Planned Course Documents

Mathematics- Kindergarten

Course: Mathematics- Kindergarten

Standards: This course is aligned to the following domains of the Kindergarten Pennsylvania Core Academic Standards for Mathematics (2014)

2.1 Numbers and Operations

A) Counting and Cardinality

B) Number & Operations in Base Ten

2.2 Algebraic Concepts

A) Operations and Algebraic Thinking

2.3 Geometry

A) Geometry

2.4 Measurement, Data, and Probability

A) Measurement and Data

Course Description:

Students focus intensively on the two critical areas specified by the Common Core State Standards for Mathematics:

● Representing and comparing whole numbers

● Describing shapes and space

Six of eight units are devoted to number and operations. They help students learn to use numbers, including written numerals, to represent quantities and solve problems; count out a given number of objects; compare sets or numerals; and model simple joining and separating situations with objects, fingers, words, actions, drawings, numbers, and equations.

The remaining two units focus on geometry. They invite students to describe and analyze the attributes of shapes in the world around them; find, count, draw, build, and compare shapes; and fit shapes together to make other shapes and complete puzzles.

Related courses:

MTSS Tier 2 and Tier 3 supports

Measurable objectives to be attained by students:

Specific objectives for this course are aligned to the Pennsylvania Core Standards for Mathematics as outlined in the Scope and Sequence for Kindergarten Mathematics.

Unit 1: Numbers to Five and Ten
Unit 2: Numbers to Ten
Unit 3: Bikes and Bugs: Double, Add & Subtract
Unit 4: Paths to Adding, Subtracting, & Measuring
Unit 5: Two-Dimensional Geometry
Unit 6: Three-Dimensional Shapes and Numbers Beyond Ten
Unit 7: Weight & Place Value
Unit 8: Computing & Measuring with Frogs and Bugs

Instructional Strategies:

Instructional Components outlined in the Framework for Teaching by Charlotte Danielson
Use of Concrete-Representational-Abstract (CRA) representations
Promote productive struggle
Promote mathematical discourse
Use precise mathematical language

Forms of Assessment to Measure Attainment of Course Objectives:

Universal Screener (Acadience)
Monitoring
Diagnostic Assessment
Curriculum-based measures
Benchmark Assessments
Formative Assessments
Summative Assessments

Estimated Instructional Time: 70 minutes

Resources:

Bridges in Mathematics, Second Edition, Published by the Math Learning Center, Salem, Oregon, 2019.

ISBN: 9781602623095

Student Resources:

Bridges in Mathematics Grade Level Student Book
Bridges in Mathematics Grade Level Home Connections
Number Corner Grade Level Student Books

Teacher Resources:

Bridges in Mathematics Grade Level Teacher Guides Units 1-8
Bridges in Mathematics Grade Level Assessment Guides
Bridges in Mathematics Grade Level Teacher Masters
Bridges in Mathematics Grade Level Teacher Masters Answer Key
Bridges in Mathematics Grade Level Student Book Answer Key
Bridges in Mathematics Grade Level Home Connections Answer Key
Bridges in Mathematics Grade Level Components and Manipulatives
Bridges Educator Site
Workplace Games and Activities
Number Corner Grade Level Teacher Guides Volumes 1-3
Number Corner Grade Level Teacher Masters
Number Corner Grade Level Teacher Masters Answer Key
Number Corner Grade Level Student Book Answer Key
Number Corner Grade Level Components and Manipulatives
Word Resource Cards

*Digital resources in italics

Technology:

mathlearningcenter.org

Other Resources: Concrete Manipulatives (i.e. number racks, five frames, ten frames)

Approved by the School Board on October 23, 2025

Unit 1

Unit 1- Numbers to 5 and 10

Unit Overview: Students will focus on the counting sequence to 20 and quantities to 10.

Standards

Number & Operations

Focus Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

K.CC.A.1. Count to 100 by ones and by tens.

K.CC.B. Count to tell the number of objects.

K.CC.B.4. Understand the relationship between
numbers and quantities connect
counting to cardinality.

Supporting Standards:

K.CC.A. Know number names and the count sequence.

K.CC.A.3. Write numbers from 0 to 20. Represent
a number of objects with a written
numeral 0- 20 (with 0 representing a
count of no objects).

K.CC.B. Count to tell the number of objects.

K.CC.B.5. Count to answer “how many?”
questions about as many as 20 things
arranged in a line, a rectangular array,
or a circle, or as many as 10 things in a
scattered configuration; given a
number from 1–20, count out that
man objects.

K.CC.C. Compare numbers.

K.CC.C.6. Identify whether the number of objects
in one group is greater than, less than,
or equal to the number of objects in
another group, e.g., by using matching
and counting strategies.

Algebraic Concepts

Supporting Standards: Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

             K.OA.A.2. Solve addition and subtraction word
   problems, and add and subtract within
   10, e.g., by using objects or drawings to
represent the problem.

K.OA.A.3. Decompose numbers less than or equal
to 10 into pairs in more than one way,
e.g., by using objects or drawings, and
record each decomposition by drawing
or equation (e.g., 5= 2 + 3 and 5 =4 + 1).

Geometry

None

Measurement, Data, and Probability

Supporting Standards: Measurement & Data

K.MD.B. Classify objects and count the number of objects in each category.

              K.MD.B.3. Classify objects into given categories;
   count the numbers of objects in each
   category and sort the categories by
   count.

Council Rock School District: Identifying Learning

Essential Questions

What can we count in our world?
How do numbers help us in our everyday lives?
Why is it important to know how many things we have?
What happens when we add more or take some away?
What can we do to know if one group has more, less, or the same as another?
Why is it important to compare numbers and objects?

Enduring Understandings

Students will understand that…

Overarching Enduring Understandings:

Knowing numbers helps us understand and describe the world around us.
Numbers tell us how many things there are.
We use counting to find out how many things are in a group.
Numbers have an order, and this order is important.
Using numbers helps us solve everyday problems.

Topical Enduring Understandings:

Counting tells us how many things are in a group.
Counting to five and ten is the first step to counting higher.
Each number represents a specific amount.
The order of numbers is important when we count.
Numbers can help us understand which group has more or less.

Content

Students will know…

One hundred
Tens
Ones
Numbers from 0 to 20
Written numerals from 0 to 20
Objects
Relationship
Numbers
Quantity

Skills

Students will be able to…

Identify numbers 1 to 10.
Count to 20.
Count with 1:1 correspondence objects up to 10.
Match numerals to quantities up to 10.
Recognize number names and write numerals 1 to 10.
Count forward from a given number within 10.

Unit 2

Unit 2- Counting to 10

Unit Overview: Students continue to develop the major concepts addressed in Unit 1 related to counting and recognizing quantities: number sequence, one-to-one correspondence, cardinality, and subitizing. Unit 2 emphasizes combinations of numbers that make 5, and also introduces the process of comparing quantities within 10.

Standards

Numbers & Operations

Focus Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

K.CC.A.1. Count to 100 by ones and by tens.

K.CC.B. Count to tell the number of objects.

K.CC.B.4. Understand the relationship between
numbers and quantities; connect
counting to cardinality.

              K.CC.B.5. Count to answer “how many?”
   questions about as many as 20 things
   arranged in a line, a rectangular array,
   or a circle, or as many as 10 things in a
   scattered configuration; given a number from 1–20, count out that many
   objects.

Supporting Standards: Counting & Cardinality

K.CC.C. Compare numbers.

             K.CC.C.6. Identify whether the number of objects
   in one group is greater than, less than,
or equal to the number of objects in
   another group, e.g., by using matching
and counting strategies.

Algebraic Concepts

Supporting Standards: Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

              K.OA.A.3. Decompose numbers less than or equal
to 10 into pairs in more than one way,
e.g., by using objects or drawings, and
record each decomposition by a
   drawing or equation (e.g., 5 = 2 + 3 and 5
   = 4 + 1).

Geometry

Supporting Standards: Geometry

K.G.B. Analyze, compare, create, and compose shapes.

K.G.B.6. Compose simple shapes to form larger
shapes.

Measurement, Data, and Probability

None

Council Rock School District: Identifying Learning

Essential Questions:

What can we count around us?
Why do we put numbers in order?
Why do we need numbers in our life?
How do we know if one group has more or less?
What happens when we add or take away objects?
How can we show numbers in different ways?

Enduring Understandings:

Students will understand that…

Overarching Enduring Understandings

We use numbers to help us understand the world around us.
Counting helps us know how many things we have.
Numbers help us compare groups of things to see if one is bigger, smaller, or the same.
Breaking apart and putting together numbers helps us understand them better.
Numbers help us solve problems and answer questions.

Topical Enduring Understandings

We can count objects to find out how many there are.
Counting to ten helps us organize and compare groups of things.
Numbers can be split into smaller numbers in different ways.
Counting connects to things we see and use every day.

Content:

Students will know…

Numbers: Ones, Tens, One hundred
Line arrangements
Rectangular arrays, Circular arrangements
Scattered configurations
Circle
Number identification
Matching strategies, Counting strategies, Objects comparison
Greater than, Less than, Equal to
Group
Pairs of numbers
Shapes composition
Numbers and quantities relationship
Quantity
Cardinality
Object
Drawing
Equation

Skills:

Students will be able to…

Count to 20
Answer "how many?" questions
Count objects with 1:1 correspondence
Count objects in a five-frame and ten-frame
Count objects in a line
Count objects in a rectangular array
Count objects in a circle
Count scattered objects
Understand how numbers and quantities are related
Connect counting to cardinality
Count a given number of objects from 1-20
Identify number of objects
Compare number of objects up to ten
Decompose numbers less than or equal to ten into pairs in more than one way
Compose simple shapes to form larger shapes

Unit 3

Unit 3- Bikes and Bugs: Double, Add and Subtract

Unit Overview: Students begin Unit 3 with an exploration of bicycles and wheels in which they begin counting by 2s. This leads them to an exploration of doubling and even numbers. They also use the five- and ten-frames to add 1 to numbers from 1 to 10, compare and order numbers, and write equations to show combinations of numbers that have a sum of 5.

Standards

Numbers & Operations

Focus Standards: Counting & Cardinality

· K.CC.B. Count to tell the number of objects.

K.CC.B.4. Understand the relationship between
numbers and quantities; connect
counting to cardinality.

K.CC.B.5. Count to answer “how many?”
questions about as many as 20 things
arranged in a line, a rectangular array,
or a circle, or many as 10 things in a
scattered configuration; given a
number from 1–20, count out that
many objects.

Supporting Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.
K.CC.A.3. Write numbers from 0 to 20. Represent
a number of objects with a written
numeral 0-20 (with 0 representing a
count of no objects).
K.CC.C. Compare numbers.

             K.CC.C.6. Identify whether the number of objects
   in one group is greater than, less than,
  or equal to the number of objects in group, e.g., by using matching and
counting strategies.

Algebraic Concepts

Supporting Standards: Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

              K.OA.A.1. Represent addition and subtraction
   with objects, fingers, mental images,
   drawings, sounds (e.g., claps), acting
   out situations, verbal explanations,
   expressions, or equations.

K.OA.A.3. Decompose numbers less than or equal
to 10 into pairs in more than one way,
e.g., by using objects or drawings, and
record each decomposition by a
drawing or equation (e.g., 5 = 2 + 3 and 5
= 4 + 1).

Geometry -
None

Measurement, Data, and Probability
None

Council Rock School District: Identifying Learning

Essential Questions

How can we use numbers to show how many things we have?
What happens when we count by 2's?
Why is it important to know how to add and subtract?
How can we show adding to or taking away 1 from a number?
Why is the order of numbers important when counting?
How can we use pictures to solve math problems?

Enduring Understandings

Overarching Enduring Understandings

Math helps us understand and describe the world around us.
Numbers tell us how many things there are.
We can use math to solve problems in everyday life.

Topical Enduring Understandings

Counting helps us know how many things are in a group.
We can compare groups to see which has more or less.
Numbers can be broken into smaller parts in different ways.

Content

Students will know…

Numbers 0-20
Written numerals
Number of objects
Counting strategies
Addition
Subtraction
Objects
Fingers
Mental images
Drawings
Sounds
Verbal explanations
Expressions
Equations
Number pairs
Decomposition
Cardinality
Five-frames
Ten-frames

Skills

Students will be able to…

Count by 1's and 2's to 20
Count forward and backward
Write numbers from 0-20
Represent a number of objects with a written numeral 0-20
Count with 1:1 correspondence to answer "how many?" questions up to 20
Compare quantities to determine whether the number of objects in one group is greater than, less than, or equal to another group
Add and subtract 1 to numbers to 10
Write equations to represent quantities in five- and ten-frames
Write equations to describe story problems involving adding and subtracting 1 and doubling
Represent addition and subtraction with objects
Decompose numbers less than or equal to ten in more than one way
Record decompositions by drawing or writing equations
Understand the relationship between numbers and quantities
Connect counting to cardinality
Double quantities
State the number before and after a number
Order numbers and quantities to 10

Unit 4

Unit 4- Paths to Adding, Subtracting and Measuring

Unit Overview: Students begin Unit 4 by building a number line to model the number sequence from 0 to 10. They continue to practice counting forward and backward between 0 and 50, starting with any number in the range. They also solve addition and subtraction problems, compute with pennies and nickels, and begin measuring length using non-standard units. The number line and measurement activities provide many opportunities for students to consider the relationships between numbers and quantities, including making comparisons about which are greater and which are less.

Standards

Numbers & Operations

Focus Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

K.CC.A.1. Count to 100 by ones and by tens.

K.CC.A.2. Count forward beginning from a given
number within the known sequence
(instead of having to begin at 1).

K.CC.B. Count to tell the number of objects.

             K.CC.B.4. Understand the relationship between
   numbers and quantities; connect
   counting to cardinality.

K.CC.B.5. Count to answer “how many?” questions
about as many as 20 things arranged in a
line, a rectangular array, or a circle, or
as many as 10 things in a scattered
configuration; given a number from 1–
20, count out that many objects.

Supporting Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

K.CC.A.3. Write numbers from 0 to 20. Represent
a number of objects with a written
numeral 0-20 (with 0 representing a
count of no objects).

K.CC.C. Compare numbers.

             K.CC.C.6. Identify whether the number of objects
in one group is greater than, less than,
   or equal to the number of objects in
   another group, e.g., by using matching
   and counting strategies.

K.CC.C.7. Compare two numbers between 1 and
10 presented as written numerals.

Algebraic Concepts

Supporting Standards: Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

K.OA.A.1. Represent addition and subtraction with
objects, fingers, mental images, drawings, sounds (e.g., claps), acting out
situations, verbal explanations,
expressions, or equations.

Geometry

None

Measurement, Data, and Probability

Supporting Standards: Measurement & Data

K.MD.A. Describe and compare measurable attributes.

              K.MD.A.1. Describe measurable attributes of
objects, such as length or weight.
   Describe several measurable attributes
   of a single object.

               K.MD.A.2. Directly compare two objects with a
   measurable attribute in common, to
   see which object has “more of”/“less
   of” the attribute and describe the
difference.

K.MD.B. Classify objects and count the number of objects in each category.

              K.MD.B.3. Classify objects into given categories;
   count the numbers of objects in each
   category and sort the categories by
   count.

Council Rock School District: Identifying Learning

Essential Questions

Why is counting important?
Why do we count in different ways?
What comes next when we start at a number?
How do we know how many things we have?
How can we tell if one group has more, less, or the same as another group?
How can using objects help us add and subtract?
How can we use numbers to measure things?

Enduring Understandings

Students will understand that…

Overarching Enduring Understandings:

Counting helps us know how many things there are.
Numbers can show if there are more, less, or the same amount of things.
Counting can start from any number, not just one.

Topical Enduring Understandings:

We can use numbers to tell how long or short something is.
We can compare numbers using a number line.
Measuring helps us compare the size of things.
We can count objects to see which group has more, less, or the same.
Every number means a certain amount of things.
We can count in different ways, like by ones or by tens.

Content

Students will know…

Number, Ones, Tens, One hundred
Counting sequence
Relationship between numbers and quantities
Objects
Cardinality
Line
Rectangular array
Circle
Scattered configuration
Objects
Number line
Penny, Nickel

Skills

Students will be able to…

Count forward and backward from 0-50
Answer "how many?" questions using 1:1 correspondence with up to 20 objects
Understand the relationship between numbers and quantities
Connect counting to cardinality
Add with sums to ten and subtract with minuends to ten
Solve story problems with objects
Arrange numbers in the correct order 0-20
Compare numbers
Measure length with non-standard units
Count using pennies and nickels

Unit 5

Unit 5- Two-Dimensional Geometry

Unit Overview: Students begin this unit by comparing a sphere and a circle, two shapes with which they are likely to be quite familiar. Students’ comparisons bring to light the difference between three-dimensional shapes and two-dimensional shapes. After this initial investigation, students spend the rest of the unit examining, identifying, comparing, and sorting two-dimensional shapes. The workplaces in this unit invite students to construct and deconstruct a variety of shapes.

Standards

Numbers & Operations

Supporting Standards: Counting & Cardinality

K.CC.C. Compare numbers.

             K.CC.C.6. Identify whether the number of objects
   in one group is greater than, less than,
   or equal to the number of objects in
   another group, e.g., by using matching
   and counting strategies.

Algebraic Concepts

Supporting Standards: Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

K.OA.A.3. Decompose numbers less than or equal
to 10 into pairs in more than one way,
e.g., by using objects or drawings, and
record each decomposition by a
drawing or equation (e.g., 5 = 2 + 3 and 5
= 4 + 1).

Geometry

Focus Standards: Geometry

K.G.A. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

           K.G.A.1. Describe objects in the environment using
   names of shapes, and describe the relative
   positions of these objects using terms such
as above, below, beside, in front of,
behind, and next to.

            K.G.A.3. Identify shapes as two-dimensional (lying
   in a plane, “flat”) or three-dimensional
   (“solid”).

K.G.B. Analyze, compare, create, and compose shapes.

           K.G.B.4. Analyze and compare two- and three-
dimensional shapes, in different sizes and
   orientations, using informal language to
describe their similarities, differences,
   parts (e.g., number of sides and
   vertices/“corners”) and other attributes
(e.g., having sides of equal length).

Supporting Standards: Geometry

K.G.A. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

K.G.A.2. Correctly name shapes regardless of their
orientations or overall size.

K.G.B. Analyze, compare, create, and compose shapes.

K.G.B.5. Model shapes in the world by building
shapes from components (e.g., sticks and
clay balls) and drawing shapes.

K.G.B.6. Compose simple shapes to form larger
shapes.

Measurement, Data, and Probability

Focus Standards: Measurement & Data

K.MD.B. Classify objects and count the number of objects in each category.

              K.MD.B.3. Classify objects into given categories;
   count the numbers of objects in each
   category and sort the categories by
   count.

Council Rock School District: Identifying Learning

Essential Questions

What shapes do you see around you every day?
How can you tell if one group has more, less, or the same number of objects as another group?
Why do some shapes look different even if they are the same kind of shape?
What makes a shape flat or solid?
How can we use words like above, below, or next to, to describe where things are?
How can you sort objects into different groups?
Why is it important to know the names of shapes?
How can we use shapes to make pictures or designs?
What are different ways that shapes be broken apart?

Enduring Understandings

Students will understand that…

Overarching Enduring Understandings

Shapes are everywhere in the world around us.
We can describe where things are by using words like above, below, and beside.
Knowing about shapes helps us understand and talk about the world.
Sorting objects into groups helps us to understand and organize them better.

Topical Enduring Understandings

Shapes can be flat (2D) or solid (3D).
Different shapes have different names and characteristics.
We can use shapes to describe things we see every day.
Shapes have parts, like sides and corners, that we can talk about.

Content

Students will know…

Categories
Numbers
Objects, Shapes, Sphere, Circle
Two-dimensional shapes
Flat
Three-dimensional shapes
Solid
Relative position terms
Similarities, Differences
Sides
Vertices
Attributes
Sizes
Orientations

Skills

Students will be able to…

Classify objects into given categories
Count the number of objects in each category
Sort the categories by count
Describe objects in the environment using names of shapes, and describe the relative position of these objects
Identify shapes as two-dimensional or three-dimensional
Analyze two- and three-dimensional shapes
Compare two- and three-dimensional shapes
Name, sort, and describe attributes of pattern block shapes
Name, identify, and analyze basic shapes (circles, squares, rectangles, triangles, hexagons, trapezoids, and rhombuses).
Construct shapes on geoboards
Draw shapes
Construct shapes
Combine simple shapes to form larger shapes

Unit 6

Unit 6- Three Dimensional Shapes and Numbers Beyond 10

Unit Overview: This unit emphasizes the two critical areas for kindergarten mathematics identified by the Common Core State Standards: number and geometry. The first two modules focus on geometry, while the last two modules focus on number and operations. To start the unit, students describe the attributes, similarities, and differences among two-dimensional and three-dimensional shapes. These early sessions also include activities in which students count and make combinations to 5. Later in the unit, students count forward and backward, read and write numerals to 20, and explore combinations to numbers from 5 to 10, with special emphasis on the 5+ and 10+ combinations. Each student receives a Student Book at the start of this unit, which they will use for independent work for the rest of the school year.

Standards

Numbers and Operations

Focus Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

             K.CC.A.3. Write numbers from 0 to 20. Represent
   a number of objects with a written
   numeral 0-20 (with 0 representing a
   count of no objects).

K.CC.C. Compare numbers.

K.CC.C.7. Compare two numbers between 1 and
10 presented as written numerals.

Supporting Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

K.CC.A.1. Count to 100 by ones and by tens.

             K.CC.A.2. Count forward beginning from a given
   number within the known sequence
   (instead of having to begin at 1).

K.CC.B. Count to tell the number of objects.

K.CC.B.4a. When counting objects, say the
number names in the standard order,
pairing each object with one and only
one number name and each name
with one and only one object.

Number & Operations in Base Ten

K.NBT.A. Work with numbers 11-19 to gain foundations for place value.

              K.NBT.A.1. Compose and decompose numbers
from 11 to 19 into ten ones and some
further ones, e.g., by using objects or
drawings, and record each
   composition or decomposition by a drawing or equation (such as 18 = 10 +
8); understand that these numbers are
composed of ten ones and one, two,
  three, four, five, six, seven, eight, or
nine ones.

K.CC.B.4b. Understand that the last number
name said tells the number of
objects counted. The number of
objects is the same regardless of
their arrangement or the order in
which they were counted.

K.CC.B.5. Count to answer “how many?”
questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10
things in a scattered configuration;
given a number from 1–20, count out
that many objects.

Algebraic Concepts

Supporting Standards: Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

K.OA.A.1. Represent addition and subtraction with
objects, fingers, mental images,
drawings, sounds (e.g., claps), acting out situations, verbal explanations,
expressions, or equations.

             K.OA.A.2. Solve addition and subtraction word
   problems, and add and subtract within
   10, e.g., by using objects or drawings to
represent the problem.

               K.OA.A.3. Decompose numbers less than or equal
   to 10 into pairs in more than one way,
e.g., by using objects or drawings, and
record each decomposition by a
   drawing or equation (e.g., 5 = 2 + 3 and 5
   = 4 + 1).

K.OA.A.5. Fluently add and subtract within 5.

Geometry

Focus Standards: Geometry

K.G.A. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

K.G.A.1. Describe objects in the environment using
names of shapes, and describe the relative
positions of these objects using terms such as above, below, beside, in front of,
behind, and next to.

K.G.A.2. Correctly name shapes regardless of
their orientations or overall size.

K.G.B. Analyze, compare, create, and compose shapes.

            K.G.B.4. Analyze and compare two- and three-
dimensional shapes, in different sizes and
   orientations, using informal language to describe their similarities, differences,
   parts (e.g., number of sides and
   vertices/“corners”) and other attributes
(e.g., having sides of equal length).

K.G.B.5. Model shapes in the world by building
shapes from components (e.g., sticks and
clay balls) and drawing shapes.

Supporting Standards: Geometry

K.G.A. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

K.G.A.3. Identify shapes as two-dimensional
(lying in a plane, “flat”) or three-
dimensional (“solid”).

Measurement, Data, and Probability

None

Council Rock School District: Identifying Learning

Essential Questions

Why is it important to know how many things we have?
How can we tell which number is bigger or smaller?
What are the different ways we can make numbers up to ten?
How do we make and break numbers from 11 to 19?
How are flat shapes and solid shapes alike and different?
Can we make new shapes by combining other shapes together?
How can we find shapes in the world around us?

Enduring Understandings

Students will understand that…

Overarching Enduring Understandings

Shapes are all around us in the world.
Knowing shapes helps us describe and understand our environment.
Shapes have special names and features.
Shapes can be flat or solid.
Knowing how many helps us make choices.
Numbers can be broken apart into smaller pieces.

Strongest 3 Topical Enduring Understandings

We can use words like above, below, and next to, to describe where shapes are.
We can tell if a shape is flat or solid.
We can build shapes using different materials.

Content

Students will know…

Numbers 0-20
Number of objects, Groups of objects
Written numerals
Quantities
Combinations to ten
Cylinders, Cubes
Tens, Ones
Spheres
Shapes
Relative positions
Two-dimensional shapes, Three-dimensional shapes
Sides
Vertices
Attributes of shapes
Similarities, Differences
Components for modeling shapes
Polydrons

Skills

Students will be skilled at…

Count to 90
Count by 10's and 1's
Count forward and backward
Write numbers from 0-20
Represent a number of objects with a written numeral 0-20
Count on from 10 and understand numbers from 11-20 as "ten and some more"
Compare and identify whether a number of objects is greater, less, or equal to another group of objects
Compare two numbers between 1-10 written as numerals
Write equations for combinations to numbers from 5-10
Describe objects using names of shapes, and describe the relative positions of these objects
Analyze two- and three-dimensional shapes
Compare two- and three-dimensional shapes
Describe attributes of shapes
Compare shapes by discussing similarities and differences
Model shapes by building shapes from components
Draw shapes
Sort shapes

Unit 7

Unit 7- Weights and Place Value

Unit Overview: Students explore weight and capacity, solve addition and subtraction story problems, and begin to develop an understanding of place value. In the first module, students measure weight and capacity and make comparisons about those measurements. In the last three modules, the focus shifts to counting and operations. Students begin to develop robust strategies for solving addition and subtraction problems and explore the concept that numbers are composed of 10s and 1s.

Standards

Numbers and Operations

Focus Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

            K.CC.A.3. Write numbers from 0 to 20. Represent a
   number of objects with a written
   numeral 0-20 (with 0 representing a
   count of no objects).

K.CC.B. Count to tell the number of objects.

K.CC.B.5. Count to answer “how many?”
questions about as many as 20 things
arranged in a line, a rectangular array, or a circle, or as many as 10 things in a
scattered configuration; given a number from 1–20, count out that many objects.

K.CC.C. Compare numbers.

              K.CC.C.6. Identify whether the number of objects
   in one group is greater than, less than,
  or equal to the number of objects in
another group, e.g., by using matching
and counting strategies.

K.CC.C.7. Compare two numbers between 1 and
10 presented as written numerals.

Supporting Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

K.CC.A.1. Count to 100 by ones and by tens.

Number & Operations in Base Ten

K.NBT.A. Work with numbers 11-19 to gain foundations for place value.

                K.NBT.A.1. Compose and decompose numbers
from 11 to 19 into ten ones and some
further ones, e.g., by using objects or drawings, and record each
   composition or decomposition by a
   drawing or equation (such as 18 = 10 +
   8); understand that these numbers
   are composed of ten ones and one,
two, three, four, five, six, seven, eight,
   or nine ones.

Algebraic Concepts

Supporting Standards: Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

             K.OA.A.1. Represent addition and subtraction with
objects, fingers, mental images,
    drawings, sounds (e.g., claps), acting out
  situations, verbal explanations,
expressions, or equations.

K.OA.A.2. Solve addition and subtraction word
problems, and add and subtract within
10, e.g., by using objects or drawings to represent the problem.

                K.OA.A.3. Decompose numbers less than or
   equal to 10 into pairs in more than one
   way, e.g., by using objects or drawings,
   record each decomposition by a drawing or equation (e.g., 5= 2 + 3 and 5
   = 4 + 1).

K.OA.A.5. Fluently add and subtract within 5.

Geometry

None

Measurement, Data, and Probability

Focus Standards: Measurement & Data

K.MD.A. Describe and compare measurable attributes.

K.MD.A.1. Describe measurable attributes of
objects, such as length or weight.
Describe several measurable attributes
of a single object.

              K.MD.A.2. Directly compare two objects with a
   measurable attribute in common, to
   see which object has “more of”/“less
   of” the attribute, and describe the
difference.

K.MD.B. Classify objects and count the number of objects in each category.

K.MD.B.3. Classify objects into given categories;
count the numbers of objects in each
category and sort the categories by
count.

Council Rock School District: Identifying Learning

Essential Questions

What can numbers tell us about the things around us?
How can we tell if something is heavier or lighter?
What does it mean when we say something weighs more or less?
What are different ways to break apart 18?
Other than counting by 1's, what are other ways that we can count?
Why is it important to know which number is bigger or smaller?
How can we show a number using objects or drawings?
What happens when we add or take away things from a group?

Enduring Understandings

Students will understand that…

Overarching Enduring Understandings

Numbers help us understand and explain our world.
Understanding weight helps us describe and compare objects in the world.
Knowing how to add and subtract helps us solve everyday problems.

Topical Enduring Understandings

We can describe objects by how heavy or light they are.
Adding means putting things together to make more.
Subtracting means taking things away to make less.
Numbers from 11 to 20 can be made up of 10 and some more.
Students will compare numbers to identify which is more, less, or equal.

Content

Students will know…

Numbers 0-20
Numerals 0-20
Objects
Number of objects
Groups of objects
Lines, arrays, circles
Scattered configurations
Comparison
Measurable attributes
Weight
Categories
Counts within categories

Skills

Students will be skilled at…

Write numbers from 0-20
Represent a number of objects with a written numeral 0-20
Connect the quantity shown in double ten-frames to the numerals 11-20 to emphasize these numbers as "ten and some more"
Count to answer "how many?" questions for up to 20 objects
Count out the correct number of objects when given a number 0-20
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in a second group
Compare two numbers between 1-10 presented as numerals
Solve addition and subtraction story problems
Count forward and backward by 10's and 1's using manipulatives (craft sticks, ten-frames, double ten-frames)
Describe measurable attributes of objects, such as weight
Compare two objects with a measurable attribute in common to see which object has "more of" or "less of" that attribute
Classify objects into given categories
Sort categories by count

Unit 8

Unit 8- Computing and Measuring with Frogs and Bugs

Unit Overview: This final unit of the kindergarten year prepares students for the work ahead in Grade 1. In the context of explorations about frogs, students build a deeper understanding of subtraction and strengthen the connections between quantity, related number combinations, and written notation to 20. The activities in this unit should help students learn to add and subtract to 5 with fluency, add to 10, and strengthen their understanding of place value by the end of the year.

Standards

Numbers and Operations

Focus Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

             K.CC.A.3. Write numbers from 0 to 20. Represent
   a number of objects with a written
   numeral 0-20 (with 0 representing a
   count of no objects).

Number & Operations in Base Ten

K.NBT.A. Work with numbers 11-19 to gain foundations for place value.

             K.NBT.A.1. Compose and decompose numbers
   from 11 to 19 into ten ones and some
   further ones, e.g., by using objects or
drawings, and record each
   composition or decomposition by a drawing or equation (such as 18 = 10 +
   8); understand that these numbers are
   composed of ten ones and one, two,
   three, four, five, six, seven, eight, or
   nine ones.

Supporting Standards: Counting & Cardinality

K.CC.A. Know number names and the count sequence.

K.CC.A.1. Count to 100 by ones and by tens.

K.CC.A.2. Count forward beginning from a given
number within the known sequence
(instead of having to begin at 1).

K.CC.C. Compare numbers.

               K.CC.C.6. Identify whether the number of
   objects in one group is greater than,
   less than, or equal to the number of
   objects in another group, e.g., by using
matching and counting strategies.

K.CC.C.7. Compare two numbers between 1 and
10 presented as written numerals.

Algebraic Concepts

Focus Standards

Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

               K.OA.A.1. Represent addition and subtraction
with objects, fingers, mental images,
   drawings, sounds (e.g., claps), acting
   out situations, verbal explanations,
   expressions, or equations.

                K.OA.A.2. Solve addition and subtraction word
   problems, and add and subtract within
   10, e.g., by using objects or drawings to
represent the problem.

K.OA.A.5. Fluently add and subtract within 5.

Supporting Standards: Operations & Algebraic Thinking

K.OA.A. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

             K.OA.A.3. Decompose numbers less than or equal
   to 10 into pairs in more than one way,
   e.g., by using objects or drawings, and record each decomposition by a
drawing or equation (e.g., 5 =2 + 3 and 5 =
4 + 1).

K.OA.A.4. For any number from 1 to 9, find the
number that makes 10 when added to
the given number, e.g., by using objects
or drawings, and record the answer with
a drawing or equation.

Geometry

None

Measurement, Data, and Probability

Supporting Standards: Measurement & Data

K.MD.A. Describe and compare measurable attributes.

K.MD.A.1. Describe measurable attributes of
objects, such as length or weight.
Describe several measurable attributes
of a single object.

K.MD.A.2. Directly compare two objects with a
measurable attribute in common, to see which object has “more of”/“less
of” the attribute, and describe the
difference.

Council Rock School District: Identifying Learning

Essential Questions

Why is it important to know how to add and subtract?
What happens when we add two groups together?
How can we use our fingers to show subtraction?
What are some ways we can solve a story problem with numbers?
What do we notice when we put together and take apart numbers from 11 to 19?
How can we measure how long something is?
How can we decide which number is bigger or smaller?

Enduring Understandings

Students will understand that…

· Overarching Enduring Understandings

· Numbers help us understand and talk about the world around us.

· We can use math to solve problems we see every day.

· Adding and taking away helps us find out how many we have.

· Topical Enduring Understandings

· We can use objects or pictures to help us add and subtract.

· We can solve problems by thinking about adding or taking away.

· Counting and measuring help us learn about size and amount.

· We can use numbers to show how things are bigger or smaller.

· Numbers can be put together and taken apart in different ways.

Content

Students will know…

Numbers 0 to 20
Written numerals
Objects
Addition, Subtraction, Word problems
Fingers
Mental images, Drawings, Sounds
Verbal explanations
Expressions, Equations
Addition and subtraction word problems
Numbers within 10, Numbers within 5, Numbers from 11 to 19
Ten, Ones

Skills

Students will be able to…

Count to 100
Write numbers from 0-20
Estimate, measure, and compare lengths
Represent a number of objects with a written numeral 0-20
Represent addition and subtraction situations with objects, manipulatives, fingers, drawings, acting out, sounds, expressions, or equations
Write equations that represent quantities
Solve addition and subtraction word problems
Add within 10
Subtract within 10
Fluently add and subtract within 5
Compose and decompose numbers from 11-19 into tens and ones
Show that the numbers from 11-19 are composed of ten ones and an additional amount of ones by writing numerals and equations

Mathematics- Grade 1

Course: Mathematics- Grade 1

Standards: Standards: This course is aligned to the following domains of the Grade 1 Pennsylvania Core Academic Standards for Mathematics (2014)

2.1 Numbers and Operations

B) Number & Operations in Base Ten

2.2 Algebraic Concepts

A) Operations and Algebraic Thinking

2.3 Geometry

A) Geometry

2.4 Measurement, Data, and Probability

A) Measurement and Data

Course Description:

Students focus intensively on the four critical areas specified by the Common Core State Standards for Mathematics in Grade One:

Addition and subtraction within 20
Whole number relationships and place value
Linear measurement in non-standard units
Reasoning with shapes and their attributes

Four of eight units are devoted to addition and subtraction within 20. They help students gain fluency with facts to 10 and develop increasingly sophisticated strategies for solving addition and subtraction combinations to 20. During these units, students' model, solve, and pose a wide variety of word problems to construct meaning for the operations of addition and subtraction, as well as an understanding of how the two are connected.

Two of the eight units focus on place value, extending the counting sequence to 120 as students learn to think of whole numbers between 10 and 100 in terms of tens and ones. Much of the work in these units engages first graders in developing, discussing, and using efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10.

The remaining two units revolve around geometry and measurement. The geometry unit challenges children to identify, describe, construct, draw, compare, compose, and sort shapes. Students also learn about fractions in the context of two-dimensional shapes. The measurement unit provides ample opportunity for students to develop an understanding of the meaning and processes of measuring time and length as they conduct duration experiments; construct, fly, and measure the flight distances of paper gliders; and investigate some of the many ways in which they have grown and changed since they were born.

Related courses:

MTSS Tier 2 and Tier 3 supports

Measurable objectives to be attained by students:

Specific objectives for this course are aligned to the Pennsylvania Core Standards for Mathematics as outlined in the Scope and Sequence for Grade 1 Mathematics.

Instructional Strategies:

Instructional Components outlined in the Framework for Teaching by Charlotte Danielson
Use of Concrete-Representational-Abstract (CRA) representations
Promote productive struggle
Promote mathematical discourse
Use precise mathematical language

Forms of Assessment to Measure Attainment of Course Objectives:

Universal Screener (Acadience)
Progress Monitoring
Curriculum-based measures
Benchmark Assessments
Formative Assessments
Summative Assessments

Estimated Instructional Time: 70 minutes

Resources:

Bridges in Mathematics, Second Edition, Published by the Math Learning Center, Salem, Oregon, 2019.

ISBN: 9781602625099

Student Resources:

Bridges in Mathematics Grade Level Student Book
Bridges in Mathematics Grade Level Home Connections
Number Corner Grade Level Student Books

Teacher Resources:

Bridges in Mathematics Grade Level Teacher Guides Units 1-8
Bridges in Mathematics Grade Level Assessment Guides
Bridges in Mathematics Grade Level Teacher Masters
Bridges in Mathematics Grade Level Teacher Masters Answer Key
Bridges in Mathematics Grade Level Student Book Answer Key
Bridges in Mathematics Grade Level Home Connections Answer Key
Bridges in Mathematics Grade Level Components and Manipulatives
Bridges Educator Site
Workplace Games and Activities
Number Corner Grade Level Teacher Guides Volumes 1-3
Number Corner Grade Level Teacher Masters
Number Corner Grade Level Teacher Masters Answer Key
Number Corner Grade Level Student Book Answer Key
Number Corner Grade Level Components and Manipulatives
Word Resource Cards

*Digital resources in italics

Technology:

Other Resources: Concrete Manipulatives (i.e. number racks, ten frames)

Mathematics- Grade 2

Course: Mathematics- Grade 2

Standards: This course is aligned to the following domains of the Grade 2 Pennsylvania Core Academic Standards for Mathematics (2014)

2.1 Numbers and Operations

B) Number & Operations in Base Ten

2.2 Algebraic Concepts

A) Operations and Algebraic Thinking

2.3 Geometry

A) Geometry

2.4 Measurement, Data, and Probability

A) Measurement and Data

Course Description:

Students focus intensively on the four critical areas specified by the Common Core State Standards for Mathematics in Grade Two:

Extending understanding of base-ten notation
Building fluency with addition and subtraction
Using standard units of linear measurement
Describing and analyzing shapes

The first unit revisits and extends addition and subtraction within 20, helping to ensure that second graders operate with understanding and fact fluency from the start of the school year.

Units 2, 3, 5, and parts of Unit 7, are devoted to place value and multi-digit addition and subtraction. During these units, students learn to count by fives, tens, and multiples of hundreds, tens and ones; read, write, and compare numbers to 1,000; and develop fluency with addition and subtraction to 100 as they solve and pose a wide variety of word problems. Later in the year, the children use concrete models and sketches, as well as strategies based on place value, properties of operations, and the relationship between addition and subtraction, to add and subtract to 1,000.

Unit 6 revolves around geometry, building foundations for understanding area, volume, congruence, similarity, and symmetry as students investigate, describe, build, draw, combine, decompose, and analyze two- and three-dimensional shapes.

Unit 4, and the first part of Unit 7, focus on linear measurement, as students construct their own rulers; estimate and measure in inches, feet, yards, centimeters, and meters; and solve problems that involve adding, subtracting, and comparing lengths.

Unit 8 revisits linear measurement in the context of science and engineering as students make and test cardboard ramps of different kinds to investigate some of the factors that cause marbles to roll farther and faster. In the process, they generate data by measuring marble roll distances multiple times, pool their data, and enter it online plots to better see, understand, and analyze how manipulating the different variables affects the outcomes.

Related courses:

MTSS Tier 2 and Tier 3 supports

Measurable objectives to be attained by students:

Specific objectives for this course are aligned to the Pennsylvania Core Standards for Mathematics as outlined in the Scope and Sequence for Grade 2 Mathematics.

Instructional Strategies:

Instructional Components outlined in the Framework for Teaching by Charlotte Danielson
Use of Concrete-Representational-Abstract (CRA) representations
Promote productive struggle
Promote mathematical discourse
Use precise mathematical language

Forms of Assessment to Measure Attainment of Course Objectives:

Universal Screener (Acadience)
Progress Monitoring
Diagnostic Assessment
Curriculum-based measures
Benchmark Assessments
Formative Assessments
Summative Assessments

Estimated Instructional Time: 70 minutes

Resources:

Bridges in Mathematics, Second Edition, Published by the Math Learning Center, Salem, Oregon, 2019.

ISBN: 9781602623507

Student Resources:

Bridges in Mathematics Grade Level Student Book
Bridges in Mathematics Grade Level Home Connections
Number Corner Grade Level Student Books

Teacher Resources:

Bridges in Mathematics Grade Level Teacher Guides Units 1-8
Bridges in Mathematics Grade Level Assessment Guides
Bridges in Mathematics Grade Level Teacher Masters
Bridges in Mathematics Grade Level Teacher Masters Answer Key
Bridges in Mathematics Grade Level Student Book Answer Key
Bridges in Mathematics Grade Level Home Connections Answer Key
Bridges in Mathematics Grade Level Components and Manipulatives
Bridges Educator Site
Workplace Games and Activities
Number Corner Grade Level Teacher Guides Volumes 1-3
Number Corner Grade Level Teacher Masters
Number Corner Grade Level Teacher Masters Answer Key
Number Corner Grade Level Student Book Answer Key
Number Corner Grade Level Components and Manipulatives
Word Resource Cards
Concept Quests

*Digital resources in italics

Technology:

Other Resources: Concrete Manipulatives (i.e. number racks, ten frames)

Mathematics- Grade 3

Course: Mathematics- Grade 3

Standards: This course is aligned to the following domains of the Grade 3 Pennsylvania Core Academic Standards for Mathematics (2014)

2.1 Numbers and Operations

B) Number & Operations in Base Ten

C) Number & Operations – Fractions

2.2 Algebraic Concepts

A) Operations and Algebraic Thinking

2.3 Geometry

A) Geometry

2.4 Measurement, Data, and Probability

A) Measurement and Data

Course Description:

Students focus intensively on the four critical areas specified by the Common Core State Standards for Mathematics in Grade Three:

Developing understanding of multiplication and division and strategies for multiplication and division within 100
Developing understanding of fractions, especially unit fractions (fractions with numerator 1)
Developing understanding of the structure of rectangular arrays and of area
Describing and analyzing two-dimensional shapes

The first unit reviews and extends work with addition and subtraction as students review facts, look for patterns, and work with larger numbers. Unit 2 transitions to multiplication by having students use a variety of rich contexts (arrays of stamps, groups of windows, and a coral reef) to develop and refine multiplication strategies and models. Unit 3 returns to addition and subtraction, this time focusing on strategies for computing with larger numbers.

In Units 4 and 5, students explore measurement, fractions, division, and multiplication of larger numbers. They estimate and make measurements in different units; explore unit fractions and equivalent fractions and begin adding and subtracting fractions; they connect multiplication to division and extend multiplication strategies to larger numbers. Their work with multiplication develops a strong understanding of area.

Unit 6 focuses on geometry, as students investigate, draw, and build two-dimensional shapes, using their properties to classify and analyze these shapes. They also connect geometry to fractions as they express the area of a shape as a unit fraction of the whole. Unit 7 brings together and extends many of the skills and concepts addressed in earlier units as students solve challenging problems that involve calculating with multi-digit numbers. They explore algorithms for addition and subtraction and dig deeper into division. Students develop strategies and models for division, many of which are based on their work with multiplication.

Unit 8 integrates mathematics and science, with a primary focus on designing and building model bridges. Students test the strength of their model bridges in systematic ways to collect data. Then they graph and analyze the data, finding the range and mean, to make conjectures and draw conclusions about effective bridge design and construction.

Related courses:

MTSS Tier 2 and Tier 3 supports
Math Enrichment and/or Acceleration

Measurable objectives to be attained by students:

Specific objectives for this course are aligned to the Pennsylvania Core Standards for Mathematics as outlined in the Scope and Sequence for Grade 3 Mathematics.

Instructional Strategies:

Instructional Components outlined in the Framework for Teaching by Charlotte Danielson
Use of Concrete Representational Abstract (CRA) representations
Promote productive struggle
Promote mathematical discourse
Use precise mathematical language

Forms of Assessment to Measure Attainment of Course Objectives:

Universal Screener (Acadience)
Progress Monitoring
Diagnostic Assessment
Curriculum-based measures
Benchmark Assessments
Formative Assessments
Summative Assessments

Estimated Instructional Time: 70 minutes

Resources:

Bridges in Mathematics, Second Edition, Published by the Math Learning Center, Salem, Oregon, 2019.

ISBN: 9781602624092

Student Resources:

Bridges in Mathematics Grade Level Student Book
Bridges in Mathematics Grade Level Home Connections
Number Corner Grade Level Student Books

Teacher Resources:

Bridges in Mathematics Grade Level Teacher Guides Units 1-8
Bridges in Mathematics Grade Level Assessment Guides
Bridges in Mathematics Grade Level Teacher Masters
Bridges in Mathematics Grade Level Teacher Masters Answer Key
Bridges in Mathematics Grade Level Student Book Answer Key
Bridges in Mathematics Grade Level Home Connections Answer Key
Bridges in Mathematics Grade Level Components and Manipulatives
Bridges Educator Site
Workplace Games and Activities
Number Corner Grade Level Teacher Guides Volumes 1-3
Number Corner Grade Level Teacher Masters
Number Corner Grade Level Teacher Masters Answer Key
Number Corner Grade Level Student Book Answer Key
Number Corner Grade Level Components and Manipulatives
Word Resource Cards
Concept Quests

*Digital resources in italics

Technology:

Other Resources: Concrete and Virtual Manipulatives

Mathematics- Grade 4

Course: Mathematics- Grade 4

Standards: This course is aligned to the following domains of the Grade 4 Pennsylvania Core Academic Standards for Mathematics (2014)

2.1 Numbers and Operations

B) Number & Operations in Base Ten

C) Number & Operations – Fractions

2.2 Algebraic Concepts

A) Operations and Algebraic Thinking

2.3 Geometry

A) Geometry

2.4 Measurement, Data, and Probability

A) Measurement and Data

Course Description:

Students focus intensively on the three critical areas specified by the Common Core State Standards for Mathematics in Grade Four:

Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends
Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers
Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry particular angle measures, and symmetry

The first two units focus on multiplication and multiplicative thinking. Unit 1 reviews and extends multiplication work from third grade and examines factors and products, as well as prime and composite numbers. Unit 2 delves deeper as students explore and extend strategies, concepts, and models related to multi-digit multiplication. Unit 3 utilizes a variety of tools to model, read, write, compare, order, compose and decompose fractions and decimals.

Units 4, 6 and 7 focus on fractions, decimals, division, and more multiplication. Various models help students understand more about operations with fractions and fraction equivalence, as well as the relationship between fractions and decimals. Students also discover the relationships between multiplication and division as they see that many multiplication strategies also apply to division problems. They solve division problems with and without remainders and begin exploring multiplication and division of simple fractions.

Unit 5 focuses on geometry and extends students’ understandings of area, volume, and symmetry. Students investigate, draw, and build two-dimensional shapes and the properties of those shapes to classify and analyze them. They also learn to use protractors to measure and construct angles.

Unit 8 integrates many key skills and concepts in the context of science and engineering by giving students the opportunity to design playgrounds. In the process, they generate and analyze data and use a line plot to represent that data.

Related courses:

MTSS Tier 2 and Tier 3 supports
Math Enrichment and/or Acceleration

Measurable objectives to be attained by students:

Specific objectives for this course are aligned to the Pennsylvania Core Standards for Mathematics as outlined in the Scope and Sequence for Grade 4 Mathematics.

Instructional Strategies:

Instructional Components outlined in the Framework for Teaching by Charlotte Danielson
Use of Concrete Representational Abstract (CRA) representations
Promote productive struggle
Promote mathematical discourse
Use precise mathematical language

Forms of Assessment to Measure Attainment of Course Objectives:

Universal Screener (Acadience)
Progress Monitoring
Diagnostic Assessment
Curriculum-based measures
Benchmark Assessments
Formative Assessments
Summative Assessments

Estimated Instructional Time: 80 minutes

Resources:

Bridges in Mathematics, Second Edition, Published by the Math Learning Center, Salem, Oregon, 2019;

ISBN: 9781602625129

Student Resources:

Bridges in Mathematics Grade Level Student Book
Bridges in Mathematics Grade Level Home Connections
Number Corner Grade Level Student Books

Teacher Resources:

Bridges in Mathematics Grade Level Teacher Guides Units 1-8
Bridges in Mathematics Grade Level Assessment Guides
Bridges in Mathematics Grade Level Teacher Masters
Bridges in Mathematics Grade Level Teacher Masters Answer Key
Bridges in Mathematics Grade Level Student Book Answer Key
Bridges in Mathematics Grade Level Home Connections Answer Key
Bridges in Mathematics Grade Level Components and Manipulatives
Bridges Educator Site
Workplace Games and Activities
Number Corner Grade Level Teacher Guides Volumes 1-3
Number Corner Grade Level Teacher Masters
Number Corner Grade Level Teacher Masters Answer Key
Number Corner Grade Level Student Book Answer Key
Number Corner Grade Level Components and Manipulatives
Word Resource Cards
Concept Quests

*Digital resources in italics

Technology:

Other Resources: Concrete and Virtual Manipulatives

Mathematics- Grade 5

Course: Mathematics- Grade 5

Standards: This course is aligned to the following domains of the Grade 5 Pennsylvania Core Academic Standards for Mathematics (2014)

2.1 Numbers and Operations

B) Number & Operations in Base Ten

C) Number & Operations – Fractions

2.2 Algebraic Concepts

A) Operations and Algebraic Thinking

2.3 Geometry

A) Geometry

2.4 Measurement, Data, and Probability

A) Measurement and Data

Course Description:

Students focus intensively on the three critical areas specified by the Common Core State Standards for Mathematics in Grade Five:

Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions)
Extending division to 2-digit divisors, integrating decimal fractions into the place value system, developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations
Developing understanding of volume

The first unit is focused on volume and includes a review of multiplication facts and multi-digit multiplication strategies. In Unit 2, students use what they know about equivalent fractions to add and subtract fractions. Unit 3 extends students’ understandings of place value and the properties of operations to help students develop powerful strategies for computing fluently with decimals. In Unit 4 they refine powerful multiplication and division strategies, including the array model and the standard algorithm for multiplication.

In Unit 5 students learn to multiply and divide fractions. Unit 6 introduces new geometric concepts, including coordinate graphing and the use of hierarchies to classify two-dimensional shapes by their properties.

In Unit 7 students develop accurate and efficient strategies for dividing whole numbers, decimals, and fractions (unit fractions by whole numbers, and whole numbers by unit fractions). Unit 8 integrates science, engineering, and math. In this final unit, students apply the understandings and skills they have developed over the year as they study solar energy and designing solar homes.

Related courses:

MTSS Tier 2 and Tier 3 supports
Math Enrichment and/or Acceleration

Measurable objectives to be attained by students:

Specific objectives for this course are aligned to the Pennsylvania Core Standards for Mathematics as outlined in the Scope and Sequence for Grade 5 Mathematics.

Instructional Strategies:

Instructional Components outlined in the Framework for Teaching by Charlotte Danielson
Use of Concrete Representational Abstract (CRA) representations
Promote productive struggle
Promote mathematical discourse
Use precise mathematical language

Forms of Assessment to Measure Attainment of Course Objectives:

Universal Screener (Acadience)
Progress Monitoring
Diagnostic Assessment
Curriculum-based measures
Benchmark Assessments
Formative Assessments
Summative Assessments

Estimated Instructional Time: 80 minutes

Resources:

Bridges in Mathematics, Second Edition, Published by the Math Learning Center, Salem, Oregon, 2019.

ISBN: 9781602625136

Student Resources:

Bridges in Mathematics Grade Level Student Book
Bridges in Mathematics Grade Level Home Connections
Number Corner Grade Level Student Books

Teacher Resources:

Bridges in Mathematics Grade Level Teacher Guides Units 1-8
Bridges in Mathematics Grade Level Assessment Guides
Bridges in Mathematics Grade Level Teacher Masters
Bridges in Mathematics Grade Level Teacher Masters Answer Key
Bridges in Mathematics Grade Level Student Book Answer Key
Bridges in Mathematics Grade Level Home Connections Answer Key
Bridges in Mathematics Grade Level Components and Manipulatives
Bridges Educator Site
Workplace Games and Activities
Number Corner Grade Level Teacher Guides Volumes 1-3
Number Corner Grade Level Teacher Masters
Number Corner Grade Level Teacher Masters Answer Key
Number Corner Grade Level Student Book Answer Key
Number Corner Grade Level Components and Manipulatives
Word Resource Cards
Concept Quests

*Digital resources in italics

Technology:

Other Resources: Concrete and Virtual Manipulatives

Mathematics- Grade 6

Course: Mathematics- Grade 6

Standards: This course is aligned to the following domains of the Grade 6 Pennsylvania Core Academic Standards for Mathematics (2014)

2.1 Numbers and Operations

D) Ratios and Proportional Relationships

E) The Number System

2.2 Algebraic Concepts

B) Expressions and Equations

2.3 Geometry

A) Geometry

2.4 Measurement, Data, and Probability

B) Statistics and Probability

Course Description:

Grade 6 begins with a unit on reasoning about area and understanding and applying concepts of surface area. It is common to begin the year by reviewing the arithmetic learned in previous grades, but starting instead with a mathematical idea that students haven’t seen before sets up opportunities for students to surprise the teacher and themselves with the connections they make. Instead of front-loading review and practice from prior grades, these materials incorporate opportunities to practice elementary arithmetic concepts and skills through warm-ups, in the context of instructional tasks, and in practice problems as they are reinforcing the concepts they are learning in the unit.

One of the design principles of these materials is that students should encounter plenty of examples of a mathematical or statistical idea in various contexts before that idea is named and studied as an object in its own right. For example, in the first unit, students will generalize arithmetic by writing simple expressions before they study algebraic expressions as a class of objects in the sixth unit. Sometimes this principle is put into play several units before a concept is developed more fully, and sometimes in the first several lessons of a unit, where students have a chance to explore ideas informally and concretely, building toward a more formal and abstract understanding later in the unit.

Related courses:

MTSS Tier 2 and Tier 3 supports
Math Enrichment and/or Acceleration

Measurable objectives to be attained by students:

Specific objectives for this course are aligned to the Pennsylvania Core Standards for Mathematics as outlined in the Scope and Sequence for Grade 6 Mathematics.

Instructional Strategies:

Instructional Components outlined in the Framework for Teaching by Charlotte Danielson
Use of Concrete-Representational-Abstract (CRA) representations
Promote productive struggle
Promote mathematical discourse
Use precise mathematical language

Forms of Assessment to Measure Attainment of Course Objectives:

Universal Screener (Acadience)
Progress Monitoring
Diagnostic Assessment
Curriculum-based measures
Benchmark Assessments
Formative Assessments
Summative Assessments

Estimated Instructional Time: 60 minutes

Student Resources: Illustrative Mathematics Grade 6 Student Book (3 volumes)

Teacher Resources: Illustrative Mathematics Grade 6 Teacher Book

Technology:

https://im.kendallhunt.com/ Resources for Families
First in Math

Other Resources: Concrete and Virtual Manipulatives

Middle School

Academic Math Grade 7

Course: Academic Math Grade 7

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This course will examine new concepts by extending previous knowledge. Topics include ratios and proportional reasoning, an in-depth study of the number system, expressions, equations, inequalities, geometry, statistics, and probability. These topics are developed conceptually and are supplemented with enrichment activities to further challenge students and to evoke abstract thinking and problem-solving skills.

Related courses:

Academic Math Grade 7 LRC is designed to implement the goals of the IEP and parallels the curriculum of Academic Math Grade 7. Successful completion of Academic Math Grade 7 will result in a recommendation to take Academic Math Grade 8

Measurable objectives to be attained by students: Specific objectives for this course are aligned to the Pennsylvania Standards for Mathematics as outlined in the course description and the linked standards.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments:

Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments:

Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes

Estimated Instructional Time: 40 daily minutes

Resources:

Text Resources:

Illustrative Mathematics: Middle School Math ISBN-10: ‎ 1792401965

Teachers are provided a Teacher’s Edition or accompanying instructor resources through a companion website.

Technology Resources:

Below is a list of technology that may be used:

● Kendall Hunt Online

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-30XIIs)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources:

Graph Paper
Various Manipulatives (i.e. Colored Pencils, Patty Paper)

Honors Math Grade 7

Course: Honors Math Grade 7

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content Grade 7

● Assessment Anchors and Eligible Content Grade 8

Course Description:

This compacted course covers both seventh and eighth grade standards in the domains of the number system, ratios and proportional reasoning, expressions and equations, functions, geometry, and statistics and probability. Algebra related topics will be studied in preparation for the formal study of Algebra 1. There will be a focus on building conceptual understanding and problem-solving skills. Challenging problems are assigned and independent work is required.

Related courses:

Upon completion of Honors Math 7 a recommendation to take Math 8 or Honors Algebra 1 in 8th grade will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 40 daily minutes

Resources:

Text Resources: Go Math, Middle School Accelerated Grade 7, ISBN 10: 1328772896

Teachers are provided a Teacher’s Edition or accompanying instructor resources through a companion website.

Technology: Below is a list of technology that may be used:

● Holt McDougal Online

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Smart Notebook

● Smart TV

● Student supplied calculators (Ti-30XIIS)

● Chromebook

● Various websites (i.e. Blooket, Khan Academy)

Other Resources:

Graph Paper
Various Manipulative (i.e. Colored Pencils, Patty Paper)

Academic Math Grade 8

Course: Academic Math Grade 8

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This course will provide a strong mathematical foundation by extending previous knowledge to prepare students for the formal study of Algebra 1. Topics include the real number system, solving multi-step step equations, functions, in-depth study of the application of geometry, statistics, probability, rate of change, slope, graphing linear equations, exponents, and scientific notation. These topics are developed conceptually and focus on application in real life situations.

Related courses:

Academic Math Grade 8 LRC is designed to implement the goals of the IEP and parallels the curriculum of Academic Math Grade 8. Upon completion of Academic Math Grade 8 a recommendation to take Concepts of Math, Algebra 1 or Accelerated Algebra 1 will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes

Estimated Instructional Time: 40 daily minutes

Resources:

Text Resources:

Illustrative Mathematics: Middle School Math, ISBN-10: ‎ 1792402112

Teachers are provided a Teacher’s Edition or accompanying instructor resources through a companion website.

Technology Resources:

Below is a list of technology that may be used:

● Kendall Hunt Online

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-30XIIs)

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources:

Graph Paper
Scatter Plot
3D figures (cone, cylinder, sphere, cube)
Various Manipulatives (ie. Colored Pencils, Patty Paper)

Honors Algebra 1 (Grades 7 and 8)

Course: Honors Algebra 1 (Grade 7 and 8)

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This course is designed to provide students with a mathematically sound understanding of the concepts of Algebra. The student will develop fundamental algebraic skills and concepts based on the structure of the system of real numbers. Topics will include equations, inequalities, problem solving, polynomials, factoring, graphs and functions, simultaneous equations, irrational numbers, square roots, relations, functions, and variation. Challenging problems are assigned, and independent work is required. Because graphing activities are integrated throughout classroom presentations and textbook activities, a graphing calculator is required for this course. We recommend the TI-84 Plus calculator.

Related courses:

Upon completion of Honors Algebra 1 a recommendation to take Accelerated Algebra 1, Accelerated Algebra 2 or Honors Algebra 2 will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may be used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 40 daily minutes

Resources:

Text Resources: Algebra 1: (Merrill Algebra 1) McGraw Hill Education, ISBN-10: ‎ 0079039898

Teachers are provided a Teacher’s Edition or accompanying instructor resources through a companion website.

Technology Resources:

Below is a list of technology that may be used:

● McGraw Hill Algebra 1 Website

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources:

Graph Paper
Scatter plot
Various Manipulatives (ie. Colored Pencils, Patty Paper)

Honors Algebra 2 (Grades 8 and 9)

Course: Honors Algebra 2 Grade 8-9

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This course covers the same material as Accelerated Algebra 2 but in greater depth. The course also covers additional topics; therefore, the pace is more rapid than that of Accelerated Algebra 2. Honors Algebra 2 reviews and extends the concepts of Honors Algebra 1 by going into more depth in studying equations, inequalities, problem solving, factoring, irrational numbers, linear equations and simultaneous equations. New topics include the study of complex numbers, functions and their inverses, polynomial, quadratic, exponential and logarithmic functions. Students should be highly motivated, able to think and process math concepts quickly and in alternate fashion.

● Because graphing activities are integrated throughout classroom presentations and textbook activities, a graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: Teacher Recommendation and at least a solid “B” in Honors Algebra 1

Upon completion of Honors Algebra 2 a recommendation to take Geometry, Accelerated Geometry, Honors Geometry or Honors Study Of Geometry will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list formative assessment strategies that may used:

Bell Ringers
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources:

Algebra 2: Big Ideas Learning, ISBN 13: 978-1-64727-421-4

Teachers are provided a Teacher’s Edition or accompanying instructor resources through a companion website.

Technology Resources: Below is a list of technology that may be used:

Big ideas
Canvas - Instructure
Chromebook
Desmos
Gimkit
Kami
Quizizzs
Quizlet
Sapling
Nearpod
Smart Notebook
Smart TV
Student Supplied calculator (Recommend the TI-84)
Various other websites (i.e. Blooket, Khan Academy)

Other Resources:

Graph Paper
Rulers

High School

Concepts in Mathematics Grade 9

Course: Concepts in Mathematics Grade 9

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

The content and instructional practices of this course are designed to transition students to the successful completion of Algebra. Pre-algebra topics will include: Number systems and operations, systems of measurement (linear, square, and cubic), ratio, and proportion, percent, probability, statistics and data analysis. Algebraic topics will include the study of expressions, properties, equations, inequalities, functions and their graphs, linear systems, properties of exponents, operations with polynomials and angle relationships. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Concepts in Mathematics LRC is designed to implement the goals of the IEP and parallels the curriculum of Concepts in Mathematics. Upon completion of Concepts in Mathematics a recommendation to take Algebra 1 will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Mathmatters 1: Glencoe, ISBN: 007868174-X‎

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources:

Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Edia

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Scatter plots, Rulers

Algebra 1, Grade 9-10

Course: Algebra 1, Grade 9-10

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This Keystone preparation course provides students with a mathematically sound introduction to Algebra 1 and is designed for the student whose past achievement indicates a need for a more gradual pace. Course content will include the following topics: operations with real numbers and expressions, linear equations and inequalities, functions, coordinate geometry, and data analysis. ● A graphing calculator is required and is an integral part of the course. TI-84 Plus CE or TI-84 Plus are the recommended calculators. ● In this course students will prepare for the Keystone Algebra 1 exam, which they will take in May.

Related courses:

Algebra 1 LRC is designed to implement the goals of the IEP and parallels the curriculum of Algebra 1. Upon completion of Algebra 1 a recommendation to take Algebra 2 will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Algebra 1 Holt McDougal, ISBN: 978-0-547-64712-8

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Nearpod

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Accelerated Algebra 1

Course: Accelerated Algebra 1

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This course is designed to give students a mathematically sound introduction to algebra. The student is given the opportunity to develop fundamental algebraic skills and concepts based on the structure of the system of real numbers such as equations, inequalities, problem solving, polynomials, factoring, graphs and functions, simultaneous equations, irrational numbers, square roots, relations, functions, and variations. ● Because graphing activities are integrated throughout classroom presentations and textbook activities, a graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators. ● In this course students will prepare for the Keystone Algebra 1 Exam, which they will take in May.

Related courses:

Upon completion of Accelerated Algebra 1 a recommendation to take Algebra 2 or Accelerated Algebra 2 will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Algebra 1 Holt McDougal, ISBN: 978-0-547-64712-8

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Nearpod

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Algebra 2

Course: Algebra 2

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This course extends the concepts learned in Algebra 1 and provides a sound introduction to Algebra 2. The topics covered in this course include the conceptual development and understanding of: operations and complex numbers, non-linear expressions and equations, patterns, relations, functions, applications of functions, and data analysis. Mathematical modeling and applications will be applied with problem solving. ● A graphing calculator is required and is an integral part of the course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: Successful Completion of Algebra 1

Algebra 2 LRC is designed to implement the goals of the IEP and parallels the curriculum of Algebra 2. Upon completion of Algebra 2 a recommendation to take Geometry will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Algebra 2: Big Ideas Learning, ISBN 13: 978-1-64727-421-4

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Nearpod

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Accelerated Algebra 2

Course: Accelerated Algebra 2

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This course reviews and extends the concepts of Accelerated Algebra 1 by going into more depth in studying equations, inequalities, problem solving, factoring, irrational numbers, linear equations, and simultaneous equations. New topics include the study of polynomial, quadratic, radical, rational, exponential, greatest integer, and logarithmic functions. Also covered in the course are linear regression lines, and scatter plotting graphs. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: At least “C” in Accelerated Algebra 1

Upon completion of Accelerated Algebra 2 a recommendation to take Geometry or Accelerated Geometry will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Algebra 2: Big Ideas Learning, ISBN 13: 978-1-64727-421-4

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Honors Algebra 2

Course: Honors Algebra 2

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

Related courses:

Prerequisite: Teacher Recommendation and at least a solid “B” in Honors Algebra 1

Upon completion of Honors Algebra 2 a recommendation to take Geometry, Accelerated Geometry, Honors Geometry or Honors Study Of Geometry will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Algebra 2: Big Ideas Learning, ISBN 13: 978-1-64727-421-4

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Geometry

Course: Geometry

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This full-year course is a study of the major ideas of geometry and the basic properties of geometric figures, without an emphasis on formal proof. Topics include angles, angle measurement, triangles, congruent triangles, quadrilaterals and other polygons, circles, parallel lines, solid figures, perimeter, area, volume, and geometric probability. An ability to perform basic algebra skills is necessary. Students who were successful in Algebra 1 will be encouraged to continue their study of mathematics with Geometry. ● This course is not appropriate for students preparing for a scientifically oriented college curriculum and does not satisfy prerequisites for Accelerated Analysis. ● A graphing calculator is required for this course. The recommended calculators are the TI-84 Plus CE or TI-84 Plus.

Related courses:

Geometry LRC is designed to implement the goals of the IEP and parallels the curriculum of Geometry. Upon completion of Geometry a recommendation to take Analysis or Trigonometry/Statistics will be made.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Geometry: McDougal Littell, ISBN 13: 978-0-618-25022-6

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Accelerated Geometry

Course: Accelerated Geometry

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

This course is a rigorous study of the concepts of geometry requiring analytical thinking in addition to factual knowledge of the material. Students develop their deductive reasoning skills throughout the course through informal justifications and arguments as well as formal proofs. All of the topics of Geometry are covered, but in greater depth. Other topics such as symbolic logic and coordinate transformation are also included. Many algebraic concepts and skills from Accelerated Algebra 2 are integrated throughout the course. ● A graphing calculator is required in the course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: At least a “C” in Accelerated Algebra 2 and plan to study Accelerated Analysis.

Upon completion of Accelerated Geometry, a recommendation to take Trigonometry/Statistics, Analysis or Accelerated Analysis will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Geometry: McDougal Littell, ISBN 13: 978-0-618-25022-6

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Honors Geometry

Course: Honors Geometry

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

Related courses:

Prerequisite: Teacher Recommendation and at least a strong “B” in Honors Algebra 2

Upon completion of Honors Geometry a recommendation to take Advanced Placement Statistics, Accelerated Analysis, Honors Analysis or Honors Study of Analysis. will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Geometry: McDougal Littell, ISBN 13: 978-0-618-25022-6

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Honors Study of Geometry

Course: Honors Study of Geometry

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Pennsylvania Academic Standards for Mathematics

● Assessment Anchors and Eligible Content

Course Description:

Related courses:

Prerequisite: Teacher Recommendation and at least a strong “B” in Honors Algebra 2 and a has GIEP

Upon completion of Honors Geometry a recommendation to take Trigonometry/Statistics, Analysis, Accelerated Analysis, Honors Analysis or Honors Study of Analysis. will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Geometry: McDougal Littell, ISBN 13: 978-0-618-25022-6

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Trigonometry

Course: Trigonometry

Standards: This course is aligned to the following standards within the Council Rock School District Framework:

● Trigonometry Framework

Course Description:

Course content includes the study of trigonometric functions both as circular functions and as ratios in similar right triangles. Throughout the course, real-life problem situations will be used to connect trigonometry to many other fields and occupations. Algebra skills will be strengthened as needed. Technology will be an integral part of instruction. Students who require a more rigorous precalculus preparation should take Accelerated Analysis, which includes all of the trigonometry presented in this course. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: Successful Completion of Accelerated Algebra 2 & Accelerated Geometry with at least “C” or Successful Completion of Algebra 2 & Geometry with at least “B”

Upon completion of Trigonometry a recommendation to take Analysis or Accelerated Stat will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Trigonometry, Prentice Hall, ISBN: 0-13-979709-2

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Statistics

Course: Statistics

Standards: This course is aligned to the following standards within the Council Rock School District Framework:

● Statistics Framework

Course Description:

Students will learn methods for displaying distributions with graphs and numbers as well as the normal distribution. They will examine relationships using scatter plots and least squares regression and correlation. They will work with designing samples and experiments in combination with some basic principles of probability. Throughout the course, real-life problem situations will be used to connect statistics to many other fields and occupations. Algebra skills will be strengthened as needed. Technology will be an integral part of instruction. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: Successful Completion of Accelerated Algebra 2 & Accelerated Geometry with at least “C” or Successful Completion of Algebra 2 & Geometry with at least “B”

Upon completion of Statistics a recommendation to take Analysis or Accelerated Statistics will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Understandable Statistics, Brase/Brase, ISBN: 0-395-90768

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Accelerated Statistics

Course: Accelerated Statistics

Standards: This course is aligned to the following standards within the Council Rock School District Framework:

● Statistics Framework

Course Description:

There will be an emphasis on organizing data, averages and variation, elementary probability, the binomial and normal distributions and inferential statistics. Throughout the course, real-life problem situations will be used to connect statistics to many other fields and occupations. Algebra skills will be strengthened as needed. Technology will be an integral part of instruction. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: Successful Completion of Accelerated Algebra 2 & Accelerated Geometry with at least “C” or Successful Completion of Algebra 2 & Geometry with at least “B”

Upon completion of Accelerated Statistics a recommendation to take Analysis or Accelerated Analysis will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Elementary Statistics: A Step by Step Approach Tenth Edition, McGrawhill, ISBN: 978-007-679-3907

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Advanced Placement Statistics

Course: Advanced Placement Statistics

Standards: This course is aligned to the following standards within The College Board:

● Pennsylvania Academic Standards for Mathematics

● Advanced Placement Statistics Standards

Course Description:

The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes. They are exploring data: observing patterns and departures from patterns; planning a study: deciding what and how to measure; anticipating patterns: producing models using probability theory and simulation, and statistical inference: confirming models. Students who successfully complete the course and take the Advanced Placement Statistics examination may receive credit, advanced placement or both, for a one semester introductory college statistics course. ● The TI-84 Plus CE or TI-84 Plus graphing calculator is required for this course.

Related courses:

Prerequisite: Successful Completion of Accelerated Algebra 2

Upon completion of Advanced Placement Statistics, a recommendation to take Honors Analysis, Honors Study of Analysis, Advanced Placement Calculus AB or Advanced Placement Calculus BC. will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: The Practice of Statistics sixth edition, Bedford, Freeman and Worth, ISBN 13: 978-1-319-26932-6

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Analysis

Course: Analysis

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Precalculus Standards

Course Description:

Topics covered include an extension of algebra skills including using functions as models for a number of applied settings; sequences and series; probability; matrices; trigonometry; linear, quadratic, exponential and logarithmic functions. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: Successful Completion of Algebra 2 and Geometry

Upon completion of Analysis a recommendation to take Accelerated Statistics will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Advanced Mathematical Concepts Precalculus with Applications, Glencoe, ISBN: 0-07-868227-4

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Accelerated Analysis

Course: Accelerated Analysis

Standards: This course is aligned to the following standards within the Common Core:

● Precalculus Standards

Course Description:

This course is designed to provide a strong foundation in pre-calculus concepts, techniques, and applications to prepare students for more advanced work in mathematics. The primary topics studied are graphical analysis; functions including polynomial, rational, exponential, and logarithmic; complex numbers; polar coordinates and complex numbers in polar form; discrete mathematics; data analysis; and trigonometry. Problems will relate abstract concepts to real world situations. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators. ● It is recommended that students electing this course complete a review packet over the summer.

Related courses:

Prerequisite: Successful Completion of Accelerated Algebra 2 & Accelerated Geometry with at least a “B” in both courses

Upon completion of Accelerated Analysis a recommendation to take Advanced Placement Calculus AB, Advanced Placement Statistics, Accelerated Calculus or Accelerated Statistics will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Precalculus with Limits: A Graphing Approach, Ron Larson, ISBN 13: 978-1-111-42764-1

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Honors Analysis

Course: Honors Analysis

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Precalculus Standards

Course Description:

This course covers the same material as Accelerated Analysis, although in greater depth and at a faster pace. It also includes limits, and parametric equations. ● Juniors intending to take AP Calculus BC Level as seniors should elect this course and must maintain a “B” average throughout this course. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators. ● It is recommended that students electing this course complete a review packet over the summer.

Related courses:

Prerequisite: Teacher Recommendation

Upon completion of Honors Analysis a recommendation to take Advanced Placement Calculus AB, Advanced Placement BC, Advanced Placement Statistics, Accelerated Calculus, Accelerated Statistics, Advanced Placement Computer Science A or Advanced Placement Computer Science Principles. will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Advanced Mathematical Concepts Precalculus with Applications, Glencoe, ISBN: 0-07-868227-4

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Honors Study of Analysis

Course: Honors Study of Analysis

Standards: This course is aligned to the following standards within the Common Core:

● Precalculus Standards

Course Description:

This course is designed for students identified as gifted and will develop GIEP goals throughout the course. This course will provide a strong foundation in pre-calculus concepts, techniques, and applications to prepare students for more advanced work in mathematics. The primary topics studied are graphical analysis; functions including polynomial, rational, exponential, and logarithmic; complex numbers; polar coordinates and complex numbers in polar form; discrete mathematics; data analysis; and trigonometry. Problems will relate abstract concepts to real world situations. An indicator of a student’s potential success in the course would be to have earned a “B” or better in both courses. This course covers the same material as Honors Analysis, although in greater depth and at a faster pace, and includes limits, and parametric equations. ● Students intending to take AP Calculus BC Level as seniors should maintain a “B” average throughout this course. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators. ● It is recommended that students electing this course complete a review packet over the summer.

Related courses:

Prerequisite: GIEP and Successful Completion of Honors Algebra 2 & Honors Geometry

Upon completion of Honors Study of Analysis a recommendation to take Advanced Placement Calculus AB, Advanced Placement BC, Advanced Placement Statistics or Accelerated Calculus will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Advanced Mathematical Concepts Precalculus with Applications, Glencoe, ISBN: 0-07-868227-4

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Accelerated Calculus

Course: Accelerated Calculus

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Accelerated Calculus Standards

Course Description:

This course is intended to provide an introduction to college mathematics. The topics covered will include functions, graphs, limits, rate of change, formal differentiation, applications of the derivative, integration, applications of integration, and transcendental functions. This course does not prepare students to take the Advanced Placement Exam in May. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators.

Related courses:

Prerequisite: Strong background in Accelerated Algebra 2, Accelerated Geometry, & Accelerated Analysis

Upon completion of Accelerated Calculus, a recommendation to take Accelerated Statistics or Advanced Placement Statistics will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Calculus of a Single Variable Eighth Edition, ISBN: 0-618-50304-8

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Advanced Placement Calculus AB

Course: Advanced Placement Calculus AB

Standards: This course is aligned to the following standards within The College Board:

● Advanced Placement AB and BC Standards

Course Description:

This course is provided as an introduction to college mathematics. The topics covered are those typically found in the first semester and some of the second semester of a college level course, including functions, graphs, limits, rate of change, formal differentiation, applications of the derivative, integration, applications of integration, and transcendental functions. This course consists of a full academic year of work in calculus and topics covered in courses at the college level. It is expected that students taking this course will seek college credit or placement by taking the Advanced Placement examination in May. ● A graphing calculator is required for this course. The TI-84 Plus CE or TI-84 Plus are the recommended calculators. ● It is recommended that students electing this course complete a review packet over the summer

Related courses:

Prerequisite: Strong background in Accelerated Algebra 2, Accelerated Geometry, & Accelerated Analysis with at least “B” in all associated courses

Upon completion of Advanced Placement Calculus AB a recommendation to take Advanced Placement Statistics, Accelerated Statistics, Advanced Placement Computer Science A or Advanced Placement Computer Science Principles will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Calculus of a Single Variable Eighth Edition, ISBN: 0-618-50304-8

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

● Canvas - Instructure

● Chromebook

● Desmos

● Gimkit

● Kami

● Quizizzs

● Quizlet

● Sapling

● Nearpod

● Smart Notebook

● Smart TV

● Student Supplied calculator (Recommend the TI-84)

● Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Advanced Placement Calculus BC

Course: Advanced Placement Calculus BC

Standards: This course is aligned to the following standards within The College Board:

● Advanced Placement Calculus AB and BC Standards

Course Description:

This course is provided as an introduction to college mathematics. The topics covered are those typically found in the first two and one-half semesters of college level courses, including functions, graphs, limits, rate of change, formal differentiation, applications of the derivative, integration, applications of integration, transcendental functions, differential equations, polar equations, vectors and parametric equations, and sequences and series. This course will cover the content in the BC level of the Advanced Placement examination which students are strongly encouraged to take in May. Graphing calculators will be used extensively in the course and are required on the Advanced Placement examination. ● The TI-84 Plus CE or TI-84 Plus are the recommended calculators. ● It is recommended that students electing this course complete a review packet over the summer

Related courses:

Prerequisite: Strong background in Honors Algebra 2, Honors Geometry & Honors Analysis This course is provided as an introduction to college mathematics.

Upon completion of Advanced Placement Calculus BC a recommendation to take Advanced Placement Statistics, Advanced Placement Computer Science A or Advanced Placement Computer Science Principles. will be made.

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: Calculus of a Single Variable Eighth Edition, ISBN: 0-618-50304-8

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

AP Classroom
Canvas - Instructure
Chromebook
Desmos
Gimkit
Kami
Quizizzs
Quizlet
Sapling
Nearpod
Smart Notebook
Smart TV
Student Supplied calculator (Recommend the TI-84)
Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Accelerated Computer Science 1

Course: Accelerated Computer Science 1

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Advanced Placement Computer Science A Standards

Course Description:

This course is open to all high school students who are at least taking Accelerated Algebra I and are interested in the study of computer programming. This entry-level course is taught using the C# (pronounced “see sharp”) language, within the Microsoft Visual Studio and will focus on the development of fundamental programming skills. The topics in this course of study include a review of the .NET Integrated Development Environment, basic structure and syntax of the C# language, an introduction to object-oriented design using classes and objects, decision-making statements, iteration structures (loops), arrays, and string manipulation. The history of computers and programming will also briefly be discussed.

Related courses:

Upon completion of Computer Science 1 with at least a “C”, students are encouraged to move on to Computer Science 2.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: C# Programming from Problem Analysis to program Design (2^nd edition), Doyle, ISBN: 1-4239-0146-0

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

AP Classroom
Canvas - Instructure
Chromebook
Desmos
Gimkit
Kami
Quizizzs
Quizlet
Sapling
Nearpod
Smart Notebook
Smart TV
Student Supplied calculator (Recommend the TI-84)
Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Accelerated Computer Science 2

Course: Accelerated Computer Science 2

Standards: This course is aligned to the following standards within the Pennsylvania Department of Education:

● Advanced Placement Computer Science A Standards

Course Description:

Students will learn the fundamental skills that are required to design and develop object-oriented applications for the Web and Microsoft Windows. This course is taught using the C# language and will serve as an extension to the concepts introduced in Computer Science 1. Additional topics in the course of study include file handling and database manipulation, methods, enumerations and structures, and an introduction to Windows forms and painting. The course will be highly project-based and geared toward real-world applications using a variety of hands-on lab exercises, case studies, and team learning tasks. It is recommended that students take Computer Science 2 before taking Advanced Placement Computer Science.

Related courses:

Prerequisite: Concurrently enrolled in a minimum of Accelerated Algebra 2 and Successful Completion of Computer Science 1

It is recommended that students take Computer Science 2 before taking Advanced Placement Computer Science.

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: C# Programming from Problem Analysis to program Design (2^nd edition), Doyle, ISBN: 1-4239-0146-0

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

Canvas - Instructure
Chromebook
Desmos
Gimkit
Kami
Quizizzs
Quizlet
Sapling
Nearpod
Smart Notebook
Smart TV
Student Supplied calculator (Recommend the TI-84)
Study Island

● Various other websites (i.e. Blooket, Khan Academy)

Other Resources: Graph Paper, Ruler, Highlighters

Advanced Placement Computer Science A

Course: Advanced Placement Computer Science A

Standards: This course is aligned to the following standards within The College Board:

● Advanced Placement Computer Science A Standards

Course Description:

This advanced course is provided as an introduction to college-level computer programming, using the Java language. It is open to students who have a solid foundation in object-oriented computer programming concepts (i.e. C#, C++, Visual Basic, and Java). A fundamental skill to the study of computer science is to develop computer programs to solve problems. A large part of this course is built around the development of computer programs or parts of programs to solve a given problem using object-oriented designs. The topics in the course of study include the use of standard Java classes, objects, data types, methods, decision making statements, string handling, the application of data storage and data processing, and other algorithms. Students will also learn to create and manipulate applications, applets, and GUI components. The course will be highly project-based and geared toward real-world applications using a variety of hands-on lab exercises, case studies, and team learning tasks. It is expected that students will seek college credit by taking the Advanced Placement Computer Science Examination (Level A) in May.

Related courses:

Prerequisite: Successful Completion of at least one year of High School English, Computer Science 2, and Accelerated Algebra 2 or Teacher Recommendation

Instructional Strategies:

Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Unit Tests
Quizzes
Mid-Term
Final

Estimated Instructional Time: 50 daily minutes

Resources:

Text Resources: C# Programming from Problem Analysis to program Design (2^nd edition), Doyle, ISBN: 1-4239-0146-0

Teachers are provided a Teacher’s Edition or accompanying instructor resources.

Technology Resources: Below is a list of technology that may be used:

Technology Resources:

●      Canvas - Instructure

●      AP Classroom

●      BlueJ

●      Java 10

●      Student Supplied Calculator (Recommended TI-84)

Advanced Placement Computer Science Principles

Course: Advanced Placement Computer Science Principles

Standards: This course is aligned to the following standards within The College Board:

● Advanced Placement Computer Science Principles Standards

Course Description:

AP Computer Science Principles offers a multidisciplinary approach to teaching the underlying principles of computation. It is open to students who have completed Algebra 2 with a strong foundation in function notation and problem solving. The course will introduce students to the creative aspects of programming, abstractions, algorithms, large data sets, the internet, cybersecurity concerns, and computing impacts. AP Computer Science Principles also gives students the opportunity to use current technologies to create innovative computational artifacts for both self-expression and problem solving. Students will develop these artifacts using the same creative processes artists, writers, computer scientists, and engineers use to bring ideas to life. It is expected that students will seek college credit by taking the Advanced Placement Computer Science Principles Examination in May.

Related courses:

Prerequisite: Successful Completion of at least one year of High School English and Accelerated Algebra 2 or Teacher Recommendation

Instructional Strategies: Below is a list of strategies for high-quality instruction in Math that may be used:

Poll The Class
Cooperative Learning
Direct Instruction
Discovery Learning
Discussion
Exploratory activities
Group work
Individual Instruction
Info Gaps
Investigative Activities
Movement Activities
Problem Solving
Real world applications
Think-Pair-Share
Whiteboard

Forms of Assessment to Measure Attainment of Course Objectives:

Formative Assessments: Below is a list of formative assessment strategies that may used:

Bell Ringers
Class Poll
Cool Downs
Exit Ticket
Homework Checks
One-on-One Check-Ins
Online Tools (Quizizz, Kahoot, Canvas Practice Quizzes)
Participation
Quick Checks
Self-rate understanding
Warm-ups
Whiteboards

Summative Assessments: Below is a list of summative assessment strategies that may be used:

Coding Tests
Quizzes

Estimated Instructional Time: 50 daily minutes

Resources:

Technology Resources:

● Canvas - Instructure

● Code HS

● AP Classroom