Kindergarten Math

PA Core Mathematics Standards
Module 1 and Module 2

•  CC.2.1.K.A.1 Students acquire the knowledge and skills needed to: Know number names and write and recite the count sequence. 
• CC.2.1.K.A.2 Students acquire the knowledge and skills needed to: Apply one-to-one correspondence to count the number of objects. 
• Module 3 and Module 4
• CC.2.1.K.A.3 Students acquire the knowledge and skills needed to: Apply the concept of magnitude to compare numbers and quantities. 
• CC.2.4.K.A.4 Students acquire the knowledge and skills needed to: Classify objects and count the number of objects in each category.  
• Module 5 and Module 6
•  CC.2.2.K.A.1 Students acquire the knowledge and skills needed to: Extend the concepts of putting together and taking apart to add and subtract within 10. 

• Numbers determine quantities.
• Numbers follow a standard order.
• The concept of first versus last when counting objects.
• Written numerals represent an amount.
• Greater than, less than, and equal to are used to compare groups.
• The concepts of same and different.
• The last number stated tells the number of objects counted.
• Attributes can include color, size, shape, and amount.
• Sort groups based on common attributes.
• Addition means to put together groups.
• Subtraction means to take from groups.
• Equations represent groups being put together or taken apart.
• Equations follow a standard format.
• Strategies for addition and subtraction include using objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
• When presented with a word problem, be able to determine when to add and when to subtract.
   

• Understand how to count and represent objects and represent each object with a number name. 
• Recognize how many objects are in a group.
• Understand that numbers can be shown in a variety of ways but that the number itself does not change.
• Written numerals correlate to how many objects are shown.
• Each successive number has a quantity that is one larger.
• Comparing groups through a variety of methods creates a foundation for comparing more difficult numbers and for adding and subtracting.
• Use attributes for classification, articulate the rule used for the classification, and compare sets based on quantity.
• Joining and taking apart groups in a variety of ways sets the foundation for future addition and subtraction.

Module 1

• Count objects, saying the number names in standard order from 0-5.
• Pair each object with only one number name and each number name with only one object.
• Count to answer "how many?" questions.
• Count out a number of objects to match a given number.

Module 2

• Say the numbers zero to five.
• Write the numbers zero to five.
• Represent a number of objects with a written numeral.
• Count to answer “how many?” questions.
• Count out a number of objects to match a given number.

Module 3

• Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group.
• Use counting and matching strategies to compare groups of objects.
• Compare numbers presented as written numerals.

Module 4

• Classify and count by color.
• Classify and count by shape.
• Classify and count by size.
• Classify, count, and sort by count.

Module 5

• Solve addition and subtraction word problems within 5 by using objects or drawings to represent the problem.
• Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
• Add and subtract within 5.

Module 6

• Solve addition and subtraction word problems within 5 by using objects or drawings to represent the problem.
• Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
• Add and subtract within 5.

• Why is it important to know the names of numbers and the order they go in?
• How can we use counting to describe the world around us?
• What patterns can we find in the number sequence?
• Why does the order in which we count objects not change the total?
• What can we learn by matching numbers to objects when we count?
• How can we use numbers and categories to describe and compare the world around us?
• How can we use addition and subtraction to solve everyday problems?
   

• L1.1 How can I represent the numbers 1 and 2 with pictures?
• L1.2 How can I represent the numbers 3 and 4 with pictures?
• L1.3 How can I represent numbers up to 5 with pictures?
• L1.4 How can I show the difference between groups of 0 and other numbers?
• L1.5 How can I use two different groups to make a group of five?
• L2.1 How can I count and write the numbers 0 and 1?
• L2.2 How can I count and write the numbers 2 and 3?
• L2.3 How can I count and write the numbers 4 and 5?
• L2.4 How can I count objects to 5 and write the correct number?
• L2.5 How can I make groups of 1 to 5 in the correct order?
• L3.1 How can I compare groups and identify the greater number by drawing objects?  
• L3.2 How can I compare groups and identify the lesser number by drawing objects?
• L3.3 How can I show two equal groups by counting and matching?
• L3.4 How can I compare numbers?
• L3.5 How can I show and compare various groups by drawing?
• L3.6 How can I write and compare numbers?
• L4.1 How can I sort objects by color and write the number of objects in each group?
• L4.2 How can I sort objects by shape and write the number of objects in each group?
• L4.3 How can I sort objects by size and write the number of objects in each group?
• L4.4 How can I sort objects by count and write the number of objects in each group?
• L5.1 How can I add to a group and represent the problem with numbers?
• L5.2 How can I subtract from a group and represent the problem with numbers?
• L5.3 How can I solve addition problems with an equation?
• L5.4 How can I solve subtraction problems with an equation?
• L5.5 How can I model addition problems by writing an equation?
• L 5.6 How can I model subtraction problems by writing an equation?
• L5.7 How can I determine whether a problem is addition or subtraction problem, solve the problem, and model it with an equation?
• L6.1 How can I represent an addition problem with objects or drawings and find the total?
• L6.2 How can I represent a subtraction problem with objects or drawings and find the total?
• L6.3 How can I solve an addition problem by putting groups together and model the problem with an equation?
• L6.4 How can I solve a subtraction problem by taking a group apart and model the problem with an equation?
• L6.5 How can I use mental images to find the total and model the groups with an addition equation?
• L6.6 How can I use mental images to take apart a group and model the subtraction problem with an equation?
• L6.7 How can I solve an addition or subtraction problem and model the problem with an equation?
   

• Two-color counters, assorted counters
• Connecting cubes of assorted colors
• Whiteboards / Smart Pals
• Crayons
• Plane shapes that include circle, square, triangle, and rectangle
• Dot plates, dot cards, dominoes
• Into Math Kindergarten Modules 1-6 Workbooks

• And
• Five
• Four
• One
• Three
• Two
• Zero
• Take apart
• Count
• Larger
• Compare
• Equal to
• Greater than
• Less than
• Match
• Put together
• Big
• Category
• Classify
• Size
• Shape
• Small
• Sort
• subtract
• Add to 
• Equation
• Join
• Minus
• Plus
• Take away
• Take from
• total

• Are You Ready? (Modules 1-6)
• Module 1: Test Form A
• Module 2: Test Form A
• Module 3: Test Form A
• Module 4: Test Form A
• Module 5: Test Form A
• Module 6: Test Form A
• * Reteach/Review with Test Form B as needed

PA Core Mathematics Standards
Module 7 and Module 8

•  CC.2.1.K.A.1 Students acquire the knowledge and skills needed to: Know number names and write and recite the count sequence. 
• CC.2.1.K.A.2 Students acquire the knowledge and skills needed to: Apply one-to-one correspondence to count the number of objects.  

Module 9 

• Will be taught during a later Unit.

Module 10

• CC.2.1.K.A.3 Students acquire the knowledge and skills needed to: Apply the concept of magnitude to compare numbers and quantities. 
• Module 11, Module 12, and Module 13
•   CC.2.2.K.A.1 Students acquire the knowledge and skills needed to: Extend the concepts of putting together and taking apart to add and subtract within 10.

• Numbers determine quantities.
• Numbers follow a standard order.
• The concept of first versus last when counting objects.
• Written numerals represent an amount.
• Greater than, less than, and equal to are used to compare groups.
• The concepts of same and different.
• The last number stated tells the number of objects counted.
• Addition means to put together groups.
• Subtraction means to take from groups.
• Equations represent groups being put together or taken apart.
• Equations follow a standard format.
• Strategies for addition and subtraction include using objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
• When presented with a word problem, be able to determine when to add and when to subtract.
• Numbers can be broken down and put together in more than one way.

• Understand how to count and represent objects and represent each object with a number name. 
• Recognize how many objects are in a group.
• Understand that numbers can be shown in a variety of ways but that the number itself does not change.
• Written numerals correlate to how many objects are shown.
• Each successive number has a quantity that is one larger.
• Comparing groups through a variety of methods creates a foundation for comparing more difficult numbers and for adding and subtracting.
• Joining and taking apart groups in a variety of ways sets the foundation for future addition and subtraction.
• Understand a group of objects can be broken into smaller groups in more than one way but still remains the total amount.

Module 7

• Count and represent numbers six to ten.
• Count and write numerals six to ten.
• Find ways to make ten.

Module 8

• Read and write numbers six to ten.
• Count to answer “how many” questions up to ten.
• Given a number, count up to ten objects.

Module 9 

• Will be taught during a later Unit.

Module 10

• Identify whether the number of objects within 10 in one group is greater than, less than, or equal to the number of objects in another group.
• Use reasoning, matching, and counting strategies to identify greater than, less than, or equal to.
• Compare two numbers between 1 and 10 presented as written numerals.

Module 11

• Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.
• Solve addition word problems within 10 by using objects or drawings.
• Solve subtraction word problems within 10 by using objects or drawings.
• Add & subtract within 10.

Module 12

• Represent addition and subtraction within 10 using objects, drawings, and equations.
• Solve addition and subtraction word problems within 10 using objects, drawings, and equations.

Module 13

• Decompose numbers (less than or equal to 10) into pairs in more than one way.
• Record each decomposition with a drawing or equation.
• Find the number that makes 10 when added to a given number.
• Understand that the last number said tells the number of objects counted.

• How can we count and show numbers from six to ten using objects, drawings, or numerals?
• What are different ways we can make the number 10 using smaller numbers?
• How can we tell if a group has more, less, or the same number of objects as another group?
• How can we use drawings, objects, or numbers to solve addition and subtraction problems up to 10?
• How can we show a group of things being put together or taken apart?
• What are different ways we can solve an addition or subtraction problem?
• How do we know if we should add or subtract in a word problem?
• Can we make the same number in more than one way?
   

• .1 How can I represent the numbers 6 and 7 with pictures?
• L7.2 How can I represent the numbers 8 and 9 with pictures?
• L7.3 How can I represent the number 10 with pictures?
• L8.1 How can I count and write the numbers 6 and 7?
• L8.2 How can I count and write the numbers 8 and 9?
• L8.3 How can I count and write the number 10?
• L8.4 How can I count in order starting and ending at any number?
• L10.1 How can I use matching to compare two groups and identify which group has the greater number of objects?
• L10.2 How can I use one-to-one comparison to compare two groups and identify which group has the lesser number objects?
• L10.3 How can I use one-to-one correspondence to compare two groups and identify if the groups have an equal number of objects? 
• L10.4 How can I compare groups of objects and numbers within ten by counting? 
• L10.5 How can I compare groups of objects by matching to determine which group is greater than, less than, or equal to the number of objects in another group? 
• L10.6 How can I compare two numerals within ten to determine which group is greater than, less than, or equal to the number of objects in another group? 
• L11.1 How can I act out joining groups to find the total?
• L11.2 How can I act out some leaving a group to find out how many are left?
• L11.3 How can I find the solution to an Add To addition problem?
• L11.4 How can I cross out objects to show how many are taken away and find how many are left?
• L11.5 How can I write an addition equation to model a problem?
• L11.6 How can I write a subtraction equation to model a problem?
• L11.7 How can I draw to represent an addition or subtraction word problem and write an equation?
• L12.1 How can I represent Put Together problems using drawings, objects, and equations?
• L12.2 How can I represent Take Apart problems using drawings, objects, and equations?
• L12.3 How can I add to a group to find how many there are now and represent the problem with numbers?
• L12.4 How can I solve subtraction word problems using objects and drawings and write questions to model the problems?
• L12.5 How can I recognize addition and subtraction word problems and solve problems using objects and drawings and writing equations?
• L13.1 How can I use two different groups of objects or drawings to represent the numbers 6 and 7 in more than one way?
• L13.2 How can I use two different groups of objects or drawings to represent the number 8 in more than one way?
• L13.3 How can I use two different groups of objects or drawings to represent the number 9 in more than one way?
• L13.4 How can I use two different groups of objects or drawings to represent the number 10 in more than one way?
• L13.5 How can I make 10 from a given number, 1-9?
   

• Two-color counters, assorted counters
• Ten frames
• Number Cards (0-10)
• Connecting cubes of assorted colors
• Whiteboards / Smart Pals
• Number tiles, number cubes
• Grid paper, lined paper, index cards
• Crayons
• String
• Dot Cards (1-10)
• Building Blocks
• Into Math Kindergarten Modules 7-13 Workbooks
   

• Six
• Seven
• Eight
• Nine
• Ten
• Compare
• Greater than
• Less than
• Equal to
• Is equal to
• Plus
• Minus
• Subtract
• Add to
• Take from
• Put together
• Take apart
• Equation
• Addend

• Are You Ready? (Modules 7-13)
• Module 7: Test Form A
• Module 8: Test Form A
• Module 10: Test Form A
• Module 11: Test Form A
• Module 12: Test Form A
• Module 13: Test Form A
  • * Reteach/Review with Test Form B as needed
     

PA Core Mathematics Standards
Module 14, Module 15, and Module 16

• CC.2.3.K.A.1 Students acquire the knowledge and skills needed to: Identify and describe two- and three-dimensional shapes.
• CC.2.3.K.A.2 Students acquire the knowledge and skills needed to: Analyze, compare, create, and compose two- and three-dimensional shapes.

• The meaning of three-dimensional shapes.
• The meaning of two-dimensional shapes.
• The attributes and names of two-dimensional shapes and three-dimensional shapes.
• The meaning of positional words.
• New shapes can be made when combining existing shapes.
• There are differences and similarities between two-dimensional and three-dimensional shapes.
   

• Correctly name shapes regardless of their orientation, location, or overall size.
• Describe objects in the environment using names of shapes, and describe the relative positions of these objects using spatial terms.
• Describe, analyze, and compare the attributes of two-dimensional shapes.

Module 14

• Correctly name and describe the characteristics of three-dimensional shapes regardless of their orientations or overall size (sphere, cube, cylinder, cone).
• Identify everyday objects resembling spheres, cubes, cylinders, and cones.
• Build three-dimensional shapes.

Module 15

• Use above and below to describe positions of objects in the environment.
• Use next to and beside to describe positions of objects in the environment.
• Use in front of and behind to describe positions of objects in the environment.

Module 16

• Identify and describe circles, squares, triangles, rectangles, and hexagons regardless of their orientations or overall size.
• Compose simple shapes to form larger shapes.
• Compare and contrast two-dimensional and three-dimensional shapes.

• How can we describe and name 2D and 3D shapes, no matter how they look or where they are?
• What shapes do we see in the world around us, and how can we build them?
• How can we use words like 'above,' 'below,' and 'next to' to describe where things are?
• How are flat shapes (2D) and solid shapes (3D) the same and different?
   

• L14.1 How can I describe the characteristics of a sphere?
• L14.2 How can I describe the characteristics of a cube?
• L14.3 How can I describe the characteristics of a cylinder?
• L14.4 How can I describe the characteristics of a cone?
• L14.5 How can I build a three-dimensional shape when given its description?
• L15.1 How can I represent and describe the position of objects by naming the shape of the objects and using the terms above and below to describe their relative positions?
• L15.2 How can I represent and describe the position of objects by naming the shape of the objects and using the terms next to and beside to describe their relative positions?
• L15.3 How can I represent and describe the position of objects by naming the shape of the objects and using the terms in front of and behind to describe their relative positions?
• L16.1 How can I identify and describe circles?
• L16.2 How can I identify and describe squares? 
• L16.3 How can I identify and describe triangles?
• L16.4 How can I identify and describe rectangles?
• L16.5 How can I identify and describe hexagons?
• L16.6 How can I compose a variety of shapes?
• L16.7 How can I compare two- and three-dimensional shapes?
   

• Various Three-dimensional shapes
• Classroom objects shaped like cubes, spheres, cylinders, and cones
• Crayons 
• Pictures of objects shaped like cones, cylinders, cubes, and spheres
• Clay or marshmallows, sticks or toothpicks
• Semantic Map (Teacher Resource Masters) 
• Large shapes (circles, squares, triangles, rectangles) in a variety of colors
• Two-dimensional shapes and objects in the classroom
• Fluency Builder: Addition Within 5 (Differentiated Instruction Blackline Masters)
• Fluency Builder: Subtraction Within 5 (Differentiated Instruction Blackline Masters) 
• Paper, index cards 
• Picture of a regular hexagon, picture of an irregular hexagon
• Pattern Blocks (Teacher Resource Masters)
• Cards showing images of two-dimensional shapes and three-dimensional shapes 
• Into Math Kindergarten Modules 14-16 Workbooks

• Curved surface
• Solid
• Sphere
• 3-dimensional shapes
• Cube
• Flat surface
• Cylinder
• Cone
• Above
• Below
• Beside
• Next to
• Behind
• In front of
• Circle
• Flat
• 2-dimensional shapes
• Square
• Triangle
• Rectangle
• Hexagon

• Are You Ready? (Modules 14-16)
• Module 14: Test Form A
• Module 15: Test Form A
• Module 16: Test Form A
  • * Reteach/Review with Test Form B as needed
     

PA Core Mathematics Standards
Module 17 and Module 18 

• CC.2.1.K.A.1 Students acquire the knowledge and skills needed to: Know number names and write and recite the count sequence.
• CC.2.1.K.A.2 Students acquire the knowledge and skills needed to: Apply one-to-one correspondence to count the number of objects.
• CC.2.1.K.B.1 Students acquire the knowledge and skills needed to: Use place value to compose and decompose numbers within 19.

Module 9

• NCTM Counting & Cardinality: Counting to 100 by ones and tens. 

• Numbers determine quantities.
• Numbers follow a standard order.
• The concept of first versus last when counting objects.
• Written numerals represent an amount.
• The last number said tells the number of objects counted.
• Adding some more ones to a group of ten creates teen numbers.
• Numbers follow a pattern within 100.
• Counting can occur by ones or tens.

• Compose and decompose numbers from 11 to 19 into ten ones and some further ones by using objects, drawings, and equations. 
• Count to answer “how many?” questions about as many as 20 things arranged in different ways.
• Write and represent numerals from 0-20.
• Find and use number patterns in the hundreds chart to count by ones and tens.
• Find a given number and count on from that number using a hundreds chart.
   

Module 17

• Compose ten ones and some more ones to 19.
• Represent numbers to 20.
• Decompose numbers to 19 into ten ones and some more ones.

Module 18

• Read and write numerals from 0 to 20 and represent a number of objects with a written numeral.
• Compose and decompose numbers from 11 to 19 into ten ones and some further ones.

Module 9

• Count to 100 by ones.
• Count to 100 by tens.
• Count forward from any number to 100
• Understand how to find a number that comes after another number.
• Understand number names.

• How can we show numbers from 11 to 19 using tens and ones?
• How can we count to 100 by ones and by tens?
• What comes next when we count, and how do we know?
• How do we read, write, and show numbers using objects and numerals?
   

• L17.1 How can I compose 10 ones and some more ones to represent numbers 11 to 14?
• L17.2 How can I compose 10 ones and some more ones to represent the number 15?
• L17.3 How can I compose 10 ones and some more ones to represent numbers 16 to 19?
• L17.4 How can I count and represent numbers to 20?
• L18.1 How can I count and write numbers up to 14 and make a group of that many objects? 
• L18.2 How can I count and write numbers up to 15 and make a group of that many objects? 
• L18.3 How can I count and write numbers up to 19 and make a group of that many objects?
• L18.4 How can I count and write numbers up to 20 and make a group of that many objects?  
• L9.1 How can I count to 100 by ones?
• L9.2 How can I count to 100 by tens?
• L9.3 How can I count forward from a given number other than 1 and stop counting at a specific number?
   

• connecting cubes 
• counters, two-color counters
• MathBoard / Smart Pals 
• ten frames
• hundreds charts
• Into Math Kindergarten Modules 17, 18, & 9 Workbooks
   

• Eleven
• Twelve
• Thirteen
• Fourteen
• More
• Ones
• Fifteen
• Sixteen
• Seventeen
• Eighteen
• Nineteen
• Twenty
• Column
• Row

• Are You Ready? (Modules 17-18, Module 9)
• Module 17: Test Form A
• Module 18: Test Form A
• Module 9: Test Form A
  • * Reteach/Review with Test Form B as needed

PA Core Mathematics Standards
Module 19 and Module 20 

• CC.2.4.K.A.1 Students acquire the knowledge and skills needed to: Describe and compare attributes of length, area, weight, and capacity of everyday objects. 

• The terms longer, taller, or shorter can be used to compare the length and height of two objects.
• Objects need to be placed at the same starting point to compare the lengths accurately.
• Things can be classified and sorted based on similar and different attributes.
• The terms heavy and light can be used to compare and describe the weight of two objects.
   

• Describe several measurable attributes of a single object.
• Compare two objects with a measurable attribute in common.

Module 19

• ​​Describe length and height by identifying longer, taller, and shorter objects.
• Directly compare two objects and describe the difference in length.

Module 20

• Describe weight as heavy or light.
• Compare two objects by weight.
• Identify more than one attribute in objects and compare two objects by more than one attribute.

• How can we tell if something is longer, shorter, or taller?
• How can we describe and compare how heavy or light things are?
• What words can we use to talk about the size and weight of objects?
• How can we compare two things using more than one attribute, like size and weight? 

• L19.1 How can I describe the height and length of objects using math language?
• L19.2 How can I compare the lengths of two objects and describe the comparison in a sentence using longer than or shorter than?
• L19.3 How can I compare the heights of two objects and describe the comparison in a sentence using taller than or shorter than?
• L20.1 How can I describe objects as heavy or light?
• L20.2 How can I identify which object is heavier or lighter and use the words heavier and lighter to describe the attributes of weight? 
• L20.3 How can I use more than one attribute to describe an object? 

• Crayons
• Classroom items such as connecting cubes, yarn, manipulatives, rulers, yard stick, balance, etc.
• Into Math Kindergarten Modules 19-20 Workbooks

• height
• length
• longer
• shorter
• taller
• heavier
• lighter
• weight

• Are You Ready? (Modules 19-20)
• Module 19: Test Form A
• Module 20: Test Form A
  • * Reteach/Review with Test Form B as needed