# Curriculum for Kindergarten

## Driven by Pedagogy, Supported by Technology (and not vice versa),

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MODULE 1 Numbers to 10

1C: Numbers to 5 in Different Configurations, Math Drawings, and Expressions

Students count in sequence to determine position or total up to 5. They relate objects to digits and see digits in a variety of fonts. They work with aligned objects, scattered objects, fingers, and the number line. Students learn strategies for counting with 1:1 match and learn that sets of objects with the same total can be aligned in different ways.

- Match a numbered set of 1, 2, or 3 cubes to an identical numbered set of cubes
- Match numbered and non-numbered sets of cubes to a number 1-3
- Match sets of cubes to numbers 1-3
- Match numbers 1-3 to their positions on a number line labeled with numbers and dot patterns
- Identify a numbered set of cubes that matches an identical set of 4 or 5 numbered cubes
- Match numbered and non-numbered sets of cubes to number 4 or 5
- Type numbers in sequence to identify 4 or 5 aligned objects
- Count 2-5 aligned objects to determine the total
- Match numbers 1-5 to arrangements of fingers displayed on a hand
- Match sets of cubes to numbers 1-5
- Identify numbered sets of cubes that match a given total up to 5
- Match numbers 1-5 to their positions on a number line labeled with numbers and dot patterns
- Align scattered objects to count and determine the total
- Count to find the total of scattered objects by matching 1:1 numbers to objects
- Identify a set of scattered objects that matches a given total up to 5
- Decompose a set of 3 objects into two groups and identify as addends

1D: The Concept of Zero and Working with Numbers 0–5

Students use digits 1-5 to sequence objects and to determine position or total. They work with aligned objects, scattered objects, and the number line. They explore the composition of the number 3 and begin using +, -, and = signs.

- Identify sets of 0 among sets of scattered objets
- Identify a set of scattered objects that matches a given total up to 5
- Sequence scattered objects numbered 1-5 in ascending order
- Continue a count sequence on a number line from a given point to reach a given position
- Identify missing numbers up to 5 on a numbered number line
- Identify the object at a given position in a set of aligned objects
- Identify the position of an object in a set of aligned objects
- Decompose a set of 3 objects into two groups and identify as addends in an equation
- Identify missing numbers in equations to show composition of 3 given a model of base-10 blocks

1E: Working with Numbers 6–8 in Different Configurations

Students count in sequence to determine position or total up to 9. They relate objects to digits and see digits in a variety of fonts. They work with aligned objects, scattered objects, fingers, and the number line. Students learn strategies for counting with 1:1 match and learn that sets of objects with the same total can be aligned in different ways.

- Identify the number of fingers up to 7 displayed on two hands
- Match numbers 0-7 to arrangements of fingers displayed on two hands
- Identify a set of aligned objects that matches a given total up to 7
- Match numbered patterns of dots to an identical numbered pattern of dots up to 7
- Identify sets of numbered cubes that match a given total of 6 or 7
- Match numbers 1-7 to their positions on a number line labeled with numbers and dot patterns
- Count objects as they move away from a set and identify the total
- Count scattered objects two different ways to arrive at the same total
- Identify the number of fingers up to 8 displayed on two hands
- Match numbers 0-8 to arrangements of fingers displayed on two hands
- Identify a set of aligned objects that matches a given total up to 8
- Identify sets of numbered cubes that match a given total up to 9
- Count objects as they move away from a set and identify the total
- Count scattered objects two different ways to arrive at the same total
- Identify the total number of scattered objects after a known total has been rearranged

1F: Working with Numbers 9–10 in Different Configurations

Students work increasingly with 0 and with numbers 6-10 to determine totals and recognize digits. They work with scattered objects, non-identical objects, fingers, and the number line.

- Determine the total of up to 9 scattered objects
- Count out a given number of objects from a larger set
- Determine the total of up to 9 scattered objects
- Match patterns of dots to their numbered position on a number line
- Determine the total of up to 9 non-identical scattered objects
- Match sets of non-identical objects to numbers up to 9
- Match numbered patterns of dots to an identical numbered pattern of dots up to 9
- Identify sets of numbered cubes that match a given total 0-10
- Identify a set of scattered objects that matches a given total up to 10
- Match numbered patterns of dots to an identical numbered pattern of dots up to 10
- Match numbers 0-10 to their position on a number line labeled with numbers and dot patterns

1G: One More with Numbers 0–10

Students use familiar representations (objects, base-10 blocks, the number line, and equations) to explore the concept of one more. They begin to count on rather than count all.

- Identify the object at a given position in a set of aligned objects
- Continue a count sequence on a number line from a given point to reach a given position
- Identify missing numbers up to 9 on a numbered number line
- Continue a count sequence on a number line from a given point
- Solve +1 equations based on a model of base-10 blocks
- Solve +1 equations based on a number line model
- Solve +1 problems based on a known total and a scenario using objects
- Solve +1 equations

1H: One Less with Numbers 0–10

Students use familiar representations (objects, base-10 blocks, the number line, and equations) to explore the concept of one less. They alternate between +1 and -1 to solve problems.

- Determine one more and one less on a number line
- Continue a count sequence on a number line from a given point counting back
- Solve -1 equations based on a model of base-10 blocks
- Solve -1 equations based on a number line model
- Solve -1 problems based on a known total and a scenario using objects
- Solve -1 equations
- Solve +1 and -1 equations based on a model of base-10 blocks
- Solve +1 and -1 equations based on a number line model
- Solve +1 and -1 problems based on a known total and a scenario using objects
- Solve +1 and -1 equations

MODULE 2 Two-Dimensional and Three-Dimensional Shapes

2A: Two Dimensional Flat Shapes

Students become familiar with the appearance and names of two-dimensional shapes. They work with squares, circles, triangles, rectangles, and hexagons. Students identify examples from among non-examples. Our sound feature allows non-readers access to shape names.

- Identify squares and circles based on an example and shape names
- Match shape names to squares and circles
- Identify squares and circles based on shape names
- Identify squares, circles, and triangles based on an example and shape names
- Match shape names to squares, circles, and triangles
- Identify squares, circles, and triangles based on shape names
- Identify squares, circles, and triangles based on shape names
- Identify triangles and rectangles based on an example and shape names
- Match shape names to triangles and rectangles
- Identify circles, triangles, and rectangles based on shape names
- Identify squares and hexagons based on an example and shape names
- Match shape names to triangles and hexagons
- Identify circles, triangles, and hexagons based on shape names
- Identify squares, circles, triangles, rectangles, and hexagons based on shape names
- Match shape names to squares, circles, triangles, rectangles, and hexagons

2B: Three-Dimensional Solid Shapes

Students explore spatial relationships by describing relative positions and directions. They use the words above, below, up, down, in front, behind, beside, and between and manipulate objects to reflect these relationships. Our sound feature helps even non-readers succeed with these language-based exercises.

- Identify positions above and below relative to an object
- Describe the relationship between two objects using the word above or below
- Place an object in a given position above or below another object
- Place two objects in given positions above or below a third object
- Move an object in a given direction up or down
- Identify the direction of a moving object as up or down
- Move an object in a given direction up or down
- Place an object in a given position in front of or behind another object (part 1)
- Place an object in a given position in front of or behind another object (part 2)
- Place an object in a given position beside or between other objects
- Place objects in given positions beside or between other objects

MODULE 3 Comparison of Length, Weight, Capacity, and Numbers to 10

3F: Comparison of Sets Within 10

Students compare two sets of objects using the words more, fewer, and same. They work with similar objects, both aligned and scattered.

Students compare two sets of objects using the words more, fewer, and same. They work with similar and dissimilar objects, both aligned and scattered, in vertical and horizontal alignments. Finally, they begin to compare numbers.

- Identify more when comparing two sets of aligned cubes that are similar and dissimilar
- Identify more when comparing two sets of cubes with or without aligning them first
- Identify more when comparing two sets of similar and dissimilar objects with or without aligning them first
- Identify more when comparing two sets of dissimilar objects with unequal alignments
- Identify more or fewer when comparing two sets of similar scattered objects
- Identify more when comparing two numbers

MODULE 4 Number Pairs, Addition and Subtraction to 10

4A: Compositions and Decompositions of 2, 3, 4, and 5

Students use familiar base-10 blocks, scenarios with objects, the number line, and equations to explore basic concepts of addition. Students determine both sums and missing addends as they gradually move from concrete models to abstract equations.

- Use cubes to represent an addition scenario based on objects and match cube patterns to addition scenarios
- Decompose a set of 3 objects into two groups and identify as addends in an equation
- Determine a missing addend in a visual model to reach a sum of 3
- Decompose a set of 4 objects into two groups and identify as addends in an equation
- Determine a missing addend in a visual model to reach a sum of 4
- Determine a missing addend in equations with a sum of 4
- Decompose a set of 5 objects into two groups and identify as addends in an equation
- Determine a missing addend in a visual model to reach a sum of 5
- Determine a missing addend in equations with a sum of 5
- Determine a missing addend in a visual model to reach sums of 3-5
- Determine a missing addend in a visual model to reach sums of 3-5
- Solve +/- equations within 5 based on movements on a number line

4B: Decompositions of 6, 7, and 8 into Number Pairs

Students use familiar base-10 blocks, scenarios with objects, the number line, and equations to extend their understanding of addition to sums of 6, 7, and 8. Students determine both sums and missing addends as they gradually move from concrete models to abstract equations.

- Identify a number line model that represents a written scenario within 8
- Decompose a set of 6 objects into two groups and identify as addends in an equation
- Complete addition equations with a sum of 6 based on a model of base-10 blocks
- Determine a missing addend in a visual model to reach a sum of 6
- Model addition scenarios to 6 on a number line and solve a related equation
- Decompose a set of 7 objects into two groups and identify as addends in an equation
- Decompose a set of 7 objects into two groups and identify as addends in an equation
- Determine a missing addend in a visual model to reach a sum of 7
- Model addition scenarios to 7 on a number line and solve a related equation
- Decompose a set of 8 objects into two groups and identify as addends in an equation
- Complete addition equations with a sum of 8 based on a model of base-10 blocks
- Determine a missing addend in a visual model to reach a sum of 8
- Model addition scenarios to 8 on a number line and solve a related equation

4C: Addition with Totals of 6, 7, and 8

Students deepen their understanding of addition by strengthening the connection between concrete objects, base-10 blocks, and equations. They determine both sums and missing addends. They record equations, including the + symbol.

- Solve addition equations to 5 based on a model of base-10 blocks
- Model addition equations to 5 with base-10 blocks and solve a related equation
- Determine a missing addend and sum in addition equations to 5 based on a scenario with objects
- Record addition scenarios with objects as equations to 5
- Use base-10 blocks to represent addition scenarios with objects to 5
- Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 6
- Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 7
- Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 8

4D: Subtraction from Numbers to 8

Students use familiar base-10 blocks, scenarios with objects, the number line, and equations to explore basic concepts of subtraction. Students determine both differences and missing subtrahends as they gradually move from concrete models to abstract equations. They also relate subtraction to addition through exploration of fact families.

- Use base-10 blocks to represent subtraction scenarios with objects within 5 and identify base-10 block patterns that represent subtraction scenarios with objects within 5
- Solve subtraction equations within 5 based on a model of base-10 blocks
- Model subtraction equations within 5 with base-10 blocks and solve a related equation
- Complete +/- equations within the fact family of 4 based on a model of base-10 blocks
- Complete +/- equations within the fact family of 5 based on a model of base-10 blocks
- Complete +/- equations within the same fact family based on a model of base-10 blocks
- Determine a missing subtrahend in subtraction equations within 5
- Identify subtraction equations within 5 that have a given difference
- Determine a missing addend or subtrahend in +/- equations within 5
- Identify +/- equations within 5 that have a given sum or difference
- Record +/- number line scenarios within 5 as equations
- Record subtraction scenarios with objects within 5 as equations with a difference of 0
- Record subtraction scenarios on a number line within 5 as equations with a difference of 0
- Use base-10 blocks to model a subtraction scenario with objects within 8 and record as an equation
- Complete +/- equations within the fact family of 6 based on a model of base-10 blocks
- Complete +/- equations within the fact family of 7 based on a model of base-10 blocks
- Identify a base-10 block model that represents a +/- scenario with objects or an equation within 9

4E: Decompositions of 9 and 10 into Number Pairs

Students use familiar scenarios with objects, base-10 blocks, and equations to extend their understanding of addition and subtraction to include 9 and 10. Students explore the composition of these totals to strengthen their awareness of number bonds.

- Solve +/- equations within 9 based on a model of base-10 blocks
- Decompose a set of 9 objects into two groups and identify as addends in an equation
- Complete addition equations to 9 based on a model of base-10 blocks
- Determine a missing addend in a visual model to reach a sum of 9
- Complete addition equations to 10 based on a model of base-10 blocks
- Match two sets of uniform objects to make a total of 10
- Determine a missing addend in a visual model to reach a sum of 10

4F: Addition with Totals of 9 and 10

Students apply their understanding of composition of 9 and 10 to solve missing-addend problems.

Students work with both addition and subtraction to reinforce understanding of underlying concepts. They represent scenarios with objects using base-10 blocks and represent base-10 blocks as equations.

- Use base-10 blocks to model an addition scenario with objects to 9 and record as an equation
- Complete +/- equations within the fact family of 9 based on a model of base-10 blocks
- Model +/- scenarios within 9 on a number line and solve a related equation
- Model +/- scenarios within 10 on a number line and solve a related equation
- Record a number line addition scenario to 10 as and equation and solve a related subtraction equation
- Complete +/- equations within the fact family of 10 based on a model of base-10 blocks
- Determine a missing subtrahend in subtraction equations from 10
- Complete +/- equations within 5 based on a model of base-10 blocks
- Complete subtraction equations within 5 based on a scenario with objects
- Record subtraction scenarios with objects within 5 as equations
- Use base-10 blocks to represent subtraction scenarios with objects within 5 and record as an equation
- Record +/- scenarios with base-10 blocks as equations within 10
- Model subtraction scenarios from 10 on a number line and solve a related equation

4H: Patterns with Adding 0 and 1 and Making 10

Students continue to complete familiar tasks, now using 0 as an addend, subtrahend, or difference. They use scenarios with objects, a number line, and equations.

MODULE 5 Numbers 10–20 and Counting to 100

5A: Count 10 Ones and Some Ones

Students differentiate a “ten” from ones using a ten-frame or rod. They begin to explore the composition of 2-digit numbers and number names. These exercises form a foundation for later learning about place value and addition strategies. Students use the vertical number line for the first time.

5C: Decompose Numbers 11–20, and Count to Answer “How Many?”

Students further their understanding of teen numbers by applying them to positions on a number line and simple equations.

5E: Represent and Apply Compositions and Decompositions of Teen Numbers

Students sort, count, add and subtract a ten and ones. They see a group of ten displayed to the right of ones as well as to the left and see both vertical and horizontal alignments of 10 objects. They solve for different positions in +/- equations in which all of the ones or a whole ten are added or subtracted.

- Sort base-10 blocks into tens and ones and determine totals
- Determine a 2-digit total based on totals of tens and ones using objects or base-10 blocks
- Solve +/- equations in the teens with and without a model of base-10 blocks
- Record +/- equations in the teens based on a model of base-10 blocks
- Complete +/- equations in the teens with and without a model of base-10 blocks