Curriculum for Kindergarten
From number recognition to counting and operations, students build the number sense and conceptual understanding they'll need for grade 1.
MODULE 1 Numbers to 10
Topic A: Identifying Same, Different, and Alike
Students consider the size, shape, and color of objects to determine whether they are the same, different, or alike. Additionally, they are introduced to dissimilar objects that "match" because of a related function, such as a sock and a shoe.
Identify two out of three objects that are the same

Identify two out of three objects that are different

Identify differences between two similar images

Identify items that belong together based on their use

Identify whether two objects have the same shape (with different colors and patterns)

Identify whether two objects have the same color (with different shapes and patterns)

Identify whether two objects have the same pattern (with the same and with different colors)

Identify whether two objects have the same pattern (with different shapes and colors)

Identify whether shape, color, or pattern is the same among two objects

Topic B: Sorting and Counting Similar Objects
Students sort similar objects based on narrow categories (such as "bears"), broad categories (such as "clothes"), and self-determined categories. They identify objects that do not belong in a group without being given the name of the category. Finally, students count to determine the total number of objects in a group.
Sort similar objects into given categories

Sort objects into self-determined groups

Identify which of four objects does not fit with the group

Identify objects that belong to a category and count the total

Count totals of objects in a category

Identify sets of objects with a given total

Identify a set of objects with a given total

Sort objects into two groups and identify totals

Topic C: 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

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

Topic D: 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 objects

Identify a set of scattered objects that matches a given total up to 5

Sequence scattered objects numbered 1-5 in ascending order (Part 1)

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

Topic E: 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.
Recognize that one more than 5 is 6

Recognize that one more than 6 is 7

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 (Part 1)

Identify sets of numbered cubes that match a given total of 6 or 7 (Part 2)

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

Recognize that one more than 7 is 8

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 (Part 1)

Identify sets of numbered cubes that match a given total up to 9 (Part 2)

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

Topic F: 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.
Recognize that one more than 8 is 9

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

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

Topic G: 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.
Solve +1 equations based on a model of base-10 blocks

Continue a count sequence on a number line from a given point

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

Topic H: 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.
Identify missing numbers on a number line numbered 9-1

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 equations (Level 1)

Solve -1 problems based on a known total and a scenario using objects

Solve -1 problems based on a known total and a scenario using objects

Solve -1 equations (Level 2)

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
Topic A: 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 positions above and below an object

Position objects above and below an object

Position an object in front of or behind an object (Part 1)

Position an object in front of or behind an object (Part 2)

Identify the lines

Identify curved lines

Identify rectangles, triangles, or circles from among a set of shapes

Identify properties of triangles

Identify properties of rectangles

Identify hexagons from among a set of shapes

Identify properties of hexagons

Identify individual 2D shapes within a larger image

Identify real world objects composed of 2D shapes

Match real world objects to their 2D shapes

Match a 2D shape to its name

Identify shapes with a given number of sides, corners, or curved lines

Identify 2D shapes and move them into positions above, below, in front of, and behind

Topic B: Three-Dimensional Solid Shapes
Students become familiar with the appearance and names of three-dimensional shapes. They work with cubes, spheres, cones, and cylinders. Students also reinforce their understanding of positions (above, below, in front of, next to, and behind). Our sound feature allows non-readers access to shape names.
Sort shapes into the categories flat and solid

Match shapes to real-world objects

Identify cylinders from among 3-D shapes

Identify cones from among 3-D shapes

Identify cubes from among 3-D shapes

Identify spheres from among 3-D shapes

Identify 3-D shapes by name

Identify 3-D shapes among real-world objects

Position 3-D shapes above, below, in front of, and behind an object

Identify objects in positions above, below, next to, and in front of

Topic C: Two-Dimensional and Three-Dimensional Shapes
Students apply their previous understanding of flat and solid shapes to distinguish between the two.
Distinguish between flat and solid shapes

Identify which shape in a set of three is not like the others

MODULE 3 Comparison of Length, Weight, Capacity, and Numbers to 10
Topic A: Comparison of Length and Height
Using familiar, real objects, students use the language of comparison (tallest, taller, longest, longer, shortest, shorter) as they explore length.
Determine which of two objects is longer or shorter

Identify the longest or shortest object in a set

Compare objects based on longer/shorter

Determine which of two objects is taller

Compare objects based on taller/tallest and shorter/shortest

Topic B: Comparison of Length and Height of Linking Cube Sticks Within 10
Students work with familiar linking cubes to count cubes to determine length of sticks. They compare lengths using longer, shorter, and the same as.
Identify the longer or shorter of two linking cube sticks (aligned and unaligned)

Identify two out of three linking cube sticks that are the same length

Build a stick of a given length of cubes or shorter, longer, the same as a given stick

Complete a statement comparing length of sticks

Identify sticks that are longer than a given length (unaligned)

Topic C: Comparison of Weight
Using familiar, real objects, students use the language of comparison (heavier, lighter, about the same) as they explore weight. To do so, they employ a virtual balance scale to compare.
Determine which of two objects is heavier or lighter

Determine which of two objects on a balance scale is heavier or lighter

Determine which of two balance scales holds objects that are about the same weight

Identify which picture of objects on a balance scale matches a description of their weight (Level 1)

Identify which picture of objects on a balance scale matches a description of their weight (Level 2)

Topic D: Comparison of Volume
Students learn the word capacity and use it to measure the amount of liquid a container can hold. Using the unit "glasses," they measure by pouring glasses into a larger container and by pouring from a larger container into glasses. They also compare measured capacities of two containers.
Identify which of two containers has a greater capacity

Measure capacity by pouring

Compare two containers based on measured capacities

Topic E: Are There Enough?
To prepare for comparing numbers, students work with real world objects to determine if there are "enough" to make pairs. They then determine whether a set of real objects has more than, fewer than, or the same as another set of objects.
Pair objects and determine whether there are enough to complete each pair

Compare paired objects to determine more, fewer, and the same as

Show more, fewer, or the same number of objects as a given set of objects

Topic F: 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.
Identify more when comparing two numbers

Identify more when comparing two sets of fingers displayed on two hands

Identify fewer when comparing two numbers

Identify fewer when comparing two sets of similar scattered objects

Count out the same number of cubes as a given set of cubes

Topic G: Comparison of Numerals
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

Compare numbers based on more/fewer

MODULE 4 Number Pairs, Addition and Subtraction to 10
Topic A: Addition with totals of 2, 3, 4, and 5
Identify totals to 4

Identify totals to 5 and state as addition (Part 1)

Identify totals to 5 and state as addition (Part 2)

Identify and use + and = signs

Solve addition equations to 5 based on a model

Solve addition equations to 5 based on a word problem

Use cubes in two colors to represent a set of real-world objects

Solve addition equations to 5 based on a model of cubes

Solve addition equations to 5

Identify correct addition sentences to 5

Topic B: Decompositions of 6, 7, and 8 into Number Pairs
Identify addition and find the sum

Solve addition equations to 6 based on a model

Solve addition equations to 6 based on a model of cubes

Solve addition equations to 7 based on a model

Model addition to 7 and solve

Solve addition equations to 7 based on a model

Solve addition equations to 8 based on a model

Model addition to 8 and solve

Topic C: 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.
Determine a missing addend and sum in addition equations to 5 based on a scenario with objects

Use cubes to represent an addition scenario based on objects and match cube patterns to addition scenarios

Solve addition equations to 5 based on a model of base-10 blocks

Determine a missing addends in equations with a sum of 4

Solve +/- equations within 5 based on movements on a number line

Determine a missing addend in equations with a sum of 4

Determine a missing addend in equations with a sum of 5

Record addition scenarios with objects as equations to 5

Use base-10 blocks to represent addition scenarios with objects to 5

Write an equation to match a number bond (total of 3, 4, or 5)

Complete addition equations with a sum of 6 based on a model of base-10 blocks

Model addition scenarios to 6 on a number line and solve a related equation

Write an equation to match a number bond (total of 6)

Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 6

Determine a missing addend in equations with a sum of 6

Decompose a set of 7 objects into two groups and identify as addends in an equation

Model addition scenarios to 7 on a number line and solve a related equation

Write an equation to match a number bond (total of 7)

Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 7

Determine a missing addend in equations with a sum of 7

Complete addition equations with a sum of 8 based on a model of base-10 blocks

Model addition scenarios to 8 on a number line and solve a related equation

Write an equation to match a number bond (total of 8)

Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 8

Determine a missing addend in equations with a sum of 8

Topic D: 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

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

Solve subtraction equations within 5 based on a model of base-10 blocks

Complete +/- equations within 5 based on a model of base-10 blocks

Determine a missing subtrahend in subtraction equations within 5

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

Solve +/- equations within 5

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

Topic E: 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.
Record a number bond based on a scenario with 9 real objects (begin with total)

Record a number bond based on a scenario with 9 real objects (unaligned)

Record a number bond based on a scenario with 9 real objects (missing total)

Record a number bond based on a scenario with 9 real objects

Record a number bond based on a scenario with 9 real objects (unaligned)

Record a number bond based on a scenario with 10 real objects (begin with total)

Record a number bond based on a scenario with 10 real objects (missing element)

Record a number bond based on a scenario with 10 real objects (missing addend)

Record a number bond based on a scenario with 10 real objects

Record a number bond based on a scenario with 10 real objects (unaligned)

Topic F: Addition with Totals of 9 and 10
Students apply their understanding of composition of 9 and 10 to solve missing-addend problems.
Solve +/- equations within 9 based on a model of base-10 blocks

Complete addition equations to 9 based on a model of base-10 blocks

Record an equation based on a model of base-10 blocks (total of 9)

Complete addition equations to 10 based on a model of base-10 blocks

Solve +/- equations within 10 based on a model of base-10 blocks

Determine a missing addends in equations with a sum of 10

Determine a missing addend in an equation with a sum of 9 or 10 based on a model of base-10 blocks

Topic G: Subtraction from 9 and 10
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

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

Complete +/- equations within the fact family of 9 based on a model of base-10 blocks

Complete +/- equations within the fact family of 10, including turnaround facts

Record a number line addition scenario to 10 as and equation and solve a related subtraction equation

Determine a missing subtrahend in subtraction equations from 10

Complete +/- equations within the fact family of 10 based on a model of base-10 blocks

Record +/- scenarios with base-10 blocks as equations within 10

Topic H: 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.
Record +/- 0 equations based on a number line model

Record subtraction scenarios on a number line within 10 as equations with a difference of 0

Complete +/- equations that include 0 in various positions

Match two sets of uniform objects to make a total of 10

Balance the scales

MODULE 5 Numbers 10 - 20 and Counting to 100
Topic A: 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.
Group objects and base-10 blocks into a ten and ones and determine totals

Determine the total number of objects or base-10 blocks grouped into a ten and ones

Determine the total number of objects by filling a 10-frame

Determine missing numbers in the second ten on a number line and identify their written name

Topic B: 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.
Represent numbers in the second ten using a rod and cubes

Position numbers to 19 on a number line

Add 1 to or subtract 1 from numbers 11-20 with and without a number line model

Determine the 2-digit total of aligned objects

Topic C: 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

Add to or subtract from numbers 11-20 with and without a model of base-10 blocks 17396

Record +/- equations with numbers 11-20 based on a model of base-10 blocks

Complete +/- equations with numbers 11-20 with and without a model of base-10 blocks
