# 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 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)

#### Sequence scattered objects numbered 1-5 in ascending order (Part 2)

#### 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

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

#### 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

### 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.