# Curriculum for Kindergarten

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

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### MODULE 1 Numbers to 10

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.

A. Identify two out of three objects that are the sameB. Identify two out of three objects that are differentC. Identify differences between two similar imagesD. Identify items that belong together based on their useE. Identify whether two objects have the same shape (with different colors and patterns)F. Identify whether two objects have the same color (with different shapes and patterns)G. Identify whether two objects have the same pattern (with different shapes and colors)H. Identify whether shape, color, or pattern is the same among two 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.

A. Sort similar objects into given categoriesB. Sort objects into self-determined groupsC. Identify which of four objects does not fit with the groupD. Identify objects that belong to a category and count the totalE. Count totals of objects in a categoryF. Identify sets of objects with a given totalG. Identify a set of objects with a given totalH. Sort objects into two groups and identify totals

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.

A. Match a numbered set of 1, 2, or 3 cubes to an identical numbered set of cubesB. Match numbered and non-numbered sets of cubes to a number 1-3C. Match sets of cubes to numbers 1-3D. Match numbers 1-3 to their positions on a number line labeled with numbers and dot patternsE. Identify a numbered set of cubes that matches an identical set of 4 or 5 numbered cubesF. Match numbered and non-numbered sets of cubes to number 4 or 5G. Count 2-5 aligned objects to determine the totalH. Match numbers 1-5 to arrangements of fingers displayed on a handI. Match sets of cubes to numbers 1-5J. Identify numbered sets of cubes that match a given total up to 5K. Match numbers 1-5 to their positions on a number line labeled with numbers and dot patternsL. Align scattered objects to count and determine the totalM. Count to find the total of scattered objects by matching 1:1 numbers to objectsN. Identify a set of scattered objects that matches a given total up to 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.

A. Identify sets of 0 among sets of scattered objectsB. Identify a set of scattered objects that matches a given total up to 5C. Sequence scattered objects numbered 1-5 in ascending order (Part 1)D. Sequence scattered objects numbered 1-5 in ascending order (Part 2)E. Continue a count sequence on a number line from a given point to reach a given positionF. Identify missing numbers up to 5 on a numbered number lineG. Identify the object at a given position in a set of aligned objectsH. Identify the position of an object in a set of aligned objects

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.

A. Recognize that one more than 5 is 6B. Recognize that one more than 6 is 7C. Identify the number of fingers up to 7 displayed on two handsD. Match numbers 0-7 to arrangements of fingers displayed on two handsE. Identify a set of aligned objects that matches a given total up to 7F. Match numbered patterns of dots to an identical numbered pattern of dots up to 7G. Identify sets of numbered cubes that match a given total of 6 or 7 (Part 1)H. Identify sets of numbered cubes that match a given total of 6 or 7 (Part 2)I. Match numbers 1-7 to their positions on a number line labeled with numbers and dot patternsJ. Count objects as they move away from a set and identify the totalK. Count scattered objects two different ways to arrive at the same totalL. Recognize that one more than 7 is 8M. Identify the number of fingers up to 8 displayed on two handsN. Match numbers 0-8 to arrangements of fingers displayed on two handsO. Identify a set of aligned objects that matches a given total up to 8P. Identify sets of numbered cubes that match a given total up to 9 (Part 1)Q. Identify sets of numbered cubes that match a given total up to 9 (Part 2)R. Count objects as they move away from a set and identify the totalS. Count scattered objects two different ways to arrive at the same totalT. Identify the total number of scattered objects after a known total has been rearranged

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.

A. Recognize that one more than 8 is 9B. Determine the total of up to 9 scattered objectsC. Count out a given number of objects from a larger setD. Determine the total of up to 9 scattered objectsE. Match patterns of dots to their numbered position on a number lineF. Determine the total of up to 9 non-identical scattered objectsG. Match sets of non-identical objects to numbers up to 9H. Match numbered patterns of dots to an identical numbered pattern of dots up to 9I. Identify sets of numbered cubes that match a given total 0-10J. Identify a set of scattered objects that matches a given total up to 10K. Match numbered patterns of dots to an identical numbered pattern of dots up to 10L. Match numbers 0-10 to their position on a number line labeled with numbers and dot patternsM. Continue a count sequence on a number line from a given point to reach a given positionN. Identify missing numbers up to 9 on a numbered number line

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.

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.

A. Identify missing numbers on a number line numbered 9-1B. Determine one more and one less on a number lineC. Continue a count sequence on a number line from a given point counting backD. Solve -1 equations based on a model of base-10 blocksE. Solve -1 equations based on a number line modelF. Solve -1 equations (Level 1)G. Solve -1 problems based on a known total and a scenario using objectsH. Solve -1 problems based on a known total and a scenario using objectsI. Solve -1 equations (Level 2)J. Solve +1 and -1 equations based on a model of base-10 blocksK. Solve +1 and -1 equations based on a number line modelL. Solve +1 and -1 problems based on a known total and a scenario using objectsM. Solve +1 and -1 equations

### MODULE 2 Two-Dimensional and Three-Dimensional 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.

A. Identify positions above and below an objectB. Position objects above and below an objectC. Position an object in front of or behind an object (Part 1)D. Position an object in front of or behind an object (Part 2)E. Identify the linesF. Identify curved linesG. Identify rectangles, triangles, or circles from among a set of shapesH. Identify properties of trianglesI. Identify properties of rectanglesJ. Identify hexagons from among a set of shapesK. Identify properties of hexagonsL. Identify individual 2D shapes within a larger imageM. Identify real world objects composed of 2D shapesN. Match real world objects to their 2D shapesO. Match a 2D shape to its nameP. Identify shapes with a given number of sides, corners, or curved linesQ. Identify 2D shapes and move them into positions above, below, in front of, and behind

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.

A. Sort shapes into the categories flat and solidB. Match shapes to real-world objectsC. Identify cylinders from among 3-D shapesD. Identify cones from among 3-D shapesE. Identify cubes from among 3-D shapesF. Identify spheres from among 3-D shapesG. Identify 3-D shapes by nameH. Identify 3-D shapes among real-world objectsI. Position 3-D shapes above, below, in front of, and behind an objectJ. Identify objects in positions above, below, next to, and in front of

Students apply their previous understanding of flat and solid shapes to distinguish between the two.

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

Using familiar, real objects, students use the language of comparison (tallest, taller, longest, longer, shortest, shorter) as they explore length.

Students work with familiar linking cubes to count cubes to determine length of sticks. They compare lengths using longer, shorter, and the same as.

A. Identify the longer or shorter of two linking cube sticks (aligned and unaligned)B. Identify two out of three linking cube sticks that are the same lengthC. Build a stick of a given length of cubes or shorter, longer, the same as a given stickD. Complete a statement comparing length of sticksE. Identify sticks that are longer than a given length (unaligned)

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.

A. Determine which of two objects is heavier or lighterB. Determine which of two objects on a balance scale is heavier or lighterC. Determine which of two balance scales holds objects that are about the same weightD. Identify which picture of objects on a balance scale matches a description of their weight (Level 1)E. Identify which picture of objects on a balance scale matches a description of their weight (Level 2)

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.

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.

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.

A. Identify more when comparing two sets of aligned cubes that are similar and dissimilarB. Identify more when comparing two sets of cubes with or without aligning them firstC. Identify more when comparing two sets of similar and dissimilar objects with or without aligning them firstD. Identify more when comparing two sets of dissimilar objects with unequal alignmentsE. Identify more or fewer when comparing two sets of similar scattered objectsF. Compare numbers based on more/fewer

### MODULE 4 Number Pairs, Addition and Subtraction to 10

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.

A. Count unlike objectsB. Count a set of objects and count two subsets by colorC. Count a set of objects and count two subsets by color; identify total in a number bondD. Count a set of objects and count two subsets by color; identify addends in a number bondE. Count a set of objects and count two subsets by color; identify number bondF. Build a number bond based on a set of objects; identify an addend in the number bond (Part 1)G. Build a number bond based on a set of objects; identify an addend in the number bond (Part 2)H. Identify the missing number in a number bond based on a set of objectsI. Build a number bond based on a set of objects; identify the total in the number bond

Students extend their understanding of number bonds to totals of 6, 7, and 8. They work with sets of similar objects in two colors to count parts (by color) and total. They then use these numbers to build number bonds based on the picture of objects.

A. Build a number bond based on a set of objects; identify an addend in the number bondB. Identify the missing number in a number bond based on a set of objectsC. Build a number bond based on a set of objects; identify the total in the number bond (total of 6)D. Color a set of objects in two colors to represent a given number bondE. Build a number bond based on a set of objects; identify the total in the number bond (total of 7)F. Build a number bond based on a set of objects; identify the total in the number bond (total of 8)G. Record a number bond based on a model students create (total of 7 or 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.

A. Determine a missing addend and sum in addition equations to 5 based on a scenario with objectsB. Use cubes to represent an addition scenario based on objects and match cube patterns to addition scenariosC. Solve addition equations to 5 based on a model of base-10 blocksD. Determine a missing addends in equations with a sum of 4E. Solve +/- equations within 5 based on movements on a number lineF. Determine a missing addend in equations with a sum of 4G. Determine a missing addend in equations with a sum of 5H. Record addition scenarios with objects as equations to 5I. Use base-10 blocks to represent addition scenarios with objects to 5J. Write an equation to match a number bond (total of 3, 4, or 5)K. Complete addition equations with a sum of 6 based on a model of base-10 blocksL. Model addition scenarios to 6 on a number line and solve a related equationM. Write an equation to match a number bond (total of 6)N. Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 6O. Determine a missing addend in equations with a sum of 6P. Decompose a set of 7 objects into two groups and identify as addends in an equationQ. Model addition scenarios to 7 on a number line and solve a related equationR. Write an equation to match a number bond (total of 7)S. Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 7T. Determine a missing addend in equations with a sum of 7U. Complete addition equations with a sum of 8 based on a model of base-10 blocksV. Model addition scenarios to 8 on a number line and solve a related equationW. Write an equation to match a number bond (total of 8)X. Represent addition scenarios with objects using base-10 blocks and record as an equation with a sum of 8Y. Determine a missing addend in equations with a sum of 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.

A. 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 5B. Complete subtraction equations within 5 based on a scenario with objectsC. Record subtraction scenarios with objects within 5 as equationsD. Use base-10 blocks to represent subtraction scenarios with objects within 5 and record as an equationE. Solve subtraction equations within 5 based on a model of base-10 blocksF. Complete +/- equations within 5 based on a model of base-10 blocksG. Determine a missing subtrahend in subtraction equations within 5H. Record subtraction scenarios with objects within 5 as equations with a difference of 0I. Record subtraction scenarios on a number line within 5 as equations with a difference of 0J. Solve +/- equations within 5K. Use base-10 blocks to model a subtraction scenario with objects within 8 and record as an equationL. Complete +/- equations within the fact family of 6 based on a model of base-10 blocksM. Complete +/- equations within the fact family of 7 based on a model of base-10 blocks

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.

A. Record a number bond based on a scenario with 9 real objects (begin with total)B. Record a number bond based on a scenario with 9 real objects (unaligned)C. Record a number bond based on a scenario with 9 real objects (missing total)D. Record a number bond based on a scenario with 9 real objectsE. Record a number bond based on a scenario with 9 real objects (unaligned)F. Record a number bond based on a scenario with 10 real objects (begin with total)G. Record a number bond based on a scenario with 10 real objects (missing element)H. Record a number bond based on a scenario with 10 real objects (missing addend)I. Record a number bond based on a scenario with 10 real objectsJ. Record a number bond based on a scenario with 10 real objects (unaligned)

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

A. Solve +/- equations within 9 based on a model of base-10 blocksB. Complete addition equations to 9 based on a model of base-10 blocksC. Record an equation based on a model of base-10 blocks (total of 9)D. Complete addition equations to 10 based on a model of base-10 blocksE. Solve +/- equations within 10 based on a model of base-10 blocksF. Determine a missing addends in equations with a sum of 10G. Determine a missing addend in an equation with a sum of 9 or 10 based on a model of base-10 blocks

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.

A. Use base-10 blocks to model an addition scenario with objects to 9 and record as an equationB. Model +/- scenarios within 9 on a number line and solve a related equationC. Model +/- scenarios within 10 on a number line and solve a related equationD. Complete +/- equations within the fact family of 9 based on a model of base-10 blocksE. Complete +/- equations within the fact family of 10, including turnaround factsF. Record a number line addition scenario to 10 as and equation and solve a related subtraction equationG. Determine a missing subtrahend in subtraction equations from 10H. Complete +/- equations within the fact family of 10 based on a model of base-10 blocksI. Record +/- scenarios with base-10 blocks as equations within 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

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.

A. Group objects and base-10 blocks into a ten and ones and determine totalsB. Determine the total number of objects or base-10 blocks grouped into a ten and onesC. Determine the total number of objects by filling a 10-frameD. Determine missing numbers in the second ten on a number line and identify their written name

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

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.

A. Sort base-10 blocks into tens and ones and determine totalsB. Determine a 2-digit total based on totals of tens and ones using objects or base-10 blocksC. Add to or subtract from numbers 11-20 with and without a model of base-10 blocks 17396D. Record +/- equations with numbers 11-20 based on a model of base-10 blocksE. Complete +/- equations with numbers 11-20 with and without a model of base-10 blocks