# Curriculum for Pre-kindergarten

Students lay the foundation of number sense and mathematical thinking as they progress through very concrete, hands-on exercises that prepare them for future success in math.

## MODULE 1 Counting to 5

### Topic A: Identifying Attributes

Students learn the meaning of same, different, alike, larger, and smaller. They identify and match objects based on size, color, shape, and even purpose.

#### Identify two out of three objects that are the same

#### Identify two out of three objects that are different

#### Identify whether two objects are the same or different

#### Identify which of two similar objects is larger

#### Identify which of two similar objects is smaller

#### Match pairs of similar items that differ in size and/or color

#### Match pairs of similar items that differ in size and color

#### Match pairs of different items that are used together

### Topic B: Sorting Objects by Attribute

Students build upon their understanding of size, color, shape, and purpose to sort dissimilar objects based on a common attribute. They must also ignore objects that do not fit the given descriptors.

#### Identify objects that belong to a given category

#### Identify objects of a given color

#### Sort objects based on two given categories (Level 1)

#### Sort objects based on two given categories (Level 2)

#### Sort objects based on two given colors

### Topic C: How Many Questions with 1, 2, or 3 Objects

Students learn to count objects with 1:1 matching by interacting with each object, either by tapping it or by moving it. They work with uniform objects that are both aligned and scattered. Automatic voice prompts give directions and guidance.

#### Count uniform objects (Part 1)

#### Count uniform objects (Part 2)

#### Align groups of uniform objects and identify the total

#### Count scattered uniform objects

### Topic D: Matching 1 Numeral with up to 3 Objects

Students match groups of uniform objects to a total written in digits. They work with both aligned and scattered objects to match objects to a number or match a number to objects. They do not necessarily count each individual object, but are encouraged to "see" the total.

#### Identify the number of aligned objects

#### Identify the number of aligned and scattered objects

#### Identify the number of scattered objects

#### Identify a group of objects with a given total

#### Counting up to 3 practice

### Topic E: Totals of 4 and 5

Students build their ability to count with 1:1 matching and move in a left to right progression. They are introduced to the concept of "a pair" and develop their visual recognition of totals without counting. Students begin to create parts (or groups) for totals of 4 or 5 objects.

#### Count to identify the total of up to 5 identical objects

#### Number up to 5 objects from left to right

#### Identify a set of objects with a given total

#### Separate pairs of objects from a group of 4

#### Separate objects into two pairs and count to reach a total of 4

#### Identify totals of up to 4 identical objects

#### Split a set of 4 objects into two groups in different ways (Part 1)

#### Split a set of 4 objects into two groups in different ways (Part 2)

#### Split a set of 5 objects into two groups in different ways (Part 1)

#### Split a set of 5 objects into two groups in different ways (Part 2)

### Topic F: Matching 1 Numeral with up to 5 Objects

Students match groups of uniform objects to a total written in digits. They work with both aligned and scattered objects to match objects to a number or match a number to objects. They do not necessarily count each individual object, but are encouraged to "see" the total.

#### Align identical objects and determine the total

#### Count a set of objects and report the total after the objects vanish

#### Determine the total of scattered identical objects

#### Identify which set of identical objects shows a given total

### Topic G: One More with Numbers 1 to 5

Students work with sets of identical objects to determine the total when one more is added. They may or may not count each object as they begin to rely on their ability to visually recognize totals up to five.

#### Determine the total after "one more" is added to a set of identical objects (Part 1)

#### Add "one more" object to a set and determine the total

#### Determine the total after "one more" is added to a set of identical objects (Part 2)

#### Determine the missing numbers on a number line numbered 1-5

### Topic H: Counting 5, 4, 3, 2, 1

Students work with sets of identical objects to determine the total when one is removed. They may or may not count each object as they begin to rely on their ability to visually recognize totals up to five.

#### Determine the total of "one less" when one object is removed from a set (Part 1)

#### Remove one object from a set and observe the total

#### Determine the total of "one less" when one object is removed from a set (Part 2)

#### Determine the missing numbers on a number line numbered 5-1

## MODULE 2 Shapes

### Topic A: Two-Dimensional Shapes

Students identify circles, squares, triangles, and rectangles of different sizes, colors, and orientation. Students also work with triangles and rectangles with different proportions. They learn the positions above, below, next to, in front of, and behind.

#### Identify circles from among a set of two-dimensional shapes

#### Identify squares from among a set of two-dimensional shapes

#### Identify triangles from among a set of two-dimensional shapes

#### Identify rectangles from among a set of two-dimensional shapes

#### Identify the position above or below a given object (Part 1)

#### Identify the position above or below a given object (Part 2)

#### Move objects up or down as instructed

#### Position a shape above or below another shape as instructed

#### Position an object next to another object as instructed

#### Identify an object based on the position near or between

#### Position an object in front of or behind another object as instructed

## MODULE 3 Counting to 10

### Topic A: How Many Questions with up to 7 Objects

Students continue developing their ability to count with 1:1 matching, moving in a left to right progression as well as from top to bottom to count objects in rows. They continue to develop their visual recognition of totals without counting.

#### Recognize that one more than 5 is 6

#### Count 6 similar aligned objects from left to right

#### Tap objects to count the total to 6

#### Identify totals of up to 6 identical objects

#### Recognize that one more than 6 is 7

#### Count 7 similar aligned objects from left to right

#### Tap objects to count the total to 7

#### Identify totals of up to 7 identical objects

#### Align groups of identical objects and identify the total

#### Count identical objects in two rows from left to right, top to bottom

### Topic B: Matching One Numeral with up to 7 Objects

Students work with groups of identical objects to split totals in different ways (a precursor to learning fact families). They count objects in different alignments, including circular, two rows, and vertical column. In the final exercise, they see that when objects are rearranged, the total remains the same.

#### Combine and split groups of 6 identical objects and determine totals

#### Split a group of 6 identical objects into two groups in different ways

#### Combine and split groups of 7 identical objects and determine totals

#### Split a group of 7 identical objects into two groups in different ways

#### Distribute and count 7 identical objects aligned in a circular arrangement

#### Distribute and count 6 identical objects aligned in two rows

#### Distribute and count 5 or 6 identical objects aligned in a column

### Topic C: How Many Questions with up to 8 Objects

Students continue developing their ability to count with 1:1 matching, moving in a left to right progression as well as from top to bottom to count objects in rows.

#### Recognize that one more than 7 is 8

#### Count 8 similar aligned objects from left to right

#### Identify totals of up to 8 identical objects

#### Align groups of identical objects and identify the total

#### Count identical objects in two rows from left to right, top to bottom

### Topic D: Matching One Numeral with up to 8 Objects

Students match groups of uniform objects to a total written in digits. They work with both aligned and scattered objects to match objects to a number or match a number to objects. Students begin to create parts (or groups) for totals of up to eight objects.

#### Identify the total of 8 identical objects aligned in two groups

#### Split a set of 8 objects into two groups in different ways

#### Identify the total of 8 identical objects aligned in a circle

#### Identify the total of 8 identical objects aligned in two rows

#### Identify the total of 7 identical objects aligned vertically

### Topic E: How Many Questions with 0 up to 9 Objects

Students are introduced to the concept of 0. They continue developing their ability to count with 1:1 matching, moving in a left to right progression as well as from top to bottom to count objects in rows.

#### Recognize that 0 is an amount that is one less than 1

#### Determine which set of identical objects has a total of 0

#### Determine totals of identical objects, including 0

#### Recognize that one more than 8 is 9

#### Count 9 similar aligned objects from left to right

#### Identify totals of up to 9 identical objects

#### Align groups of identical objects and identify the total

### Topic F: Matching One Numeral with 0 up to 9 Objects

Students work with groups of identical objects to split totals in different ways (a precursor to learning fact families). They count objects in different alignments, including circular and rows. In the final exercise, they see that when objects are rearranged, the total remains the same.

#### Combine and split groups of 9 identical objects and determine totals

#### Split a group of 9 identical objects into two groups in different ways

#### Count 7 identical objects aligned in a circular arrangement

#### Distribute and count 9 identical objects aligned in a circular arrangement

### Topic G: How Many Questions with up to 10 Objects

Students continue developing their ability to count with 1:1 matching, moving in a left to right progression as well as from top to bottom to count objects in rows.

#### Recognize that one more than 9 is 10

#### Count 10 similar aligned objects from left to right

#### Identify totals of up to 10 identical objects

#### Align groups of identical objects and identify the total

#### Count identical objects in two rows from left to right, top to bottom

### Topic H: Matching One Numeral with up to 10 Objects

Students work with groups of identical objects to split totals in different ways (a precursor to learning fact families). They count objects in different alignments, including circular and two rows. In the final exercise, they see that when objects are rearranged, the total remains the same.

#### Combine and split groups of 10 identical objects and determine totals

#### Split a group of 10 identical objects into two groups in different ways

#### Distribute and count 10 identical objects aligned in two rows

## MODULE 4. Comparison of Length, Weight, Capacity, and Numbers to 5

### Topic A: Comparison of Length

Students are introduced to the terms "taller," "higher," and "about the same" regarding height and length. They work with familiar objects to make determinations about height or weight, eventually manipulating objects to create the desired height or weight.

#### Determine which of two objects is taller

#### Determine which of two objects is longer or shorter

#### Identify two objects that are about the same height

#### Identify two objects that are about the same length

#### Identify an object that is about the same length or height as a given object

#### Add cars or take them away to make a train the same length as a given train

#### Add cubes or take them away to make a tower the same height as a given tower

### Topic B: Comparison of Weight

Students are introduced to the terms "heavier," "lighter," and "about the same" regarding weight. They first work with familiar objects to make determinations about weight based on intuition. Then, they learn how a balance scale (see-saw) works and use that to determine comparative weights.

#### 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 C: Identifying Objects That Are First and Last

Students are introduced to the terms "first" and "last," then use this knowledge to identify which items are first and last in a series of 5 or less. Then, students are introduced to the concept of one-to-one correspondence.

#### Develop the concept of "first" and "last"

#### Identify objects that are first and last in a series

#### Begin to understand the concept of one-to-one correspondence

### Topic D: Comparing Sets

Students are introduced to the concepts of "more," "less," "same," and "different." Given two sets of 5 or less objects, students will compare the number of items in each group and identify which shows more or less, or same or different amounts.

#### Determine which of two sets shows "more"

#### Determine which of two sets shows "fewer"

#### Identify the number of cubes in two given stacks and compare them

#### Begin to understand the concepts of "same" and "different" amounts of objects

#### Determine if two sets of base-10 cubes show the same amount

## MODULE 5 Addition and Subtraction Stories

### Topic A: Contextualizing Addition Stories to Solve

Students count identical objects aligned in a row. Then additional objects, identical except for the color, are added to the row. Students count those objects and then determine the total.

#### Count two groups of objects and determine the total (Part 1)

#### Count two groups of objects and determine the total (Part 2)

### Topic B: Contextualizing Subtraction Stories to Solve

Students count identical objects aligned in a row. Then some of the objects are taken away (balloons pop, pears are eaten, etc.). Students count the remaining objects to determine the difference.

#### Determine the number of objects at different points in a subtraction scenario (Part 1)

#### Determine the number of objects at different points in a subtraction scenario (Part 2)

### Topic C: Decontextualizing Addition Stories to Solve Using Fingers, Objects, and Drawings

Students move toward more abstract thinking by using cubes to represent real objects (birds, balloons, apples, etc.). They build understanding that the number of cubes represents the objects with 1:1 matching and can be used in determining totals in simple addition stories.

#### Match cubes 1:1 with objects aligned in a row (Level 1)

#### Match cubes 1:1 with objects aligned in a row (Level 2)

#### Determine the number of objects represented by cubes

#### Match cubes 1:1 with objects aligned in a row (Level 3)

#### Determine the number of objects represented by cubes in an addition scenario (Level 1)

#### Determine the number of objects represented by cubes in an addition scenario (Level 2)

#### Determine the total of two groups of objects based on their representation in cubes

### Topic D: Decontextualizing Subtraction Stories to Solve Using Fingers, Objects, and Drawings

Students move toward more abstract thinking by using cubes to represent real objects . They build understanding that the number of cubes represents the objects with 1:1 matching and can be used in determining totals in simple subtraction stories.