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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

Build an understanding of the word "same." The identify which two objects are the same when shown three objects
Identify two out of three objects that are the same

Identify two out of three objects that are different

Practice the difference between "same" and "different." Then look at three objects and choose two objects that are different
Identify two out of three objects that are different

Identify whether two objects are the same or different

Practice comparing objects. Look at two objects and tell whether they are the same or different
Identify whether two objects are the same or different

Identify which of two similar objects is larger

Practice comparing objects. Look at two objects that look alike but are different sizes. Tell which one is larger
Identify which of two similar objects is larger

Identify which of two similar objects is smaller

Practice comparing objects. Look at two objects that look alike but are different sizes. Tell which one is smaller
Identify which of two similar objects is smaller

Identify which of two similar objects is larger or smaller

Practice comparing objects. Look at two objects that look alike but are different sizes. Tell which one is larger or smaller
Identify which of two similar objects is larger or smaller

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

Match pictures that show the same object. The objects may be different sizes or different colors, but are alike because they show the same object
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 similar objects that differ in size and color. Look at pictures and match the pictures that show the same object, even if the color or size is different
Match pairs of similar items that differ in size and color

Match pairs of different items that are used together

Match pairs of different objects to show which ones are used together. Instead of matching the same objects, this time you match objects based on what objects go together or what objects are used together
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.

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.

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.

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

Practice counting up to 5 identical objects in a row. Click the number that shows the answer
Count to identify the total of up to 5 identical objects

Number up to 5 objects from left to right

Number up to five objects from left to right by clicking on the numbers in order, up to a given number
Number up to 5 objects from left to right

Identify a set of objects with a given total

Creatures called numberlings are holding stones. Click on the numberlings with a given number of stones to practice identifying a set of objects with a given total
Identify a set of objects with a given total

Separate pairs of objects from a group of 4

Practice grouping objects in pairs by putting two objects in each group. Recognize that a pair means two
Separate pairs of objects from a group of 4

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

Practice grouping objects in two pairs and then counting to find the total of four. Click on the correct number to tell how many
Separate objects into two pairs and count to reach a total of 4

Identify totals of up to 4 identical objects

Practice subitizing up to four objects. Try to tell how many without counting each object
Identify totals of up to 4 identical objects

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

Practice splitting 4 objects in two different ways. See that 4 objects can be split into 1 and 3 or 2 and 2
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)

Practice splitting 4 objects in two different ways. See that 4 objects can be split into 1 and 3 or 2 and 2
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)

Practice splitting 5 objects in two different ways. See that 5 objects can be split into 1 and 4 or 2 and 3
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)

Practice splitting 5 objects in two different ways. See that 5 objects can be split into 1 and 4 or 2 and 3
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.

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.

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.

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

Practice recognizing circles. Then find and click on the circles in a set of shapes to feed them to the creature
Identify circles from among a set of two-dimensional shapes

Identify squares from among a set of two-dimensional shapes

Practice recognizing squares. Then find and click on the squares to feed them to the creature
Identify squares from among a set of two-dimensional shapes

Identify triangles from among a set of two-dimensional shapes

Practice recognizing triangles. Then find and click on the triangles to feed them to the creature
Identify triangles from among a set of two-dimensional shapes

Identify rectangles from among a set of two-dimensional shapes

Practice recognizing rectangles. Then find and click on the rectangles to feed them to the creature
Identify rectangles from among a set of two-dimensional shapes

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

Practice the positional words "above" and "below." Help guide a spaceship through space by telling it to go above or below an asteroid
Identify the position above or below a given object (Part 1)

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

Practice the positional words "above" and "below" by tapping the space above or below the birds
Identify the position above or below a given object (Part 2)

Move objects up or down as instructed

Practice the words "up" and "down" by dragging handles up or down to reveal a space scene
Move objects up or down as instructed

Position a shape above or below another shape as instructed

Practice the words "above" and "below." Listen to the directions telling where to put the given shapes
Position a shape above or below another shape as instructed

Position an object next to another object as instructed

Practice the meaning of the positional phrase "next to" by positioning objects next to other objects
Position an object next to another object as instructed

Identify an object based on the position near or between

Practice the meaning of the positional words "near" and "between" by locating a hiding creature based on a spoken clue
Identify an object based on the position near or between

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

Practice the positional terms "in front of" and "behind" by placing objects in front of or behind other objects
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

Learn that one more than 5 is 6. Count a row 5 objects, then see one more object added to the row. Learn that the next number after 5 is 6 as a 6 tile is placed beside the 5 tile
Recognize that one more than 5 is 6

Count 6 similar aligned objects from left to right

Count up to 6 similar objects that are in a row. Practice one-to-one correspondence by clicking on each object as you count
Count 6 similar aligned objects from left to right

Tap objects to count the total to 6

Count 6 objects that are not in a row, and click on the number that tells how many
Tap objects to count the total to 6

Identify totals of up to 6 identical objects

Count up to 6 objects, then click on the number that tells how many
Identify totals of up to 6 identical objects

Recognize that one more than 6 is 7

Learn that one more than 6 is 7. Count a row 6 objects, then see one more object added to the row. Learn that the next number after 6 is 7 as a 7 tile is placed beside the 6 tile
Recognize that one more than 6 is 7

Count 7 similar aligned objects from left to right

Count up to 7 similar objects that are in a row. Practice one-to-one correspondence by clicking on each object as you count
Count 7 similar aligned objects from left to right

Tap objects to count the total to 7

Count 7 objects that are not in a row, and click on the number that tells how many
Tap objects to count the total to 7

Identify totals of up to 7 identical objects

Count up to 7 similar objects that are in a row. Click on the number that tells how many
Identify totals of up to 7 identical objects

Align groups of identical objects and identify the total

Learn that it is easier to count objects when they are in a row. Line up 6 or 7 objects in a row, then count. Click on the number that tells how many
Align groups of identical objects and identify the total

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

Practice counting up to 6 objects that are placed in two rows by counting left to right and top to bottom
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

Count how many pencils a girl has, then count how many pencils a boy has. Then, put all of the pencils together and count how many there are altogether
Combine and split groups of 6 identical objects and determine totals

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

Split 6 flowers into two groups in different ways. First, split the flowers into two groups of 3. Then split the flowers into a group of 1 and a group of 5
Split a group of 6 identical objects into two groups in different ways

Combine and split groups of 7 identical objects and determine totals

Count how many pencils a girl has, then count how many pencils a boy has. Then, put all of the pencils together and count how many there are altogether
Combine and split groups of 7 identical objects and determine totals

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

Split 7 flowers into two groups in different ways. First, split the flowers into a group of 3 and a group of 4. Then split the flowers into a group of 1 and a group of 6
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 7 balls to 7 children who are standing in a circle. Then count the balls and click on the number to tell how many
Distribute and count 7 identical objects aligned in a circular arrangement

Distribute and count 6 identical objects aligned in two rows

Practice one-to-one correspondence. Distribute 6 bowls of food to 6 pets who are sitting in two rows. Then count the bowls to tell how many
Distribute and count 6 identical objects aligned in two rows

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

Practice counting objects that are in a column. Sew 5 or 6 buttons on a jacket. Then count the buttons and click on the number to tell how many
Distribute and count 5 or 6 identical objects aligned in a column

Distribute a given number of identical objects

Practice counting out a given number of objects. The directions will show a number to tell how many objects to give to Dino. Count out that many objects from a larger set of objects
Distribute a given number of identical objects

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 one-to-one with up to 4 objects. This will help students model story problems using cubes as a model
Match cubes 1:1 with objects aligned in a row (Level 1)

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

Practice modeling a situation with cubes. Look at a picture of up to 4 objects. Place the correct number of cubes to model the number of objects
Match cubes 1:1 with objects aligned in a row (Level 2)

Determine the number of objects represented by cubes

Practice modeling a situation with cubes. Look at a picture of up to 4 objects. Place the correct number of cubes to model the number of objects. Then, the objects will be hidden. Look at the number of cubes, and tell how many objects are hidden
Determine the number of objects represented by cubes

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

Practice one-to-one correspondence and modeling. Model different colored objects with different colored cubes. Make sure the number of cubes matches the number of objects
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)

Model addition situations with cubes. Use a different colored cubes for different colored objects. Then, the objects will be hidden. Find how many objects there are altogether by counting the cubes
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)

Practice modeling with cubes. Listen to a description telling a number of objects and model the number of objects using cubes. Then, set up addition problems with sums to 5 by modeling the two addends with cubes
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

Use cubes to model an addition story problem. Then solve the problem by finding the total number of cubes
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.