
Course Content
A. Sorting, Ordering, and Classifying
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A.01. Identify objects that are the same.
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A.02. Recognize objects that are different.
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A.03. Distinguish between objects that are the same and different.
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A.04. Classify shapes by color.
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A.05. Sort objects by color.
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A.06. Classify shapes by shape.
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A.07. Classify and sort objects by multiple attributes.
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A.08. Count shapes within a Venn diagram.
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A.09. Sort shapes into a Venn diagram based on attributes.
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A.10. Place numbers up to 10 in sequential order.
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A.11. Place numbers up to 20 in sequential order.
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A.12. Develop logical reasoning skills through classification and sorting activities.
B. Positions
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B.01. Identify objects that are inside or outside a defined space.
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B.02. Recognize the top, middle, and bottom positions.
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B.03. Understand the concepts of above and below.
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B.04. Locate solid figures that are above or below a reference point.
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B.05. Identify objects that are on the left, in the middle, or on the right.
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B.06. Understand the terms beside and next to.
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B.07. Locate solid figures that are beside or next to another object.
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B.08. Determine locations on a grid using coordinates.
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B.09. Use directional language (e.g., forward, backward, up, down) to describe movement.
C. Comparing
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C.01. Determine if there are enough objects to satisfy a need.
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C.02. Compare two groups of objects using matching to determine “fewer” and “more.”
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C.03. Compare two groups of objects by counting to determine “fewer” and “more.”
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C.04. Compare quantities within a mixed group of objects.
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C.05. Differentiate between “fewer,” “more,” and “the same” quantities.
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C.06. Compare two numbers up to 10 using comparison vocabulary and symbols.
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C.07. Compare three numbers up to 10 and arrange them in order.
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C.08. Compare two numbers up to 20.
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C.09. Apply comparison skills to real-world scenarios, such as comparing heights or lengths.
D. Numbers and Counting up to 3
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D.01. Verbally count to 3 in the correct sequence.
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D.02. Identify written numbers up to 3.
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D.03. Choose the correct number when heard, up to 3.
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D.04. Count a set of stickers up to 3.
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D.05. Represent numbers up to 3 using objects.
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D.06. Count objects arranged on ten frames, up to 3.
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D.07. Show numbers on ten frames up to 3.
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D.08. Demonstrate one-to-one correspondence when counting up to 3.
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D.09. Subitize quantities up to 3 (instantly recognize the number without counting).
E. Numbers and Counting up to 5
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E.01. Identify written numbers up to 5.
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E.02. Choose the correct number when heard, up to 5.
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E.03. Verbally count to 5 in the correct sequence.
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E.04. Count a set of stickers up to 5.
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E.05. Count a set of cubes up to 5.
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E.06. Show numbers with cubes up to 5.
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E.07. Represent numbers up to 5 using objects.
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E.08. Count objects arranged on ten frames, up to 5.
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E.09. Show numbers on ten frames up to 5.
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E.10. Determine “one more” than a number using pictures, up to 5.
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E.11. Determine “one more” than a number on ten frames, up to 5.
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E.12. Identify “one more” than a given number up to 5.
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E.13. Determine “one less” than a number using pictures, up to 5.
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E.14. Determine “one less” than a number on ten frames, up to 5.
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E.15. Identify “one less” than a given number up to 5.
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E.16. Determine the number that comes next in a sequence, up to 5.
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E.17. Identify ordinal numbers up to fifth.
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E.18. Apply counting skills to solve simple real-world problems involving quantities up to 5.
F. Numbers and Counting up to 10
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F.01. Identify written numbers up to 10.
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F.02. Choose the correct number when heard, up to 10.
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F.03. Verbally count to 10 in the correct sequence.
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F.04. Count a set of stickers up to 10.
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F.05. Count a set of cubes up to 10.
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F.06. Show numbers with cubes up to 10.
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F.07. Represent numbers up to 10 using objects.
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F.08. Count objects arranged on ten frames, up to 10.
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F.09. Show numbers on ten frames up to 10.
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F.10. Determine “one more” than a number using pictures, up to 10.
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F.11. Determine “one more” than a number on ten frames, up to 10.
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F.12. Identify “one more” than a given number up to 10.
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F.13. Determine “one less” than a number using pictures, up to 10.
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F.14. Determine “one less” than a number on ten frames, up to 10.
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F.15. Identify “one less” than a given number up to 10.
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F.16. Determine “one more and one less” than a number using pictures, up to 10.
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F.17. Determine “one more and one less” than a number on ten frames, up to 10.
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F.18. Identify “one more and one less” than a given number up to 10.
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F.19. Determine the number that comes next in a sequence, up to 10.
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F.20. Use a number line to find the next number, up to 10.
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F.21. Count up and down to find the next number, up to 10.
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F.22. Count to fill a ten frame.
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F.23. Read and interpret tally marks up to 10.
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F.24. Identify numbers on a number line, up to 10.
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F.25. Determine the numbers that come before, after, and between given numbers, up to 10.
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F.26. Count forward and backward from a given number, up to 10.
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F.27. Convert numbers written in words to digits, up to 10.
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F.28. Convert numbers written in digits to words, up to 10.
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F.29. Write digits given numbers in words, up to 10.
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F.30. Write numbers in words given digits, up to 10.
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F.31. Complete a number sequence, up to 10.
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F.32. Identify ordinal numbers up to tenth.
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F.33. Use estimation skills to approximate quantities up to 10 in real-world contexts.
G. Numbers and Counting up to 20
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G.01. Identify written numbers up to 20.
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G.02. Verbally count to 20 in the correct sequence.
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G.03. Count objects arranged on ten frames, up to 20.
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G.04. Show numbers on ten frames up to 20.
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G.05. Represent numbers up to 20 using objects.
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G.06. Identify “one more” than a given number up to 20.
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G.07. Identify “one less” than a given number up to 20.
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G.08. Identify “one more and one less” than a given number up to 20.
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G.09. Count up and down to find the next number, up to 20.
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G.10. Read and interpret tally marks up to 20.
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G.11. Identify numbers on a number line, up to 20.
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G.12. Determine the numbers that come before, after, and between given numbers, up to 20.
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G.13. Count forward and backward from a given number, up to 20.
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G.14. Convert numbers written in words to digits, up to 20.
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G.15. Convert numbers written in digits to words, up to 20.
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G.16. Write digits given numbers in words, up to 20.
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G.17. Write numbers in words given digits, up to 20.
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G.18. Complete a number sequence, up to 20.
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G.19. Count groups of tens and ones up to 20.
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G.20. Write numbers representing tens and ones up to 20.
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G.21. Compose teen numbers using a ten and some ones.
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G.22. Decompose teen numbers into a ten and some ones.
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G.23. Compare and order numbers up to 20 using visual aids and manipulatives.
H. Numbers and Counting Beyond 20
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H.01. Count objects arranged on ten frames, up to 30.
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H.02. Identify numbers on a number line, up to 30.
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H.03. Count groups of tens and ones up to 30.
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H.04. Count groups of ten.
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H.05. Verbally count to 100.
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H.06. Count on a hundred chart.
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H.07. Count up and down to find the next number, up to 100.
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H.08. Complete a number sequence, up to 100.
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H.09. Count forward and backward from a given number, up to 100.
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H.10. Estimate quantities to the nearest ten, up to 100.
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H.11. Recognize place value in two-digit numbers (tens and ones).
I. Skip-Counting
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I.01. Describe the concept of skip-counting by twos.
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I.02. Skip-count by twos.
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I.03. Skip-count by twos using ten frames.
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I.04. Describe the concept of skip-counting by fives.
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I.05. Skip-count by fives.
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I.06. Describe the concept of skip-counting by tens.
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I.07. Skip-count by tens.
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I.08. Describe the concept of skip-counting by twos, fives, and tens.
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I.09. Skip-count by twos, fives, and tens.
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I.10. Use skip-counting to solve simple problems involving repeated addition.
J. Addition Skill Builders
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J.01. Practice adding 0 to a given number.
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J.02. Practice adding 1 to a given number.
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J.03. Practice adding 2 to a given number.
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J.04. Practice adding 3 to a given number.
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J.05. Practice adding 4 to a given number.
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J.06. Practice adding 5 to a given number.
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J.07. Practice adding 6 to a given number.
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J.08. Practice adding 7 to a given number.
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J.09. Practice adding 8 to a given number.
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J.10. Practice adding 9 to a given number.
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J.11. Practice adding 10 to a given number.
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J.12. Use mental math strategies to quickly recall addition facts.
K. Addition Up to 5
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K.01. Use cubes to physically combine and add numbers with sums up to 5.
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K.02. Represent the decomposition of numbers up to 5 using words.
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K.03. Add numbers using cubes, with sums up to 5.
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K.04. Add numbers using pictures, with sums up to 5.
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K.05. Match addition sentences to corresponding models (pictures or objects), with sums up to 5.
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K.06. Interpret addition sentences by describing what the corresponding model shows, with sums up to 5.
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K.07. Represent the decomposition of numbers up to 5 using addition sentences.
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K.08. Add two numbers, with sums up to 5.
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K.09. Make a specific number using addition, with sums up to 5.
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K.10. Complete addition sentences to find the missing addend, with sums up to 5.
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K.11. Solve addition word problems with supporting pictures, with sums up to 5.
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K.12. Solve simple addition word problems, with sums up to 5.
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K.13. Create their own addition word problems based on given scenarios, with sums up to 5.
L. Addition Up to 10
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L.01. Use cubes to physically combine and add numbers with sums up to 10.
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L.02. Represent the decomposition of numbers up to 10 using words.
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L.03. Decompose a number up to 10 into its addends.
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L.04. Add numbers using cubes, with sums up to 10.
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L.05. Add numbers using pictures, with sums up to 10.
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L.06. Match addition sentences to corresponding models (pictures or objects), with sums up to 10.
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L.07. Interpret addition sentences by describing what the corresponding model shows, with sums up to 10.
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L.08. Represent the decomposition of numbers up to 10 using addition sentences.
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L.09. Add two numbers, with sums up to 10.
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L.10. Make a specific number using addition, with sums up to 10.
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L.11. Complete addition sentences to find the missing addend, with sums up to 10.
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L.12. Complete addition sentences to make 10 using models.
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L.13. Complete addition sentences to make 10.
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L.14. Write addition sentences to represent given scenarios, with sums up to 10.
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L.15. Solve addition word problems with supporting pictures, with sums up to 10.
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L.16. Solve simple addition word problems, with sums up to 10.
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L.17. Add doubles using models.
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L.18. Add doubles (e.g., 1+1, 2+2).
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L.19. Add doubles by completing the sentence (e.g. 3 + 3 =__).
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L.20. Add using doubles plus one (e.g., 3 + 4 = 3 + 3 + 1).
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L.21. Add using doubles minus one (e.g., 4 + 3 = 4 + 4 – 1).
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L.22. Add three numbers, with sums up to 10.
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L.23. Create and solve complex addition word problems with multiple steps, with sums up to 10.
M. Addition Up to 20
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M.01. Add numbers using pictures, with sums up to 20.
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M.02. Interpret addition sentences by describing what the corresponding model shows, with sums up to 20.
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M.03. Add one-digit numbers, with sums up to 20.
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M.04. Add any two numbers, with sums up to 20.
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M.05. Make a specific number using addition, with sums up to 20.
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M.06. Complete addition sentences to find the missing addend, with sums up to 20.
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M.07. Solve addition word problems, with sums up to 20.
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M.08. Identify related addition facts (e.g., 5 + 3 = 8, 3 + 5 = 8).
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M.09. Apply addition strategies (e.g., counting on, making ten) to solve problems efficiently, with sums up to 20.
N. Subtraction Skill Builders
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N.01. Practice subtracting 0 from a given number.
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N.02. Practice subtracting 1 from a given number.
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N.03. Practice subtracting 2 from a given number.
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N.04. Practice subtracting 3 from a given number.
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N.05. Practice subtracting 4 from a given number.
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N.06. Practice subtracting 5 from a given number.
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N.07. Practice subtracting 6 from a given number.
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N.08. Practice subtracting 7 from a given number.
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N.09. Practice subtracting 8 from a given number.
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N.10. Practice subtracting 9 from a given number.
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N.11. Practice subtracting 10 from a given number.
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N.12. Use mental math strategies to quickly recall subtraction facts.
O. Subtraction Up to 5
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O.01. Take away cubes to represent subtraction, with numbers up to 5.
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O.02. Subtract numbers using cubes, with numbers up to 5.
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O.03. Subtract numbers using pictures, with numbers up to 5.
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O.04. Match subtraction sentences to corresponding models (pictures or objects), with numbers up to 5.
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O.05. Interpret subtraction sentences by describing what the corresponding model shows, with numbers up to 5.
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O.06. Subtract numbers, with numbers up to 5.
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O.07. Complete subtraction sentences to find the missing subtrahend or difference, with numbers up to 5.
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O.08. Solve subtraction word problems with supporting pictures, with numbers up to 5.
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O.09. Solve simple subtraction word problems, with numbers up to 5.
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O.10. Create their own subtraction word problems based on given scenarios, with numbers up to 5.
P. Subtraction Up to 10
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P.01. Take away cubes to represent subtraction, with numbers up to 10.
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P.02. Subtract numbers using cubes, with numbers up to 10.
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P.03. Subtract numbers using pictures, with numbers up to 10.
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P.04. Match subtraction sentences to corresponding models (pictures or objects), with numbers up to 10.
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P.05. Interpret subtraction sentences by describing what the corresponding model shows, with numbers up to 10.
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P.06. Subtract numbers, with numbers up to 10.
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P.07. Make a specific number using subtraction, with numbers up to 10.
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P.08. Complete subtraction sentences to find the missing subtrahend or difference, with numbers up to 10.
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P.09. Write subtraction sentences to represent given scenarios, with numbers up to 10.
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P.10. Solve subtraction word problems with supporting pictures, with numbers up to 10.
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P.11. Solve simple subtraction word problems, with numbers up to 10.
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P.12. Compare addition and subtraction strategies and identify when each is most appropriate, with numbers up to 10.
Q. Subtraction Up to 20
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Q.01. Subtract numbers using pictures, with numbers up to 20.
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Q.02. Interpret subtraction sentences by describing what the corresponding model shows, with numbers up to 20.
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Q.03. Subtract numbers, with numbers up to 20.
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Q.04. Make a specific number using subtraction, with numbers up to 20.
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Q.05. Complete subtraction sentences to find the missing subtrahend or difference, with numbers up to 20.
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Q.06. Solve subtraction word problems, with numbers up to 20.
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Q.07. Identify related subtraction facts (e.g., 8 – 3 = 5, 8 – 5 = 3).
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Q.08. Apply subtraction strategies (e.g., counting back, using a number line) to solve problems efficiently, with numbers up to 20.
R. Understand Multiplication
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R.01. Define multiplication as repeated addition.
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R.02. Count equal groups of objects.
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R.03. Identify multiplication expressions that represent equal groups.
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R.04. Write multiplication sentences to describe equal groups.
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R.05. Identify multiplication expressions for objects arranged in arrays.
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R.06. Write multiplication sentences to describe arrays.
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R.07. Illustrate multiplication problems using concrete objects and drawings.
S. Understand Division
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S.01. Define division as sharing equally into groups.
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S.02. Divide objects by counting equal groups.
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S.03. Write division sentences to represent equal groups.
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S.04. Write division sentences to represent arrays.
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S.05. Solve simple division problems using manipulatives and visual aids.
T. Fractions
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T.01. Understand the concept of equal parts of a whole.
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T.02. Identify halves of shapes and objects.
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T.03. Identify quarters of shapes and objects.
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T.04. Discriminate between halves and quarters.
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T.05. Create halves by dividing objects or shapes.
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T.06. Create quarters by dividing objects or shapes.
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T.07. Create halves and quarters of various objects and shapes.
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T.08. Apply fraction concepts to real-world sharing and partitioning scenarios.
U. Patterns
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U.01. Recognize and extend color patterns.
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U.02. Recognize and extend size patterns.
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U.03. Recognize and extend shape patterns.
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U.04. Identify the next shape in a pattern.
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U.05. Complete a pattern.
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U.06. Create their own patterns.
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U.07. Recognize and extend growing patterns.
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U.08. Identify the next shape in a growing pattern.
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U.09. Identify the next row in a growing pattern.
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U.10. Describe the rule or relationship within a pattern.
V. Two-Dimensional Shapes
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V.01. Name common two-dimensional shapes.
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V.02. Identify circles.
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V.03. Identify triangles.
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V.04. Identify squares and rectangles.
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V.05. Identify hexagons.
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V.06. Select specified two-dimensional shapes from a group of shapes.
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V.07. Identify shapes with curved parts.
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V.08. Count the number of sides and corners on a shape.
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V.09. Compare the number of sides and corners between different shapes.
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V.10. Understand the basic concept of symmetry.
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V.11. Identify pictures that exhibit symmetry.
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V.12. Compose new shapes by combining two-dimensional shapes.
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V.13. Relate 2D shapes to everyday objects in their environment.
W. Three-Dimensional Shapes
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W.01. Distinguish between two-dimensional and three-dimensional shapes.
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W.02. Name common three-dimensional shapes.
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W.03. Identify spheres.
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W.04. Identify cubes and cuboids.
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W.05. Identify cones.
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W.06. Identify cylinders.
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W.07. Identify pyramids.
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W.08. Select specified three-dimensional shapes from a group of shapes.
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W.09. Identify the two-dimensional shapes traced from the faces of solids.
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W.10. Recognize three-dimensional shapes in real-world objects.
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W.11. Categorize real-world objects based on their corresponding 3D shapes.
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W.12. Build simple structures using various 3D shapes.
X. Measurement
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X.01. Compare objects to determine which is long and which is short.
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X.02. Compare objects to determine which is tall and which is short.
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X.03. Compare objects to determine which is wide and which is narrow.
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X.04. Compare objects to determine which is light and which is heavy.
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X.05. Compare containers to determine which holds more and which holds less.
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X.06. Compare objects based on size, weight, and capacity.
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X.07. Measure objects using non-standard units (e.g., paperclips, blocks).
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X.08. Measure length using cubes.
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X.09. Build cube trains to measure length.
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X.10. Measure height using cubes.
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X.11. Build cube trains to measure height.
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X.12. Estimate the length, height, or weight of an object before measuring.
Y. Time
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Y.01. Match digital clocks to corresponding times (hour).
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Y.02. Match digital clocks to corresponding times (half-hour).
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Y.03. Match analogue clocks to corresponding times (hour).
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Y.04. Match analogue clocks to corresponding times (half-hour).
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Y.05. Match analogue and digital clocks showing the same time (hour).
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Y.06. Match analogue and digital clocks showing the same time (half-hour).
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Y.07. Read analogue clocks and write the time (hour).
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Y.08. Read analogue clocks and write the time (half-hour).
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Y.09. Understand the difference between A.M. and P.M.
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Y.10. Associate times with common everyday events.
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Y.11. Compare different clocks and identify which shows an earlier or later time.
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Y.12. Identify the four seasons.
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Y.13. Name the days of the week in order.
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Y.14. Name the months of the year in order.
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Y.15. Read and interpret a calendar.
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Y.16. Determine the duration of simple activities using time measurements.
Z. Data and Graphs
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Z.01. Identify the correct picture graph that represents a given data set.
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Z.02. Interpret data presented in picture graphs.
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Z.03. Identify the correct tally chart that represents a given data set.
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Z.04. Interpret data presented in tally charts.
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Z.05. Identify the correct table that represents a given data set.
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Z.06. Interpret data presented in tables.
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Z.07. Collect and organize data using simple methods such as surveys and observations.
AA. Money
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AA.01. Identify and state the value of 1p, 2p, 5p, and 10p coins.
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AA.02. Identify and state the value of 20p, 50p, £1, and £2 coins.
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AA.03. Identify and state the value of all common coins.
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AA.04. Count a group of 1p coins.
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AA.05. Count a group of 1p and 2p coins.
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AA.06. Count a group of 1p, 2p, and 5p coins.
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AA.07. Count a group of 1p, 2p, 5p, and 10p coins.
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AA.08. Create equivalent groups of coins with the same value.
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AA.09. Exchange groups of coins for a single coin of equivalent value.
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AA.10. Perform coin exchanges involving different denominations.
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AA.11. Compare the value of two groups of coins and determine which is greater.
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AA.12. Solve simple word problems involving money and making purchases.
BB. Probability
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BB.01. Determine if an event is more or less likely to occur based on available information.
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BB.02. Describe the likelihood of simple events using terms like “certain,” “impossible,” “likely,” and “unlikely.”
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BB.03. Conduct simple experiments to explore probability and outcomes.
CC. Vocabulary
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CC.01. Define and use the terms “sum” and “difference” in mathematical contexts.
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CC.02. Explain the relationship between addition and the term “sum.”
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CC.03. Explain the relationship between subtraction and the term “difference.”
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CC.04. Use appropriate mathematical vocabulary to describe problem-solving strategies and solutions.