Math

Our math curriculum is heavily based on the Singapore math program, but is supplemented with other materials. The Singapore math program is very light on memorization and very heavy on general analytical skills, so we observe that many of the children need practice in addition to the official Singapore curriculum. If you are curious about the Singapore math program, you can find summaries of it at:

and you can find a supplier of the course & work books at:

Order of Instruction

Below is the order of objectives within the Singapore Math Program. Each heading (1A, 1B, 2A, etc.) nominally corresponds to one semester of math class, although we hope to proceed faster. Math classes start in Kindergarten, so 1A is the start of Kindergarten, assuming no prior knowledge of math.

1A

  1. Numbers 0 to 10
    1. Count within 10, including zero
    2. Read and write the numerals 0 to 10 and the corresponding words
    3. Compare numbers within 10
    4. Understand "more" and "less"
    5. Sequence numbers from 0 to 10
    6. Count from an arbitrary number within 10
    7. Count backwards from 10 to 0
    8. Review
  2. Number Bonds
    1. Identify parts in a whole
    2. Make up number stories to illustrate number bonds within 10
    3. Divide a set of objects into two parts in multiple ways
    4. Write number bonds for a given number within 10
    5. Find number pairs that make 2, 3, 4, or 5
    6. Find number pairs that make 6, 7, 8, 9, and 10
    7. Mind the missing part of a number bond
    8. Review
  3. Addition
    1. Understand the meaning of addition
    2. Associate addition with the whole-part concept
    3. Write addition using "+" and "="
    4. Relate number bonds to addition sentences to number stories
    5. Write two addition facts for a given number bond
    6. Relate addition facts within 10 to number bonds
    7. Explore number bonds and addition facts
    8. Practice addition facts
    9. Use "Count on" strategy to add two numbers within 10, one of which is 1, 2, or 3
    10. Practice counting on from 1, 2, and 3
    11. Review number pairs that make 10
    12. Addition facts game
  4. Subtraction
    1. Understand the meaning of subtraction
    2. Associate subtraction with the part-whole concept
    3. Make number stories for subtraction
    4. Compare addition to subtraction
    5. Write subtraction sentences using "-" and "="
    6. Practice
    7. Make number stories for subtraction
    8. Find the missing part of a set using subtraction
    9. Use "taking away" as a method of subtraction"
    10. Relate subtraction facts within 10 to number bonds
    11. Write a family of 4 addition and subtraction facts for given number bonds.
    12. Recall subtraction facts within 5
    13. use the "count back" strategy to subtract 1, 2, or 3 from a number within 10
    14. Practice counting back 1, 2, or 3
    15. Recognize numbers that differ by 1 or 2
    16. Review number-pairs that make 10
    17. Recall addition facts within 10
  5. Ordinal Numbers
    1. Name a position using ordinal numbers 1st through 10th
    2. Compare ordinal numbers to numbers
    3. Find an ordinal position from the left or from the right
    4. Review
  6. Numbers to 20
    1. Count to 20 by building up from 10
    2. Relate numbers 11 to 10 to a ten + ones
    3. Read and write numerals and number words for 11 to 20
    4. Count back from 20
    5. Compare numbers within 20
    6. Order numbers within 20
    7. Add two 1-digit numbers using the "make 10" strategy
    8. Add a 2-digit number within 20 and a 1-digit number
    9. Subtract a 1-digit number from a 2-digit number within 20 when there are not enough ones by subtracting from the 10
    10. Add 1, 2, or 3 to a number within 20 by counting on
    11. Subtract 1, 2, or 3 from a number within 20 by counting back
    12. Review
  7. Shapes
    1. Recognize and name the four basic shapes: circle, triangle, square, and rectangle

Sort and classify 2-dimensional shapes according to shape, size, or color

  1. Describe or continue a pattern according to one or two attributes such as shape, size, or color
  2. Fit matching pieces together to form a basic shape
  1. Length
    1. Compare the lengths of two or more objects
    2. Estimate and measure length in non-standard units
  2. Weight
    1. Compare the weights of two or more objects
    2. Estimate and measure weight in non-standard units
    3. Review

1B

  1. Comparing Numbers
    1. Use the language of "more than" and "less than"
    2. Compare two numbers that differ by one, within 10
    3. Compare two numbers by subtraction
    4. Solve picture problems involving comparison by subtraction
  2. Graphs
    1. Make simple picture graphs using one-to-one-representation
    2. Read and interpret data presented as a picture graph
  3. Numbers to 40
    1. Count within 29
    2. Read and write the numerals 30-40 and the corresponding number words
    3. Interpret numbers within 40 as tens and ones
    4. Count on or count back 1, 2, 3
    5. Compare and order numbers up to 10
    6. Interpret a 2-digit number in terms of tens and ones
    7. Find out what number is 1 more than (or 1 less than) a given number
    8. Find out what number is 10 more than (or 10 less than) a given number
    9. Add a 1-digit number to a 2-digit number without renaming
    10. Subtract a 1-digit number to a 2-digit number without renaming
    11. Add a ten and subtract a ten
    12. Use the "count on" strategy to add two numbers within 40, one of which is 1, 2, or 3
    13. Use the "count back" strategy to subtract 1, 2, or 3 from a number within 40
    14. Add a 2-digit number and a 1-digit number using the "make 10" strategy
    15. Subtract a 1-digit number from a 2-digit number using the "subtract from ten" strategy
    16. Add three single-digit numbers
    17. Review
  4. Multiplication
    1. Recognize equal groups
    2. Find the total number in a collection of groups by repeated addition
    3. Use mathematical language such as "four threes" and "two groups of five" to describe equal groups
    4. Use picture cutouts or other manipulatives to illustrate the meaning of multiplication
    5. Make up number stories for given multiplication sentences
    6. Understand the concept of equal groups
    7. Work out multiplication facts within 40 by repeated addition
    8. Solve picture problems by multiplication
    9. Review
  5. Division
    1. use picture cutouts or other manipulatives to illustrate the sharing concept of division
    2. Solve picture problems involving division
    3. use picture cutouts or other manipulatives to illustrate the grouping concept of division
    4. Solve picture problems involving division
    5. Recognize and name one half of a whole which is divided into 2 equal parts
    6. Recognize and name one quarter of a whole which is divided into 4 equal parts
    7. Recognize halves and quarters
    8. Recognize patterns
  6. Time
    1. Tell the times on the hour
    2. Sequence events according to time
    3. Tell the times at half past the hour
    4. Review
  7. Numbers to 100
    1. Count by tens
    2. Read and write numerals and number words for tens
    3. Count within 100 by making tens
    4. Read and write numerals and number words for numbers within 100
    5. State the number which is: 1 more than; 10 more than; 1 less than; 10 less than a given number
    6. Compare two numbers within 100
    7. Arrange a group of numbers within 100 in ascending or descending order
    8. Count on by ones or tens from a given number
    9. Count back by ones or tens from a given number
    10. Add a 2-digit number and a 1-digit number without renaming
    11. Add a 2-digit number and a 1-digit number using the "make ten" strategy
    12. Subtract a 1-digit number from a 2-digit number without renaming
    13. Subtract a 1-digit number from a 2-digit number using the "subtract from ten" strategy
    14. Subtract tens from a 2-digit number
    15. Subtract a 2-digit number from another 2-digit number in two steps by first subtracting the tens and then subtracting the ones
    16. Review
  8. Money
    1. Recognize and name coins
    2. Count coins
    3. Change a coin for an equivalent set of coins of smaller denominations
    4. Recognize bills (notes) and count
    5. Change a bill for an equivalent set of bills of smaller denominations
    6. Compare the amount of money in 2 or 3 sets of coins or bills
    7. Read the price of an item and prepare payment
    8. Solve simple picture problems involving money within $20
    9. Review

2A

  1. Looking Back
    1. Relate 2-digit numbers to tens and ones
    2. Read and write 2-digit numbers and corresponding number words
    3. Count on by 1, 2, 10, or 20 to a number less than 100
    4. Count back by 1, 2, 10, or 20 from a number less than 100
    5. Recognize and use the symbol ">" for "is greater than" and the symbol "<" for "is less than"
    6. Compare and order numbers less than 100
    7. Practice
  2. Hundreds, Tens, and Ones
    1. Understand the hundreds place
    2. Relate two digit numbers to hundreds, tens, and ones
    3. Relate hundreds, tens, and ones to currency bills
    4. Relate 3-digit numbers to number discs
    5. Read and write 3-digit numbers and corresponding number words
    6. Compare and order numbers less than 1000
    7. Count up by 1's, 10's, or 100's
    8. Count back by 1's, 10's, or 100's
    9. Evaluate number patterns
  3. Addition and Subtraction
    1. Review the part-whole concept of addition and subtraction
    2. Review addition and subtraction of 1-digit numbers and tens
    3. Compare sets by subtraction
    4. Relate "more than" and "less than" to addition and subtraction
    5. Review addition and subtraction of 2-digit numbers without renaming
    6. Solve word problems involving mental addition and subtraction within 100
    7. Add one,s tens, or hundreds
    8. Add within 100 without renaming using the formal algorithm for addition
    9. Add numbers within 1000 without renaming
    10. Solve word problems involving addition within 1000 without renaming
    11. Subtract ones, tens, and hundreds
    12. Subtract within 100 without renaming using the formal algorithm for subtraction
    13. Subtract numbers within 1000 without renaming
    14. Solve word problems involving subtraction within 1000 without renaming
    15. Practice
    16. Add ones or tens to a 3-digit number
    17. Add numbes within 1000 with renaming in the ones
    18. Add numbers within 1000 with renaming in the tens
    19. Practice
    20. Solve word problems involving addition of 2-digit numbers with renaming once
    21. Add numbers within 1000 with renaming twice
    22. Add three numbers within 1000
    23. Solve word problems which involve addition within 1000
    24. Subtract ones or tens from a 3-digit number
    25. Subtract numbers within 1000 where the tens are renamed, using the subtraction algorithm
    26. Practice
    27. Subtract numbers within 10000 where the hundreds are renamed
    28. Subtract numbers within 1000 where there is renaming twice
    29. Solve word problems
    30. Practice
    31. Subtract from a 3-digit number where renaming occurs twice before ones can be subtracted
  4. Length
    1. Understand the meter as a unit of measurement
    2. Estimate the length of an object as equal to, longer than, or shorter than 1 meter
    3. Measure length to the nearest meter
    4. Estimate lengths longer than a meter
    5. Add and subtract lengths
    6. Understand the centimeter as a unit of measurement
    7. Measure length to the nearest centimeter
    8. Compare lengths in centimeters
    9. Measure curved lengths
    10. Use a measuring tape
    11. Draw a straight line of a given length in centimeters
    12. Understand the yard and foot as units of measurement

2B

3A

3B

4A

4B

5A

5B

6A

6B