Strand B- Number Sense Grade Three Mental Math Strand B- Number Sense Grade Three

Double Facts If you know that 6 + 6 = 12, then applying the doubles strategy to adding numbers in the 10s, you know 60 + 60 = 120. If you know that 3 + 3 = 6, then you know that 30 + 30 = 60.

Double Facts 40 + 40 70 + 70 90 + 90 50 + 50 20 + 20 10 + 10 80 + 80 30 + 30 60 + 60

Double Facts 20 + 30 30 + 40 40 + 20 30 + 50 30 + 60 10 + 50 20 + 70 50 + 20 80 + 10 70 + 20

Double Facts 200 + 200 400 + 400 300 + 300 900 + 900 600 + 600 800 + 800 700 + 700 100 + 100 200 + 400 300 + 500

Near Doubles This strategy is also called “doubles plus one.” The strategy is to double the smaller number and add one. Example: 6 + 7 is (6 + 6) +1. Now, apply this strategy to 10s and 100s. Example: 60 + 70 is (60 + 60) + 10.

Near Doubles 30 + 40 50 + 60 80 + 90 30 + 20 20 + 30 60 + 70 70 + 80 10 + 20 50 + 40 30 + 10

Near Doubles 400 + 500 400 + 300 200 + 100 700 + 800 800 + 900 900 + 800 300 + 200 600 + 700 300 + 100 500 + 200

Doubles Plus Two Strategy A: doubling the smaller plus 2 - Example: 4 + 6 is double 4 plus 2 more. Extension to Grade Three level: 40 + 60 is double 40 plus 20 more. Strategy B: doubling the number between -Example: 5 + 7 is (5+1) + (7 – 1) = 12 50 + 70 is (50 + 10) + (70 – 10) = 120

Doubles Plus Two 40 + 60 60 + 80 90 + 70 30 + 10 20 + 40 50 + 30 60 + 40 70 + 90 10 + 30 40 + 20

Doubles Plus 2 100 + 300 700 + 500 300 + 500 700 + 900 800 + 600 600 + 400 300 + 100 500 + 300 600 + 800 500 + 700

Plus or Minus 0 You already know 5 + 0 = 5. You can extend that to You can also extend that to 500 + 0 = 500 or 500 – 0 = 500. 0 + 90 300 - 0 20 + 0 0 + 500 900 - 0

Plus or Minus 0 80 – 0 700 + 0 500 – 0 0 + 30 600 – 0 0 + 80 900 + 0 700 – 0 0 + 400 100 – 0

Make 10 or 100 This strategy is used with addends of 8 or 9 or 80 or 90. Example: 9 + 6 –- think: 9 + 1 (from the 6) = 10 and then 10 + 5 = 15 Or: 9 + 6 = (9 + 1) + 5 = 10 + 5 = 15

Make 10 or 100 8 + 5 9 + 2 8 + 6 8 + 3 9 + 5 5 + 8 9 + 4 4 + 8 9 + 6 8 + 2

Make 10 or 100 80 + 20 80 + 40 20 + 90 40 + 90 30 + 90 80 + 10 90 + 20 60 + 80 90 + 10 80 + 30

Plus 2s or “Next Even/Odd” Number You know that 5 + 2 = 7 because when adding 2, you jump to the next odd number since 5 is an odd number. Another example is: 6 + 2 = 8 because adding 2 to an even number means you jump to the next even number which is 8. This can be applied to 10s and 100s. Example: 70 + 20 = 90 40 + 20 = 60

Plus 2s or “Next Even/Odd” Number 60 + 20 30 + 20 40 + 20 50 + 20 10 + 20 20 + 20 80 + 20 30 + 60 50 + 30 70 + 10

Plus 2s or “Next Even/Odd” Number 200 + 700 600 + 200 300 + 200 200 + 400 800 + 200 500 + 200 100 + 200 700 + 100 300 + 300 400 + 300

Plus 3s or “Adding 2 and Then 1” When adding 3 to a single digit number, think “next even/odd and then next number.” Example: 6 + 3 is (6 + 2) + 1 = 9 8 + 3 5 + 3 9 + 3 3 + 3 1 + 3 7 + 3 2 + 3 4 + 3

Plus 3s 50 + 30 30 + 60 90 + 30 20 + 30 80 + 30 30 + 10 30 + 70 40 + 30 30 + 50 70 + 20

Plus 3s 400 + 300 700 + 300 300 + 800 200 + 300 600 + 300 100 + 300 900 + 300 300 + 500 300 + 100 300 + 400

Front End Addition Add the highest place values and then add the sums of the next place values. Example: 45 + 17 -- think 40 + 10 and 5 + 7 or 50 + 12 = 62.

Front End Addition 15 + 66 74 + 19 33 + 21 + 42 25 + 11 + 43 41 + 13 + 24 65 + 72 18 + 88 22 + 13 + 51 34 + 16 73 + 21

Front End Addition 24 + 31 + 14 34 + 11 + 52 24 + 12 + 33 19 + 42 66 + 51 21 + 72 33 + 15 42 + 13 24 + 14 62 + 33

Finding Compatibles Find pairs of numbers that add to powers of ten to make the addition easier. Example: 3 + 8 + 7 Think: 3 + 7 is 10 plus 8 is 10 + 8 = 18. Example: 20 + 40 + 80 Think: 20 + 80 is 100, so 100 and 40 is 140.

Finding Compatibles 6 + 9 + 4 2 + 3 + 8 4 + 6 + 2 1 + 9 + 5 5 + 6 + 5 3 + 7 + 4 9 + 8 + 1 5 + 9 + 5 8 + 3 + 2 5 + 3 + 7

Finding Compatibles 10 + 60 + 90 30 + 50 + 70 80 + 30 + 20 60 + 30 + 40 80 + 20 + 70 60 + 30 + 70 40 + 70 + 60 90 + 80 + 10 30 + 70 + 40 40 + 60 + 40

Break Up and Bridge think 45 and 30 is 75 + 8 = 83 Start with the first number and add the values in the place values beginning with the larger of the second number. (You may want to use the 100s chart as a tool to teach this strategy.) Example: 45 + 38 think 45 and 30 is 75 + 8 = 83

Break Up and Bridge 37 + 45 72 + 28 25 + 76 38 + 43 59 + 15 66 + 27 23 + 52 45 + 62 54 + 21 73 + 54

Break Up and Bridge 54 + 33 82 + 24 67 + 32 43 + 31 15 + 59 27 + 72 45 + 37 42 + 34 71 + 16 36 + 22

Compensation Change one number to 10, carrying out the addition and then adjusting the answer to compensate for the original change. Example: 52 + 9 Think– 52 plus 10 is 62, but I added 1 too many, to take me to the next 10 to compensate, so I subtract one from my answer, 62 to get 61 OR 52 + 9 = (52 + 10) – 1 = 61

Compensation 43 + 9 56 + 8 79 + 2 48 + 5 65 + 29 13 + 48 49 + 27 3 + 78 11 + 45 15 + 84 2 + 97

Compensation 27 + 94 48 + 31 29 + 56 5 + 84 2 + 97 8 + 65 9 + 34 48 + 22 35 + 3 54 + 7

Subtraction – Doubles Use addition double facts to help find the answers to related subtraction combinations. Example: 12 – 6 Think – 6 + _____ = 12 120 – 60 Think – 60 + _____ = 120

Subtraction – Doubles 60 – 30 100 – 50 20 – 10 40 – 20 120 – 60 180 – 90 140 – 70 160 – 80 80 - 40

Subtraction – Doubles 200 – 100 800 – 400 1000 – 500 1200 – 600 1600 – 800 1800 – 900 400 – 200 600 – 300 1400 – 700

Subtraction – Near-Doubles When the part being subtracted is close to half of the total, we can think of an addition double fact, and then adjust it by 1 to find the answer. Example: 9 -4 Think– 4 + 4 = 8, 4 + 5 = 9, so 9 – 4 = 5 Example: 90 – 40 Think – 40 + 4- = 80, 40 + 50 = 90, so 90 – 40 = 50