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Strategy Guide

Make Friendly Numbers

Add near 10s and 100s

Round the second number UP to the nearest 10 or 100. Add that instead, it's easier. Then subtract the bit you added extra.

Example

346 + 99
Round 99 up to 100
346 + 100 = 446
Added 1 too many → 446 − 1 = 445

Subtract near 10s and 100s

Round the number you're subtracting UP to the nearest 10 or 100. Subtract that instead. Then add back the extra you took away.

Example

500 − 99
Round 99 up to 100
500 − 100 = 400
Took 1 too many → 400 + 1 = 401

Compensation

Same idea as near 10s but with any near-round number. Round, calculate, then adjust. The key question: did you add or subtract too many?

Example

347 + 198
Round 198 up to 200
347 + 200 = 547
Added 2 too many → 547 − 2 = 545

Bridge Through

Bridge through 10

When adding, jump to the next 10 first, then add the rest. Split the second number into two parts to make it work.

Example

27 + 8
27 + 3 = 30 (bridge to 30)
Then + 5 more
30 + 5 = 35

Bridge through 100 or 1,000

Same idea but jumping to the next hundred or thousand. Split the number you're adding to land on the round number first.

Example

87 + 24
87 + 13 = 100 (bridge to 100)
Then + 11 more
100 + 11 = 111

Break It Apart (Partition)

Partition to Add

Split both numbers into tens and ones. Add the tens together, then add the ones. Then combine.

Example

34 + 52
30 + 50 = 80
4 + 2 = 6
80 + 6 = 86

Partition to Subtract

Split the number you're subtracting. Take away the tens first, then the ones.

Example

76 − 34
76 − 30 = 46
46 − 4 = 42

Partition to Multiply (2-digit × 1-digit)

Split the 2-digit number into tens and ones. Multiply each part by the single digit, then add the results together.

Example

34 × 3
30 × 3 = 90
4 × 3 = 12
90 + 12 = 102

Partition to Divide (2-digit ÷ 1-digit)

Split the dividend into two parts that both divide evenly by the divisor. Divide each part, then add the answers.

Example

45 ÷ 3
Split 45 into 30 + 15
30 ÷ 3 = 10
15 ÷ 3 = 5
10 + 5 = 15

Count Up Instead

Find the Difference

When two numbers are close together, don't subtract, count up from the smaller to the larger. It's much faster.

Example

52 − 47
Count up: 47 → 52
That's just 5 steps
Answer = 5

Difference within 100 or 1,000

Same idea with bigger numbers. If the gap is small, counting up is faster than subtracting.

Example

1,003 − 997
Count up: 997 → 1,003
That's just 6 steps
Answer = 6

Double It. Halve It.

Double then Double Again (× 4)

Multiplying by 4 is the same as doubling twice. Double the number, then double your answer.

Example

7 × 4
Double 7 = 14
Double 14 = 28

Division Strategies

Fact Families

Every multiplication fact gives you two division facts. If you know 6 × 7 = 42, you automatically know 42 ÷ 6 = 7 and 42 ÷ 7 = 6.

Example

63 ÷ 9 = ?
Think: what × 9 = 63?
7 × 9 = 63
So 63 ÷ 9 = 7

Inverse Thinking

Division is just multiplication backwards. Turn the division into a missing factor problem and use your tables knowledge.

Example

48 ÷ 6 = ?
Flip it: ? × 6 = 48
8 × 6 = 48
So 48 ÷ 6 = 8

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