Questions: Near Doubles Facts Within 20

Question 1

A student knows that 7 + 7 = 14. Using the near-doubles strategy, what is 7 + 8?

• A. 15 — because 8 is one more than 7, so the sum is one more than 14
• B. 14 — use the doubles fact directly since 8 is close to 7
• C. 16 — round 8 up to 9 and use 7 + 9 instead
• D. You must count from 1 to find a fact you haven't memorized

Answer: (A)

The near-doubles strategy uses a known doubles fact as a launching pad. Since 7 + 7 = 14, and 8 is one more than 7, the answer is one more than 14 — which is 15. You do not start over from 1; you take a single hop from a fact already in memory. Option B ignores the 'one more' step; option D defeats the whole purpose of the strategy.

Question 2

Which of these problems is best solved using the near-doubles strategy?

• A. 4 + 9 — the addends are five apart
• B. 6 + 6 — this is already a doubles fact
• C. 5 + 6 — the addends are exactly one apart
• D. 3 + 8 — the addends are five apart

Answer: (C)

Near-doubles applies when the two addends are exactly one apart — making one a neighbor of the other. 5 + 6 qualifies perfectly: use 5 + 5 = 10 and add 1 to get 11. Options A and D have addends too far apart for this strategy. Option B is already a doubles fact, so no strategy is needed.

Question 3

The near-doubles strategy for 6 + 7 works because 7 is exactly one more than 6, so the sum is exactly one more than the known fact 6 + 6 = 12.

• T. True
• F. False

Answer: True

This is precisely how the strategy works. 6 + 7 = (6 + 6) + 1 = 12 + 1 = 13. The logic is that replacing the second 6 with a 7 adds exactly one to the total. This is the 'one hop from a known fact' that makes the strategy fast and reliable.

Question 4

To use the near-doubles strategy, you should first count both addends on your fingers to confirm they are one apart before using the doubles fact.

• T. True
• F. False

Answer: False

The strategy does not require finger-counting. You recognize from the numbers themselves that they are one apart (e.g., 8 and 9 look like neighbors), recall the doubles fact for the smaller number, and add one. Counting on fingers would be slower and would miss the whole efficiency the strategy provides.

Question 5

Explain how you would use the near-doubles strategy to solve 9 + 8, and why this is faster than counting up from 1.

Model answer: Recognize that 9 and 8 are one apart. Recall the doubles fact 8 + 8 = 16 (or 9 + 9 = 18). Since 9 is one more than 8, the answer is one more than 16 — which is 17. (Alternatively: 9 + 9 = 18, and 8 is one less than 9, so the answer is 18 − 1 = 17.) This is faster than counting from 1 because you start from a fact already in memory and take just one step, instead of performing 17 individual counting actions.

The core insight is that you are using an existing mental shortcut (the doubles fact) rather than rebuilding the answer from scratch. This is a first example of the broader mathematical habit: always look for something nearby that you already know.