What You'll Learn
- Recall doubles from 1 + 1 through 9 + 9
- Identify addition expressions whose addends differ by one or two
- Adjust a nearby double without changing the total incorrectly
- Connect doubling to equal groups and multiplication by two
The Reasoning Behind Doubles and Near-Doubles
A double combines two equal addends: 6 + 6 = 12. Doubles produce even totals because two equal groups can be paired with nothing left over. The sequence 2, 4, 6, 8, and onward grows by two each time because increasing each matching addend by one adds two to the total.
A near-double uses an equal-pair fact as an anchor. In 6 + 7, replace the 7 temporarily with 6 to see 6 + 6 = 12, then restore the one-unit difference: 12 + 1 = 13. The adjustment is justified because 7 is exactly one more than 6.
Either neighboring double may work. For 7 + 8, the lower anchor gives 7 + 7 + 1 = 15; the upper anchor gives 8 + 8 − 1 = 15. These expressions agree because shifting one unit from one addend to the other can create equal groups while preserving the total.
When addends differ by two, their midpoint can form a useful double. For 5 + 7, move one from 7 to 5: 6 + 6 = 12. This compensation method differs from simply rounding one addend, because the opposite addend changes in balance and the original total remains constant.
Earlier addition facts supply the anchors, complements help when a double crosses ten, and Stage 2 regrouping explains teen totals such as 8 + 8 = 16. Doubling also previews multiplication: two groups of 7 contain 14 altogether, written later as 2 × 7 or 7 × 2.
Why This Skill Matters
Doubles compress repeated counting into a stable pattern and offer reference points for many nearby sums. The strategy also introduces equal groups, even numbers, compensation, and the distributive reasoning used in multiplication.
Choosing an anchor trains attention to relationships between numbers. Instead of treating 8 + 9 as isolated, it becomes one more than a known structure, 8 + 8.
Where You Will Use Doubles and Near-Doubles
Two shelves holding 8 books each contain 16 books. If one extra book is placed on the second shelf, the new total is the near-double 8 + 9 = 17. The equal arrangement provides the anchor; only the change needs fresh calculation.
Pairs also appear in wheels on bicycles, matching rows of seats, and equal game turns. When the groups differ slightly, a near-double describes both the symmetry and the small adjustment.
See the Strategy in Action
Read the strategy, then prove you can use it: every example ends with a matching problem on new numbers that you answer and check right here. Answer it and press New numbers for as many fresh problems as you like.
Recall an exact double
7 + 7
- 1 I see two equal groups of 7.
- 2 The doubles sequence tells me the total after 12 is 14.
- 3 I can verify by making 7 + 3 + 4 = 10 + 4.
7 + 7 = 14
Your turn — try it on new numbers
9 + 10 = ?
Use the lower double
6 + 7
- 1 I anchor at 6 + 6 = 12.
- 2 The second addend is one larger than 6, so I add one.
6 + 7 = 13
Your turn — try it on new numbers
3 + 2 = ?
Use the upper double
8 + 9
- 1 I know the upper double 9 + 9 = 18.
- 2 The first addend is one below 9, so I subtract one.
8 + 9 = 17
Your turn — try it on new numbers
8 + 7 = ?
Balance a two-apart pair
5 + 7
- 1 The addends are two apart, with 6 between them.
- 2 I move one from 7 to 5, forming 6 + 6 without changing the total.
- 3 The double of 6 is 12.
5 + 7 = 12
Your turn — try it on new numbers
8 + 8 = ?
Self-Check: Errors to Avoid
Forgetting the adjustment
Using 6 + 6 for 6 + 7 finds only 12. Compare the actual addend with the anchor and restore the extra one to reach 13.
Adjusting in the wrong direction
If 8 + 9 is anchored to 9 + 9, the original is one smaller, so subtract one. Say “lower anchor plus” or “upper anchor minus” before calculating.
Changing only one side during compensation
Turning 5 + 7 into 6 + 7 increases the total. To preserve it, move one: increase 5 to 6 while decreasing 7 to 6.
Pro Tips
- • Recite doubles as connected even totals, not as unrelated flash-card answers.
- • For addends one apart, decide whether the lower-plus-one or upper-minus-one anchor feels clearer.
- • For addends two apart, move one unit toward the midpoint to form equal addends.
- • Sketch two equal rows and mark the extra object when a near-double is confusing.
Practice Exercises
Work each problem mentally, then type the answer and check it. Nothing is marked correct until you enter a value that actually equals the result, and every problem keeps its mental-steps note in reach if you get stuck.
- 1. 2 + 2 = ?
- 2. 5 + 5 = ?
- 3. 8 + 8 = ?
- 4. 6 + 7 = ?
- 5. 7 + 8 = ?
- 6. 8 + 9 = ?
- 7. 4 + 5 = ?
- 8. 3 + 3 = ?
- 9. 9 + 9 = ?
- 10. 5 + 6 = ?
- 11. 4 + 6 = ?
- 12. 5 + 7 = ?
- 13. 6 + 8 = ?
- 14. 3 + 4 = ?
- 15. 7 + 7 = ?
- 16. 2 + 4 = ?
- 17. 1 + 1 = ?
- 18. 9 + 8 = ?
Drill Stage 6 with unlimited problems
Type your answer and press Enter. Every problem is generated on the spot and uses exact doubles and near-doubles. Get it wrong and the steps below show how that exact problem is solved mentally.
- Correct
- 0 / 0
- Accuracy
- —
- Best streak
- 0
- Time
- 0:00
Problem 1
3 + 4 = ?
Stage 6 Questions
Which double should anchor a near-double?
Either neighboring double is valid. Use the lower double and add, or the upper double and subtract; choose the fact you recall most securely.
Why are all doubles even?
A double consists of two equal groups, so its objects can be arranged in pairs with no unpaired object remaining.
Are addends two apart still near-doubles?
Yes. Their midpoint creates an exact double by balanced compensation, as 5 + 7 becomes 6 + 6.