Doubles
A double is a number added to itself. 6 + 6 is double 6, and it makes 12. Draw it as two equal rows of 6, and the two rows match exactly.
The doubles up to 10 + 10 are worth knowing by heart: 1 + 1 = 2, 2 + 2 = 4, 3 + 3 = 6, and on up to 10 + 10 = 20. Each double is an even number, because it is two equal rows.
Two equal rows of 6 make 12.
One more than a double
6 + 7 is nearly a double. Put a row of 6 above a row of 7. The 6 in the top row match 6 in the bottom row, and 1 is left over.
So 6 + 7 is double 6 and 1 more: 12 + 1 = 13. When the two numbers are next to each other in counting, the sum is called a near double: it is always the double of the smaller number and 1 more.
The two rows match for 6 places, which is double 6, and 1 is left over: 12 + 1 = 13.
6 + 6 = double 6 = 12
Make 6 + 7
Where the rows match, the pairs make the double. A square past the end of the top row is one more than the double, and a gap under it is one less.
Two equal hops of 6 reach 12, which is double 6. One more hop of 1 lands on 13.
Or one less than a double
You can start from the bigger number instead. 6 + 7 is also double 7 and 1 less: 14 − 1 = 13. Both ways give 13.
Double the smaller number and add 1, or double the bigger number and take 1 away. Doubling the bigger number and then adding 1 is the usual mistake: 14 + 1 = 15 counts 1 too many.
Two equal hops of 7 reach 14, which is double 7. A hop back of 1 lands on 13.
Bigger numbers
Near doubles work for bigger numbers too. 36 + 37 is double 36 and 1 more. To double 36, split it into tens and ones: double 30 is 60 and double 6 is 12, so double 36 is 72. Then 72 + 1 = 73.
Double 36, split into tens and ones: 30 + 30 = 60 and 6 + 6 = 12, so 36 + 36 = 72.
Double 36 is 72, and one more is 73.
Worked example: Two Classes of Almost the Same Size
Question Class 3A has 38 pupils and Class 3B has 39 pupils. (a) What is double 38? (b) How many pupils are in the two classes altogether?
1.39 is 1 more than 38. So 38 + 39 is double 38 and 1 more.
39 is 1 more than 38, so the total is double 38 and 1 more. 2.Double 38 by splitting it into 30 and 8. Double 30 is 60 and double 8 is 16.
Double 30 is 60 and double 8 is 16. 3.(a) 60 + 16 = 76, so double 38 is 76.
(a) 60 + 16 = 76, so double 38 is 76. 4.(b) 76 + 1 = 77, so there are 77 pupils altogether. Check: double 40 is 80, and 80 − 2 − 1 = 77.
(b) 76 + 1 = 77 pupils altogether.
Answer: (a) 76; (b) 77 pupils
Common mistakes
- Stopping at 76. That is two classes of 38, but Class 3B has 1 more pupil, so 1 must still be added.
- Doubling 39 to get 78 and then adding 1. Double 39 already counts 1 pupil too many, so 1 must be taken away: 78 − 1 = 77.
More adding and subtracting in your head problems, worked step by step →