Some facts sit right next door to a double. 7 + 8 is almost 7 + 7.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Use the double, then adjust
7 + 7 is 14. The 8 is one more than 7, so the answer is one more than 14.
So 7 + 8 = 15. You never counted. You used a fact you already had.
Either neighbor works
You could also use 8 + 8 = 16 and take one away. Both roads reach 15.
Step 2: Try It Yourself
Set the parts one apart and compare with the double.
First part and Second part
7
8
Total
15
7 and 8 make 15.
How many
15 and 5 make 20. There are 5 empty spaces.
7 and 8 make 15.
Step 3: In Real Life
Two shelves of books
One shelf holds 7 books. The next holds 8. 7 + 7 is 14. One more is 15. You knew the double, so you knew its neighbor.
Step 4: Watch an Example
One step at a time.
Watch Leo Use a Near Double
Leo is asked for 6 + 7.
- Step 1
He notices the two numbers are only one apart.
Step 5: Your Turn
Practice makes it stick.
Two Boxes
Problem 1 of 2
One box holds 8 pencils. The other holds 9. How many pencils in all?
pencils
Football Teams
Problem 2 of 2
One team has 5 players. The other has 6. How many players are on the field?
players
Use the Double Next Door
Say the double first, then adjust by one.
1 of 4
4 + 5 = ?
2 of 4
7 + 8 = ?
3 of 4
9 + 8 = ?
4 of 4
6 + 5 = ?
Show the Missing Part
Build it, then check.
15 is 7 and how many? Show that part.
How many
Step 6: Quick Check
Show what you know.
Question 1 of 2
8 + 9 = ?
Question 2 of 2
You know 6 + 6 = 12. What is 6 + 7?
What You Learned
- A near double sits one away from a double.
- Recall the double, then add or take away one.
- Using a fact you know beats counting every time.
For the grown-up
This lesson is where the child solves near-double facts such as 7 + 8 by recalling the double and adjusting by one. Fluency within twenty is not speed for its own sake. Facts that come without thinking free up the working memory that the next four years of mathematics need, and a child recomputing 8 + 6 every time has nothing left over for the problem it sits inside.
Watch for finger counting that has gone underground — a pause, a glance away, lips moving. The strategy has not gone; it has just got quieter.
Short and often beats long and rare. Two minutes of the facts they nearly know is worth more than twenty minutes of the ones they already do.
What makes two numbers near doubles — Two numbers are near doubles when they are one apart, like 6 and 7, or two apart, like 6 and 8. You do not add them from scratch. You find the double hiding inside them, then fix the difference. For 6 + 7, the double is 6 + 6 = 12, and 7 is one more than 6, so the answer is one more: 13.
Two doubles to choose from — For 6 + 7 you could use the double of 6 and add one, or use the double of 7 and take one away: 7 + 7 = 14, then 14 - 1 = 13. Both routes land on 13. Pick whichever double you know better. Getting the same answer two ways is good evidence you are right.
The slip to watch for — The common mistake is adjusting in the wrong direction — using 6 + 6 = 12 and then taking one away instead of adding one. Guard against it by asking whether the answer should be bigger or smaller than the double before you calculate. 6 + 7 has more in it than 6 + 6, so the answer must be bigger. That check takes a second and catches the error every time.
Lean on the double next door — 7 + 8. Not a double, but nearly one. You know 7 + 7 = 14. 8 is one more than 7. So the answer is one more than 14. 7 + 8 = 15