Doubles and Near-Doubles Strategies - Second Grade Mathematics

Among all addition facts, doubles facts are the easiest and most enjoyable to memorize because they possess a satisfying rhythm and appear everywhere in the natural world: two hands with 5 fingers each, an egg carton with two rows of 6, or a spider with two sets of 4 legs. Once you memorize your doubles facts, they become powerful anchor facts that unlock dozens of nearby facts through the near-doubles strategy. In this chapter, you will master all doubles facts up to 10 + 10, learn how to adjust sums by adding or subtracting one or two, and use visual symmetry models to solve addition problems in a split second.

The Core Doubles Facts up to 10 + 10

A doubles fact occurs when a number is added to itself: two equal addends combined into one sum.

The Complete Doubles Roster:
 1 +  1 =  2   (Eyes on a face)
 2 +  2 =  4   (Tires on a car)
 3 +  3 =  6   (Legs on an insect)
 4 +  4 =  8   (Legs on a spider)
 5 +  5 = 10   (Fingers on two hands)
 6 +  6 = 12   (Eggs in a dozen)
 7 +  7 = 14   (Days in two weeks)
 8 +  8 = 16   (Crayons in two 8-packs)
 9 +  9 = 18   (Holes in a golf course)
10 + 10 = 20   (Fingers and toes combined)

Visual Symmetry of Doubles

Notice how every single doubles sum is an even number ending in 0, 2, 4, 6, or 8. Because both groups are identical, they can always be lined up in two perfectly balanced rows with zero leftovers. This visual symmetry helps your brain remember that a double can never equal an odd number like 13 or 17.

Rhythmic Chanting and Mental Recall

Practicing doubles as a rhythmic chant helps lock them into auditory memory: "6 plus 6 is 12, 7 plus 7 is 14, 8 plus 8 is 16." Once these ten facts are second nature, you are equipped to use the near-doubles strategy.

The Doubles-Plus-One Strategy

A near-doubles fact, also called a doubles-plus-one fact, consists of two consecutive numbers that sit side by side on the number line, such as 6 + 7 or 8 + 9.

Solving 7 + 8 using Doubles-Plus-One:

Step 1: Notice that 8 is just 1 more than 7.
        7 + 8 = 7 + (7 + 1)

Step 2: Recall the familiar double:
        7 + 7 = 14

Step 3: Add the extra 1:
        14 + 1 = 15

Visual Model:
Row 1: [O][O][O][O][O][O][O]       (7)
Row 2: [O][O][O][O][O][O][O] + [O] (7 + 1 = 8)
Total: 14 + 1 = 15

Thinking "Double the Smaller Number and Add 1"

Whenever two numbers differ by 1, look at the smaller number, double it, and add 1. For 5 + 6: think 5 + 5 = 10, plus 1 more is 11. For 8 + 9: think 8 + 8 = 16, plus 1 more is 17. For 6 + 7: think 6 + 6 = 12, plus 1 more is 13. Every doubles-plus-one sum is an odd number because an even double plus 1 always equals an odd number.

The Doubles-Minus-One Strategy

You can also solve near-doubles by doubling the larger number and subtracting 1.

Solving 7 + 8 using Doubles-Minus-One:

Step 1: Look at the larger number: 8.
Step 2: Pretend both numbers are 8:
        8 + 8 = 16
Step 3: Since you only had 7 (which is 1 less than 8), subtract 1:
        16 - 1 = 15

Choosing Your Favorite Path

Both strategies yield the exact same correct answer of 15. Some students prefer doubling the smaller number and adding 1, while others prefer doubling the larger number and subtracting 1. Having multiple mental pathways makes you a more flexible mathematician.

Doubles-Plus-Two Facts

What if the numbers differ by 2, such as 6 + 8?

Solving 6 + 8:
Method A (Doubles-Plus-Two):
Double the smaller: 6 + 6 = 12.
Add the extra 2: 12 + 2 = 14.

Method B (The Number in the Middle):
The number between 6 and 8 is 7.
Take 1 from 8 and give it to 6: both become 7!
7 + 7 = 14!

The Sharing-to-Make-Doubles Method

Method B above is called the sharing method. When two numbers have an even gap of 2 (like 5 and 7, or 7 and 9), you can take 1 from the larger number and give it to the smaller number. This turns both numbers into their common middle number: 7 + 9 becomes 8 + 8 = 16!

Practice Exercises

Exercise 1: Identify the double fact and the extra amount used to solve 8 + 9 using the doubles-plus-one strategy, and state the final sum.

Exercise 2: Solve 6 + 7 using both the doubles-plus-one strategy and the doubles-minus-one strategy. Show the steps for both methods.

Exercise 3: Use the sharing method (finding the middle number) to solve 7 + 9 as a double fact. Explain how the numbers were adjusted.

Exercise 4: Explain why the sum of any doubles-plus-one problem must always be an odd number.

Solutions and Explanations

Solution to Exercise 1: To solve 8 + 9 using doubles-plus-one, identify the smaller number, which is 8. The core double fact is 8 + 8 = 16. Since 9 is 1 more than 8, add the extra 1 to the double: 16 + 1 = 17. The final sum is 17.

Solution to Exercise 2: For the doubles-plus-one method, double the smaller number: 6 + 6 = 12, then add 1 to get 13. For the doubles-minus-one method, double the larger number: 7 + 7 = 14, then subtract 1 to get 13. Both methods correctly produce 13.

Solution to Exercise 3: In the problem 7 + 9, the number directly between 7 and 9 on the number line is 8. Take 1 from 9 (leaving 8) and give it to 7 (making it 8). The problem transforms into the double fact 8 + 8 = 16.

Solution to Exercise 4: Any number doubled is even because it consists of two identical, equal groups with no leftover units. When you add 1 to any even number, that single unit has no partner to pair with, creating a collection with an odd number of items. Therefore, an even double plus 1 is always odd.