Doubles Doubles I Can Add Doubles

Doubles and Doubles‑Plus‑One: A Simple Strategy for Adding Numbers Quickly

When students first learn addition, they often rely on counting on fingers or drawing pictures. While these methods work for small numbers, they become cumbersome as the sums grow larger. A powerful mental‑math tool that bridges the gap between basic counting and fluency is the doubles strategy—using known double facts (like 6 + 6 = 12) to solve nearby addition problems. So by mastering doubles, doubles‑plus‑one, and doubles‑minus‑one, learners can add numbers swiftly and confidently. This article explains the concept, shows how to apply it, offers practice exercises, and answers common questions Small thing, real impact..

What Are Doubles?

In mathematics, a double is the sum of two identical numbers. The doubles facts form a small, memorable set:

These facts are usually among the first addition facts children memorize because they follow a clear pattern: each double is simply twice the addend. Knowing them by heart provides a foundation for more complex mental calculations Turns out it matters..

Using Doubles to Add Nearby Numbers

Once the doubles are internalized, they become stepping stones for solving problems where the addends are close but not identical. The two most useful extensions are doubles‑plus‑one and doubles‑minus‑one.

Doubles‑Plus‑One

If you need to add two numbers that differ by one (e.g., 6 + 7), you can:

1. Identify the smaller number (6).
2. Recall its double (6 + 6 = 12).
3. Add one more to account for the extra + 1 (12 + 1 = 13).

Thus, 6 + 7 = 13. The same logic works for any pair like 4 + 5, 9 + 10, etc.

Doubles‑Minus‑One

For pairs where the larger number is one more than the smaller (e.g., 8 + 7), you can:

1. Identify the larger number (8).
2. Recall its double (8 + 8 = 16).
3. Subtract one to remove the extra + 1 (16 − 1 = 15).

So, 8 + 7 = 15. This also works for 5 + 4, 10 + 9, and so on Easy to understand, harder to ignore..

Both extensions rely on the same core idea: start from a known double, then adjust by ± 1.

Step‑by‑Step Guide to the Doubles Strategy

Below is a concise procedure you can teach or follow when faced with an addition problem.

1. Look at the two addends.

   • Are they the same? → Use the double directly.
   • Do they differ by exactly one? → Use doubles‑plus‑one or doubles‑minus‑one.
   • If the difference is larger, consider breaking the problem into a double plus a remaining chunk (see “Beyond ±1” later).

2. Identify the base number for the double.

   • For doubles‑plus‑one, the base is the smaller addend.
   • For doubles‑minus‑one, the base is the larger addend.

3. Recall the double fact.

   • If you haven’t memorized it yet, you can quickly compute it by multiplying the base by 2 (e.g., 7 × 2 = 14).

4. Adjust by ± 1 as needed Easy to understand, harder to ignore..

   • Add 1 for doubles‑plus‑one.
   • Subtract 1 for doubles‑minus‑one.

5. Write or say the final sum.

Beyond ±1: Using Doubles as a Building Block

When the addends differ by more than one, you can still take advantage of doubles by splitting the problem:

Example: 9 + 6

1. Find the double of the smaller number: 6 + 6 = 12.
2. Determine how much more the larger number is than the smaller: 9 − 6 = 3.
3. Add that difference to the double: 12 + 3 = 15.

Alternatively, you could double the larger number and subtract the excess:

• Double 9 = 18.
• Excess = 9 − 6 = 3.
• 18 − 3 = 15.

Both routes give the same result and reinforce the flexibility of the doubles concept Practical, not theoretical..

Why the Doubles Strategy Works: A Brief Cognitive Explanation

The doubles strategy taps into two well‑studied aspects of arithmetic cognition:

1. Fact Retrieval: Small, repetitive facts like doubles are stored in long‑term memory and can be recalled automatically, reducing the load on working memory.
2. Derived Fact Strategy: Once a base fact is known, learners can derive related facts by applying simple transformations (adding or subtracting 1). This mirrors how experts use known relationships to solve new problems quickly.

Research shows that children who receive explicit instruction in doubles and derived facts develop faster fluency and fewer errors than those who rely solely on counting The details matter here..

Practice Problems

Try solving each using the doubles method. Check your answers afterward.

Set A: Identical Addends (Pure Doubles)

1. 4 + 4 = __
2. 7 + 7 = __
3. 11 + 11 = __

Set B: Doubles‑Plus‑One

1. 5 + 6 = __
2. 8 + 9 = __
3. 12 + 13 = __

Set C: Doubles‑Minus‑One

1. 9 + 8 = __
2. 6 + 5 = __
3. 13 + 12 = __

Set D: Using Doubles as a Chunk

1. 10 + 7 = __
2. 14 + 9 = __
3. 3 + 11 = __

Answers:

• Set A: 8, 14, 22
• Set B: 11, 17, 25
• Set C: 17, 11, 25