Making a Ten Strategy - Second Grade Mathematics

In our base-ten number system, ten is the most celebrated benchmark number: it fills a ten-frame, creates a ten rod, and rolls numbers smoothly into the next decade. Because adding any single-digit number to ten is effortless (such as 10 + 4 = 14 or 10 + 7 = 17), the making-a-ten strategy is one of the most powerful mental tools you will ever learn. By breaking apart one addend to lend a few units to the other, you can transform difficult addition problems into simple ten-plus facts. In this chapter, you will master the making-a-ten strategy using ten-frames, number bonds, and mental decomposition.

The Magic of Adding to Ten

Consider how easy it is to add any number to ten: 10 + 1 = 11 10 + 2 = 12 10 + 5 = 15 10 + 8 = 18

The Ten-Plus Superpower:
Whenever one addend is 10, the ones digit of the other addend
simply takes over the zero in the ones place!
    10 + 6 = 16

Why We Want to Make a Ten

Because adding to ten is instantaneous, mathematicians look for opportunities to turn non-ten problems into ten-plus problems. If you have 8 + 5, you can ask yourself: "How can I rearrange these numbers so that 8 becomes a friendly 10?"

The Make-a-Ten Strategy Step by Step

Let us examine how to solve 8 + 5 step by step using the making-a-ten method.

Solving 8 + 5 by Making a Ten:

Step 1: Ask how many 8 needs to make 10.
        8 needs 2 more.

Step 2: Decompose the second addend (5) to give 2 to the 8.
        5 breaks into 2 and 3.

Step 3: Combine 8 and 2 to make 10.
        (8 + 2) = 10

Step 4: Add the remaining 3 to 10.
        10 + 3 = 13

Visual Ten-Frame Model:
Frame 1 (Needs 2): [X][X][X][X][X]    Frame 2 (Lends 2): [O][O][O][ ][ ]
                   [X][X][X][O][O]                       [ ][ ][ ][ ][ ]
                   (Full 10!)                            (3 remain)
Total: 10 + 3 = 13

Number Bonds Show the Split

You can draw a number bond under the second addend to show how it is partitioned: Under the number 5, draw two branches leading to 2 and 3. The equation transforms: 8 + 5 = (8 + 2) + 3 = 10 + 3 = 13.

Using the Associative Property

This strategy relies on the associative property of addition, which says you can regroup addends in parentheses without changing the sum: 8 + (2 + 3) = (8 + 2) + 3 = 10 + 3 = 13.

Making a Ten with 9, 8, and 7

The making-a-ten strategy is most effective when one of the addends is close to ten: 9, 8, or 7.

When Adding 9: Always needs 1 to make 10.
  9 + 6 = 9 + (1 + 5) = (9 + 1) + 5 = 10 + 5 = 15

When Adding 8: Always needs 2 to make 10.
  8 + 7 = 8 + (2 + 5) = (8 + 2) + 5 = 10 + 5 = 15

When Adding 7: Always needs 3 to make 10.
  7 + 6 = 7 + (3 + 3) = (7 + 3) + 3 = 10 + 3 = 13

The "Nines Rule" (Steal 1, Drop 1)

When adding 9 to any single digit, the answer always begins with a 1 in the tens place, and the ones digit is always 1 less than the number being added to 9. Look at the pattern: 9 + 4 = 13 (4 drops to 3) 9 + 7 = 16 (7 drops to 6) 9 + 8 = 17 (8 drops to 7) Understanding that 9 steals 1 to make 10 explains why the other digit drops by 1!

Practice Exercises

Exercise 1: Use the make-a-ten strategy to solve 9 + 5. State how many 9 needed, how 5 was decomposed, and the final sum.

Exercise 2: Solve 8 + 6 by making a ten. Draw or write out each step using parentheses to show the associative regrouping.

Exercise 3: Solve 7 + 5 by making a ten. Explain how you chose to break apart the number 5.

Exercise 4: Explain why someone would choose the make-a-ten strategy instead of counting on fingers to solve 8 + 7.

Solutions and Explanations

Solution to Exercise 1: To solve 9 + 5, 9 needs 1 more to make 10. Decompose 5 into 1 and 4. Combine 9 and 1 to make 10: (9 + 1) = 10. Then add the remaining 4: 10 + 4 = 14. The final sum is 14.

Solution to Exercise 2: To solve 8 + 6, 8 needs 2 to make 10. Break 6 into 2 and 4. Using parentheses: 8 + 6 = 8 + (2 + 4) = (8 + 2) + 4 = 10 + 4 = 14.

Solution to Exercise 3: To solve 7 + 5, start with 7, which needs 3 to make 10. Decompose 5 into 3 and 2. Join 7 and 3 to create 10, then add the remaining 2 to obtain 10 + 2 = 12.

Solution to Exercise 4: Solving 8 + 7 by counting on fingers requires tracking seven separate finger taps, which is slow and easy to miscount. Making a ten is a mental structure that transforms 8 + 7 into (8 + 2) + 5 = 10 + 5 = 15 in less than two seconds, guaranteeing accuracy and building place value fluency.