Making Ten to Add (e.g., 8 + 5 = 10 + 3) - First Grade Mathematics
Adding across ten can feel like climbing a steep hill, but there is a friendly shortcut that makes it simple: the Make-a-Ten strategy! Ten is our favorite benchmark number because adding anything to ten is effortless: 10 + 3 is 13, 10 + 7 is 17, and 10 + 4 is 14. In this chapter, you will learn how to take a few units from one addend and give them to the other addend so you can create a ten. Once you have a ten, you can add the remaining ones in a single step!
The Magic of Borrowing to Make Ten
Look at the problem 8 + 5. The number 8 is so close to 10; it only needs 2 more to become a complete ten!
The Make-a-Ten Transformation for 8 + 5:
Start with: 8 + 5
/Decompose 5: 2 3 (Break 5 into 2 and 3!)
Give 2 to 8: (8 + 2) + 3
Make Ten: 10 + 3 = 13!
Seeing it on Double Ten-Frames
Picture two ten-frames side by side: Frame 1 holds 8 red counters (it has 2 empty boxes). Frame 2 holds 5 yellow counters. Take 2 yellow counters from Frame 2 and move them into the empty boxes of Frame 1. Now Frame 1 is completely full (10), and Frame 2 has 3 counters left! You instantly see: 10 + 3 = 13!
Double Ten-Frame Demonstration:
Frame 1 (was 8, now FULL): Frame 2 (was 5, now 3):
+---+---+---+---+---+ +---+---+---+---+---+
| R | R | R | R | R | | Y | Y | Y | | |
+---+---+---+---+---+ +---+---+---+---+---+
| R | R | R | Y | Y | | | | | | |
+---+---+---+---+---+ +---+---+---+---+---+
10 Tens + 3 Ones = 13!
Using Make-a-Ten with 9
The number 9 is the greatest fan of the Make-a-Ten strategy because it needs only ONE unit to become 10!
Solving 9 + 6:
9 needs 1 to make 10.
Borrow 1 from 6 (leaving 5):
9 + 6 becomes 10 + 5 = 15!
Solving 9 + 4:
Borrow 1 from 4 (leaving 3):
9 + 4 becomes 10 + 3 = 13!
Solving 9 + 7:
Borrow 1 from 7 (leaving 6):
9 + 7 becomes 10 + 6 = 16!
The "Nine Takes One" Chant
Whenever you see a 9 in an addition problem, think: "Nine takes one from its neighbor!" The neighbor becomes one smaller, and you have your teen number instantly!
The Three Steps of Making Ten
Follow this clear three-step routine for any problem: Step 1: Identify the addend closest to 10 (usually 9, 8, or 7). Step 2: Figure out how many it needs to make 10, and split that amount off from the other addend. Step 3: Combine to make 10, and add the leftover ones to name the teen number!
Practice Exercises
Exercise 1: Solve 8 + 6 by making a ten. How many does 8 need to make 10? How do you split 6? What is the final equation and sum?
Exercise 2: Solve 9 + 5 by making a ten. Show how 9 borrows 1 to make 10 + 4.
Exercise 3: Solve these equations mentally using the make-a-ten strategy: 8 + 4 = __ 7 + 5 = __ 9 + 8 = __ 8 + 7 = __
Exercise 4: Explain why transforming 8 + 5 into 10 + 3 makes the problem easier to solve in your head.
Solutions and Explanations
Solution to Exercise 1: The number 8 needs 2 to make 10. Split 6 into 2 and 4. Combine 8 and 2 to make 10: 10 + 4 = 14. The sum is 14.
Solution to Exercise 2: The number 9 needs 1 to make 10. Split 5 into 1 and 4. Give the 1 to 9 to make 10, leaving 4. Then 10 + 4 = 14.
Solution to Exercise 3: 8 + 4 = 12 (8 needs 2, 4 becomes 2: 10 + 2 = 12) 7 + 5 = 12 (7 needs 3, 5 becomes 2: 10 + 2 = 12) 9 + 8 = 17 (9 needs 1, 8 becomes 7: 10 + 7 = 17) 8 + 7 = 15 (8 needs 2, 7 becomes 5: 10 + 5 = 15)
Solution to Exercise 4: Transforming 8 + 5 into 10 + 3 makes it easier because our base-ten number system makes adding to 10 instant: 10 plus any single digit simply forms that teen number (10 + 3 = 13) without requiring any finger counting.