Friends of 10: Combinations that Equal 10 - First Grade Mathematics

In first grade, the number 10 is like the superhero of mathematics. Almost every advanced addition and subtraction strategy you will learn later—including adding large numbers and doing mental math—relies on knowing which numbers pair together to make 10. These special pairs are affectionately known as the "Friends of 10." Just like two best friends who go everywhere together, each number from 0 to 10 has a unique partner that joins with it to make a complete ten. In this chapter, you will master all the Friends of 10 and learn how to spot them instantly.

The Rainbow of Ten

A wonderful way to visualize all the combinations that equal 10 is the Rainbow of Ten.

The Rainbow of 10:
  0 ---- 1 ---- 2 ---- 3 ---- 4 ---- 5
  |      |      |      |      |      |
  |      |      |      |      |   (5 + 5)
  |      |      |      |   (4 + 6)
  |      |      |   (3 + 7)
  |      |   (2 + 8)
  |   (1 + 9)
(0 + 10)
  |      |      |      |      |      |
 10 ---- 9 ---- 8 ---- 7 ---- 6 -----+

The Pairs That Make 10:

0 and 10 are friends: 0 + 10 = 10 1 and 9 are friends: 1 + 9 = 10 2 and 8 are friends: 2 + 8 = 10 3 and 7 are friends: 3 + 7 = 10 4 and 6 are friends: 4 + 6 = 10 5 is friends with itself: 5 + 5 = 10!

Seeing Friends of 10 on a Ten-Frame

A ten-frame is the most reliable tool for finding the missing friend of 10.

Finding the Partner for 7:
+---+---+---+---+---+
| * | * | * | * | * |  -> 5 filled
+---+---+---+---+---+
| * | * | O | O | O |  -> 2 filled, 3 EMPTY (O)
+---+---+---+---+---+
Filled Boxes = 7  |  Empty Boxes = 3  |  7 + 3 = 10!

Count the Empty Boxes!

Whenever you place counters on a ten-frame, the empty boxes immediately reveal the missing partner. If you place 8 counters on a ten-frame, you will see 2 empty spaces. That proves that 8 needs 2 to make 10 (8 + 2 = 10).

The Ten-Finger Secret

You have the ultimate ten-frame attached to your own wrists: your ten fingers!

Finding Friends of 10 with Fingers:
Hold up all 10 fingers.
Fold down 4 fingers:
How many fingers are still standing? 6 fingers!
That proves: 4 + 6 = 10!

Quick Finger Fluency

Fold down any number of fingers, and count the fingers still standing up. If you fold down 1 finger, 9 are standing (1 + 9 = 10). If you fold down 3 fingers, 7 are standing (3 + 7 = 10). You always have your ten fingers with you to check your work!

Practice Exercises

Exercise 1: Find the missing Friend of 10 in each equation: 8 + __ = 10 4 + __ = 10 1 + __ = 10 5 + __ = 10

Exercise 2: You place 6 red counters on a ten-frame. How many yellow counters do you need to add to fill the frame completely? Write the addition equation.

Exercise 3: Write out all six basic pairs of numbers that add up to 10.

Exercise 4: A student says that 3 and 8 are Friends of 10. Is the student correct? Explain why or why not, and identify the true friend of 3.

Solutions and Explanations

Solution to Exercise 1: 8 + 2 = 10 4 + 6 = 10 1 + 9 = 10 5 + 5 = 10

Solution to Exercise 2: You need 4 yellow counters. Since 6 boxes are filled with red counters, there are 4 empty boxes remaining in the ten-frame. The addition equation is 6 + 4 = 10.

Solution to Exercise 3: The six basic pairs that add up to 10 are: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5.

Solution to Exercise 4: The student is not correct. 3 + 8 equals 11, which is one more than 10. The true Friend of 10 for the number 3 is 7, because 3 + 7 = 10.