Fact families and basic addition and subtraction facts

This article explains how to use fact families to help children learn the basic addition and subtraction facts (with single-digit numbers), and also contains a complete example lesson with exercises and word problems about fact families where the sum is 13 or 14.

What is a fact family?

A fact family is a group of math facts using the same numbers.  In the case of addition/subtraction, you use three numbers and get four facts.  For example, you can form a fact family using the three numbers 10, 2, and 12: 10 + 2 = 12, 2 + 10 = 12,  12 − 10 = 2, and 12 − 2 = 10.

Where do we use fact families?

We can use fact families to reinforce or learn the connection between addition and subtraction, and to help children memorize the basic addition & subtraction facts. The two videos below explain several strategies for learning addition and subtraction facts, including number rainbows and fact families.

After the videos, there follows a complete lesson with many exercises and word problems about fact families with 13 and 14 (where the sum is 13 or 14), taken from my book Math Mammoth Add & Subtract 2-A.

A Lesson on Fact Families - sums with 13 and 14

1. Fill in. In each fact family, color the marbles so they match the numbers in it.

Fact families with  13

 10, 3, and 13 10  +  3  = _____     3  +  10 = _____ 13  −  10  = _____ 13  −   3   = _____
 9, _____, and 13 9  + ____ = 13 ____ + ____ = _____ _____ − ____ = ____ _____ − ____ = ____
 8, ____, and 13 8  + ____ = 13 ____ + ____ = _____ _____ − ____ = ____ _____ − ____ = ____
 7, ____, and 13 7  + ____ = 13 ____ + ____ = _____ _____ − ____ = ____ _____ − ____ = ____

2. Connect with a line the problems that are from the same fact family. You don't need to

 13 − 7 = 5 + = 12 11 − 3 = 8 + = 13 12 − 3 = 7 + = 11 11 − 4 = 11 − 8 = 5 + = 13 12 − 5 = 6 + = 13 9 + = 12 12 − 7 = 13 − 6 = 3 + = 12 13 − 5 = 3 + = 11 4 + = 11

3. Fill in. In each fact family, color the marbles so they match the numbers in it.

Fact families with  14

 10, 4, and 14 10  +  4  = _____     4  +  10 = _____ 14  −  10  = _____ 14  −   4   = _____
 9, _____, and 14 9  + ____ = 14 ____ + ____ = _____ _____ − ____ = ____ _____ − ____ = ____
 8, ____, and 14 8  + ____ = 14 ____ + ____ = _____ _____ − ____ = ____ _____ − ____ = ____
 7, ____, and 14 7  + ____ = 14 ____ + ____ = _____ _____ − ____ = ____ _____ − ____ = ____

4. Subtract.

 a. 13 − 8 = ____    14 − 6 = ____ b. 13 − 5 = ____   13 − 4 = ____ c. 12 − 7 = ____   13 − 7 = ____ d. 12 − 9 = ____   14 − 9 = ____

5. Find the missing numbers.

 a.  9 + = 14 b.  6 + = 14 c.  6 + = 12 d.  − 9 = 4 e.  − 7 = 7 f.  − 9 = 3 g.  14 − = 8 h.  12 − = 7 i.  13 − = 8

6. Solve the word problems.

 a.  Ted arranged his toy cars in rows. The first row had     seven cars, the second had seven, and the third row     had four. How many cars does Ted have? b. If you have 14 strawberries and I have eight,     how many more do you have? c.  Dad has six cherries and Mom has five more than him.     How many cherries does Mom have? d.  At first Mom had 20 apples to make a pie,      but she gave each of the four children one apple      before she made the pie. How many apples      did she have left for the pie?

7. Figure out the patterns and continue them!

a.
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40

48

56

64 72 _____ _____ _____ _____

b.
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17 21 25 29 _____ _____ _____ _____ _____

This lesson is taken from Maria Miller's book Math Mammoth Add & Subtract 2A, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

Math Mammoth Add & Subtract 2-A

A self-teaching worktext for 2nd grade that covers “easy” additions and subtractions within 0-100; such as 24 + 5 and 89 − 7, or adding or subtracting whole tens; memorizing the basic addition facts of single-digit numbers, and learning to use them with subtraction.