Fact Families: Addition and Subtraction | 1st Grade Math

Fact Families: Addition and Subtraction - Grade 1 Math
Grade 1 Math  ›  Addition & Subtraction  ›  Lesson 12
Grade 1 Math - Addition and Subtraction

Fact Families: Addition and Subtraction

Learn how the same three numbers can make related addition and subtraction facts. Use parts and a whole to build fact families and connect addition to subtraction.

This first grade math lesson uses fact families, part-part-whole models, and related addition and subtraction equations to help students recognize number relationships and use known facts to solve new problems.

Fact families Related facts Addition and subtraction Parts and whole Grade 1 math

๐ŸŽฏ What You Will Learn

Find the parts and whole
Recognize which two numbers combine to make the whole.
Build related facts
Use the same three numbers in addition and subtraction equations.
Connect addition and subtraction
Use an addition fact to understand a related subtraction fact.
Check a fact family
Decide whether equations really use the same part-part-whole relationship.
For parents & teachers — standards alignment: “Fact family” is a common classroom way to represent related addition and subtraction facts; it is not itself the name of a Common Core standard. This lesson aligns with the Grade 1 CCSS 1.OA.B cluster: it directly supports 1.OA.B.4 by connecting subtraction to an unknown-addend relationship and supports 1.OA.B.3 when students use the fact that switching addends does not change a sum. Formal property names are not required from Grade 1 students.

๐Ÿง  Key Vocabulary

fact family — a group of related addition and subtraction facts built from the same part-part-whole relationship.
part — one of the amounts that combine to make the whole.
whole — the total made by combining the parts.
related facts — equations connected by the same numbers and number relationship.
addition fact — an addition equation such as 3 + 5 = 8.
subtraction fact — a subtraction equation such as 8 − 3 = 5.

๐Ÿ  Parts, Parts, and Whole

A fact family begins with one part-part-whole relationship. If the parts are 3 and 5, the whole is 8.

๐Ÿ”„ Four Related Facts

When the two parts are different, the same three numbers usually make two addition equations and two subtraction equations.

3 + 5 = 8 5 + 3 = 8 8 − 3 = 5 8 − 5 = 3
Important pattern: Addition can use the two parts in either order. In the related subtraction facts, start with the whole and subtract one part to find the other part.

๐Ÿ‘ฏ A Special Case: Doubles

If the two parts are the same, switching the parts does not make a new equation. For the family 4, 4, 8, there are only two distinct equations: 4 + 4 = 8 and 8 − 4 = 4.

4 + 4 = 8 8 − 4 = 4
Common mistake: Subtraction does not work like addition when the order changes. From 3 + 5 = 8, the related subtraction facts begin with 8: 8 − 3 = 5 and 8 − 5 = 3.

๐ŸŒŸ 25 Worked Examples

✏️ Try each problem first. Then tap “Show solution” to check the complete relationship.
1 Meet a fact family
Use the numbers 2, 3, and 5.
✨ Show solution ๐Ÿ™ˆ Hide solution

The parts are 2 and 3, and the whole is 5. The related equations are 2 + 3 = 5, 3 + 2 = 5, 5 − 2 = 3, and 5 − 3 = 2. These four equations form a fact family.

2 Build four related facts
Write the fact family for 2, 4, and 6.
✨ Show solution ๐Ÿ™ˆ Hide solution

The whole is 6. Use both orders for addition, then start both subtraction equations with 6: 2 + 4 = 6, 4 + 2 = 6, 6 − 2 = 4, 6 − 4 = 2.

3 Parts 3 and 5
Write the fact family for 3, 5, and 8.
✨ Show solution ๐Ÿ™ˆ Hide solution

Three and five are the parts, and 8 is the whole. 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5, 8 − 5 = 3.

4 A family with 1
Write all related facts for 1, 7, and 8.
✨ Show solution ๐Ÿ™ˆ Hide solution

The addition facts are 1 + 7 = 8 and 7 + 1 = 8. The subtraction facts are 8 − 1 = 7 and 8 − 7 = 1.

5 Make a family to 10
Write the fact family for 4, 6, and 10.
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Four and six make 10. So the family is 4 + 6 = 10, 6 + 4 = 10, 10 − 4 = 6, and 10 − 6 = 4.

6 A family beyond 10
Write the fact family for 2, 9, and 11.
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The whole is 11. 2 + 9 = 11, 9 + 2 = 11, 11 − 2 = 9, 11 − 9 = 2.

7 Parts 5 and 8
Write the fact family for 5, 8, and 13.
✨ Show solution ๐Ÿ™ˆ Hide solution

The whole is 13. The four related equations are 5 + 8 = 13, 8 + 5 = 13, 13 − 5 = 8, and 13 − 8 = 5.

8 Two close parts
Write the fact family for 6, 7, and 13.
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Six plus seven makes 13. The family is 6 + 7 = 13, 7 + 6 = 13, 13 − 6 = 7, and 13 − 7 = 6.

9 A larger family
Write the fact family for 7, 9, and 16.
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The whole is 16. 7 + 9 = 16, 9 + 7 = 16, 16 − 7 = 9, 16 − 9 = 7.

10 Another family within 20
Write the fact family for 8, 9, and 17.
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Eight and nine are the parts. The four facts are 8 + 9 = 17, 9 + 8 = 17, 17 − 8 = 9, and 17 − 9 = 8.

11 Start from an addition fact
If 4 + 7 = 11, write the two related subtraction facts.
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Because 11 is the whole, subtraction starts with 11. The related subtraction facts are 11 − 4 = 7 and 11 − 7 = 4.

12 Start from a subtraction fact
If 12 − 5 = 7, write the related addition facts.
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The three numbers are 5, 7, and 12. The related addition facts are 5 + 7 = 12 and 7 + 5 = 12.

13 Find the three family numbers
What three numbers are used in the fact family for 6 + 8 = 14?
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The two addends are 6 and 8, and their sum is 14. The family numbers are 6, 8, and 14.

14 Does this equation belong?
Does 9 − 3 = 6 belong to the fact family 3, 6, 9?
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Yes. Nine is the whole, and subtracting one part, 3, leaves the other part, 6. Yes, 9 − 3 = 6 belongs to the family.

15 An equation that does not belong
Does 6 − 3 = 9 belong to the fact family 3, 6, 9?
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No. The subtraction equations in this family must start with the whole, 9. A correct related fact is 9 − 3 = 6. So 6 − 3 = 9 does not belong.

16 Why subtraction starts with the whole
Why does the subtraction in the family 4, 5, 9 start with 9?
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Because 9 is the whole. Subtraction takes away one part from the whole to find the other part. For example, 9 − 4 = 5.

17 Switch the addition order
If 3 + 8 = 11, what happens when the addends switch places?
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The sum stays the same: 8 + 3 = 11. This gives the second addition fact in the family.

18 A special doubles family
Use the numbers 4, 4, and 8. How many different equations are in this fact family?
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Because the two parts are the same, switching them does not create a new equation. The two different equations are 4 + 4 = 8 and 8 − 4 = 4. So there are 2 distinct equations, not 4.

19 Another doubles family
Write the distinct fact-family equations for 7, 7, and 14.
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The repeated part means the two addition equations would be identical, and the two subtraction equations would also be identical. The distinct equations are 7 + 7 = 14 and 14 − 7 = 7.

20 Read a part-part-whole model
A model shows parts 5 and 7 with whole 12. Write the fact family.
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Read the two parts first for addition and the whole first for subtraction: 5 + 7 = 12, 7 + 5 = 12, 12 − 5 = 7, 12 − 7 = 5.

21 Spot the mistake
A student uses 3 + 8 = 11 and writes 8 − 3 = 11. What is wrong?
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The subtraction started with a part instead of the whole. The whole is 11, so a related subtraction fact is 11 − 8 = 3.

22 Use addition to know subtraction
You know 9 + 4 = 13. What is 13 − 9?
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The addition fact says 9 and 4 are the parts of 13. If 9 is removed from the whole 13, the other part is 4. Answer: 13 − 9 = 4.

23 Use a family to subtract
You know 8 + 7 = 15. Use the fact family to find 15 − 8.
✨ Show solution ๐Ÿ™ˆ Hide solution

Since 8 and 7 are the parts of 15, subtracting 8 from 15 leaves 7. Answer: 15 − 8 = 7.

24 Create the complete family
Write all the related equations for 1, 9, and 10.
✨ Show solution ๐Ÿ™ˆ Hide solution

The complete family is 1 + 9 = 10, 9 + 1 = 10, 10 − 1 = 9, and 10 − 9 = 1.

25 Challenge: check the relationship
Do 4, 9, and 13 form an addition-subtraction fact family? Explain.
✨ Show solution ๐Ÿ™ˆ Hide solution

Yes. The two smaller numbers combine to make the largest: 4 + 9 = 13. Therefore the related equations are 4 + 9 = 13, 9 + 4 = 13, 13 − 4 = 9, and 13 − 9 = 4.

๐ŸŽฎ Independent Practice — 30 Problems

  1. Write the four related facts for 2, 5, and 7.
  2. Write the four related facts for 3, 4, and 7.
  3. Write the four related facts for 1, 8, and 9.
  4. Write the four related facts for 5, 6, and 11.
  5. Write the four related facts for 5, 7, and 12.
  6. Write the four related facts for 6, 8, and 14.
  7. Write the four related facts for 7, 9, and 16.
  8. Write the four related facts for 8, 9, and 17.
  9. Write the four related facts for 8, 10, and 18.
  10. Write the four related facts for 9, 10, and 19.
  11. In the family 4, 7, 11, which number is the whole?
  12. In the family 3, 8, 11, which two numbers are the parts?
  13. Use 5 + 9 = 14 to write one related subtraction fact.
  14. Use 13 − 6 = 7 to write one related addition fact.
  15. Complete the family: 4 + 8 = 12, 8 + 4 = 12, 12 − 4 = 8, 12 − 8 = □.
  16. Complete the family: 7 + 6 = 13, 13 − 7 = 6, 13 − 6 = 7, □ + 7 = 13.
  17. Which equation belongs to the family 2, 7, 9: 9 − 2 = 7 or 7 − 2 = 9?
  18. Which equation does NOT belong to the family 5, 8, 13: 13 − 8 = 5 or 8 − 5 = 13?
  19. True or false: In a fact family, the subtraction equations begin with the whole.
  20. True or false: Addition can switch the order of the two parts and keep the same sum.
  21. Fix the mistake: 4 + 5 = 9, so 5 − 4 = 9.
  22. Use the family for 6, 9, and 15 to find 15 − 6.
  23. Use the family for 7, 8, and 15 to find 15 − 7.
  24. Name the three family numbers in 3 + 9 = 12.
  25. Name the three family numbers in 16 − 7 = 9.
  26. Write the distinct equations for the doubles family 5, 5, 10.
  27. How many distinct equations are in the doubles family 6, 6, 12?
  28. Explain why 14 − 5 = 9 is related to 5 + 9 = 14.
  29. Do 6, 8, and 15 form a fact family? Explain.
  30. Challenge: Write a fact family using the numbers 7, 10, and 17.

๐Ÿ† Lesson Test — 15 Questions

  1. Write the four related facts for 2, 6, and 8.
  2. Write the four related facts for 4, 5, and 9.
  3. Write the four related facts for 7, 8, and 15.
  4. You know 6 + 9 = 15. Write one related subtraction fact.
  5. You know 14 − 6 = 8. Write one related addition fact.
  6. In the family 5, 7, 12, which number is the whole?
  7. In the family 4, 9, 13, which two numbers are the parts?
  8. Use 3 + 8 = 11 to find 11 − 3.
  9. True or false: You can switch the numbers in a subtraction equation the same way you switch addends in addition.
  10. Which equation belongs to the family 4, 6, 10: 10 − 4 = 6 or 6 − 4 = 10?
  11. Fix the mistake: 3 + 7 = 10, so 7 − 3 = 10.
  12. A doubles family uses 5, 5, and 10. How many distinct equations does it have, and what are they?
  13. Explain how knowing 8 + 4 = 12 helps you know 12 − 8.
  14. Do 5, 9, and 14 form a fact family? Explain.
  15. Challenge: Write the complete fact family for 9, 10, and 19.

๐Ÿ” Complete Answer Key

Answer-key note: When a question asks for one related equation, more than one correct choice may be possible. The key gives a valid example and notes common alternatives where useful.
๐Ÿ”‘ Show practice answer key ๐Ÿ™ˆ Hide practice answer key

Practice Answers

1. 2 + 5 = 7; 5 + 2 = 7; 7 − 2 = 5; 7 − 5 = 2
2. 3 + 4 = 7; 4 + 3 = 7; 7 − 3 = 4; 7 − 4 = 3
3. 1 + 8 = 9; 8 + 1 = 9; 9 − 1 = 8; 9 − 8 = 1
4. 5 + 6 = 11; 6 + 5 = 11; 11 − 5 = 6; 11 − 6 = 5
5. 5 + 7 = 12; 7 + 5 = 12; 12 − 5 = 7; 12 − 7 = 5
6. 6 + 8 = 14; 8 + 6 = 14; 14 − 6 = 8; 14 − 8 = 6
7. 7 + 9 = 16; 9 + 7 = 16; 16 − 7 = 9; 16 − 9 = 7
8. 8 + 9 = 17; 9 + 8 = 17; 17 − 8 = 9; 17 − 9 = 8
9. 8 + 10 = 18; 10 + 8 = 18; 18 − 8 = 10; 18 − 10 = 8
10. 9 + 10 = 19; 10 + 9 = 19; 19 − 9 = 10; 19 − 10 = 9
11. 11
12. 3 and 8
13. Possible answer: 14 − 5 = 9. (14 − 9 = 5 also works.)
14. Possible answer: 6 + 7 = 13. (7 + 6 = 13 also works.)
15. 4
16. 6
17. 9 − 2 = 7
18. 8 − 5 = 13
19. True
20. True
21. Correct related subtraction: 9 − 5 = 4 (or 9 − 4 = 5).
22. 9
23. 8
24. 3, 9, and 12
25. 7, 9, and 16
26. 5 + 5 = 10; 10 − 5 = 5
27. 2 distinct equations
28. Because 5 and 9 are the parts that make 14; subtracting one part from 14 gives the other part.
29. No. 6 + 8 = 14, not 15.
30. 7 + 10 = 17; 10 + 7 = 17; 17 − 7 = 10; 17 − 10 = 7
๐Ÿ… Show test answer key ๐Ÿ™ˆ Hide test answer key

Test Answers

1. 2 + 6 = 8; 6 + 2 = 8; 8 − 2 = 6; 8 − 6 = 2
2. 4 + 5 = 9; 5 + 4 = 9; 9 − 4 = 5; 9 − 5 = 4
3. 7 + 8 = 15; 8 + 7 = 15; 15 − 7 = 8; 15 − 8 = 7
4. Possible answer: 15 − 6 = 9. (15 − 9 = 6 also works.)
5. Possible answer: 6 + 8 = 14. (8 + 6 = 14 also works.)
6. 12
7. 4 and 9
8. 8
9. False
10. 10 − 4 = 6
11. Correct related subtraction: 10 − 7 = 3 (or 10 − 3 = 7).
12. 5 + 5 = 10; 10 − 5 = 5
13. Eight and 4 are the parts of 12, so subtracting 8 from 12 leaves the other part, 4.
14. Yes. 5 + 9 = 14.
15. 9 + 10 = 19; 10 + 9 = 19; 19 − 9 = 10; 19 − 10 = 9

๐Ÿ’ก Common Mistakes to Watch For

Starting subtraction with a part
In a fact family, subtraction begins with the whole.
Thinking subtraction can simply switch order
3 + 5 and 5 + 3 have the same sum, but the related subtraction facts must start with the whole, 8.
Using numbers that do not make one whole
Check that the two parts really add to the whole.
Writing four copies in a doubles family
When both parts are equal, there are only two distinct equations.
For parents & teachers — Texas connection: This lesson supports TEKS 1.3(D) and 1.3(E) through addition/subtraction fact strategies and explanations with number sentences. It also supports the addition-property component of TEKS 1.5(G) when students switch the order of addends. The next MathLattice lessons treat the equal sign and unknowns explicitly, so those topics are intentionally kept limited here.

๐Ÿ”— Related Lessons

Lesson 11 — Doubles, Near Doubles & Easier Facts
Review known addition facts before connecting them to subtraction facts. Lesson 10 — Subtraction Strategies Within 20
Review how addition can help solve subtraction.

๐Ÿ–จ️ Printable Companion

A free Fact Families Practice Pack will be connected here as the MathLattice printable library grows. It will include part-part-whole models, fact-family cards, related-equation practice, doubles-family special cases, error analysis, mixed practice, and an answer key.

← Lesson 11: Doubles, Near Doubles & Easier Facts Grade 1 Math Hub Next: Equal Sign & True/False Equations →

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