You know that 6 + 8 = 14. Which of the following is also part of the same fact family?
A6 + 6 = 12
B14 - 8 = 6
C8 + 6 = 12
D14 + 6 = 20
A fact family uses the same three numbers — here, 6, 8, and 14. The four related facts are: 6+8=14, 8+6=14, 14-8=6, and 14-6=8. Option B (14-8=6) is one of the subtraction facts in the family. Option C is a distractor with a wrong sum. Option A uses different numbers entirely. Option D adds instead of subtracting, producing an unrelated result.
Question 2 Multiple Choice
A student learns that 9 + 4 = 13. Their teacher says they now know 3 more facts for free. Which statement best explains why?
ABecause addition and subtraction always produce numbers in the same family
BBecause 9, 4, and 13 have a part-whole relationship that works in all four directions
CBecause 13 is always connected to 9 in the times tables
DBecause you can always add 3 to find the next fact
The three numbers 9, 4, and 13 form one relationship: 9 and 4 are parts, 13 is the whole. That single relationship can be expressed four ways: 9+4=13, 4+9=13, 13-9=4, and 13-4=9. This is the essence of a fact family — one relationship, four facts. The student doesn't need to memorize each separately; understanding the part-whole structure gives them all four.
Question 3 True / False
In a fact family, the largest number is always the result of adding the other two numbers together.
TTrue
FFalse
Answer: True
The largest number in any fact family is the whole — the sum of the two parts. For example, in the family 3, 5, 8: 3+5=8 and 5+3=8. When you subtract, you always subtract a smaller number (a part) from the largest number (the whole). This is why the top number on the fact-family triangle is always the whole — it is always the largest of the three.
Question 4 True / False
Nearly every fact family has exactly four different equations.
TTrue
FFalse
Answer: False
Most fact families have four equations, but when the two parts are equal (like 5, 5, and 10), the two addition facts are identical (5+5=10 and 5+5=10) and the two subtraction facts are identical (10-5=5 and 10-5=5). This gives only two unique equations, not four. When the whole is formed by doubling one part, the family collapses to fewer distinct facts.
Question 5 Short Answer
Explain why knowing one fact in a fact family automatically gives you the other three, using the numbers 7, 6, and 13 as an example.
Think about your answer, then reveal below.
Model answer: Because all four facts describe the same part-whole relationship: 7 and 6 are parts, 13 is the whole. Knowing 7+6=13 tells you the parts and the whole, so you can immediately write 6+7=13 (swap the parts), 13-7=6 (remove one part from the whole to get the other), and 13-6=7 (same logic). The relationship is the same in all four directions.
This question targets the core insight: a fact family isn't four separate facts to memorize — it's one relationship written four ways. A student who truly understands this can reconstruct any missing fact from any known fact in the family, rather than treating each equation as an isolated piece of information.