A student knows that 6 + 7 = 13. Which subtraction fact can they figure out immediately — without any new calculation?
A13 − 9 = 4, because 9 is close to 7
B13 − 6 = 7, because they already know 6 and 7 belong together with 13
C7 − 6 = 1, because 7 and 6 are both in the problem
D6 − 7 cannot be solved with positive numbers
The fact family for 6, 7, and 13 includes 6 + 7 = 13, 7 + 6 = 13, 13 − 7 = 6, and 13 − 6 = 7. Knowing the three numbers in the family means all four equations come for free — no new calculation needed. 13 − 6 = 7 is part of the same family as 6 + 7 = 13.
Question 2 Multiple Choice
How many different equations belong to the fact family for the numbers 4, 9, and 13?
ATwo — one addition and one subtraction
BThree — two additions and one subtraction
CFour — two additions and two subtractions
DSix — three additions and three subtractions
Every fact family has exactly four members: 4 + 9 = 13, 9 + 4 = 13, 13 − 9 = 4, and 13 − 4 = 9. There are two additions (using the commutative property) and two subtractions. There are not six because subtraction is not commutative — 4 − 9 and 9 − 4 are not valid positive-number equations in this family.
Question 3 True / False
If you know the fact 8 + 5 = 13, then you automatically know what 13 − 5 equals, without doing any new calculation.
TTrue
FFalse
Answer: True
8, 5, and 13 form a fact family. The equation 8 + 5 = 13 tells you that 13 is the whole, and 8 and 5 are its two parts. Knowing the whole and one part, you can always find the missing part: 13 − 5 = 8. No separate calculation is needed because subtraction is built into the same three-number relationship.
Question 4 True / False
Subtraction facts is expected to be memorized separately from addition facts because subtraction works in a mostly different way.
TTrue
FFalse
Answer: False
This is the core misconception the fact family concept is designed to fix. Subtraction facts are not separate — they come from the same three-number relationship as addition facts. A student who knows all addition families within 20 already has access to all corresponding subtraction facts. The operations are two views of the same underlying number relationship.
Question 5 Short Answer
Why does a fact family have four equations instead of two, and how does knowing the family save you work?
Think about your answer, then reveal below.
Model answer: Addition is commutative (order doesn't change the sum), so each family has two addition equations. Subtraction gives two more equations — one for each part being subtracted from the whole. Knowing the family means you only need to learn three numbers once to unlock four related facts.
The power of fact families is that they collapse what might seem like four separate memorization tasks into one: the relationship among three numbers. Once a student sees 4, 9, and 13 as a group, they can write any of the four equations from that group. This is more efficient than treating addition and subtraction as separate inventories of facts.