Mathematics
Grade 6
15 min
Fact families
Fact families
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1
Introduction & Learning Objectives
Learning Objectives
Define a fact family and identify its core components.
Generate all four related facts for a given set of three numbers in an addition/subtraction fact family.
Generate all four related facts for a given set of three numbers in a multiplication/division fact family.
Explain the relationship between inverse operations (addition/subtraction and multiplication/division).
Identify missing numbers in fact family equations.
Use fact families to check the accuracy of their calculations.
Apply the concept of fact families to solve simple word problems.
Ever noticed how some numbers just 'belong' together? 🤔 Like 3, 5, and 8? They can make addition and subtraction facts!
In this lesson, you'll discover 'fact families' – groups of rela...
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Key Concepts & Vocabulary
TermDefinitionExample
Fact FamilyA group of three numbers that are related through addition and subtraction, or through multiplication and division. These three numbers can be used to form four different math facts.The numbers 3, 5, and 8 form a fact family because 3 + 5 = 8, 5 + 3 = 8, 8 - 3 = 5, and 8 - 5 = 3.
Inverse OperationsOperations that 'undo' each other. Addition is the inverse of subtraction, and multiplication is the inverse of division.If you add 5 to 3 to get 8, you can 'undo' it by subtracting 5 from 8 to get 3.
Addition FactA mathematical statement showing the sum of two numbers.For the fact family of 3, 5, 8, an addition fact is 3 + 5 = 8.
Subtraction FactA mathematical statement showing the difference between two numbers.For the fact family of 3, 5, 8...
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Core Formulas
Addition/Subtraction Fact Family Rule
If $a + b = c$, then $b + a = c$, $c - a = b$, and $c - b = a$.
This rule shows how three numbers are connected through addition and subtraction. The two smaller numbers (addends) add up to the largest number (sum). The largest number is always the starting point for subtraction.
Multiplication/Division Fact Family Rule
If $a \times b = c$, then $b \times a = c$, $c \div a = b$, and $c \div b = a$.
This rule shows how three numbers are connected through multiplication and division. The two smaller numbers (factors) multiply to get the largest number (product). The largest number is always the dividend in division.
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Challenging
Two numbers in a multiplication/division fact family are 4 and 24. All three numbers in the family are distinct positive integers. Which number could NOT be the third number in the family?
A.6
B.96
C.20
D.The third number could be either 6 or 96.
Challenging
If m, n, and p are three distinct positive integers that form a multiplication/division fact family, and p is the largest number, which equation must always be true?
A.m ÷ n = p
B.p ÷ m = n
C.m × p = n
D.n ÷ p = m
Challenging
A rectangular garden has an area of 72 square feet. Its length is 9 feet. The relationship between area, length, and width forms a fact family. Which of the following equations is NOT part of this fact family?
A.9 × 8 = 72
B.72 ÷ 9 = 8
C.8 × 9 = 72
D.72 - 9 = 63
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