Unknown Factors and Fact Families
Print 3rd grade unknown factor worksheets: fact family triangles, missing numbers in multiplication and division equations, and division as a missing factor.
Worksheet version 1 of 12. The answer key matches the current version.
Find the number that makes each equation true. Use the multiplication facts you know to help with division.
Part A. Find the missing number in each triangle. Then write the four facts in its family.
× =
× =
÷ =
÷ =
× =
× =
÷ =
÷ =
× =
× =
÷ =
÷ =
× =
× =
÷ =
÷ =
Part B. Write the missing number in each box.
Part C. Write each division as a multiplication with a missing factor, then solve it.
q) 72 ÷ 9 = □
9 × = 72, so 72 ÷ 9 =
r) 48 ÷ 8 = □
8 × = 48, so 48 ÷ 8 =
About this worksheet
A fact family is the set of multiplication and division facts made from the same three numbers. With 6, 8 and 48 you can write 6 × 8 = 48, 8 × 6 = 48, 48 ÷ 6 = 8 and 48 ÷ 8 = 6. On a fact family triangle the product sits at the top and the two factors sit at the bottom: multiply the bottom numbers to get the top, or divide the top by one bottom number to get the other.
An unknown can sit anywhere in an equation. In 8 × □ = 48, ask "8 times what makes 48?". In □ ÷ 3 = 7, the box is the number being shared, so multiply: 3 × 7 = 21. In 56 = 7 × □, the equal sign comes first, but the question is the same. Each version has 12 equations, two with the box in each of six places, and every fact is within 10 × 10.
The last part turns division into a missing-factor problem. To find 72 ÷ 9, ask "9 times what equals 72?". That is how most children find division facts once they know their times tables.
Practice aligned to CCSS 3.OA.A.4 and 3.OA.B.6.
Before this: equal groups and sharing. Next: division facts and multiplication facts 6 to 9. More practice: multiplication worksheets, division worksheets and 3rd grade math worksheets.
Related Math Worksheets
Print 3rd grade equal groups worksheets: write multiplication for pictures of equal groups, share dots on plates and circle groups to divide. 12 versions.
Print 4th grade worksheets finding factor pairs within 100, listing multiples, and classifying prime vs composite numbers, with clean printable answer keys.
Print 2nd grade array worksheets: add equal rows or columns of dots, draw arrays, and write repeated addition sentences.
Single-digit multiplication problems for third graders. Print a clean sheet to build times-table fluency, and check each product by dividing.
Free printable 3rd grade worksheet for two-digit by one-digit multiplication, bridging single-digit times tables and larger multi-digit problems.
Free printable 3rd grade mental-math worksheet for multiplying a one-digit number by a multiple of ten, like 9 x 80.