Multiplication and divisionGrades 2–3
Fact family worksheets for multiplication and division
Each fact family worksheet shows a triangle with three related numbers and four equations to finish: two multiplication and two division facts, or two addition and two subtraction facts. Choose the type, the largest number and the count.
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On this page
The idea behind a fact family
Three numbers can be tied together by four facts. Take 6, 7 and 42: the facts 6 × 7 = 42 and 7 × 6 = 42 describe multiplication, while 42 ÷ 6 = 7 and 42 ÷ 7 = 6 describe the same relationship turned around. Children who see this stop treating division as a separate, harder topic. A division fact becomes a multiplication fact with a missing number, and that is exactly how most adults solve one in their heads.
These sheets suit second and third graders. The addition version is a good fit when subtraction first appears, and the multiplication version helps when a class begins division.
What the sheet looks like
Every item is a small triangle. The biggest number (the sum or the product) sits at the top, and the two parts or factors sit at the bottom corners. Next to the triangle are four equations with the numbers already written in and the answer left blank. Students therefore practice both operations in each family and see that the same three numbers keep reappearing. Items are numbered and printed two across.
Settings
- Fact families for has two choices: Multiplication and division, or Addition and subtraction. The page opens on multiplication.
- Largest factor or part runs from 5 to 20 and limits the two numbers at the bottom of the triangle. With a limit of 10, products reach 90. Since the two bottom numbers are always different and at least 2, you will not see squares such as 5 × 5, and no family involves 0 or 1.
- Number of problems accepts 4 up to 12 families. The default of ten fills a page nicely.
For a first lesson, set the largest number to 5 so products stay small, then widen to 10 as the facts firm up. For the addition version, a limit near 10 matches first-grade work, and 20 suits a second grader practicing within 40.
Worked example: the family of 6, 7 and 42
Suppose the triangle shows 42 on top and 6 and 7 at the bottom.
- Complete 6 × 7 = ___. The student recalls or counts up to 42.
- Complete 7 × 6 = ___. The answer is again 42. This is a chance to point out that order does not change a product.
- Complete 42 ÷ 6 = ___. Ask: "6 times what makes 42?" The answer is 7.
- Complete 42 ÷ 7 = ___. Now it is 7 times what? The answer is 6.
Encourage students to say the multiplication question out loud for each division fact. That habit is the real skill the worksheet is building.
Checking the answer key
Look for these patterns when marking.
- Division answers equal to the product. A student wrote 42 for 42 ÷ 6. They likely copied the top number, which means they have not yet connected division with the triangle.
- Right product, swapped quotients. If 42 ÷ 6 shows 6, check that the child understands the answer is the other bottom number, not the divisor.
- Wrong facts that repeat. If 7 × 8 is wrong in every family it appears in, move to a focused drill with the 9 times table sheet or the 12 times table sheet for that factor.
Once families are secure, multiplication and division word problems are the natural next step, because they ask the student to choose the operation from a story.