Multiplication
Multiplication and division array facts
Use one rectangular array to write two multiplication equations and two related division equations.
Preview and downloadFact family practice
Multiplication and division fact families
Connect two multiplication facts with two exact divisions in each of six triangles. Choose first factors from 2–11; the other factor is from 2–9.
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Use the product at the top of the triangle and the two factors below to complete two multiplication equations and two division equations.
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Customize this worksheetWhat the choices control
Choose one or more first factors from 2–11. The other factor comes from 2–9, whether or not it is checked. Products can reach 99, and every division is exact.
Every family keeps four equation rows. When its two parts or factors are equal, swapping them changes nothing: there are only two distinct equations, each written twice.
Learning objective
What this activity builds
Use the inverse relationship between multiplication and division to connect factors with a product.
Worked example
What four equations connect 4, 7 and 28?
4 × 7 = 28; 7 × 4 = 28; 28 ÷ 7 = 4; 28 ÷ 4 = 7.
The factors can switch places in a multiplication. Dividing the product by either factor gives the other factor, with no remainder.
Teaching notes
Make the practice count
- The selected checkboxes control the first factor only. The second factor comes from 2–9, so selecting 11 can produce a family such as 11, 8 and 88.
- Build an array, then turn it to connect the two multiplication rows. Use the same array to explain division into rows or columns.
- Both division equations begin with the product. All operands are positive, and every generated division is exact; there is no division by zero.
- Equal factors produce only two different equations even though four rows stay on the page. Explain the repeated facts instead of inventing a new factor.
- Six distinct unordered factor pairs appear on each sheet. A selected factor need not appear on every sheet, and a new seed can change the families or their order.
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Use six number triangles to write two additions and two subtractions per family. Choose first addends from 1–12; the other addend is from 1–9.
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