Multiplication Grid

Free puzzles to print

Each set: a Learn sheet with a worked example, 10 puzzles from easiest to hardest, and the answers.

• Level 3

  Ages 8–10 · Grades 3–4

  

  A 3 × 3 table with one or two outside numbers missing, each found by one division. Then 4 × 4 tables where one found number helps find the next. Then every outside number is hidden. The child looks for the one number from 2 to 10 that divides two answers in the same row. The hardest are 5 × 5 and need that more than once.

  On the sheet: “Find the missing factors. Then fill every square.”

  Print Level 3 (Letter)Other paper size: A4

• Level 4

  Ages 10–12 · Grades 5–6

  

  Factors from 2 to 12. The easiest are 5 × 5 tables with four to six outside numbers hidden, found one after another by dividing. Then every outside number is hidden, so a number that divides two answers is needed. Then 6 × 6 tables with every outside number hidden. The hardest show only 7 to 9 inside numbers and need that step three times or more.

  On the sheet: “Find the missing factors. Then fill every square.”

  Print Level 4 (Letter)Other paper size: A4

The thinking it works on

• Knowing multiplication facts

  Recalls or looks up products to 10 × 10, and to 12 × 12 at Level 4.

  Steel and Funnell (2001) found that 8- and 9-year-olds mixed recall with working facts out. The 10- to 12-year-olds mostly recalled smaller facts and fell back on slower methods for larger ones. Source

• Dividing to undo multiplying

  Uses division to undo multiplication.

  Mulligan and Mitchelmore (1997) followed girls in grades 2 and 3 solving multiplication and division word problems. They found three intuitive models at work: counting one by one, adding in groups, and multiplying. The model a child chose reflected the structure she saw in the problem. Source

• Listing factor pairs

  Lists every factor pair of a product.

• Reasoning with two clues

  Finds the one number that fits two answers at once.

• Seeing how rows and columns build a table

  Understands how rows and columns build each square.

  Battista and colleagues (1998) found that many students do not yet see a grid of squares as rows and columns at once, as adults assume. They described levels in how students come to see it. Source

Where is this thinking used?

• Arranging chairs: Rows and columns that make a given number of seats.
• Recipes: Scaling a recipe up or down by a whole number.
• Gardening: Planting in neat rows to fill a bed.
• Money: Working out the price of one item from the cost of several.