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W.3 Multiplication and division facts up to 12: complete the sentences

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Understanding multiplication and division facts

Multiplication is a way to find the total when you combine equal groups. Division is splitting a total into equal groups to find how many are in each group or how many groups you can make.

Examples:
  • If 4 boxes contain 6 crayons each, multiplication finds the total: 4 × 6 = 24 crayons.
  • If 24 crayons are shared equally among 4 boxes, division finds the amount per box: 24 ÷ 4 = 6 crayons.
Note

Multiplication and division are inverse operations. They undo each other, just like addition and subtraction.

Building fact families up to 12

A fact family is a set of four related multiplication and division facts that use the same three numbers. Mastering these families helps you solve problems fluently.

Example fact family for 3, 8, and 24:
  • 3 × 8 = 24
  • 8 × 3 = 24
  • 24 ÷ 3 = 8
  • 24 ÷ 8 = 3
Note

If you know one multiplication fact, you automatically know three other facts in its family.

Strategies for finding unknown numbers

In a number sentence with a missing factor or missing total, you can use related facts or the inverse operation to find the unknown number.

How to complete the sentences:
  • If 7 × ? = 56, think: 56 ÷ 7 = 8. So, 7 × 8 = 56.
  • If ? ÷ 9 = 4, think: 4 × 9 = 36. So, 36 ÷ 9 = 4.
  • If 11 × 12 = ?, calculate: 10 × 12 = 120, plus 1 × 12 = 12. 120 + 12 = 132.
Note

When the total is missing, multiply. When a factor or the number of groups is missing, divide.

Applying facts in different situations

Multiplication and division facts can describe arrays, repeated addition or subtraction, and comparisons. Understanding these situations builds number sense.

Examples in context:
  • Array: A 5 by 7 array shows 5 × 7 = 35 total items.
  • Repeated Addition: 6 × 4 is the same as 4 + 4 + 4 + 4 + 4 + 4.
  • Comparison: “8 times as many” means multiply. If Emma has 3 stamps and Ria has 8 times as many, Ria has 8 × 3 = 24 stamps.
  • Measurement Division: How many 4-foot ropes can you cut from a 36-foot rope? 36 ÷ 4 = 9 ropes.
Note

Look for key words like “total,” “each,” “equal groups,” “times as many,” and “shared equally” to decide whether to multiply or divide.

Fluency with facts from 0 to 12

Fluency means you can recall basic multiplication and division facts quickly and accurately. This provides a strong foundation for more complex math.

Key facts to know fluently:
  • Rules of 0 and 1: Any number × 0 = 0. Any number × 1 = itself.
  • Doubles: 6 × 6 = 36, 8 × 8 = 64.
  • Fives: Count by 5s. 5 × 9 = 45.
  • Tens: 10 × 7 = 70. A number times ten ends in a zero.
  • Squares: 7 × 7 = 49, 12 × 12 = 144.
Note

Practice with flashcards, games, and timed drills in short sessions to build speed without stress. Accuracy comes first.