Stage 3 multiplication and division

Strategies

Students can:

  • select and apply appropriate mental, written and calculator strategies to solve multiplication and division questions

Activities to support the strategies

Students need to be aware that there are a number of strategies that they can use to solve multiplication and division questions. More competent students would know that they can use multiplication to solve a problem and division to double check that same question.

Some activities for developing mental computation in multiplication and division are detailed below.

Activity 1 – developing mental computation

Students in pairs can play a game of Dice Tables.

View and print – multiplication and division table (PDF 24.32KB)

  • The two students need three 1 to 6 dot dice, 2 sets of coloured counters and a dice table’s board.
  • The first player rolls the dice and chooses two of the three numbers to multiply to match a number on their dice tables board, e.g. if the student rolls 4, 5 and 3 they could make 4 x 5 = 20 or 4 x 3 = 12 or 5 x 3 = 15.
  • They place a counter on the chosen multiple. Students alternate turns. The aim is to be the first to get 4 counters in a row, column, diagonal or square.

Dice to 100

  • Students in pairs can play a game of Dice to 100.
  • Two students need two 1 to 6 dot dice.
  • The students take turns to roll two dice and multiply the numbers. The total for each round is added onto the previous round. The first person to 100 is the winner.
  • Variation: Use a 10- or 12-sided dice and a larger target number.

Activity 2 – halving and doubling

Introduce halving and doubling as strategies that can be used to solve multiplication and division problems involving three-digit numbers.

Work through examples to demonstrate the strategy:

  • To divide an even three-digit number by 4, students could find half of the number and halve again.
  • E.g. to find the answer to 324 divided by 4

Ask – Can you use the halving or doubling strategy to find the answer?

  • How would you use this strategy?
  • What is half of 324? (162) is this the answer to the question?
  • What is half of 162?
    • To divide a number by 5, students could divide by 10 and double the answer.

E.g. to find the answer to $4 divided by 5

Ask – Can you use the halving or doubling strategy to find the answer?

  • How would you use this strategy? (divide by 10 then double)
  • What is $4/$4.00 divided by 10? (40c)
  • What is double 40?

Activity 3 – solving word problems

Pose this problem for the students to solve

  • On the way to school four children found a $50 note. They handed it to the school principal. They will each get an equal share of the money if no one claims it.

Investigate the strategies used by asking these questions:

  • How much would each child get?
  • What strategy did you use to find each share?
  • Can you use doubling or halving?
  • Which operation would you use to check if your answer is correct?
  • How much would each child get if $5 was found?
  • How much would each child get if 50c was found?

Repeat using other division problems, each time discussing the strategies the students used. Emphasise that students should use multiplication to check their answers to division problems.

Pose this problem for the students to solve in pairs:

It takes four oranges to fill a small juice bottle with juice. If I bought a box containing 93 oranges, how many bottles could be filled? How many oranges left over?

Students in pairs, discuss how they would solve this problem. They determine two different strategies that could be used. Each pair explains the two strategies they would use.

  • Students are presented with a variety of multiplication and division problems involving three- and four-digit numbers. Students first estimate their answer before solving, to compare mental and written strategies.

Students discuss the strategies they used and determine which strategy is the most efficient.

Discuss:

  • How accurate was your estimation?
  • How did your estimation help?
  • Which operation did you use?
  • Can you describe your strategy?
  • Is your strategy efficient?
  • How did you check whether your answer is correct?
  • Students can write other word problems for their partner to solve
  • Check their answers with a calculator

References

Australian curriculum reference: ACMNA122

Identify and describe properties of prime, composite, square and triangular numbers ACMNA123: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers.

NSW syllabus reference: MA3-6NA

Selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation.

NSW literacy continuum reference: SPEC11M5

Aspects of speaking, Cluster 11, Marker 5: Uses active listening strategies such as rephrasing ideas and clarifying and repairing breakdowns in communication.

NSW numeracy continuum reference:

Aspect 5: Multiplication & Division; Multiplication and division as operations.

Resources

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