Lollies, lollies, lollies

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Purpose

This problem solving activity has a number focus.

Achievement Objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.
Student Activity

Decorative image of liquorice allsorts.Each day, from Monday to Friday, Sam, Nikau and Maia were given the same number of lollies. Each day they shared them the same way.
Nikau got twice as many lollies as Sam.
Maia got three times as many lollies as Sam.

If Maia got a total of 18 lollies on Tuesday and Wednesday, how many lollies did Nikau get for the whole five days?

How many lollies would Sam need to get on Saturday if he wanted to have 39 lollies altogether?

Specific Learning Outcomes
  • Solve problems that involve multiplication and division
  • Use equations to express a problem
Description of Mathematics

In this problem students use logic, number operations and relational (algebraic) thinking as they seek a solution.

This is one of six Number problems: Lollies! and More Lollies, Level 1; Sharing Lollies, Level 2; Lollies, Lollies, Lollies, Level 3; and Still More Lollies, Level 4.  At each level, these problems become more algebraic in their focus.

Required Resource Materials
Activity

The Problem

Each day, from Monday to Friday, Sam, Nikau and Maia were given the same number of lollies. Each day they shared them the same way.
Nikau got twice as many lollies as Sam.
Maia got three times as many lollies as Sam.

If Maia got a total of 18 lollies on Tuesday and Wednesday, how many lollies did Nikau get for the whole five days?

How many lollies would Sam need to get on Saturday if he wanted to have 39 lollies altogether?

Teaching Sequence

  1. Pose first part of the problem to the class.
    Each day, from Monday to Friday, Sam, Nikau and Maia were given the same number of lollies. Each day they shared them the same way.
    Nikau got twice as many lollies as Sam.
    Maia got three times as many lollies as Sam.
  2. Ask some simple questions to get the students thinking about the problem.
    If Sam got ten lollies how many did Nikau and Maia get?
    If Maia got 30 lollies how many did Nikau and Sam get?
  3. Ask the students to use number sentences to express their answers. Share and discuss. Encourage them, as necessary, to use counters to model the solutions.
  4. Give the students time to think about the first part of the problem and to discuss it with their friends.
  5. Ask the students for their solutions to the first part.
  6. Pose the rest of the problem for the students to work on in pairs. Have the students use number sentences in their written record of the solution.
  7. As the students work ask questions that focus on their choice of number operation and their use of number sentences to record their answer.
    Why did you use multiplication?
    What number operation have you selected? Why?
    Tell me what this number sentence tells us.
    Could you write another equation to illustrate this problem?
  8. Share solutions to the problem discussing the different approaches used.

Extension

Have students write their own problem for others to solve.

Solution

Maia got 18 in two days, so 9 lollies a day.
Maia got three times as many lollies as Sam, so Sam got 3 lollies a day.
Nikau got 6 (= 2 x 3) lollies per day.

So over a five-day period Sonny got 5 x 6 = 30 lollies.

Sam got 3 lollies a day, so he got 15 from Monday to Friday. 15 + 24 = 39. Sam needs 24 lollies on Saturday.

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Level Three