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Level Three > Number and Algebra

Lollies, Lollies, Lollies

Keywords:
Achievement Objectives:

Achievement Objective: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
Achievement Objective: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.

Specific Learning Outcomes: 

Solve problems that involve multiplication and division

Use equations to express a problem

Description of mathematics: 

This problem is one of six problems that go from Level 1 to Level 4 and slowly change from being completely number oriented to being completely algebraically oriented. The aim of these problems is to show how a simple idea can be taken and extended to cover a range of Levels and Achievement Objectives. The problems, including this one are Lollies! (Level 1), More Lollies (Level 1), Sharing Lollies (Level 2), Sharing More Lollies (Level 2) and Still More Lollies (Level 4).

In practice, complicated problems that can be solved algebraically often have quite simple numerical ideas underlying them. Of course, the same thing can be said for any apparently difficult problem in mathematics. The ideas that are used at any level are based on ones found earlier. That is just the way that the subject builds itself up and manages to deal with ever more complicated situations.

Required Resource Materials: 
Copymaster of the problem (English)
Copymaster of the problem (Māori)
Activity: 

The Problem

On Monday, Sam, Sunny and Sylvia shared some lollies that their Mum had given them. Sunny got twice as many lollies as Sam. Sylvia got three times as many lollies as Sam.

Their mother gave them the same number of lollies each day up to (and including) Friday. If Sylvia got a total of 18 lollies on Tuesday and Wednesday, how many lollies did Sunny 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. Read the first part of the problem to the class.
    On Monday, Sam, Sunny and Sylvia shared some lollies that their Mum had given them. Sunny got twice as many lollies as Sam. Sylvia got three times as many lollies as Sam.
  2. Ask some simple questions to get the students thinking about the problem.
    If Sam has ten lollies how many have Sunny and Sylvia got?
    If Sylvia has 30 lollies how many does Sunny and Sam have?
    Ask the students to use number sentences to express their answers. Share and discuss.
  3. Pose the first part of the problem to the class.
  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. Tell the students that you want them to 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.
  8. Share solutions to the problem discussing the different approaches used.

Other Contexts

This problem could be posed in a number of contexts. Money, marbles could replace the lollies.

Solution

For Sylvia to get 18 over two days she must have got half of that on one day. So she gets 9 lollies a day. As Sylvia gets three times as many lollies as Sam, then Sam only gets 3 lollies a day. But then Sunny gets 6 (= 2 x 3) lollies a day.

So over a five-day period Sunny gets 5 x 6 = 30 lollies.

Sam gets 3 lollies a day, so he gets 15 from Monday to Friday. So what does he have to add to 15 to get 39? Just 24. So Sam need 24 lollies on Saturday.

AttachmentSize
Lollies.pdf39.97 KB
LolliesMaori.pdf45.99 KB

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