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Level Two > Number and Algebra

Sharing More Lollies

Keywords:
Achievement Objectives:

Achievement Objective: Use simple additive strategies with whole numbers and fractions.
Achievement Objective: Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols.

Specific Learning Outcomes: 

Solve problems that involve halves and thirds

Used the terms greater than and less than in the solution of the problem

Description of mathematics: 

There are two aims of this problem. The simplest is that it is one problem that will fit the Achievement Outcomes suggested below. In solving it you always have to refer back to Sam and his situation, as this is the only way that you can link what Sunny gets to what Sylvia gets.

On the other hand, this problem is the first 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), Lollies, Lollies, Lollies (Level 3) and Still More Lollies (Level 4).

Actually we could have given the idea more twists. We leave that for you to do.

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: 
A bag of lollies to interest the students in the problem.
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 half as many lollies as Sam got. Sylvia got a third as many lollies as Sam got. Their Mum gave them the same number of lollies each day up to (and including) Friday.

  1. If Sunny got 9 lollies on Wednesday, how many lollies did Sylvia get on Thursday?
  2. Is the number of lollies that Sylvia got over Monday, Tuesday, Wednesday and Thursday, less than the number Sunny got for the days Thursday and Friday?
  3. How many days does it take for the number of lollies Sunny got, to be greater than the number Sam got on Friday?

Lesson Sequence

  1. Read the problem situation to the class.
    "On Monday, Sam, Sunny and Sylvia shared some lollies that their mother had given them. Sunny got half as many lollies as Sam got. Sylvia got a third as many lollies as Sam got. Their mother gave them the same number of lollies each day up to (and including) Friday."
  2. Ask some warm-up questions to get the students thinking about halves and thirds in the context of this problem.
    If Sam had 12 lollies can you work out how many Sylvia has? Explain.
    What about Sunny? Explain.
  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 possibly discuss it with their friends.
  5. Ask the students for their thoughts about how they will solve the first part.
  6. Share solutions.
  7. Let the students work on rest of the problem in pairs.
  8. As the students work ask questions that focus on their choice of problem solving strategy and their understanding of fractions.
    Can you tell me what you are doing?
    Why did you decide to solve the problem that way?
    What is a third? What is a half?
    How do you know when you have third?
    Which student would you like to be? Why?
  9. Share solutions to the problem. Discuss the different approaches used by the students. Highlight the use of greater than and less than in the discussion of the problem.

Other Contexts

Use objects that are of current interest with the class, for example, marbles, cards.

Solution

Sunny gets half as many lollies as Sam. So Sam gets twice as many lollies as Sunny. If Sunny got 9 lollies, then Sam got 18.
Now Sylvia gets a third of Sam’s number. This is 6.
On any four days Sylvia will get 6 + 6 + 6 + 6 = 24. On any two days, Sunny will get 9 + 9 = 18. Since 24 > 18, then Sylvia gets more than Sunny. It is not true to say that Sylvia gets less than Sunny.
Sam got 18 lollies on Friday. Sunny gets 9 lollies a day. On two days Sunny gets 9 + 9 = 18 which equals the number of lollies that Sam got on Friday. Over three days, Sunny gets 27 lollies. Since 27 > 18, then it takes Sunny 3 days to get more lollies than Sam.

 

AttachmentSize
SharingMoreLollies.pdf50.84 KB
SharingMoreLolliesMaori.pdf62.12 KB

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