Solve problems that involve halves and thirds.
Devise and use problem-solving strategies (draw, act) to explore situations mathematically
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 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). 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.
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. If Sam got 18 lollies on Wednesday, how many lollies did Sunny get on Thursday?
How many lollies did Sylvia get that week?
- Ask some quick warm-up questions to get the students thinking about halves and thirds.
Show a piece of paper and ask the students to find a third of it. How do you know you have a third?
Show the students 6 counters and ask the students to find a third of them? How do you know? How did you work it out?
- Pose the problem to the class.
- Give the students time to think about the problem and possibly discuss it with their friends.
- Ask the students for their thoughts about how they will solve the problem.
- Let the students work on the problem in pairs.
- 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?
- Share solutions to the problem. Discuss the different approaches used by the students.
This problem could be posed in a number of contexts. Money, time, temperature or length could replace the lollies.
Now Sunny gets half as many lollies as Sam. But Sam got 18 and half of 18 is 9. So Sunny got 9 lollies. Using blocks and dividing them into two equal piles, easily achieves the halving.
Since Sam got 18 lollies on any day and Sylvia gets a third of that, then Sylvia gets 6 lollies. Five lots of six is thirty.