Still More Lollies
Solve problems that involve simple linear relationships
Write simple linear expressions
Devise and use problem-solving strategies to explore situations mathematically
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), Sharing More Lollies (Level 2) and Lollies, Lollies, Lollies (Level 3).
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.
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 plus two lollies.
Their Mum gave them the same number of lollies each day up to (and including) Friday. Altogether, their Mum gave them 70 lollies. How many lollies did Sam get on Monday?
Teaching Sequence
- Read the first part of the problem to the class.
On Monday, Sam, Sunny and Sylvia shared some lollies that their Mother had given them. Sunny got twice as many lollies as Sam. Sylvia got three times as many lollies as Sam plus two lollies. - 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 Sunny got ten lollies how many does Sunny and Sam have?
Ask the students to use number sentences to express their answers. Share and discuss. At this stage you might want to talk about the use of a letter or empty box to represent the unknown number in the problem.
Sam s
Sunny 2s
Sylvia 3s + 2 - Pose the problem to the class.
- Give the students time to think about how they will solve the problem and to discuss it with their friends.
- Tell the students that you want them to use number sentences in their written record of the solution.
- As the students work ask questions that focus on their choice of number operation and their use of number sentences to record their answer.
What number operation have you selected? Why?
Tell me what this number sentence tells us. - Share solutions to the problem discussing the different approaches used.
Extension to the problem
Ask the students to make up similar story problems for others to solve.
Solution
One way to do this problem is to let the number of lollies that Sam gets equal s. Then Sunny gets 2s and Sylvia gets 3s + 2. On any one day they all get s + 2s + (3s + 2) = 6s + 2.
Over 5 days they get 5(6s + 2) = 30s + 10. But this is 70. So we have to solve 30s + 10 = 70. Taking 10 from both sides gives 30s = 60. Now we can divide both sides by 30 or simply guess the answer. Whatever way we go we get s = 2. And that is how many lollies Sam got on Monday.
Alternatively we could say that 70 lollies in five days is 70/5 = 14 in one day. Now we only have to solve 6s + 2 = 14. From there 6s = 12 and so s = 2.
This problem doesn’t have to be done by algebra though. Whatever Sam gets, Sunny gets twice as much and Sylvia gets three times as much (forgetting the plus 2 for a minute). Now one lot plus two lots plus three lots is six lots. With the two we get six lots plus two. Again six lots plus two equals 14 and we can get one lot equals two from there.
| Attachment | Size |
|---|---|
| Still More Lollies.pdf | 40.7 KB |
| Still More LolliesMaori.pdf | 53.62 KB |
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