More Lollies
Solve problems up to 20 using subtraction and addition.
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), Sharing Lollies (Level 2).
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.
The Problem
On Monday, their Mum gave Sam and Sylvia 7 lollies. Sam got 2 lollies. How many lollies did Sylvia get?
Their Mum gave Sam the same number of lollies each day up to (and including) Friday. Altogether she gave them both Sam and Sylvia 20 lollies. How many lollies did Sylvia get that week?
Lesson Sequence
- Review the days of the week. See if the students can recite the sequence using different starting days. Also ask for the sequence backwards.
- Pose the problem to the class.
- Ask volunteers to retell the problem using their own words to check that everyone understands what is required.
- As the students work on the problem (in pairs or individually) as them to explain their thinking.
How did you start the problem?
What have you found out?
Are you convinced that you are correct?
Can you convince me? - Share solutions.
Other Contexts
This problem could be posed in a number of contexts using items which are of current interest to the students.
Extension to the Problem
Make up similar story problems of your own.
Solution
By putting 7 blocks down to represent lollies, then taking 2 blocks away for Sam’s share, we get 5 blocks. So Sylvia had 5 lollies.
Since Sam had 2 lollies on Monday, he must have had 2 lollies on every other day up to Friday. So Sam had 2 + 2 + 2 + 2 + 2 = 10 lollies. Now altogether Sam and Sylvia got 20 lollies. So Sylvia got 20 – 10 = 10 lollies.
| Attachment | Size |
|---|---|
| MoreLollies.pdf | 41.96 KB |
| MoreLolliesMaori.pdf | 54.71 KB |
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