This problem solving activity has a number (all operations) focus.
On Monday, Sam and Sylvia have 7 lollies.
They are not equally shared.
2 of the lollies are Sam's.
How many lollies are Sylvia's?
Sam has the same number of lollies each day up to (and including) Friday.
Altogether Sam and Sylvia have 20 lollies.
How many lollies are Sylvia's that week?
- Solve problems up to 20 using subtraction and addition.
Students apply addition and early multiplication strategies (e.g. repeated addition, skip counting) to solve this problem.
This is one of six problems: Lollies! Number, Level 1; More Lollies, Number, Level 1; Sharing More Lollies, Number, Level 2; Lollies, Lollies, Lollies, Number, Level 3; and Still More Lollies, Algebra, Level 4. At each level, these problems become more algebraically-focused.
- Copymaster of the problem (Māori)
- Copymaster of the problem (English)
- Counters
- A 7-day calendar
The Problem
On Monday, Sam and Sylvia have 7 lollies. They are not equally shared. 2 of the lollies are Sam's. How many lollies are Sylvia's?
Sam has the same number of lollies each day up to (and including) Friday. Altogether Sam and Sylvia have 20 lollies. How many lollies are Sylvia's that week?
Teaching Sequence
- Review the days of the week.
- Pose the problem to the class and have students retell in their own words what they have to find out. You might use the calendar and the lollies to model the problem.
- Have students suggest how they might record/show their solutions.
- As the students work on the problem (in pairs or individually) ask them to explain their thinking.
How did you start the problem?
How many lollies did Sam/Sylvia have by the end of the week? How do you know?
What have you found out?
How do you know that you are correct?
Can you show me that you have solved the problem? - Share solutions.
Extension
When combined and then shared fairly at the end of four days, Sam and Sylvia each get 6 lollies. If Sam has 2 lollies each day, how many does Sylvia have each day?
Vary the number of days, number of lollies each and fair share amounts.
Solution
Students may use a range of representations to show that:
7 - 2 = 5. Sylvia has 5 lollies.
On 5 days Sam has 2 + 2 + 2 + 2 + 2 = 10 lollies (or 2 lollies x 5 days). So Sylvia has 20 – 10 = 10 lollies.
Solution to the Extension
6 lollies each is 12 altogether. Sam has 2 + 2 + 2 + 2 = 8. Sylvia has 12 - 8 = 4, which is 1 lolly each day.