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Not a Polite Question

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

Whole Numbers Only

Can you work out how many of each kind of pencil this student bought?


Add up all 5 equations given below. What do you notice? Solve the system and find the values of a, b, c , d and e. b + c + d + e = 4 a + c + d + e = 5 a + b + d + e = 1 a + b + c + e = 2 a + b + c + d = 0

Sweet Shop

Age 11 to 14
Challenge Level

Why do this problem?

This problem provides a useful context for equations and especially simultaneous equations.

There is also an opportunity to discuss the issue of redundant information.

Possible approach

Jonathan Linton sent us these slides which aim to present the problem in an accessible way for students.

Key questions

How much does one lollypop cost?
Would it be a good idea to see what Kenny bought next?
What did Nathan and Judy both buy?
Would it be helpful to write it all out as equations?
Would it be a good idea to call the sweets b, c, m and l?

Possible extension

Learners could go on to Letter Land or invent their own sweet shop questions.

Possible support

Suggest starting by working out the cost of lollipops from what Liam bought. Next look at what Kenny bought. Then continue through the other children's purchases.