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Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Good Work If You Can Get It

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?

This problem encourages students to think of different ways in which it can be solved. This can be done using trial and improvement, but preferably, and more efficiently, by creating some linear equations. The very fact that the six men have names beginning with the letters A to F should make an algebraic solution stand out!

Possible approach

You could introduce the problem to the class, and give them a little bit of time to work in pairs to suggest ways it could be tackled. Then come together again to share possible strategies and discuss any difficulties that might arise.

Once students have had a chance to develop clear strategies for working on the problem allow them some time in pairs to develop and discuss their answers.

Allow some time for feed back at the end and to explore and discuss both learners' methods and their answers.

Key questions

Have you thought of making a table to show how long each man worked?
Have you thought of making some algebraic equations from the information given?
Is your strategy the quickest way to work out the answer?

Possible extension

Learners could follow-up with this harder problem, How Many Miles to Go?

Possible support

Suggest making a table and tackle the problem using trial and improvement. Alternatively, those who find the wordiness of the problem an overwhelming difficulty could try Pyramids.