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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Negative Dice

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

Playing Connect Three

Age 11 to 14 Challenge Level:

Why do this problem?

In these games, students have the opportunity to practise adding and subtracting positive and negative numbers in an engaging context.
As students become hooked on the game, they may also like to explore winning strategies (or more realistically, a strategy that improves their chances of winning) and consider the probability of getting different numbers.

Teachers may find it interesting to read the NCETM Mathemapedia Entry:
Games as challenges to stimulate curiosity and support learning

Possible approach

This printable worksheet may be useful: Playing Connect Three

In this problem there are two games; the first uses dice with positive numbers, and the second uses dice with a mixture of both positive and negative numbers.

The games could be introduced using an interactive whiteboard or projector, and inviting two volunteers to play.

After the introduction students could play in pairs at individual computers, or this  worksheet could be printed for students to play away from the computers.

This spreadsheet can be used to simulate throwing the two dice in the second game.

Key questions

Are there some numbers that we should be aiming for? Why?

Are certain numbers easier to 'cover' than others? Why?

Do certain numbers contribute to more winning lines?

Possible extension

Following on from this problem, students could take a look at:
Consecutive Negative Numbers

Possible support

The article Adding and Subtracting Negative Numbers offers several models that can be used to help students understand addition and subtraction of positive and negative numbers.

The game Up, Down, Flying Around might be a good preparation for Playing Connect Three.