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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?

Connect Three

Age 11 to 16 Challenge Level:

Why do this problem?

In this problem, 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 strategies that improve their chances of winning, and consider the probability of getting different numbers.

Possible approach


This printable worksheet may be useful: Connect Three.

Demonstrate how to play the game to the whole class, perhaps by inviting two volunteers to have a go. (You can click the purple cog in the top right corner to access the settings menu, and choose whether to play against the computer or not.)

After the introduction students could play in pairs on a computer or tablet, or if computers are unavailable, this worksheet could be printed and handed out instead - students will need dice or spinners with the correct numbers. 

Once students have had an opportunity to play the game a few times, discuss the key questions below, and then perhaps allow students a couple more games to try out any strategies they have thought of.

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 support

Students may wish to play First Connect Three before trying this version.

The article Adding and Subtracting Positive and 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.

 

Possible extension


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