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Route to Infinity

Can you describe this route to infinity? Where will the arrows take you next?

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Eight Hidden Squares

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?


Age 11 to 14 Challenge Level:

Why do this problem?

This problem offers students a chance to consolidate their understanding of coordinates whilst challenging them to think strategically.

Possible approach

Demonstrate the problem to the class, either using the interactivity, or with a grid drawn on the board.

Give students about 10 minutes to work on the problem, either at computers, or on paper in pairs - taking it in turns to choose where the giraffe is and give the distances. Pairs can keep score of the number of guesses each student required to find the giraffe - the one with the lowest total wins.

Ask the class to share efficient strategies/useful ideas. Encourage the students to consider all the points that satisfy each condition, and to look at the shape of this locus. Re-emphasise that the problem is to develop a strategy to find the giraffe with the minimum number of guesses.

Return to the computers/pairs to work on the suggested strategies. Provide squared paper for rough jottings.

If students are familiar with coordinates in 4 quadrants, the game can be an excellent context for practising these - working on paper with suitable grids.

Key questions

Which points satisfy the conditions given so far?
How can you narrow down the possibilities?

Possible extension

Play the game on a grid with axes from -9 to 9. Restrict the guessing to the central square -5 to 5, but insist that the giraffe is lost outside this central square. Students are allowed one 'final answer' guess outside the square to locate the giraffe.

Possible support

Encourage students to draw the situtation on squared paper, and colour code points that are possible/impossible; looking at the result of each new piece of information.