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### Number and algebra

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# Treasure Hunt

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

Possible approach

*You may find it useful to print off these grids* *if your students do not have access to the interactivity. *

*This problem featured in an NRICH Primary webinar in November 2021, and in an NRICH Primary and Secondary webinar in September 2022.*

Demonstrate the Level 1 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 treasure is and give the distances). Pairs can keep score of the number of guesses each student required to find the treasure - the one with the lowest score 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 treasure with the minimum number of guesses (at Levels 1 and 2, with the appropriate strategy, it is always possible to find the treasure in fewer than
four 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 four quadrants, the Level 2 game can be an excellent context for practising these. (The level can be changed by clicking on the purple cog in the top right of the interactivity.) Encourage students to do their work on paper.

Which points satisfy the conditions given so far?

How can you narrow down the possibilities?

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

Possible extension

The Level 3 game provides an interesting challenge: the searching area is restricted to the pink region, although the treasure may be anywhere on the grid. Users are allowed one 'final answer' guess outside the pink region to locate the treasure.

The Level 4 game provides a challenging context in which to think about 3-dimensional coordinates and it can be explored in 3D Treasure Hunt.

Again, the challenge is to develop a strategy to find the treasure with the minimum number of guesses (at Levels 3 and 4, with the appropriate strategy, it is always possible to find the treasure in fewer than five guesses).