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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Rhombus It

Why play this game?

This game offers an excellent opportunity to practise visualising shapes and angles on grids and also encourages students to look at strategies using systematic approaches. Describing strategies to others is always a good way to focus and clarify mathematical thought.

### Possible approach

### Key questions

### Possible support

### Possible extension

The computer follows an algorithm (which may or may not be random) to place its pieces.
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Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 11 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Why play this game?

This game offers an excellent opportunity to practise visualising shapes and angles on grids and also encourages students to look at strategies using systematic approaches. Describing strategies to others is always a good way to focus and clarify mathematical thought.

*This game featured in the NRICH Primary and Secondary webinar in April 2023.*

*This printable worksheet may be useful: *Rhombus It

Start with a demonstration playing against a student rather than against the computer. Students may be surprised when the winning rhombus isn't aligned with the grid. This leads to discussions about what makes a rhombus a rhombus.

After a demonstration of the game, students could be left to play for a while in pairs, either on the computer or on a paper grid. Give them the option of reducing the size of the board if they seem overwhelmed!

Bring the class together for a discussion of their thoughts on the game. Did anyone consistently win or lose? Can anyone think of any good strategies which might help them win?

Once ideas have been shared the group can return to playing in pairs, or they can play a game together against the computer, trying, as a class to decide on the best move at each stage. Ask each student to explain the reasoning behind the moves they choose.

One aspect of developing a winning strategy that could be considered is the number of distinctly different starting points ($6$ on a $5 \times 5$ board) and the number of different rhombuses that can be drawn that include each of those points. That is, "Is there a good place to start and why?". This is a great investigation, with the capacity to expand by changing the sizes of the starting
grid, and which leads back into the game itself.

Working on the properties of a rhombus offers an opportunity to look at gradients to establish whether a shape is a rhombus.

With classes who never arrive together or on time, this and other interactive games can be used on the Interactive White Board to engage the early arrivers and set up a relaxed mathematical atmosphere.

- Is your move a good one? Why did you make it?
- Why do you think the computer made that move? Was it a good one?
- How do you know this is a rhombus?

The computer follows an algorithm (which may or may not be random) to place its pieces.

By studying the moves over a series of games can you work out the computer's strategy?

Do you think that it is random or deterministic (i.e. the computer will always play in a certain position given a certain configuration of pieces)?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?