Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# 3 by 3 Mathdokus

### Why do this problem?

### Possible approach

### Key questions

### Possible support

### Possible extension

## You may also like

### Pebbles

### It Figures

### Bracelets

Or search by topic

Age 7 to 14

Challenge Level

- Problem
- Student Solutions
- Teachers' Resources

Mathdoku grids are a motivating context for learners to develop fluency with number bonds, and factors and multiples, as well as providing an opportunity to reason mathematically.

*The 4 by 4 version of this problem featured in the NRICH Primary and Secondary webinar in October 2022.*

Display the interactivity and, without saying much else, invite learners to consider what they notice and what questions they would like to ask. Give them time to think on their own, then talk to a partner, before drawing everyone together. Facilititate a whole group discussion, using the points raised to explain how the Mathdoku grid works. It would be useful to introduce the vocabulary of 'cages' and squares. Alternatively, you might like to watch this demonstration video, which you could pause as you wish.

Ask for suggestions about where we might start. Which square might we fill in first? Emphasise that you are particularly interested in their reasoning. How do they know that the number they are offering *must* go in that square? Can they convince the rest of the class and you?

If you have not watched the introductory video, you may wish to demonstrate how to seek help from the interactivity if learners are not sure which square is possible. (Clicking on 'Show me a square I can solve' will result in a yellow box appearing around a square which is solvable. Clicking on 'Give me a hint about this square', will suggest how you might go about working out the number in that square.)

You can continue in this way with the whole group for as long as you feel is appropriate. Once everyone has got the idea, you can ask learners to complete the grid in pairs, either using the interactivity on a tablet or computer, or using a printed copy (clicking on the purple cog in the top right allows you to select a version of the grid which you can print using the browser printing option). As they work, listen out for examples of children's watertight reasoning, which could be shared with the whole class in the plenary.

You may wish to display a new grid in the plenary for the class to solve together, so they have chance to practise creating chains of reasoning using their knowledge of number and calculation.

What are the *possible options* for this square? How do you know?

Is there any other information in the grid that could help us narrow down the possibilities?

Can you convince me/someone else that this number *must* go in this square?

The interactivity has built-in hints which will help all learners access this challenge. Many children will find it useful to have paper and pencil to hand to jot down possibilities for the square they are working on (this could be a print-out of the grid, but could simply be plain paper).

Once learners have tried all the grids in the interactivity (see the Settings menu), or on paper, you could offer them larger grid sizes: 4 by 4, 5 by 5 and 6 by 6. You could also challenge them to create their own Mathdoku in pairs. Their grid must have a unique solution and they can give it to another pair to solve.

Learners may also like to have a go at one of NRICH's Sudokus, which contain the numbers 1-9 in each row, column and three by three grid (currently they are paper based only). A First Product Sudoku would be a good starting point.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?