We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Roll over the Dice
Age 7 to 11 Challenge Level
Roll over the Dice
You will need a 5 by 5 square and a dice.
Place your dice in the top left hand corner.
Whatever number is on the top of the dice, write it down on the square.
Follow the green line on this grid as a route by rolling your dice, writing down the numbers on top of the dice as you move along. You can see in this video how it might be started. Have a good look at what's happening and then carry it on in a similar way.
When you've filled all 25 squares with numbers, EXPLORE!
What do you notice?
What little change can you make to the rules to explore again?
Why do this problem?
This activity was initially developed for Wild Maths, our sister site, to encourage learners to be creative mathematicians. Mathematics is certainly a creative subject. It involves spotting patterns, making connections, finding new ways of looking at things and using what you already know in new contexts. Creative mathematicians play around with
examples, draw pictures, have the courage to experiment and ask good questions. (Wild Maths is aimed at individual learners, rather than teachers so the notes below only appear on NRICH.)
I found it good to just show the video and ask the pupils what it is they notice. This way, you can establish what is happening and discuss the 'rules' of the activity. When the simple rules have been agreed, some pupils may be happy recording their trials on paper.
When they have completed the 25 squares they can offer you further observations. When all observations have been shared and discussed it's a matter of asking them to suggest one small change in the instructions and to carry out their new versions (each child maybe making their own changes). Then further sharing and discussing is important.
What changes have you made?
Tell me about what you've noticed in your new version.
Can they make predictions about what the results will be following their change in the game (the dimensions of the rectangle, the way the dice moves etc.)?
Some children may need help recording their routes and/or manipulating the dice.
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NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.