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?
The first person who is unable to cross out a number loses.
Here is an interactive version of the game in which you drag the numbers from the left hand grid and drop them on the right hand grid. Alternatively, click on a number in the left hand grid and it will transport to the earliest empty location in the right hand grid. You can rearrange the numbers in the right hand grid by dragging and dropping them in position. The integer in the top right hand
corner grows with the number of factors/multiples you have in a row.
Do you have any winning strategies?
Are there any numbers you shouldn't go to?
Use a smaller number board, eg $1-50$ (or $1-49$ in a square). Here is a large $1-50$ grid and here is
a sheet of smaller grids which could be given to pupils. This makes the mental calculations much easier, without watering down the mathematics. The lesson could focus on accuracy of calculation - with teacher interventions to get pupils sharing their mental strategies.
Handouts for teachers are available here (Word document, pdf), with the problem on one side and the notes on the other.
You may prefer to use an alternative version of the interactivity which distinguishes between factors and multiples by colour:
Full Screen Version