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Draw a number line on a piece of paper, marked from $0$ to $20$, like this:
(You could print off this sheet of number lines.)
This challenge is a game for two players. The first player chooses two numbers in this grid and either multiplies or divides them.
They then mark the answer to the calculation on the number line. The second player then chooses two numbers and either $\times$ or $\div$, and marks that number in a different colour on the number line.
If the answer is too big or too small to be marked on the number line, the player misses a go.
The winner is the player to get four marks in a row with none of their opponent's marks in between.
What good ways do you have of winning the game?
Does it matter if you go first or second?
[This game is adapted from a SMILE Centre card.]
This game gives children the opportunity to estimate answers to calculations in a motivating context, and gives plenty of practice in multiplication and division. Playing strategically involves higher-order thinking and the need to think ahead.
You could play the game on the board against another adult (or a child who has been told the rules), but without saying anything about the rules to the whole group. You could write down each calculation as you go along. Invite the class to watch the game in action and after a few moves, ask them to suggest what they think the rules might be. How might the game be won? Having discussed the possibilities as a whole class, explain the rules as described in the problem itself and set the children off playing in pairs on some number lines.
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?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?