Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
If you are a teacher click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on ...
On my calculator I divided one whole number by another whole number and got the answer $3.125$.
I know that both numbers were less than $50$, but can't remember what they were.
Can you work out what they were?
Once you've had a chance to think about it, click below to see how four different pupils began working on the task.
Here is Gemma and Flo's work:
Richard wrote the following:
"I multiplied $3.125$ by $1$, then I tried multiplying $3.125$ by $2$, then I multiplied $3.125$ by $3$ ..."
Here is the start of Thomas' work:
Can you take each of these starting ideas and develop it into a solution?
Click here for a poster of this problem.
Allow pairs to work on the task so that you feel they have made some progress, but do not worry if they have not completed it or if they report being stuck. The aim at this stage is for everyone to 'get into' the problem and work hard on trying to solve it, but not necessarily to achieve a final solution.
At a suitable time, hand out this (doc pdf ) to
pairs. Suggest to the class that when they've finished or can't make any further progress, they should look at the sheet showing three approaches used by children working on this task. Pose the question, "What might each do next? Can you take each of their starting ideas and develop them into a solution?". You may like pairs to record their work on large sheets of paper, which
might be more easily shared with the rest of the class in the plenary.