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Carrying Cards


These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it.
children holding numbers
Each child in blue is holding a number which is four more than the child in the same row wearing red.
The children in yellow shirts each have a number which is double the number of the child in the same row wearing red.
Some of the numbers that the children in red, blue or yellow shirts are holding have got rubbed off. What should the numbers be?
Can you work out how the numbers that the children in green are holding have been worked out? What are the two missing numbers?
If there was another row of four children standing behind the fourth row, what numbers would they be holding?

Why do this problem?

This problem will give  pupils experience of looking for, and explaining, number patterns, and it could lead into algebra.   It  would also make a good introduction to spreadsheet use.

Possible approach

You could introduce this problem practically in the classroom with children holding small whiteboards, for example.  Rather than wearing coloured shirts, the children could have particular coloured pens or they might wear 'bibs' or ribbons usually used for sports matches.  Arrange the sixteen children in four rows of four as in the picture and write the given numbers on the appropriate whiteboards.
 
You could present the challenge orally for the whole class to solve together, but giving time for learners to talk to each other in pairs or small groups as well. During the main problem-solving time, it may be better for the sixteen children to return to their seats so they too can be fully involved in the solutions.  
 
In the plenary, you can invite the pupils to stand in the grid formation again and everyone can participate in building up the numbers on the whiteboards.  Encourage learners to explain how they know what the number on each board is, and draw attention to the fact that each number might be worked out in several different ways.  Invite four more children to stand behind the back row so that the last question can be answered.
 
You could end with a final challenge for the class to solve:  Invite four more children to come up and stand in a row some way behind the fifth row.  On the board which is held by the child standing behind numbers $1$, $2$, $3$, $4$ and $5$, draw a shape or write 'any number' or write 'a number'.  Explain that this is a number, any number - you don't know what it is.  Can the group write expressions on the other three whiteboards?

Key questions

What do you know about the red/blue/yellow numbers?
How will that help you work out what this number should be?
What do you notice about the green numbers?
Can you make the green numbers from any of the other numbers?

Possible extension

Some children may enjoy the challenge of creating a spreadsheet which represents the children.

Possible support

It might help to have some cards or pieces of paper available which state the relationships between the different coloured numbers so that children can refer to them as they work.