### Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

### Noah

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

### Five Coins

Ben has five coins in his pocket. How much money might he have?

# I'm Eight

## I'm Eight

When I went into a classroom earlier this week a child rushed up to tell me she was 8 that day.

Well, Happy Birthday to everyone who has a birthday today!

This challenge is about finding a variety of ways of asking questions which make 8.

You might think of 6 + 2, or 22 - 14 or...

However, try to create examples that use all the different mathematical ideas that you know about.

Perhaps you could challenge yourself to find ways of making 8 that you think no-one else will have thought of.

If you are not 8 years old, you might like to use your age instead of 8.

### Why do this problem?

This number activity can be stated very simply but has huge potential. It simulates pupils' curiosity, engaging them in thoughtful work and motivating them to challenge and deepen their own understanding of number.

You could build further on children's natural curiosity by encouraging them to ask "I wonder what would happen when...?". If you are interested in pursuing curiosity in particular, then please see the 'Further note' at the bottom of this page.

### Possible approach

You could begin by introducing the task and giving time for children to record one way of making 8 on a mini whiteboard, on their own.  Then invite them to record another way.  Then another way.  Continue this so that they have at least five examples.  Then ask them to turn to a partner and share ideas.

Bring everyone together and ask how they felt being asked for another example, then another, then another... This way of working often encourages learners to challenge themselves in a way that asking for a particular number of examples all at once doesn't do.  This raises children's awareness of the range of examples open to them rather than immediately opting for the first one that sprang to mind.  (See John Mason's Open University course booklet Working On Your Own Mathematics, 2017, for more information about this approach.)

Invite pairs to share their ideas and record them on the board for all to see. You may find it helpful to try to group their suggestions into the four rules of number: addition, subtraction, multiplication and division, if applicable. The prompts you use will depend on the sorts of statements offered by the children, and how varied they are.  If, for example, most statments use exactly two numbers, point this out and ask children to try to use three or four numbers to get 8. If they have used addition only, suggest that they could start with a biggish number and then take some away and then have to take some more away in order to end up with only 8. They may be motivated to create examples that they think no-one else will have thought of.

Allow plenty of time for pairs or individuals to work further on the task.  A mini plenary might draw attention to those contributions that follow a particular pattern e.g. 1 + 7, 2 + 6 ... , encouraging children to write 'etc' to indicate that there were some more if they thought so. This activity could be left 'simmering' so that you come back to it later in the week and leave a space on your working wall for contributions in the meantime.

### Key questions

Tell me what you are doing here.
How have you got these?
Could you find any more like that?

### Possible extension

You might find that, for example, a pupil continues with lots and lots of subtractions, raising the starting number by just one each time. It is useful to allow that to happen for a while as there are some fruitful conversations to be had about the patterns and how long they will continue.  However, after a suitable period, encourage them to venture further. You might deliberately drop in a prompt about a certain area of mathematics (e.g. halves), even if the class has not formally been taught that topic.  You may be surprised!

### Possible support

If a pupil has eight objects then they can make a start on this activity by putting the eight into a number of groups and say "this, plus this, plus this, makes 8".

### Further note

You may be interested in the following talks given by Professor Susan Engels, which focus on encouraging curiosity and are available on YouTube:
The Rise and Fall of Curiosity - the extract from 23.50 to 37.15 on adult encouragement and teacher behaviour is particularly worth viewing;
The Hungry Mind: The Origins of Curiosity - the extract from 8.22 to 12.29 on children asking questions is especially useful.