### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Tiles on a Patio

How many ways can you find of tiling the square patio, using square tiles of different sizes?

### Pebbles

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?

# Shape Draw

## Shape Draw

This challenge is designed to be worked on with a friend or in a small group.

You will need to print off and cut out the eight cards from this sheet.

Can you use the information on the cards to draw the one shape which is being described?

Did you need all the information that was given?  Why or why not?

#### Why do this problem?

This activity will help to consolidate learners' understanding of properties of quadrilaterals, area, perimeter and symmetry.  It could be a useful assessment task.

#### Possible approach

Give pairs or small groups copies of  the cards and simply explain that their task is to draw the shape that is being described.  Try not to say anything more at this stage.  Stand back and observe the children as they begin the task.  You may like to have centimetre squared paper available, should learners ask for it.

As you move around the room, watch out for those who have an organised approach.  Perhaps they are discussing each card in turn and agreeing what it tells them.  Perhaps they have noticed some cards which together help narrow down the possibilities.   Bring the class together to share thoughts so far (a mini-plenary) which will help some children 'get off the ground' and others by giving them chance to articulate their ideas.

Alternatively, if you would like to place more emphasis on drawing/construction, you could introduce the task slightly differently.  Ask each group to place all the cards face down and then turn over one card.  In pairs, learners then draw a single shape that fits that criterion and then compare their drawing with other pair/s in the group. The group then turns over a second card and each pair modifies their drawing so that the new shape meets both criteria.  Pairs can compare for a second time.  This process is repeated until all the cards have been turned over.

Having given time for learners to complete the task, the plenary could focus on whether all the information was needed.  Were there any cards that were superfluous?  Which ones?  Why?

#### Key questions

What does this card tell you about the shape?
What do we know now?
How are you keeping track of what you know so far?

#### Possible extension

Some learners might relish the challenge of creating their own version of this task.  You may wish to stipulate that there must be one solution, or perhaps you'd like them to create a task which has two or more possible outcomes.  Of course, once a new activity is completed it must be tried out!

#### Possible support

You could give some children a sheet with some possible shapes on it, one of which is the solution.  That way, the task becomes one which involves comparing and contrasting, rather than creating.