Why do this problem?
This activity is an engaging way for younger children to practise their number bonds to six and their understanding of odd and even numbers. It also provides an opportunity for children to begin thinking about working systematically, as well as giving pupils the freedom to record their ideas in different ways.
As a class, talk through the different types of house and ask children what they notice. If they don't suggest it, point out that semi-detached houses have to come in pairs, and terraced houses have to come in groups of three or more. Ask the children for suggestions of what types of house we could build if there are going to be three houses on the road. Write or draw these options on the
whiteboard, explaining that for this task we aren't worried about the order of the houses, only the number of different types of house. Do pupils have any ideas for how we could record these ideas? How can we tell that we've found all of the possibilities?
In pairs, provide pupils with pictures of the different types of house
(at least six pictures of each type) and some paper on which they can record their ideas. Give children time to work together to find different combinations of six houses. As you walk around the room, discuss with pupils how they are
keeping track of their ideas. How are they making sure they don't get the same combination twice? At the end of the lesson, ask some pairs to discuss the way they approached the problem. How can we work systematically to be sure we've found all of the options?
How are you keeping track of your ideas?
Tell me about this arrangement.
How do you know you've found all the different possibilities?
Is it possible to have three semi-detached houses? Or two terraced houses? How do you know?
Depending on how the pupils have approached this activity, you may be able to ask them for ideas as to what other things they could now explore. If not, you can suggest looking at the possible combinations for five or seven houses.
Using multilink cubes as well as pictures of the different types of house might be help some children imagine the houses being 'attached'. If there are children who find recording their ideas difficult, taking photos of the different combinations might allow these children to focus on the activity rather than the recording.