# Sort the Street

Here is a picture of nine of the houses in my street:

Find as many different ways to sort them into groups as you can.

You may like to use this interactivity to drag the houses into groups.

Thank you to everybody who sent in their thoughts about these houses.

Lauren and Toby from Llandovery Prep School in Wales each sent in a solution like this:

There are 3 houses with green doors.

There are 3 houses with blue doors.

There are 3 houses with black doors.

There are 3 houses with 3 storeys.

There are 4 houses with grey rooves.

There are 5 houses with red rooves.

There are 3 houses with small chimneys.

There are 6 houses with big chimneys.

There are 3 houses with 3 windows.

There are 6 houses with 5 windows.

Well spotted! I wonder how many different ways of sorting the houses that gives us?

Elijah from the Independent Jewish Day School wrote in with these solutions:

There are 3 houses with blue doors

There are 3 houses with green doors

There are 3 houses with black doors

There are 3 houses with 3 small windows

There are 3 houses with 5 small windows

There are 3 houses with 4 small windows and one big window

There are 3 houses big houses

There are 3 houses medium houses

There are 3 houses small houses

There are 6 houses with a door on the right

There are 3 houses with a door in the middle

There are 4 houses with a grey roof

There are 5 houses with a red roof

Well done for spotting all of these differences, Elijah. How many ways of sorting the houses does that give us?

Noah from Goodwyn School came up with these eight solutions:

Door colour - blue, green or black

Number of windows - 3 or 5

Roof colour - grey or brown

Amount of floors - 2 or 3

Position of door - right or middle

Number of sections in window - 4 or 6

Positioning of windows

Height of roof - small or big

Thank you for sending us these ideas, Noah - that's eight different ways we could sort the houses.

If you would like to get in touch with us with some different ways of sorting these houses, please email us with your ideas.

**Why do this problem?**

This low threshold high ceiling problem is ideal for children to work on in pairs or small groups as this will encourage them to talk about what they are doing, which is a great assessment opportunity for you. Its open-ended nature is a reason in itself to try it in the classroom. Some pupils may surprise you with their inventiveness! The task encourages learners to identify what is the same and what is different as they compare the images. Being able to articulate sameness and difference is a key mathematical skill.

### Possible approach

*This problem featured in the NRICH Primary and Secondary webinar in September 2022.*

To introduce the problem, invite the children to chat in pairs about what they notice about the houses. Then, sort the houses according to a particular criterion using the interactivity and invite the class to work out how they have been sorted. This will help them to grasp the focus.

### Key questions

What is the same about these houses? Are there any others like that?

Why have you grouped the houses in this way?

### Possible extension

Some children will enjoy the challenge of finding two or more criteria which fit some houses, perhaps also extending to more than two groups. For example, rather than just "these houses have five windows" and "these houses don't have five windows", some might say "these houses have five windows and are tall"; "these houses have five wondows but aren't tall/are short" and "these houses don't have five windows".

The problem Sets of Numbers offers an opportunity for more experienced learners to apply the skill of identifying what is the same and what is different to numbers. (The numbers themselves could be changed to suit the class.)

### Possible support

You could model one way to approach this activity by taking two houses and asking what the same is about them, as suggested in the key questions. Children can then add more houses to the pair by looking for those that fit this criterion.

*If you are looking for copies of the old style houses you can print them here*.