Sort the street
Sort the houses in my street into different groups. Can you do it in any other ways?
Problem
Here is a picture of nine of the houses in my street:
For accessibility: A 3-by-3 grid filled with houses.
The first house has a green door, a grey roof, 2 floors, a chimney on the left-hand side and 3 medium sized windows.
The second house has a black door, a grey roof, 2 floors, a chimney on the left-hand side, and 5 small windows.
The third house has a blue door, a grey roof, 3 floors, a chimney on the left-hand side, and 4 medium-sized windows and 1 large window.
The fourth house has a blue door, an orange roof, 2 floors, a chimney on the left-hand side, and 3 medium-sized windows.
The fifth house has a black door, an orange roof, 2 floors, a chimney on the left-hand side, and 5 small windows.
The sixth house has a green door, an orange roof, 3 floors, a chimney on the right-hand side, and 4 medium-sized windows and 1 large window.
The seventh house has a black door, an orange roof, 2 floors, a chimney on the right-hand side, and 3 medium-sized windows.
The eighth house has a green door, a grey roof, 3 floors, a chimney on the right-hand side, and 4 medium-sized windows and 1 large window.
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.
Getting Started
Student Solutions
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.
Camille from The Field School in Washington DC, USA found a way of sorting these houses that nobody else had suggested:
Chimney Placement; Chimney on Left, Chimney on Right
Well spotted, Camille!
If you would like to get in touch with us with some different ways of sorting these houses, please email us with your ideas.
Teachers' Resources
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.
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.