Cutting it out
I cut this square into two different shapes. What can you say about
the relationship between them?
Age
5 to 11
Challenge level
Problem
So, I started with a $10$ by $10$
green square,
I marked the half-way point along
the top edge,
I then drew a line from that point
to a corner at the base.
Image
Image
Image
Then I cut the corner piece out
along that line and made a change of colour, so I ended up with
these two shapes:
Image
What can you say about these two
shapes?
Can you say something about the
relationship between them?
Do you have any other ideas about
these two shapes?
What about starting with a rectangle like this ...
Image
Then you could mark it at half-way or elsewhere ...
Image
Image
What can you say now?
Getting Started
It might help to cut out your own shapes from a square piece of
card or paper.
Have you thought about measuring the shapes in some way?
Have you thought about measuring the shapes in some way?
Student Solutions
This activity probably gave a number of classes a good chance to explore shapes and their properties. It did not easily lend itself to solutions being sent in. However Angus, Gabs and Abi told us that they made rectangles.
Holly and Amy told us that they worked it out by using their brains and said;
It always helps us with maths or other subjects.
If you do have a go at this investigation, no matter how far you get, do send in your ideas. Teachers, you may want to send in a summary of your group's findings.
Teachers' Resources
Cutting it Out
So, I started with a $10$ by $10$ green square,
I marked the half-way point along the top edge,
I then drew a line from that point to a corner at the base.
Image
Image
Image
Then I cut the corner piece out along that line and made a change of colour, so I ended up with these two shapes:
Image
What can you say about these two shapes?
Can you say something about the relationship between them?
Do you have any other ideas about these two shapes?
What about starting with a rectangle like this ...
Image
Then you could mark it at half-way or elsewhere ...
Image
Image
What can you say now?
Why do this problem?
This problem is good for pupils to be able to explore the relationships between 2D shapes. The open-ended nature of the task means that pupils can pursue whatever excites them and some may surprise you. When different examples have been tried there is a chance to compare, analyse and possibly generalise.
Possible approach
It would be good to demonstrate how the two shapes are made from a square to begin this activity. Either using a drawing programme on the interactive whiteboard, or by having a large square made from card pinned on the board, show the children the process. Preferably do this in silence so that the group has to watch what you're doing very carefully. Once you have the two shapes, ask pairs to
talk about what you did. Share ideas amongst the whole group so that you clarify the 'rules' you were using.
Then, encourage pairs or small groups to discuss the relationships between the two shapes. You could ask children to consider what is the same and what is different about them. Give them plenty of opportunities to explore, discuss, argue, etc. You may like to bring them together to discuss what they've found out, which might include theories about area, side length, perimeter ... Encourage
learners to state reasons for the relationships and how they know.
They can then be introduced to generating their own two shapes in a similar way and they may have particular theories to test. Will the same relationship hold for different shapes? Will the same relationships hold for a line drawn differently in the square? Encourage these types of 'what if ...?' questions.
If learners made posters of their findings, the work could make an informative and engaging display.
Key questions
Tell me about your shapes.
What is the same about the shapes?
What is different about the two shapes?
What can you tell me about what you've found connecting the two shapes?
Possible extension
It might appeal to some children to investigate cutting into more than two pieces.