Shape Mapping
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
why?
Age
7 to 11
Challenge level
Problem
In this problem you're going to explore the changes that have happened to a shape and then choose a shape that shows the same change but with a different start.
Here's an example:
Image
|
is to | Image
|
as
Image
is to A, B, C or D below?
|
Image
A
|
Image
B
|
Image
C
|
Image
D
|
Well let's look at this first one together.
We need to decide what changed the square into a rectangle. I see that it appears to have been stretched to be twice as wide. We now have to look to see if there is a shape that looks as if that triangle has been stretched in the same way. Maybe you can see straight away.
We could look at the four suggestions.
A Looks smaller
B Could be OK
C Not as high
D Just two of them
B is the one which is stretched twice as wide.
Here are some for you to try.
1.
Image
|
is to | Image
|
as
Image
is to:
|
Image
A
|
or |
Image
B
|
or |
Image
C
|
or |
Image
D
|
2.
Image
|
is to | Image
|
as
Image
is to
|
Image
A
|
or |
Image
B
|
or |
Image
C
|
or |
Image
D
|
3.
Image
|
is to | Image
|
as
Image
is to
|
Image
A
|
or |
Image
B
|
or |
Image
C
|
or |
Image
D
|
When you've done these, you might like to invent some for yourself.
Get one or two ready for someone else to do.
Getting Started
Look carefully at the first two shapes. How would you
describe the change?
Try comparing the new shape to A, B, C or D. How would you describe each of these changes?
It might help to talk to someone else about your ideas.
Try comparing the new shape to A, B, C or D. How would you describe each of these changes?
It might help to talk to someone else about your ideas.
Student Solutions
Several of you sent very clearly explained solutions to Shape Mapping, including Dante from Newton Prep, Jack and Jemma from Eastwood Primary, and Jamie from Great Sankey High School. Dante says:
1. the small circle is to C because the triangle is elongated sideways and so is C
2.the triangle is to B because the square has a quarter taken off it and so does B
3.the u-shape is to B because if you rotate the first shape 180 degrees clockwise and add the shape you on to the highest point on the right of the original shape, that will also happen with the u-shape and B
Fantastic! Jamie also sent in his own challenge for us:
Image
as ...
Image
is to
Image
What do you think?
Can you explain why?
Thanks Jamie!
Teachers' Resources
This activity might seem quite straightforward but there is an opportunity to have worthwhile discussions about why some suggestions are not correct.
For example in the first worked one:
Image
|
could be said to relate to | Image
|
such that it is just two of the first square put together. In which case you could argue that
Image
|
relates to | Image
|
in the same way. Then you would be able to discuss what else has happened in the first that does not happen in the second.