This is a level 3 link geometry activity from the Figure It Out series.
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investigate symmetry
FIO, Geometry and Measurement Link, Punch a Pattern, page 2
hole punch
classmate
In this activity, students use symmetry to determine how to fold squares of paper and make a series of holepunch patterns.
It’s a good idea to precut lots of squares before setting a group to work on this activity because they will get through quite a few! If you cut the squares 10 cm x 10 cm (memo cube size), you will get 6 from a recycled A4 sheet. This size is fine for most of the problems, although students may prefer to work with larger squares
when trying to create the pattern in question 1g, which requires some tricky folding.
At first, let the students experiment and use trial and improvement to make each pattern. After they have made several, encourage them to look back at the holes and folds and see what they can observe. Ideas might include:
You could give the students a photocopy of the page in the student book and have them predict the folds by sketching the lines of symmetry. If they have problems with this, suggest that they draw dotted lines between each hole and its buddy and then draw the line that goes through the midpoint of the dotted line,
at right angles to it. This is the axis of symmetry or mirror line. They can check their predictions by folding a paper square, using the lines they drew as guides, then punching a hole in it.
Ask “What strategies are you using to help you work out where the folds go?” Ideas might include:
Encourage your students to notice and explain relationships and to make predictions:
• If I fold a piece of paper in half, in half again, and in half again, and then punch a hole through all the layers, how many holes will I have? Can you convince me you’re right without using the paper and punch? (The answer is 8. See if the students realise that if they punch a hole through 8 layers, they will get 8 holes. So the number of holes tells them the number of layers.)
After the activity, encourage reflective thinking by asking questions such as:
Activity One
1. Here are the folding lines you will need to make for each of the patterns:
2. a.–b. Practical activity
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/punch-pattern at 10:49pm on the 26th February 2024