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3. Dynamic imagery
Uses dynamic imagery to visualise manipulation of shapes by transforming and rearranging.
Computer shapes
Computer shapes
Materials: Electronic device which has a drawing tool function (e.g. Word, PowerPoint).
Activity: Students use a drawing tool function on their device to create a 2D shape. Use control functions to make a copy of the shape and slide the shape beside the original. Ask students to identify their original and the copy. Are they identical? What action did you take to get from the first to the second shape?
Then ask students to use the rotate function to change the position of their shape. Ask, what is the same now? What has changed?
Trial this with a variety of 2D shapes and discuss which shapes appear to stay the same and which appear to look different.
Related key ideas: Symmetry, orientation, transformation, visualisation.
Variation: Use digital technology to replicate many of the same shape to see which shapes tessellate, with and without rotations. Why does this happen? What makes shapes fit together?
Tangram challenge
Tangram challenge
Materials: Multiple sets of tangram pieces (BLM template or commercially produced), Appendix 5.
Activity: Show students the completed tangram and ask, what shape is the puzzle? How is it partitioned? How do the pieces fit together? What shapes do you recognise?
Using a puzzle, ask students to reassemble the completed square. Ask, what strategies did you use to put them back together? Which parts were easy/difficult and why?
Present the students with the two-way table in Appendix 5. Students work in pairs or small groups to work out which of the problems are possible
Related key ideas: Symmetry, orientation, transformation, visualisation.
Variation: Challenge students to create as many symmetrical shapes as possible using the tangram pieces. Present students with examples of tangram pictures that they need to recreate (see examples below).
Picture turns
Picture turns
This task has been adapted from PASMAP Book 1 (Mulligan & Mitchelmore 2016a) with permission from the authors.
Materials: Pattern/attribute blocks, A4 Paper, split pins.
Activity: Students choose two blocks to create a shape which they will trace around onto paper and cut out. Using a split pin, fasten the shape onto another piece of paper. While the shape is in its starting position, students trace around the shape so it is recorded onto the paper below.
Ask the students to turn their shape a quarter turn clockwise and trace around it. Repeat this process in quarter turns until the shape has reached its original position. How many times did we turn/rotate our shape to get back to the starting position? Do you think the same thing will happen if we go anticlockwise? Repeat the quarter turns anticlockwise. What did you notice? What is the same?
Remove the split pin and shape. Look at the drawings on the paper. What do you notice about the drawings? Are there parts which are the same/different? Why? Look at different combinations across the class and discuss what happens to the different shapes when rotating them.
Related key ideas: Transformation, symmetry, visualisation.
Variation: Investigate which attribute blocks have or don’t have rotational symmetry. What features do they have in common?
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