Growth Point 4

Properties of Shape Growth Points activities

4. Definition of shapes using properties

States and understands conditions for defining key shapes.

Fold-a-shape

Materials: A4 paper.

Activity: Each student has their own piece of paper. Ask students, what do you notice about the shape the outline of the paper makes? Get students to run their fingers around the outside border and identify the attributes of the rectangle. Next get students to fold their page vertically.

Ask students, what shape do you have now? Why do we still call this a rectangle? How is it the same as the last shape? How is it different?

Now unfold the page back to its original size. Ask students to roll up the bottom left corner to the line which has been created in the centre of the page (see example below). This will create a sharp corner in the bottom right corner.

sk students, what shape do you have now? Why do we call this a quadrilateral? How is it the same as the last shape? How is it different?

Next roll the top left corner down to sit on the fold. Then fold the extra piece under so that it forms a smooth edge.

You should now have an equilateral triangle. Ask, what shape have you created? What has changed? What attributes does this shape have that are the same/different as the last two?

Fold the triangle so that two vertices meet, which will create a midpoint along the third side. Mark the midpoint with a dot using pencil. Repeat this on the other side. Where the two folds meet is the centre of the triangle. Again, mark it with a pencil.

Find the vertex that is opposite the midpoint you created. Fold it down so that it touches this point. Ask, what shape have you made? Why is it called a trapezium? Does it have any similarities to the previous shapes we have created?

Now unfold the vertex so that you have a triangle again. Using the same vertex, fold it again but this time stop at the midpoint in the centre of the triangle. What shape is this? It is also a trapezium, but it is different. What is different/the same about it?

Fold the last two vertices into the same midpoint. What shape is this now? Why is it called a hexagon? What are its special properties?

At the end, ask students to make posters about the various shapes they created and the properties they have.

Related key ideas: Features, properties, classification.

Exploring sides

This task has been adapted from PASMAP Book 1 (Mulligan & Mitchelmore 2016a) with permission from the authors.

Materials: Hexagon pattern/attribute blocks and cut-up shapes from Appendix 1.

Activity: Look at the cut-up shapes from Appendix 1. Ask students to sort the shapes into two groups: those which have sides of equal length, and those which don’t. How can you check that the sides are the same length? What is the same/different about the shapes in each group?

Draw students’ attention to the hexagon and ask them to compare it to the hexagon block. What is the same/different about the two hexagons? Why are they both called hexagons?

As a class, develop a set of rules for naming shapes.

Related key ideas: Features, attributes, classification.

Fitting shapes together

This task has been adapted from PASMAP Book 1 (Mulligan & Mitchelmore 2016a) with permission from the authors.

Materials: Cut-up shapes from Appendix 1 (bottom two rows only).

Activity: Students choose one of the shapes provided. Students then find another shape in the collection that is identical. Ask students to join their two shapes together to make a new shape.

Draw around the two shapes to show the new shape that has been made. Ask, how many different shapes can you make using those two identical shapes? What is the same/different about the shapes? Which shapes give you the most/least number of possibilities?

Related key ideas: Features, attributes, symmetry, orientation.

Exploring corners

This task has been adapted from PASMAP Book 1 (Mulligan & Mitchelmore 2016a) with permission from the authors.

Materials: Pattern/attribute blocks, bendy straws (or pipe cleaners).

Activity: Refer to ‘Square corners’ activity. Use bendy straws to show how the corners are formed when investigating squares. How did you make a right angle using the straws? How much did you have to bend or turn the arms? What position are they in?

Investigate the collection of pattern blocks. What do you notice about the corners of these shapes? Do any of them have right angles? (use the straws to prove/disprove). What other corners did you need to make?

As they bend and turn the straws, ask students to place their straw on a piece of paper and draw the corner they have found. What do you notice about all of your corners? Are they the same size? How do you think this affects the way a shape looks? It is important to get students to notice that the angle is the amount of turn between straws, not the length of the straws.

As a class, come up with a definition to describe a corner.

Related key ideas: Properties.

Triangle corners

This task has been adapted from PASMAP Book 1 (Mulligan & Mitchelmore 2016b) with permission from the authors.

Materials: Bendy straws (pipe cleaners), geoboards, rubber bands.

Activity: Refer to ‘Exploring corners’ activity. Using the straws, ask students to start with their straw bent so that both arms are touching. Students turn the arms of their straw until they get to a right angle. How do you know it is a right angle? Can you make one smaller/bigger?

Ask students to make a hypothesis, do you think the corners in triangles make bigger or smaller angles than a square? Students then make a variety of triangles using the geoboards and test the corners using their straws. Have a class discussion about what they have found.

Related key ideas: Properties.

Variation: Using geodot paper, students draw in the triangles they have made and measure the corners.

Using triangular grid paper, students investigate all the different corners they can make using various quantities of combined triangles.

Shape paths

This task has been adapted from PASMAP Book 1 (Mulligan & Mitchelmore 2016b) with permission from the authors.

Materials: Pattern/attribute blocks, pencil and paper.

Activity: Refer to ‘Exploring corners’ activity and the class definition of corners. Look at the collection of blocks. Brainstorm as a class all of the language you might use to describe corners and the sides of shapes.

In pairs, Student 1 use1 language (e.g. half turn, right angle, quarter turn, straight line) to describe a path to Student 2, so that the Student 2 can follow instructions to draw a shape.

For example, saying ‘Straight, right angle turn/half turn, straight, right angle/half turn, straight, right angle turn/half turn, straight, right angle/half turn’ will result in drawing a square or rectangle.

Related key ideas: Properties.

Variation: Use a variety of grid paper to draw the shapes and give more specific instructions.

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