Growth Point 2

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

Materials: Collection of 4 coloured counters per pair.

Activity: As a class, discuss the terms ‘front, back, left, right’ and how these movements can be enacted. Play a game of Simon Says using these words to move students around the room.

In pairs, students nominate one student to be the walker and one to place the counters. Student 1 places the counter on the floor where their partner is standing. Teacher then gives Simon Says directions again. Student 2 will follow these directions (e.g. take two steps forward) and Student 1 will place the counter on the floor where the student has stopped. Repeat this three times so that all four counters have been placed on the floor where Student 2 has stopped each time.

Go on a gallery walk and look at how the counters have been placed by different groups. Ask, what do you notice? Are they all the same? Why is there more space between some people’s counters? (Notice the size of steps, with each step being a ‘unit’ of measure).

Discuss how you can describe each step. It can be described as a slide (or translation) and that slides are like a step in the same direction.

Related key ideas: Transformation, partitioning, visualisation.

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

Materials: Collection of four coloured counters per pair, grid paper, one six-sided die, one blank die labelled with directional language (e.g. forward, back, left, right).

Activity: Reflect on the activity ‘Sliding people’. Ask, how did we describe each step? (as a slide or translation). Explain that the steps in this activity are represented by the grid paper so that all steps are the same size. In pairs, students play a game where Student 1 rolls the two dice to give the directions (e.g. two slides forward) and Student 2 slides the counter across the grid paper.

Related key ideas: Transformation, partitioning, visualisation.

Variation: Ask students to colour or mark their pathway as they go and then record their movements at the end of the game.

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

Materials: Unifix.

Activity: Patterns are often created by repeating transformations. In pairs, students choose the three identical unifix that can be joined together to create a base for their pattern. Describe that this will be their ‘unit of repeat’. Each student now needs to create a unifix train that is four units of repeat long.

Place the trains side-by-side. Ask, what do you notice? Why are they identical? Students then slide one train across, one unifix at a time until it matches itself again. This is called slide symmetry. How many unifix did you need to slide before they matched again? (i.e. the identical unit of repeat). How many times can you do this? Why does this happen?

Students gallery-walk around the room and investigate sliding with the other trains that pairs of students have made.

Related key ideas: Transformation, symmetry, visualisation.

Variation: Make trains of different ‘unit’ lengths and describe the translation. Prompt students to make a connection between the length of the unit and how many slides they require before their trains match.

Make one ‘unit’ which students can transfer onto grid paper using coloured pencils. Students then iterate that unit along the paper, repeating and recording their pattern.

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

Materials: Clock with movable hands or student-made clocks or spinners.

Activity: Look at the clock (or circle). What do you notice about the way the hands move? Discuss the term ‘turning’ and the words students can use to describe turns. Teacher then gives instructions for students to turn the hands or spinner (e.g. full turn, half turn clockwise, quarter turn anticlockwise). Encourage students to mark in the turns as they go, to show where the hand stopped.

Play a game of Simon Says using these words so that students can act out the turns used when performing translations.

Related key ideas: Transformation, visualisation.

This task has been adapted from PASMAP Book 2 (Mulligan & Mitchelmore 2016b) with permission from the authors.

Materials: Square grid paper, coloured square tiles or cubes.

Activity: Give each pair a set of 24 tiles or cubes (two colours, 12 of each). Ask them to assemble them so that they are in a four by six array that shows the two colours forming a pattern. Go on a gallery walk around the room.

How many different patterns are there? How are they the same/different? Which directions are the patterns going in? Are there any patterns that have not been made? Encourage the students to create/look for patterns that have more than two tiles or cubes in a repeating unit.

Students then choose a pattern to represent a repeating pattern using square grid paper. Ask students to outline the ‘units of repeat’ on their grid paper. Ask, what do you notice? Explore the idea of two-dimensional patterns, meaning those that are both horizontal and vertical. Explain that patterns like these are called ‘tessellations’ because they repeat without having gaps or overlaps.

Related key ideas: Transformation, symmetry, visualisation.

Variation: Go on a hunt for tessellations around the school. Where do we see them? What is the same/different about the various tessellations we have found?