This unit explores the teaching and learning of tiling patterns and tessellations. It is intended to support teachers working on the GCSE Linked Pair Pilot and is subject content for the Methods qualification. You will be invited to consider tiling patterns of polygons and what is important when developing students’ understanding of why polygons tessellate. You will then explore some strategies and activities which may support you in the planning of a group of lessons to include in your scheme of work focussing on tiling patterns and tessellations.
Objectives related to this topic are:
- solve problems in the context of tiling patterns and tessellations
- Resource sheets
- a laptop with Geogebra software (available as a free download)
- a digital camera
Activity 1: Getting Started
Many learners will engage with this topic because it can be made relevant to things they see around them. Working with a partner make a list of examples of tessellations that can be seen in your local environment – this could be tiles on the floor, windows in the school or you might know of some notable examples in your locality (perhaps in a local church or shopping centre).
You may want to take pictures of these tessellations in school to show to learners as an introduction to the topic (What is the same and what is different about these pictures?)
Activity 2: Sample learning activities
As a team use the following resource sheets to explore the suggested learning activities:
Tessellations 1 – Target 360
In this activity the teacher invites learners to select combinations of numbers that total 360
Tessellations 2 – Multiple representation activity
This activity may help the teacher to find out what pupils know already. Learners match diagrams, words and symbols. You may wish to create a poster by sticking down the cards and annotating the arrangement.
Tessellations 3 – Always, sometimes, never activity
Learners decide if statements relating to tessellation are always, sometimes or never true
Tessellations 4 – Additional activities to support ‘Always Sometimes Never’ Activity
This activity includes two Geogebra files to explore two of the statements form the Always, sometimes never activity in Tessellations 3.
Tessellations 5 – tessellation pictures
This resource can be used to encourage learners to use their knowledge of tessellations and tiling with real life patterns. You may choose to substitute these pictures with ones you took as part of Activity 1
Tessellations 6 – Duals
Learners explore the tessellating patterns that can be generated by drawing the duals of regular and semi-regular tessellations
Tessellations 7 – Working on an examination question
Learners are given a diagram from an examination question. They are given a framework in which to write down things that they know, and suggest possible questions that they could answer before being shown the questions that were posed in the examination.
Activity 3: So what’s good about these activities?
Read ‘Eight Principles for Effective Teaching’ on resource sheet Tessellations 8 (taken from Malcolm Swan in the Standards Unit ‘Improving Learning in Mathematics’ resource).
In pairs or small groups discuss the ways in which the sample activities fit and don’t fit with these principles.
Collect other Tessellation activities which fit with some of the Eight Principles. Sort these activities into a progression which can be developed into a unit of work to be included into your team’s scheme of work.
Embedding in practice
Hooks for Learning
At the end of the session, spend time recording some actions. What do you need to do:
- Next day?
- Next week?
- Next year?