Attractive Tablecloths

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Problem, Clue, Solution, Teachers' note

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Lesson idea. This problem encourages students to look at the structure of several symmetric patterns in the context of tablecloths and to explain how to generate rules for finding the number of colours required. There are five 5x5 square tablecloths to work through, each satisfying a different symmetry rule.

Teaching approach. This lesson idea is about applying and consolidating^(ta).

The collection of NRICH activities are designed to develop students capacity to work as a mathematician. Exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, justifying, proving are all at the heart of mathematical thinking.

This particular resource has been adapted from an original NRICH resource. NRICH promotes the learning of mathematics through problem solving. NRICH provides engaging problems, linked to the curriculum, with support for teachers in the classroom. Working on these problems will introduce students to key mathematical process skills. They offer students an opportunity to learn by exploring, noticing structure and discussing their insights, which in turn can lead to conjecturing, explaining, generalising, convincing and proof.

The Teachers’ Notes provided focus on the pedagogical implications of teaching a curriculum that aims to provoke mathematical thinking. They assume that teachers will aim to do for students only what they cannot yet do for themselves. As a teacher, consider how this particular lesson idea can provoke mathematical thinking. How can you support students' exploration? How can you support conjecturing, explaining, generalising, convincing and proof?.

Resource details
Title	Attractive Tablecloths
Topic
Teaching approach
Learning Objectives	Applying and consolidating
Format / structure
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Table of contents
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Related ORBIT Wiki Resources	The following NRICH resources have the teaching approach "[[Teaching Approaches/|]]": Some use of "" in your query was not closed by a matching "". The following NRICH resources have the topic "[[Topics/|]]": Some use of "" in your query was not closed by a matching "".
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Files and resources to view and download	The following parts are available: Problem, Clue, Solution, Teachers' note. The original problem is available on the NRICH website here.
Acknowledgement	The NRICH website http://nrich.maths.org publishes free mathematics resources designed to challenge, engage and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support for teachers by publishing Teachers’ Resources for use in the classroom.
License	CC-By, with kind permission from NRICH. This resource was adapted from an original NRICH resource.