Drawing a regular 3.5-sided polygon - Encouraging thinking skills (KS3 & KS4)

Oct 20, 2026

Training material for MathsConf 32 (Summer 2023) by Greg Thomas, focused on encouraging thinking skills in KS3 and KS4 through challenging geometry tasks. The sessions aim to push students beyond comfort zones and prompt careful use of mathematical definitions and language. Activities include exploring prime numbers, building reasoning with sums of integers, finding maxima, interpreting multiple representations, and creatively constructing regular 3.5-sided and other fractional-sided polygons to generate conjectures and investigate rotational and angle patterns.

LanguageEnglish

CategoryExam

FormatPPTX

Pages25

Reading Time1 h 3 min

AccessFree to download

Welcome

Aims

Thinking skills (and you thought you knew maths)

Prime numbers

Where a + b + c = 10

Find the highest value you can

Multiple representations

Let’s get creative

Draw a regular 3.5-sided polygon

Draw regular 4.5- and other fractional-sided polygons

Where does the 3.5 fit in?

Conjectures about regular n-gons

Discussion points

Who to use it with

How to adapt and differentiate

Level 2 Certificate in Further Mathematics (L2FM)

Why choose L2FM

Who is it for

Qualification aims

Resources

Planning, Teaching and Assessment tabs

MathsConf past presentations

All About Maths pages

Get in touch

Drawing a regular 3.5-sided polygon: Encouraging thinking skills (KS3 & KS4) Greg Thomas MathsConf 32 1 Summer 2023 Copyright © AQA and its licensors. All rights reserved. Welcome 2 Aims: To move students outside of their comfort zone To encourage thinking skills To make you consider mathematical definitions and language 3 Thinking skills (and you thought you knew maths) Copyright © AQA and its licensors. All rights reserved. Prime numbers What’s your definition of a prime number? 4 Copyright © AQA and its licensors. All rights reserved. Where a + b + c = 10 (and a, b and c are integers) 5 Find the highest value you can: Copyright © AQA and its licensors. All rights reserved. 6 What are these multiple representations of? Copyright © AQA and its licensors. All rights reserved. Use a protractor, pencil and ruler to draw a regular 5-sided polygon. Copyright © AQA and its licensors. All rights reserved. 7 Let’s get creative Use a protractor, pencil and ruler to draw a regular 3.5-sided polygon. Copyright © AQA and its licensors. All rights reserved. 8 Let’s get creative Use a protractor, pencil and ruler to draw a regular 4.5-sided polygon. Copyright © AQA and its licensors. All rights reserved. 9 Let’s get creative Copyright © AQA and its licensors. All rights reserved. 10 Where does the 3.5 fit in? What conjectures could students make about regular n-gons? If given a regular 3.2-gon, what would the angles be? How many sides would it have? How many rotations would it take for the last side to meet the first side? How are a 3-gon, a 3.5-gon and a 3.2-gon the same/different? Add a 4.7-gon to the picture. Why do some have lots of rotations and others only have one or two? What type of regular n-gon will have many rotations before the last side meets with the first side? What type will have few rotations? How do the angle measures change as n-increases? Why? Can we build a regular ∏-gon? If so, what would it look like? If not, why not? Copyright © AQA and its licensors. All rights reserved. 11 Questions to consider Copyright © AQA and its licensors. All rights reserved. 12 Polygons Copyright © AQA and its licensors. All rights reserved. 13 How did you feel when you were given this task? Credit: © iStock.com/picture Copyright © AQA and its licensors. All rights reserved. 14 Discussion points Who might you use this with in the classroom? How might you adapt it? How might you differentiate it? What are the key questions? (Patterns within the ball of string) Copyright © AQA and its licensors. All rights reserved. 15 Human stars with a ball of string Credit: © iStock.com/malerapaso Copyright © AQA and its licensors. All rights reserved. 16 Level 2 Certificate in Further Mathematics L2FM is intended to be taught alongside or after GCSE Maths Higher tier (not as a replacement). It is designed to prepare students for the rigour of A-level Maths and Further Maths but doesn’t infringe upon the content of AS. It features demanding topics including matrices and differentiation. It doesn’t discount against GCSE Maths and does not get any performance points. Copyright © AQA and its licensors. All rights reserved. 17 Why choose Level 2 Further Maths? (L2FM) It’s for more able maths students, with a focus on higher-level thinking and reasoning. It is designed to stretch students, supporting what they learn in GCSE Maths. It gives students the chance to encounter more challenging maths, useful for those likely to study maths after GCSE. With over 25,000 entries each year, we help students realise their potential. Copyright © AQA and its licensors. All rights reserved. 18 Who is it for? We designed the L2FM qualification to: fill the gap for high-achieving students needing more stretch and challenge than GCSE Maths provides focus on higher-order technical proficiency, rigorous argument and problem-solving skills and to help prepare students for further study of maths expose students to a wider range of maths problems encourage more students to continu

FAQs

What learning aims does the session state for encouraging thinking skills?

It aims to move students outside their comfort zone, encourage thinking skills, and make students consider mathematical definitions and language.

How does the activity use the idea of drawing regular fractional-sided polygons?

Students are instructed to use a protractor, pencil, and ruler to draw a regular 3.5-sided polygon, then extend the work to other regular n-gons and related constructions.

What kinds of questions are suggested when investigating regular n-gons and the 3.5 case?

The slide prompts conjectures about regular n-gons, explores angles for a 3.2-gon, compares 3-gon/3.5-gon/3.2-gon, considers rotations for sides to meet, and asks how angle measures change as n increases.

Oct 20, 2026

Uploaded by Lucas Martin