YEAR 9 SPRING TERM PROJECT – POLYGONS and SYMMETRY
Focus of the Project
These investigations are all centred on the theme polygons and symmetry allowing students to develop their
geometric thinking and reasoning skills over a period of time. Students should be encouraged to develop their
reasoning and communication skills, such as when exploring tessellations and the underlying angles in polygons
reasoning. The tasks here develop much of the geometry studied up until this point and serve as an excellent way to
consolidate skills and knowledge from Year 7 and 8.
How to run this project
Schools are free to run this project in whatever way fits their curriculum and allocation. For example, some schools
have “Maths days” where some of the tasks could be used. Others may wish to use lesson time at the beginning or
end of half terms to start some tasks and then let the students work through them as homeworks, either as
individuals or in small groups. You might want to set aside a regular slot within other lessons to allow students to
share their progress so far and discuss other options for continuing the project.
How to mark this project
As ever, we would never impose a system of schools, but this particular project would seem to lend itself very well to
peer-assessment. In addition, students could be asked to work in pairs or groups to develop their own marking
criteria. If the work is being done during lesson times, then progress can be checked and plenaries could be used to
reinforce key findings; perhaps students could be asked to share something they have discovered during that lesson.
Links to MM KS3 Programme of Study
This project has direct links to:
Year 7 Unit 10-12 – Properties of triangles, quadrilaterals and 2D shapes in rich contexts
Year 7 Unit 9 – Angles and angle properties
Year 9 Unit 11 – Angles in polygons
Links to National Curriculum KS3 Programme of Study
This project meets the requirements of the develop fluency, reason mathematically and solve problems elements
of the new KS3 Curriculum.
Several other elements of the Curriculum are directly met when using these projects:
 Use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, including regular
polygons.
 Apply properties of angles around a point
 Describe, sketch and draw using conventional terms and notations: regular polygons and polygons which are
reflectively and rotationally symmetric.
 Illustrate properties of triangles, quadrilaterals and other plane shapes using appropriate language
Suggested tasks for this Project
Tile patterns
This is a simple pattern investigation using tiles as the main manipulative or pictorial representation. Students could
use cubes or other manipulatives to support their learning.
Students explore patterns by considering the following questions (the list is not exhaustive and can be readily
changed or adapted and the idea of rotational symmetry can also be added to the list of questions):
Pattern A
(a) How many lines of reflection symmetry does pattern A have?
(b) Swap the position of one coloured tile and one white tile so that the new pattern has no lines of symmetry.
Draw the pattern you have made.
(c) Starting from pattern A again, change the colour of one tile so that the number of lines of symmetry doesn’t
change. Which tile do you change?
(d) Starting from pattern A, change the colour of 3 tiles so that the new pattern has 2 lines of reflection
symmetry. Draw the new pattern and its lines of symmetry.
(e) Rearrange the coloured tiles in pattern A to make a different pattern with 4 lines of reflection symmetry.
Draw the pattern.
(f) Use one white tile and 8 coloured tiles to make a square pattern with
(i)
(ii)
4 lines of reflection symmetry
1 line of reflection symmetry
Draw the patterns you have made.
(g) Can you make a square pattern using 8 coloured tiles and one white tile with no lines of symmetry? If so,
draw your square.
NRich also has a very nice tile pattern investigation here: http://nrich.maths.org/1886
Using tangrams
Using tangrams, students could be asked to explore which symmetrical shapes and designed could be make. This
could be for either reflective and rotational symmetry, or a combination of the two. Students will need to be
introduced to the correct notation and language of rotational symmetry.
Some examples:
Using Ls
This is another fairly open-ended task that can incorporate reflection or rotation symmetry or both. Given two L
shapes such as those below, how many ways are there of combining them to make shapes with reflection or rotation
symmetry or both. The L shapes can be modified to change the level of difficulty in the question OR more L shapes
can be added.
Regular polygons
In this task students are asked to explore regular polygons for reflective and rotational symmetry. This task offers
the chance to consolidate knowledge of polygons, regular polygons and angle facts.
Tessellations
Students learn about angles in polygons during the spring of Year 9. This task enables students to make connections
between angles in polygons and tessellation pattern.
Firstly, students could be asked to explore regular polygons and find which ones tessellate AND WHY.
Students should use interior angle facts to give reasons for their discoveries:
The next stage is to explore semi-regular tessellations. For these, students are permitted to use two or more regular
polygons to make a repeating pattern. There are a number of these tessellations:
Once again, students should discuss their findings in the context of interior angles, noting that the same shapes in
the same order meet at each meeting point.
The alphabet
In this task students are asked to explore the letters of the alphabet and to determine which have reflective
symmetry, which have rotational symmetry, which have both and which have neither.
This then lends itself well to using a Venn diagram to represent results. Venn diagrams for small letters and capital
letters could be produced for comparison.