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Symmetry on the National Curriculum:
On the national curriculum, symmetry makes its appearance in year two, and it is practised throughout a student’s education.
The learning outcome for students is that:
- Students should be able to identify lines of symmetry in 2-D shapes and identify the properties of each shape including the number of sides and faces.
- Students should also draw lines and shapes using a straight edge and be able to read and write names for shapes that are appropriate for their word reading and spelling.
The Line of Symmetry:
What is it?
The line where the shape is cut exactly in half. This means that if you were to cut the shape in half (using your line of symmetry) both halves would be equal. If you were then to place them back together, the shape would still be the same.
Why do we use it?
The line of symmetry is a fundamental part of geometry, the world, and shapes. As mentioned above, a line of symmetry aids with measuring in equal parts, but it also helps us identify how to rotate, translate, and reflect other shapes.
Symmetry is in nature, but many people often do not recognise it, examples of symmetry in the world would be butterflies, flowers, feathers, some insects, animals, buildings.
The 2-D Shapes: Identifying the line of and their sides.
In maths, especially geometry, a 2-D shapes stands for a two-dimensional shape. These shapes are flat, and only have two dimensions: length and width. 2-D shapes do not have any thickness and usually only have two faces.
The 2-D shapes below are what students are expected to learn thoughout thir education. Three dimmesnional (3-D) shapes are also approached in KS1 and KS2.
Rectangles have only two lines of symmetry. But four sides.
There are four lines of symmetry in a square. There are also four corners.
Octagons have eight lines of symmetry and eight sides.
An equilateral (equal on both sides) triangle has three lines of symmetry and three sides.
Regular hexagons have six lines of symmetry and six sides.
A regular pentagon has five lines of symmetry and five sides too!
A circle can have as many lines of symmetry as you want – this is due to having no corners. However, a semi-circle has one line.
Activities for your classroom.
Understanding symmetry can sometimes be a challenge for those students who are not “visual learners”. To help, Emile has come up with seven activities that might be useful for your classroom.
This one can help make class more fun. Ask your students to write their names on paper along with a line of symmetry wherever they want – have them come up with funky shapes to decorate your classroom or assembly hall. To challenge those working at GD, ask them to have their line of symmetry across their name and at an angle.
Draw the Image
On your IWB using whatever graphics program you have available, draw a line of symmetry and a shape. Challenge your class to copy what you have drawn and draw what the shape would look like if the symmetry line were to cut the shape.
Are they still equal?
One of the classic symmetric activities is using paper planes.
There are lots of instructions online showing different ways of folding paper planes, and almost all of them need to use the knowledge of symmetry. Try to organize a competition within your class to see who can fold the best paper plane that flies the furthest.
Prepare some papers, fold them in half and ask your pupils to draw “half of a person” with the middle of the person meeting the fold.
Ask your pupils to cut out the people with scissors, unfold the paper and colour them. Let pupils vote for the one that looks the best. These when painted can make great classroom displays hung on washing lines or directly with blue-tack.
If you want to extend the activity, you can fold the papers in a curtain effect several times and have the dolls holding hands, to produce the classic paper doll look.
Prepare some images of national flags of different countries and ask pupils to identify the ones that have lines of symmetry.
Apps like Geometry with Emile can help your pupils answer hundreds of questions on symmetry without any marking. Challenge another class and see whose students work the hardest, make the most progress or are the best at geometry.
We have prepared some free printable worksheets for your classroom, you simply just have to download them below.
Can you students identify the trick question?