Dear Family, your Operation Maths guide to Symmetry
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Dear Family, below is a brief guide to understanding the topic of symmetry, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about symmetry. The digital resources are organised according to approximate class level:
Understanding Symmetry
Symmetry is introduced in second class and is a stand-alone maths topic in only second to fourth classes. That said, it also features as part of the topic of 2-D shapes in fifth and sixth classes where the children in those classes are asked to “classify 2-D shapes according to their lines of symmetry”.
While there are different types of symmetry (which children will explore deeper in second level maths), the primary curriculum specifies line symmetry, also known as mirror symmetry, reflective or reflection symmetry.
In school, the children will often have the chance to use special child-safe mirrors to explore this concept, and to look at the mirror image of arrangements of various items. It would be really valuable for the children to be able to do something similar at home, with any suitable small mirrors that might be available (Tip: mirrors with straight outside edges rather than curved edges are better for this, eg a small mirror from the lid of a make-up pallet). Draw your child attention to the way in which the pattern appears to be reversed e.g. in the image above the order of the real cubes is orange, yellow, green, but in the reflection we see green, yellow, orange.
Practical Suggestions for Supporting Children
- Symmetry at home: explore the symmetry that is all around you:
- Look for examples of symmetry in clothes, furniture, windows, dishes, ornaments, doors, etc.
- If going for a walk, look out for examples of symmetry in nature eg flowers, leaves.
- Is there symmetry in any of the numbers we write? What about letters of the alphabet; lower-case and/or upper case (capital letters)? What about the letters in your name?
- Take some time to use mirrors to explore symmetry (as mentioned above, small square, or rectangular, cosmetic mirrors are ideal for this). Using the mirrors the children can create and check symmetrical patterns using cubes, counters, objects etc. They can look for symmetry in numbers and capital letters (eg the letters on the cover of their Operation Maths book, other books, newspapers, boxes, food containers etc). Can your child answer the following questions?
- What letters or numbers look the same in the mirror? What shapes or images look the same in the mirror?
- Can you put the mirror along the middle of any letters and numbers so that they look complete? Does this work with any other shapes or images?
- For some shapes/numbers/letters, is there more than one than one way, that the mirror can be placed?
- Using the mirrors the children can create and check symmetrical patterns using pieces of lego, blocks or other suitable objects etc.
- Place a mirror to the right or left of the arrangement. Describe what can be seen in the reflection.
- Change the position of the mirror, perhaps above or below the arrangement. Does the reflection in the mirror look the same? Is it different? How? Why?
- Repeat using different items and/or arrangements. Ask your child to predict what the mirror image will look like before they actually look into the mirror.
- If your child has his/her Operation Maths twenty frame at home (free with Operation Maths 1 and 2) it can be used to create a symmetry challenge (see below). One person uses counters, lego pieces, buttons etc, to make an arrangement and the other person makes its mirror image. You could also do something similar with a chessboard/draughtboard and the playing pieces.
- Art and Maths are often very connected, and this is especially the case with symmetry. Why not try making a symmetrical butterfly, symmetry painting and/or your name as symmetrical art? For more art ideas search Google for symmetry art for kids. Older children could also explore mirror writing and how Leonardo da Vinci used it.
Digital Resources for Second Classes
In second class, the children are being introduced to simple symmetry. If your child knows very little about symmetry already, a good starting point is to watch some of the videos below.
Symmetry: A series of video lessons from White Rose Maths, including for Year 2, Lines of Symmetry, Draw the Whole.
Intro to Symmetry: A YouTube video that introduces and explores reflectional (mirror) symmetry.
Symmetry Land: Learn about lines of symmetry through this song from Numberock
Symmetry Painter: This simple activity allows you to paint on one side and watch as the symmetrical image magically appears on the other side!
Symmetry Matching: 3 different games where you choose the matching symmetrical half.
Symmetry Sorting: 3 different games where you decide if the image shown is symmetrical or not symmetrical.
I know it – Symmetry: Interactive quiz for Grade 1. After, you could try the Grade 2 quiz
Pattern Blocks: Use these interactive pattern blocks to make numerous designs, pictures etc on one side of the screen. And then challenge yourself, or another, to complete the symmetrical image on the other side.
Symmetry: A selection of simple games from ixl.com. You can do a number of free quizzes each day without having a subscription.
Math Games: a simple symmetry game ideal for beginners.
Digital Resources for Third and Fourth Classes
NB: Children in these classes may also enjoy the links for second class above
Symmetry: A series of video lessons from White Rose Maths, including for Year 4 Lines of Symmetry and Complete a Symmetric Figure.
Khan Academy – Symmetry: Watch the videos and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other topics/grades.
Vertical and Horizontal Lines of Symmetry: learn about different types of lines of symmetry from Mashup Math
Symmetry Shapes: You will be shown a shape and you must create the reflection or mirror image of the shape as reflected in the line of symmetry. Click on the grid squares to colour them in, and then click check to see if you are correct.
Symmetry Counters: Similar to the game above, an arrangement of counters will be shown and you move the other counters to create the reflection or mirror image of the arrangement, as reflected in the line of symmetry.
Symmetry Invaders: Can you complete the symmetrical images to win this space invaders-type game?
I know it – Symmetry: Interactive quiz for Grade 3. After, you could try the Grade 4 or Grade 5 quiz
IXL: A selection of symmetry games from ixl.com. You can do a number of free quizzes each day without having a subscription.
Maths is Fun: Background information on reflection (mirror) symmetry
Math Games: a whole suit of symmetry games, for a range of class levels; start with second class and work your way up.
Line Symmetry Quiz: Identify the number of lines of symmetry in each shape by dragging the answers into the correct places.