Rich tasks
These are open-ended activities.
- The first task challenges students to find whether it is possible to create 50 different symmetrical patterns with two colours on a 3 x 3 grid. Students can then explore how many patterns they can make on a 4 x 4 grid.
- The second task asks students to find examples of symmetry in photographs.
The tasks can be given at the start of a topic, done as the students gain enough knowledge to complete it, inserted into a topic at an appropriate place, or given as a homework task.
Animals like symmetry
- Photo wall
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1. Animals like symmetry
- Ensure students understand the concept of symmetry and then encourage students to be systematic in their approach to this activity so that they don’t inadvertently repeat a pattern or overlook a possible combination.
- Students could be divided into groups where each participant is asked to find all the possible patterns with one square shaded, two squares shaded etc. Students who work more quickly could then be given tasks with more possible combinations.
- Encourage students to share and compare the patterns they have created. This might include discussion around whether patterns are actually different or whether they are the same pattern in a different orientation.
2. Photo wall
- Students could find symmetrical photos on the internet or take their own if they have access to digital equipment
Symmetry page 278
- Know that when a shape has line symmetry the two halves fold exactly onto each other.
- Use a mirror to check that a shape is symmetrical and find where the lines of symmetry lie.
- Know that when a shape is rotated (turned) around a point, and looks the same in more than one place, it has rotational symmetry.
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Teacher notes
- Depending on prior knowledge and experience students will need to practise locating the lines of symmetry within an object using a mirror, or finding rotational symmetry by turning a tracing on a piece of paper or sheet of firm plastic over the original image. Eventually students will be able to manipulate mental images to determine the reflective and rotational symmetry of a shape, however it is important to provide and encourage the use of these materials for as long as necessary.
Teachers may choose to revise fractions using some of the natural links that arise when exploring symmetrical shapes, for example, the practicals ‘Animal symmetry’ and ‘Circle symmetry’ on page 279 of the student book. The lines of symmetry in a symmetrical shape create pieces of equal size, so students can be encouraged to notice that one mirror line creates two equal pieces and each piece is ½ of the original shape.
Making patterns page 283
- Create symmetrical patterns using reflections, translations and rotations.
- Identify the transformation which has created the pattern and predict the next item in the pattern.
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Teacher notes
- At Level 2 the mathematical vocabulary of translation, reflection or rotation is introduced. Some students may need to have a visual prompt available or be reminded that: translation = slide; reflection = flip and rotation = turn, but they should also be encouraged to use the mathematical term.
- Encourage students to create and look for reflective patterns across horizontal, vertical and diagonal mirror lines.
- Sometimes students may notice that the same image has both reflective and rotational symmetry. Encourage students to look closely at these examples and discuss why this is true for some shapes and not others.
- Advising students to begin at the mirror line or centre of rotation and work out when drawing a reflected or rotated image can be helpful.
- Encourage students to pay particular attention to angle and distance of an image across a mirror line. Using grid paper is useful especially for students who are having difficulty.
- Students may also need mirrors, tracing paper or firm plastic to check patterns they are creating or completing, so it is a good idea to have these available.
Tessellations page 286
- Know that shapes tessellate if they fit together without overlapping or gaps.
- Create a simple tessellating pattern with geometric shapes.
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Teacher notes
- Not all shapes will tessellate. Sometimes students will notice that a tessellation with one shape will create a “gap” that could be filled with another shape. Talk about these observations and encourage students to think about the properties of shapes that can and those that cannot tessellate.
- There are many interesting examples of tessellating pictures online. While students at this level will only be tessellating simple shapes, it is interesting for them to see how clever and complex these tiled patterns can become.
