Measurement & Geometry

Chapter 15 | Symmetry and transformations

These are problem solving open-ended questions related to the transformations of reflection, rotation, translation and enlargement. The tasks can be used at any point in the chapter. They can be given at the start of a topic and done as the students gain enough knowledge to complete them, inserted into a topic at an appropriate place or given as homework or extension.

Draw and answer questions about reflections, rotations and translation of objects.
Recognise the invariant properties under reflection, rotation and translation. This is further developed in book 2.

Teaching ideas

Rotation

Rotating shapes (Teacher resource sheet 31)
- This link displays shape cards with a letter on each vertex of the shape.
- You could print these out and then push a pencil through the middle to illustrate the rotation.
- You could ask the students questions such as “Which letter will be in the bottom left-hand corner if the shape is rotated clockwise by 90º? What will it look like?

Translation

A game of four directions
Pair the students up.
Give each student a grid.
Each student places their counter on the bottom left hand corner of their grid.
The students now sit back to back.
The first student slides their counter to a new position and describes the movement to the other student using words like “slide the counter 3 squares to the right and 2 squares up.” The second student moves their counter following the instructions.
Both check that their counters are in the same place.
Swap roles.

Reflection

What time is that? (Teacher resource sheet 30)
- This link displays some clocks reflected in a mirror.
- Tell students they are at the hairdressers and they can only see the reflection of the clock in the mirror. They have to be home by a 10 o’clock, b 11 o’clock, and c 1/4 to 3. The hairdresser tells them they will be finished in 5 minutes, plus it takes 15 minutes to get home. Will they get there in time?
Cut outs
You could give the students some cut out shapes and ask them to flip them over the mirror line to see what the reflection looks like.
Emergency
Ask students to write the word AMBULANCE as they see it in the rear view mirror of a car. Discuss the fact that some ambulances have it written so that you can read it when you look in the rear view mirror.

Teacher notes

Rotation

Students often have difficulty visualizing rotation. It is useful to have some shapes with letters or shapes in corners for them to work with until they get more practice at visualizing. Suggest that they try to visualize first and then rotate the shape to check.
Emphasise that the centre of rotation always stays in the same place as a shape rotates.

Translation

Use a counter on a grid or game board to demonstrate the sliding movement from one place to another. Ask students to give examples of how they would describe the movement to another person.

Reflection

Students often get confused between finding lines of symmetry and drawing reflections. Point out that when we draw a reflection of a shape in the mirror line, the resulting shape is symmetrical.
Emphasise the results of page 252 Activity 3 question 13. Shape, angles, lengths and area do not change. Only orientation changes.
Some students will draw a translation of the shape instead of a reflection. Encourage them to check using a mirror or check that each corresponding point on the shape and its image are the same distance (perpendicular or at right angles) from the mirror line.
Some students find reflecting in diagonal lines difficult. Again encourage them to check using a mirror. Some may find it easier to draw the image points the same distance (perpendicular) from the mirror line to create an outline.
For the Puzzles on page 252 encourage students to decide which digits look the same when reflected and also if any digits are a reflection of another, such as 2 and 5.