1. This is a discussion activity to explore enlargement with a centre.
Students work in pairs or small groups and use the questions offered as prompts for their discussion. Mini-whiteboards may help students to record and explain their thoughts.
The questions in this presentation are prompts and are meant to be supplemented by questions from the teacher and other students in the class. My idea when putting this together was to link the change in the position of the line of an enlarged shape with the change in its length.
This is based on the Rays of Enlargement activity from the Strategy publication Teaching Mental Mathematics from Level 5: Shape and Space
I used Cabri to generate the images used in this PowerPoint – the interactive and dynamic elements of the dynamic geometry software add another (probably more important) element to enlargement and, when I use this with students, I use Cabri to explore how the final shapes change as the centre changes.
If you use this activity with a group please let me know how it goes.

2. How much longer than the 1st line is the 2nd line?
16cm
12cm
8cm
4cm
4th
3rd
1st
2nd
Where’s the 4th line going to be?
Where’s the 10th line going to be?
How much longer than the 1st line is the 3rd line?
How do you know?

3. How much longer than the 1st line is the 2nd line?
How much longer than the 1st line is the 3rd line?
Where’s the 3rd line going to be?
3rd
4th
2nd
1st
5cm
10cm
15cm
20cm
Where’s the 4th line going to be?
Where’s the 10th line going to be?
How would you work out where the 31st line will be?

4. How much longer than the 1st line is the 2nd line?
How much longer than the 1st line is the 3rd line?
How do you know where the second, third and fourth lines are going to be?
16cm
12cm
8cm
4cm
1st
2nd
3rd
4th

5. Combining all three diagrams
How do you know the size and position of the 17th triangle?
The 25th…?
The 103rd…?
16cm
12cm
8cm
4cm
5cm
10cm
15cm
20cm
How much bigger than triangle 1 is triangle 2?
How much bigger is triangle 3 than triangle 1? Than triangle 2?
What will the dimensions of the 10th triangle be?
And how far along the line will the top vertex be?