Links to Lesson Resources (Members Only)
Students recap the length and area scale factor using two similar pentagons. For example, to work out the area of the larger pentagon marked x, encourage students to begin by finding the length scale factor using a matching pair of sides. From this, they can work out the area scale factor using the relationship AreaS.F.= LengthS.F.2.
Students should clearly show how they worked out the area scale factor as a similar approach will be needed later in the lesson when finding the volume scale factor.
Prompts / Questions to consider
In the central part of the lesson, present the three cubes on the board and ask students to work in pairs to consider any relationship between the cube lengths, surface areas and volumes.
After a few minutes of processing time and small group discussions, present the table below and ask students to complete it using their ideas so far.
Solution
Using the table above as a guide, students should now be able to define the relationship between the length and volume scale factor as VolumeS.F.= LengthS.F.3
At this point, the teacher could work through questions 1 and 2 on the second slide as shown in the video above with the class attempting Q3 on mini-whiteboards.
Prompts / Questions to consider
The plenary challenges students to work out the volume of a frustum by considering it as two similar square-based pyramids. Students could prove that the two pyramids are mathematically similar using angles in parallel lines.
All students should include clear diagrams as part of their work as this will help them identify how to use the relevant scale factors.
Prompts / Questions to consider
More able students could work with shapes involving fractional scale factors and consider the relationship between the volume and area scale factors. Less able students may benefit from working with solids with integer scale factors.
How to teach problem solving with angles in polygons through scaffolding.
Explore geometric series in our A-Level Maths tutorial. Perfect for students/teachers, with resources to download at mr-mathematics.com.