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This lesson has five grade 8 and 9 maths problems for higher-ability students. Each question requires students to connect multiple high-level topics within a single problem.

The five questions connect the following topics:

- Solving quadratic equations arising from algebraic fractions
- Deriving the equation of a tangent to a circle using circle theorems.
- Using the Cosine rule, special triangles and surds are used to calculate a perimeter of a triangle.
- Calculating the volume, mass and density of a composite solid involving a frustum and hemisphere
- Using interpolation to compare a histogram with a box plot.

Here is a sample of three questions from the five.

Click here to view the video.

In this question, students make a comparison between two crops of beans. To make this comparison, they will need to use interpolation to estimate the interquartile range and median from the histogram.

Their comparison should use these values to comment on the spread and measure the central location for each crop.

Students work out the average density of the composite solid. To do this, they begin by working out the individual volumes of the frustum and hemisphere.

Should the students need further prompts, I encourage them to present the information within a table as shown below.

By laying out the information in this way, most students could calculate the total volume and mass of the composite solid.

My name is Jonathan Robinson, and I am passionate about teaching mathematics. I am Head of Maths in the South East of England and have taught for over 15 years. I am proud to have helped teachers worldwide continue engaging and inspiring their students with my lessons.

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