Problem solving with complex 2D shapes
I can use my understanding of 2D shapes to solve problems.
Problem solving with complex 2D shapes
I can use my understanding of 2D shapes to solve problems.
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Lesson details
Key learning points
- When problem solving, consider whether any elements are familiar from other areas of maths.
- Keep the goal in mind, it is easy to get distracted by too much information.
- The size of a sector of a pie chart can be scaled to reflect the population size.
Keywords
Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.
Compound shape - A compound shape is a shape created using two or more basic shapes.
Composite shape - A composite shape is an alternative for a compound shape.
Pie chart - A pie chart (pie graph) is a circular graph where sectors represent different groups proportionally.
Common misconception
For the problems with squares inscribed inside circles, pupils may think that the length of the square is equal to the diameter of the circle.
This would be the case if the circle was inscribed inside a square. But when the square is inscribed inside a circle, the diagonal length of the square is equal to the diameter of the circle.
To help you plan your year 10 maths lesson on: Problem solving with complex 2D shapes, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Problem solving with complex 2D shapes, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the 2D and 3D shape: compound shapes unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.A is a circular graph where sectors represent different groups proportionally.
Q2.Jacob wants to plot a pie chart to represent the data in the table. What angle for the sector representing 'museum' should Jacob use?
Q3.A circle has diameter 10 cm. Its area is ____$$\pi$$ cm².
Q4.The diagram shows a sector of a circle with radius 10 cm. The angle at the centre of the sector is 70°. Which calculation would find the area of the sector?
Q5.The diagram shows a sector of a circle with radius 12 cm. The angle at the centre of the sector is 60°. The area of the sector is $$\pi$$ cm².
Q6.The diagram shows a sector of a circle with radius 12 cm. The angle at the centre of the sector is 60°. The perimeter of the sector is cm (to one decimal place).
Assessment exit quiz
6 Questions
Q1.The diagram shows a square inscribed inside a circle. The length of the square is 6 cm. What is the diameter of the circle?
Q2.The diagram shows a square inscribed inside a circle. The diameter of the circle is 6 cm. Work out the length of the square.
Q3.The diagram shows a square inscribed inside a circle. The length of the square is 8 cm. The area of the circle is $$\pi$$ cm².
Q4.The diagram shows a square inscribed inside a circle. The diameter of the circle is 8 cm. The area of the square is cm².
Q5.The diagram shows a square inscribed inside a circle. The diameter of the circle is 12 cm. Which calculation would find the area of the shaded region?
Q6.The diagram shows a square inscribed inside a circle. The length of the square is 12 cm. The area of the shaded region is cm² (to one decimal place).