Geometrical Reasoning, Golden Ratio, Algebra - solving quadratics
Key Stage: 4 ★★★
If the three triangles in the diagram have the same area, can you show that the sides of the rectangle are divided in the golden ratio
This problem offers opportunities to experience several key problem-solving processes including making a useful transformation into a simpler task and making use of algebra to represent the situation before interpreting results as meaningful solutions within the problem context.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
Key Stage: 4 ★★★
If the three triangles in the diagram have the same area, can you show that the sides of the rectangle are divided in the golden ratio
This problem offers opportunities to experience several key problem-solving processes including making a useful transformation into a simpler task and making use of algebra to represent the situation before interpreting results as meaningful solutions within the problem context.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
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Another nice lesson idea from n-rich, this link is on the topic of triangles and the golden ratio. I like these lesson ideas as they teach the topic in an interesting and different way and come with a full set of teacher notes, hints for pupils and solutions for ease of planning. Would make an ideal investigation lesson as a paired or group work task.
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