I created this question to challenge the students in my higher ability Year 11 class. The question connects simultaneous equations to density, volume, surface area and rearranging formula.
Each individual topic is fairly straight forward on its own. The challenge is to connect them together within a single problem. To begin with, I posed the question to the class and asked the students to discuss in pairs or small groups a strategy for solving the problem.
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After a few minutes we decided to work the problem backwards. To work out the surface area we need the radius. We work out the radius we can use the volume. To find the volume we need to work out the value of y. To work out y we need to set up and solve a pair of simultaneous equations.
At this point about half the class began working independently either on their own or in pairs to set up the two equations. The other half needed sone help setting up the two equations with x and y. I prompted them to consider the mass of spheres A and B and the volume of sphere C.
When the students had set up the simultaneous equations almost all the class were able to complete the problem with no further help.
I wanted this problem to emphasise the need for developing a strategy to solving a problem. By working the problem backwards students were able to identify the starting point and how it would lead on further workings.
My name is Jonathan Robinson and I passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.
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