Maths Subject Knowledge: Proportion, Ratio and Scaling

Syllabus

• Week 1

  Proportional reasoning

  • Introduction to proportional reasoning

    In this first activity, you'll understand that proportional reasoning is about multiplication. We introduce the idea of proportionally scaling up and down.

  • Using different methods

    You've been introduced to the basics of proportional reasoning, now let's apply these approaches to a common problem of scaling up and down recipes.

  • Applications: value for money

    To finish the first week, we look at an everyday situation: when shopping, how do you know you are getting value for money from multipacks?

• Week 2

  Ratios

  • Introduction to ratio

    This week we look at ratio and using proportional reasoning to solve ratio problems.

  • Using different methods: ratios

    We'll now use the techniques we've looked at so far, and the three ways of solving problems, to take some new examples.

  • Sharing amounts using ratio

    We build upon our examples so far to consider ratios with three parts and ratio problems that involve sharing an amount using a ratio.

  • Further ratio problems

    For the final two examples this week, we use bar modelling to solve a problem of sharing and a problem that requires making ratios compatible.

• Week 3

  Applications of proportional reasoning

  • Conversion of units

    This week we are looking at applications of proportional reasoning in daily life, science and engineering.

  • Proportionality represented with graphs

    Graphs can be a useful approach to solving proportional reasoning problems. Over the next few steps you'll look at how to use graphs and represent proportionality with graphs.

  • Compound measures

    Our third group of examples are known as compound measures. We look at common problems in physics such as speed, density and pressure.

  • Checking proportionality

    We look at a question of proportionality and return to the starting problem for the week to help assess whether a problem can be solved using proportional reasoning or not.

• Week 4

  Taking proportional reasoning further

  • Proportional reasoning of area

    This week we look at proportional reasoning applied to area and volume. We start be looking at area and a simple, but effective way of converting linear scale factors to area scale factors.

  • Proportional reasoning with 3D objects

    Now we look at volume scale factors when using proportional reasoning with 3D objects and proportionality of surface area.

  • Test your understanding

    We revisit the watery problem from the start of the week, before providing you the opportunity to test your new understanding of proportional reasoning.

  • Reviewing your professional development

    Review your professional development and plan your next steps to sustain and develop the way you plan for learning.

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