Maths Subject Knowledge: Proportion, Ratio and Scaling

Syllabus

• Week 1

  From 8 Jun 2020

  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

  From 15 Jun 2020

  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

  From 22 Jun 2020

  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

  From 29 Jun 2020

  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.

  • Completing the course

    Well done for reaching the end of the course. We revisit the watery problem from the start of the week, before providing you the opportunity to test your new understanding of proportional reasoning.

Who will you learn with?