Mastering Ratio and Proportion using Ratio Tables at PGHS

The mathematics department have been working collaboratively to improve the teaching and learning of mathematics through a ‘mastery’ approach.

We all strive to teach identified topics with an agreed approach for understanding so that if students move sets or change teachers, they are not confused by different teaching styles. Our new approach for year 7 is using ratio tables to teach ratio, direct proportion and multiplicative reasoning. The aim is to embed this through KS3 and KS4 but we are only at the start of our journey here.

We have identified other topics within mathematics that we will use with this approach. We will then use this across the curriculum in other subjects that use direct proportion, for example, Science, Food Technology and Art.

One of our aims is to use different representations and thus help learners understand mathematical concepts via multiple channels in a better way.

The following areas of mathematics can also use ratio tables:

Fractions
Percentages
Best value for money
Conversions
Recipe problems
Construction, measuring and scale
Straight line graphs and calculating the gradient
Scatter diagrams
Enlargement and similarity
Rates
Trigonometry
Capture, recapture

Below is an example of how direct proportion can be taught using the ratio tables moving from the unitary method.

Example of a solving a recipe question using a ratio table.

Ant is making a spicy soup for 11 people. He uses 25ml of Tabasco sauce. Bea is making the same soup for 33 people. How much Tabasco sauce should she use?

Example of using a ratio table for similar shapes

Example of using a ratio table for money conversions.

6 Australian Dollars are worth 27 Argentine Pesos. What are 20 Australian Dollars worth?

What I really like about ratio tables are the use of fractions. Students will need to be confident with:

converting fractions from mixed numbers to improper fractions and vice versa.
Understanding that dividing by 2 is the same as multiplying by a half etc.
Converting between fractions and decimals.
Multiplying by fractions.
Simplifying fractions.
Understanding that multiplication can make the outcome smaller and not always bigger.

The above skills will improve their fluency in fractions.

Mrs Sweeney

Curriculum Leader for Mathematics