# GMC3: Working with proportion

This list contains a collection of resources to help meet General Mathematical Competency 1 (GMC1). More resources to support T level Science can be found on our T Level science resource packages page.

**GMC3 states:**

Students should:

- Be able to test for situations where two variables are directly proportional
- Be able calculate magnification from the size of the image and the size of the object
- Understand that an empirical formula represents the simplest ratio of atoms of each element in a compound and to be able to calculate an empirical formula
- Understand how to use the empirical formula and relative molecular mass to work out the molecular formula of a compound
- Understand the link between balanced equations and the ratio of moles of a substance in a reaction.
- Recognise other types of proportionality: inverse, square, inverse square
- Appreciate the different representations of different kinds of proportionality: numerical, algebraic and graphical representation
- Understand the links between fractions, percentages, ratios and proportion

### Comparing strategies for proportion problems

This lesson develops the concept of direct proportion and its application to problems. The works addresses the following problems that students might have:

- Use of inappropriate additive strategies in scaling problems
- Inefficient strategies such as not using a single multiplier for solving proportionality problems
- See multiplication as making numbers bigger, and division as making numbers smaller

The activity involves working on three situations requiring proportional reasoning:

- Scaling a recipe
- Pricing for tins of paint
- Enlarging a photograph

Students make an initial attempt at the problems. There are then examples of both correct and incorrect student work, providing opportunities for peer assessment and discussion. This work leads to developing efficient methods for working with proportional reasoning.

### Classifying proportional and non-proportional situations

This lesson develops the concept of identifying when two quantities vary in direct proportion to each other. Students enhance their ability to:

- Distinguish between direct proportion and other functional relationships
- Solve proportionality problems using efficient methods

The lesson begins with students answering questions set in the following contexts:

- An exchange rate transaction
- A mobile phone bill
- A car journey at constant speed
- Painting a room

Having worked on the questions, students must then classify each as either proportional or having a constant ratio

There is then a collaborative activity in which students must classify a situation as showing either direct proportion or not. There is a mixture of practical and mathematical contexts, drawing together a wide range of topics.

### Using proportional reasoning

This lesson develops the concept of classifying relationships between two quantities. In particular, students will:

- Describe a ratio relationship between two quantities
- Compare ratios expressed in different ways
- Use proportional reasoning to solve a real-world problem

An introductory task looks at two examples of mixing orange with soda. Students must determine if there will be a difference in taste between the two mixes.

There is a collaborative activity that represents mixing orange with soda using picture cards. There are also instruction cards for mixing the two ingredients. The cards must be placed in order so that the resulting drinks go from the weakest to strongest taste of orange.

### Developing Proportional Reasoning N6

In this resource students reflect on the reasoning they currently use when solving proportion problems, examine proportion problems and appreciate their multiplicative structure and create their own variants of proportion problems. Proportional reasoning is notoriously difficult for many students and many have difficulty in recognising the multiplicative structures that underlie proportion problems. Instead, they use addition methods, or informal methods using doubling, halving and adding.

This session aims to expose and build on this prior learning. Students are given four direct proportion problems to solve, taken from different areas of the mathematics curriculum. They then compare their methods for solving these with methods produced by other students. This leads to a discussion that compares the use of more primitive informal methods that use adding, doubling and halving with the use of more sophisticated methods that use multiplication.