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- Use scale factors (review)
- Understand direct proportion
- Calculate with pressure and density
- Understand inverse proportion
- Ratio problems (review)

For higher-attaining pupils:

- Construct complex direct proportion equations
- Construct inverse proportion equations

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Gradient of a Line Practise the skill of finding the gradients of straight lines by counting squares and dividing rise by run.
- Graph Paper Flexible graph paper which can be printed or projected onto a white board as an effective visual aid.
- Scale Factors Video The scale factor, area factor and volume factor of similar shapes are quite different.
- Similar Shapes Questions about the scale factors of lengths, areas and volumes of similar shapes.
- Direct and Inverse Proportion A self-marking exercise in solving direct and inverse variation problems.
- Compound Units Practise using compound units such as speed, unit pricing and density to solve problems.

Here are some exam-style questions on this topic:

- "
*At depths below 900 metres, the temperature of the water in the sea is given by the formula:*" ... more - "
*The graph gives information about how the charging time in hours of an electric car relates to its range given as a distance in kilometres.*" ... more - "
*The following table shows corresponding values for two variables \(x\) and \(y\).*" ... more - "
*(a) Sketch a graph on the axes below left that shows that \(y\) is directly proportional to \(x\).*" ... more - "
*At a constant temperature, the volume of a gas \(V\) is inversely proportional to its pressure \(p\). By what percentage will the pressure of a gas change if its volume increases by 15% ?*" ... more - "
*Which of the following statements are correct if \(xy = c\) and \(c\) is a constant.*" ... more - "
*The circumference of the red circle is 80% of the circumference of the blue circle.*" ... more - "
*The graph shows the temperature (\(T\)) of an unidentified flying object over a period of 10 seconds (\(t\)).*" ... more - "
*The three boxes pictured below are mathematically similar.*" ... more - "
*Two similar pentagonal based pyramids have surface areas 200 cm*" ... more^{2}and 50 cm^{2}respectively. - "
*If \(a\) is inversely proportional to \(b\) and \(b\) is directly proportional to \(c^2\) find a formula for \(a\) in terms of \(c\) given that \( a=20 \) and \(c = 4 \) when \(b = 8 \).*" ... more

Here are some Advanced Starters on this statement:

**Square in Rectangle**

Find the area of a square drawn under the diagonal of a rectangle more**Temperature Sum**

Can you explain why 0^{o}C + 0^{o}C does not equal 64^{o}F more**Three Right Triangles**

Calculate the lengths of the unlabelled sides of these right-angled triangles. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.
- Ratio A ratio is a relationship between two numbers of the same kind. In layman's terms a ratio represents, simply, for every amount of one thing, how much there is of another thing. This topic presents a number if different ways pupils can represent ratios and apply their meaning to problem solving situations.

Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.

If six girls can plant 90 trees in a day. How many trees can ten girls plant in a day? The unitary method.

Work out the date for various given amounts of time after the beginning of the year.

The height of this giraffe is three and a half metres plus half of its height. How tall is the giraffe?

A lamp and a bulb together cost 32 pounds. The lamp costs 30 pounds more than the bulb. How much does the bulb cost?

A puzzle about a restaurant bill. Exactly where did the missing pound go?

It is called Refreshing Revision because every time you refresh the page you get different revision questions.

Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.