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These are the topics related to the standard: Analyze proportional relationships and use them to solve real-world and mathematical problems."

Here are some specific activities, investigations or visual aids picked out. Click anywhere in the grey area to access the resource.

- Algebra In Action Real life problems adapted from an old Mathematics textbook which can be solved using algebra.
- Ratio A self marking exercise on using ratio notation, reducing a ratio to its simplest form and dividing a given quantity into a number of parts in proportion to a given ratio.
- Ratio Video Learn to work with ratios including dividing a quantity in a given ratio.
- 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.
- Unit Pricing Calculate the unit cost of items to earn jigsaw pieces that make a joke.

Here are some exam-style questions on this statement:

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*Which of the following statements are correct if \(xy = c\) and \(c\) is a constant.*" ... more - "
*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

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

- Fractions A fraction is a part of a number. Fractions are either vulgar or decimal. Vulgar fractions can be proper, improper or mixed. Equivalent fractions have the same value. Pupils, at all stages of their learning, should practise using fractions. From dealing with halves, the most basic fraction, to manipulating algebraic fractions containing surds, this topic is always relevant. Proficiency also depends on reasonable numeracy skills particularly the multiplication tables and finding the lowest common multiple of two numbers. Pupils also need to be able to convert vulgar fractions to decimals and percentages and vice versa. Be wary of teaching the 'rules' for manipulation fractions by rote. Pupils need to understand the reason why and the time-honoured key to understanding starts with the imaginary pizza and the much-used fraction wall.
- Percentages Percentages provide a useful and common way to express a part of a quantity. The word is derived from the Latin per centum meaning “by the hundred”. Although percentages are usually used to express numbers between zero and one, any ratio can be expressed as a percentage. Pupils begin working with common percentages such as 50%, 25% and 10% and practise estimating percentages to get a better understanding of the concept. They then learn how to convert percentages to decimals and vulgar fractions and vice versa. More advanced problem solving may include percentage change and how it is applied in real life to discounts and interest. A study of the use of percentages in the media can provide many discussion points and can provide a stimulus for classroom display work.
- 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.