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National Curriculum: Ratio, proportion and rates of change - KS3 - Activities

Created on 15 October 2013 by ncetm_administrator
Updated on 14 April 2016 by ncetm_administrator


Ratio (mathematical moments)

This is a collaborative task to support pupils to develop concepts about equivalent ratios. (You need to be logged in to the National STEM Centre website to access this document)

Understanding ratio (Learning mathematics in context):

This is a collaborative task on combining quantities in a given ratio. Pupils will learn to: identify the ratio of two quantities and use the notation. Understanding of the meaning of ratio and equivalent ratios will be developed. Pupils combine quantities and divide quantities in a given ratio.

Proportion (mathematical moments)

This activity is intended to give pupils the opportunity to explore the proportional relationships between numbers using a relatively familiar resource (a multiplication grid) and make links with other areas of mathematics. (You need to be logged in to the National STEM Centre website to access this document)

Toad in the whole:

This activity uses proportion and the understanding of the multiplicative relationships between quantities to solve a problem that superficially appears a simple question of adding amounts of money.

Mixing Lemonade:

This activity uses ratio and proportional reasoning to determine the relative strength of mixing cordial with water. There are a range of ways of determining the answer using fractions, percentages or pie charts to illustrate the answer.

Calculating scales for scale drawing (Learning Mathematics in Context):

This activity develops pupils understanding of scales written in the form 1:x. It develops the ability to carry out calculations involving scales using a variety of units.

Developing Proportional Reasoning (Improving Learning in Mathematics N6):

Pupils 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 pupils.

Using Percentages to Increase Quantities (Improving Learning in Mathematics N7):

Pupils make links between percentages, decimals and fractions, represent percentage increase and decrease as multiplication and recognise the inverse relationship between increases and decreases using proportional reasoning.

Four on the road:

This activity involves using graphical representations to solve speed, time and distance problems.


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