New
New
Lesson details
Key learning points
- There may be a relationship between quantities A and B and a relationship between quantities B and C
- Therefore there is a relationship between A and C
- If A : B and B : C then A : B : C and A : C
- When the common quantity is not the same in each ratio, equivalent ratios can be used
- For example, if A:B and 2B:5C then 2A:2B:5C and 2A:5C
Keywords
Proportion - A part to whole (sometimes part to part) comparison. If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.
Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
LCM - LCM is an abbreviation for lowest common multiple.
Lowest common multiple - The lowest common multiple is the lowest number that is a multiple of two or more numbers.
Common misconception
Combining ratios without using equivalent ratios to equate the common part.
Pupils may need to spend extra time finding equivalent ratios and looking at when it is ok to combine ratios or not.
Using objects or bar models to show the ratios can help pupils to visualise the concept better.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.LCM is an abbreviation for lowest common .
LCM is an abbreviation for lowest common .
Q2.What is the ratio of hearts : smileys?
What is the ratio of hearts : smileys?
Q3.What is the HCF of 24 and 18?
What is the HCF of 24 and 18?
Q4.What is the ratio of hearts : smileys? (Give your answer in its simplest form)
What is the ratio of hearts : smileys? (Give your answer in its simplest form)
Q5.What is the LCM of 4 and 6?
What is the LCM of 4 and 6?
Q6.Match each ratio to an equivalent ratio.
Match each ratio to an equivalent ratio.
Assessment exit quiz
6 Questions
Q1.What is LCM an abbreviation for?
What is LCM an abbreviation for?
Q2.Given these bar models, what is the ratio of hearts to suns?
Given these bar models, what is the ratio of hearts to suns?
Q3.Given that squares : circles = 4 : 3 and circles : triangles = 1 : 5, find the ratio of squares : triangles.
Given that squares : circles = 4 : 3 and circles : triangles = 1 : 5, find the ratio of squares : triangles.
Q4.a : b = 2 : 5, b : c = 6 : 7. Find the ratio a : b : c
a : b = 2 : 5, b : c = 6 : 7. Find the ratio a : b : c
Q5.A box contains 212 sweets which are either hearts (h), stars (s) or bottles (b). The ratio of hearts to stars is 5 : 3. The ratio of stars to bottles is 4 : 7. How many stars are in the box?
A box contains 212 sweets which are either hearts (h), stars (s) or bottles (b). The ratio of hearts to stars is 5 : 3. The ratio of stars to bottles is 4 : 7. How many stars are in the box?
Q6.b = 4a, c = 5b, find the ratio of a : c
b = 4a, c = 5b, find the ratio of a : c
