Writing equations from ratios
I can write equations involving ratios.
Writing equations from ratios
I can write equations involving ratios.
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Lesson details
Key learning points
- Ratios can be written as fractions.
- A ratio can be used to write an equation.
- This equation is another way of representing how the two quantities are connected.
- Either of the quantities can be the subject.
Keywords
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.
Coefficient - A numerical coefficient is a constant multiplier of the variables in a term.
Equation - An equation is used to show 2 expressions that are equal to each other.
Common misconception
When $$x : y$$ are in the ratio 1 : 2 pupils write the equation as $$x = 2y$$
The bar models shown in this lesson can help to support pupils with this.
To help you plan your year 10 maths lesson on: Writing equations from ratios, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Writing equations from ratios, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Explore more key stage 4 maths lessons from the Ratio unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Prior knowledge starter quiz
6 Questions
Q1.Which of the following is the correct way of writing the ratio 1 to 2?
Q2.There are 36 cans of drink and bags of sweets in a vending machine. The ratio of cans : bags is 2 : 1. 4 of each are sold. What is the ratio of cans : bags now? (In its simplest form)
Q3.There are 56 vehicles in a car park. The ratio of cars : vans is 5 : 2. 4 more vans enter the car park. What is the ratio of cars : vans now? (Give your answer in its simplest form)
Q4.The ratio of adults to children at an athletics club is 8 : 5. 8 adults leave, the ratio is now 4 : 3. How many children are members of the club?
Q5.3 bags contain counters in the ratio 6 : 3 : 5. Some counters are taken out of 1 bag and put into the other 2. The ratio of counters is now 6 : 5 : 10. What is the minimum number of counters removed?
Q6.The ratio of the number of £1 coins to £2 in Sam’s money box is 3 : 2. Their gran gives them 6 more £1 coins, the ratio is now 2 : 1. How much money was in Sam’s money box originally?
Assessment exit quiz
6 Questions
Q1.The 3 in $$3a$$ is the .
Q2.What is the equation of $$y$$ in terms of $$x$$?

Q3.What is the equation of $$y$$ in terms of $$x$$?

Q4.Match each ratio of $$x$$ : $$y$$ to the correct equation of $$y$$ in terms of $$x$$.
1 : 4 -
$$y=4x$$
4 : 1 -
$$y={1\over4}x$$
3 : 2 -
$$y={2\over3}x$$
2 : 3 -
$$y=1.5x$$
3 : 5 -
$$y={5\over3}x$$