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Year 10
Higher

Algebraic ratios

I can form equations from algebraic ratios and solve to find an unknown.

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New
New
Year 10
Higher

Algebraic ratios

I can form equations from algebraic ratios and solve to find an unknown.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Equivalent ratios have a scalar multiplier.
  2. Two equations can be written which are simultaneous.
  3. This can be set equal to each other and then solved.

Keywords

  • Proportionality - Proportionality means when variables are in proportion if they have a constant multiplicative relationship.

  • 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.

  • Factorise - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

Common misconception

When $$x : y$$ are in the ratio 1 : 2 pupils write the equation as $$x = 2y$$

Show that the equation $$x = 2y$$ in a ratio table would mean the multiplier from $$y$$ to $$x$$ would be times by 2, this would mean when $$y=1 x=2$$ which is 2 : 1 not 1 : 2

Pupils will need to be confident solving equations, including quadratic equations so you may want to remind pupils or include some recall of these skills prior to the lesson.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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6 Questions

Q1.
A numerical coefficient is a constant of the variables in a term.
addition
subtraction
Correct answer: multiplier
Q2.
What is the equation of $$y$$ in terms of $$x$$?
An image in a quiz
Correct answer: $$y=3x$$
$$y={1\over4}x$$
$$y={1\over3}x$$
$$y=4x$$
Q3.
What is the equation of $$y$$ in terms of $$x$$?
An image in a quiz
$$y=5x$$
Correct answer: $$y={1\over6}x$$
$$y={1\over5}x$$
$$y=6x$$
Q4.
Match each ratio of $$x$$ : $$y$$ to the correct equation of $$y$$ in terms of $$x$$.
Correct Answer:3 : 1,$$y={1\over3}x$$

$$y={1\over3}x$$

Correct Answer:1 : 3,$$y=3x$$

$$y=3x$$

Correct Answer:4 : 5,$$y=1.25x$$

$$y=1.25x$$

Correct Answer:5 : 4,$$y=0.8x$$

$$y=0.8x$$

Correct Answer:4 : 3,$$y=0.75x$$

$$y=0.75x$$

Q5.
The ratio of adults to children at a running club is 8 : 5. Which of the following are correct equations linking adults and children?
Correct answer: $$c={5\over8}a$$
$$c={8\over5}a$$
$$a={5\over8}c$$
Correct answer: $$a={8\over5}c$$
Q6.
$$4x-6y = 3x-2y$$. What is the ratio of $$x:y$$?
Correct Answer: 4 : 1, 4:1

Exit quiz

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6 Questions

Q1.
To factorise is to express a term as the of its factors.
Correct Answer: product
Q2.
Which of these are equivalent ratios to the ratio 3 : 5
4 : 6
5 : 3
13 : 15
Correct answer: 30 : 50
Correct answer: 27 : 45
Q3.
Given that $$2x-7$$ : $$6-3x$$ is equivalent to 3 : 5 which of the following equations are also true.
Correct answer: $$\frac{2x-7}{6-3x}=\frac{3}{5}$$
Correct answer: $$\frac{6-3x}{2x-7}=\frac{5}{3}$$
$$\frac{2x-7}{3}=\frac{5}{6-3x}$$
Correct answer: $$\frac{2x-7}{3}=\frac{6-3x}{5}$$
$$\frac{2x-7}{6-3x}=\frac{5}{3}$$
Q4.
Work out the value of $$x$$ given that $$7 : 10 + x = 2 : x$$
Correct Answer: 4
Q5.
Given that $$x>0$$ Work out the value of $$x$$ given that $$3x+1 : x+3 = 2x+4 : x+2$$
Correct Answer: 5
Q6.
Given that $$x>0$$ Work out the value of $$x$$ given that $$x : 2x+7= 2x+5 : 10x+13$$ Give your answer as a decimal.
Correct Answer: 3.5