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Year 10
Higher

Problem solving with algebraic ratios

I can use my knowledge of ratio to solve problems.

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New
New
Year 10
Higher

Problem solving with algebraic ratios

I can use my knowledge of ratio to solve problems.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. It is important to preserve the relationship between the parts of a ratio.
  2. There is a functional relationship between the quantities in a ratio.
  3. This relationship can be represented algebraically.

Keywords

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

  • Coordinates - Coordinates are a set of values that show an exact position.

  • Expression - An expression contains one or more terms, where each term is separated by an operator.

  • Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

Common misconception

Procedural understanding of sharing in a ratio where pupils add the parts, divide the amount by this and then multiply by each part without considering the information in the question.

In the lesson encourage pupils to look for keywords in the question which indicate if the amount given is the total, one part or the difference. The use of a bar model to display the information can also be used to help pupils.

When working with ratios in geometry a sketch can be really important. Being able to plot the coordinates accurately in relation to each other without having to have a complete coordinate grid will be key to success. Mini-whiteboards could help.
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.
Which of the following are expressions?
Correct answer: $$4x+5y$$
$$4x$$
Correct answer: $$4x + 5$$
$$4x=5y$$
Correct answer: $$4(2x +5)$$
Q2.
What is the length of AB?
An image in a quiz
Correct Answer: 9, nine
Q3.
Which of the following are equivalent ratios to 3 : 9?
Correct answer: 27 : 81
Correct answer: 1 : 3
Correct answer: 1.5 : 4.5
Correct answer: 12 : 36
36 : 117
Q4.
Point A and B are on a straight line. The coordinates of point A are (2, 3). Point B is 2 to the right and 4 below point A. What are the coordinates of point B?
$$(0, -1)$$
Correct answer: $$(4, -1)$$
$$(0, 7)$$
$$(4, 7)$$
Q5.
There are 42 cars and vans in a car park in the ratio of 5 : 2. How many vans are there?
Correct Answer: 12, 2 vans, twelve, twelve vans
Q6.
Bag A contains $$b$$ beads, bag B contains two more than bag A and bag C contains twice as many as bag B. Which of the following is the correct expression for the number of beads in bag C?
$$b+2$$
$$b-2$$
$$2b+2$$
Correct answer: $$2(b+2)$$

Exit quiz

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6 Questions

Q1.
Which are of the following are expressions?
$$2y=3x$$
Correct answer: $$2y - 3x$$
Correct answer: $$2(y + 3)$$
$$2y$$
Correct answer: $$2y-3$$
Q2.
The points A, B, C and D are in order on a straight line. AB : BD = 2 : 7, AC : CD = 15 : 3. Find the ratio of AB : BC : CD
Correct Answer: 4 : 11 : 3, 4:11:3
Q3.
The points A, B and C are on a straight line. The coordinates of A are (6, 2). The coordinates of B are (8, 5). Given that AB : BC = 1 : 2. Find the $$x$$ coordinate of C.
Correct Answer: 12, twelve, x = 12, x=12
Q4.
The ratio of red to yellow sweets in a bag is 2 : 3. The ratio of hearts to stars in the bag is 3 : 1. What is the probability of picking out a red heart? (Give your answer as a decimal)
Correct Answer: 0.3
Q5.
The ratio of gravel to water in this fish tank is 1 : 5. What volume of water is in the tank?
An image in a quiz
$$5000 cm^3$$
$$6 000 cm^3$$
$$24 000 cm^3$$
Correct answer: $$25 000 cm^3$$
Q6.
There are red and green counters in a bag in the ratio of 1 : 2. 2 are taken at random, the probability that 2 red counters are taken is $$8\over75$$. How many green counters are there?
Correct Answer: 34, 34 green, 4 green counters