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Year 11
Higher

Abstract direct proportion

I can identify, write and solve direct proportion questions involving algebra.

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New
New
Year 11
Higher

Abstract direct proportion

I can identify, write and solve direct proportion questions involving algebra.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Direct proportion equations are of the form y = kx
  2. k is the constant of proportionality and it is also the gradient of the graph.
  3. To find the gradient, k, you can use a set of coordinates (pair of values).

Keywords

  • Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship.

  • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.

Common misconception

We use the term 'multiplicative relationship' when talking about direct proportion. Pupils may need reminding that division is equivalent to multiplying by the reciprocal.

Allow opportunities to explore division of a number and multiplication of its reciprocal. Remind pupils that any non-zero number multiplied by its reciprocal is equal to 1.

To help overcome the misconception use mini-whiteboards. Give the class an number and ask them to write the reciprocal on their board. These can be tailored to the class, eg. stick to integers and unit fractions for lower ability and include mixed numbers, algebra and surds for higher ability.
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.
Two variables are inversely proportional if there is a multiplicative relationship between one variable and the reciprocal of the other.
Correct Answer: constant
Q2.
Which of the following is an example of inverse proportion?
The number of cans of drink and the number of boxes bought
Correct answer: The time taken to fill a lorry and the number of people packing the lorry
The number of metres run and the number of kilometres run
The number of euros exchanged and the number of dollars
The amount of flour needed and the number of biscuits being made
Q3.
Which of the following is an equation representing inverse proportion?
$$y={{{5}\over{x}}-1}$$
$$y={{{x}\over{5}}}$$
Correct answer: $$y={{{5}\over{x}}}$$
$$y={{{5}\over{x}}+1}$$
Q4.
A graph representing inverse proportion will appear in how many quadrants when plotted on a pair of axes?
Correct Answer: 2, two, 2 quadrants, two quadrants
Q5.
The smaller the dividend, the to the origin the graph will be.
Correct Answer: closer
Q6.
Which of the following is the graph of $$y={{{3.5}\over{x}}}$$?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz

Exit quiz

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6 Questions

Q1.
Any non-zero number multiplied by its reciprocal is equal to .
$$-1$$
0
Correct answer: 1
2
Q2.
Which of the following tables show direct proportion?
An image in a quiz
Correct answer: a
Correct answer: b
c
Correct answer: d
Q3.
Match the numbers to their reciprocals.
Correct Answer:5,$$1\over5$$

$$1\over5$$

Correct Answer:$$2\over5$$,$$5\over2$$

$$5\over2$$

Correct Answer:$$1\over2$$,2

2

Correct Answer:$$3\over4$$,$$4\over3$$

$$4\over3$$

Correct Answer:$$1\over4$$,4

4

Q4.
Decide which of the following would share a directly proportional relationship.
Correct answer: The time taken to mow a lawn and the size of the lawn
The time taken to run a 5 k race and the speed at which its run
Correct answer: The number of metres of ribbon bought and the cost of the ribbon
The cost of hiring a coach and the cost per person
Q5.
$$h$$ is directly proportional to $$g$$. When $$g$$ = 12, $$h$$ = 7.2. Find $$h$$ when $$g$$ = 28.
Correct Answer: 16.8
Q6.
$$g$$ is directly proportional to $$h$$. When $$g$$ = 17, $$h$$ = 93.5. Find $$g$$ when $$h$$ = 45.1.
Correct Answer: 8.2