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- Year 11•
- Higher
Finding the constant of proportionality for direct proportion
I can use the general form for a directly proportional relationship to find k.
- Year 11•
- Higher
Finding the constant of proportionality for direct proportion
I can use the general form for a directly proportional relationship to find k.
Lesson details
Key learning points
- Direct proportion equations are of the form y = kx
- k is the constant of proportionality and it is also the gradient of the graph.
- To find the gradient, k, you can use two sets of coordinates (pairs of values).
Keywords
Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship
Common misconception
Failing to recognise that x/2 is the same as 1/2 × x and therefore shows a directly proportional relationship where the value of k is 1/2.
It is useful to go back to looking at unit fractions. E.g. 2/3 = 1/3 × 2 and 7/9 = 1/9 × 7, etc. And, then look at algebraic terms leading up to for example, 2x/3. 'What is the the multiplier?'
To help you plan your year 11 maths lesson on: Finding the constant of proportionality for direct proportion, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Finding the constant of proportionality for direct proportion, 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.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Direct and inverse proportion unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Any non-zero number multiplied by its is equal to 1.
Q2.Which of the following tables show direct proportion?
Q3.Match the numbers to their reciprocals.
$$1\over8$$ -
8
$$8\over3$$ -
$$3\over8$$
$$1\over3$$ -
3
6 -
$$1\over6$$
$$6\over5$$ -
$$5\over6$$
Q4.Decide which of the following would share a directly proportional relationship.
Q5.$$h$$ is directly proportional to $$g$$. When $$g$$ = 17, $$h$$ = 93.5. Find $$h$$ when $$g$$ = 25.
Q6.$$h$$ is directly proportional to $$g$$. When $$h$$ = 17, $$g$$ = 93.5. Find $$g$$ when $$h$$ = 60.5.
Assessment exit quiz
6 Questions
Q1.When dealing with equations of direct proportion we use the equation $$y = kx$$. What does $$k$$ represent?
Q2.Which of the following equations represent $$y$$ being directly proportional to some form of $$x$$?
Q3.Match each equation to its correct value of $$k$$.
$$y={x\over6}$$ -
$$1\over6$$
$$y={\sqrt6{x}}$$ -
$${\sqrt6}$$
$$y={5x\over6}$$ -
$$5\over6$$
$$y={\sqrt5{x}}$$ -
$${\sqrt5}$$
$$y={6x\over5}$$ -
$$6\over5$$
Q4.$$y$$ is directly proportional to $$x$$. When $$x$$ = 13, $$y$$ = 52. Write an equation connecting $$x$$ and $$y$$.
Q5.$$y$$ is directly proportional to $$x$$. When $$x$$ = 6, $$y$$ = 13.2. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 14.
Q6.$$y$$ is directly proportional to $$x$$. When $$x$$ = 6, $$y$$ = 13.2. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$x$$ when $$y$$ = 123.2.