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- Year 11•
- Higher
Abstract direct proportion
I can identify, write and solve direct proportion questions involving algebra.
- Year 11•
- Higher
Abstract direct proportion
I can identify, write and solve direct proportion questions involving algebra.
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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 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 you plan your year 11 maths lesson on: Abstract 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: Abstract 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.
Licence
Prior knowledge starter quiz
6 Questions
Q1.Two variables are inversely proportional if there is a multiplicative relationship between one variable and the reciprocal of the other.
Q2.Which of the following is an example of inverse proportion?
Q3.Which of the following is an equation representing inverse proportion?
Q4.A graph representing inverse proportion will appear in how many quadrants when plotted on a pair of axes?
Q5.The smaller the dividend, the to the origin the graph will be.
Q6.Which of the following is the graph of $$y={{{3.5}\over{x}}}$$?




Assessment exit quiz
6 Questions
Q1.Any non-zero number multiplied by its reciprocal is equal to .
Q2.Which of the following tables show direct proportion?

Q3.Match the numbers to their reciprocals.
5 -
$$1\over5$$
$$2\over5$$ -
$$5\over2$$
$$1\over2$$ -
2
$$3\over4$$ -
$$4\over3$$
$$1\over4$$ -
4