- Year 11•
- Higher
Abstract inverse proportion
I can identify, write and solve inverse proportion questions involving algebra.
- Year 11•
- Higher
Abstract inverse proportion
I can identify, write and solve inverse proportion questions involving algebra.
These resources will be removed by end of Summer Term 2025.
Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
These resources were created for remote use during the pandemic and are not designed for classroom teaching.
Lesson details
Key learning points
- Inverse proportion equations are of the form y = k ÷ x^n
- k is the constant of proportionality.
- To find k, you can use a pair of values.
Keywords
Inversely proportional - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.
Common misconception
For all direct and inverse proportions, the multiplicative relationship is with x and y.
The multiplicative relationship whether direct or inverse can be shown as y and x^n. Show a ratio table of y and 1/x^2 and a table of y and 1/x. The inverse multiplicative relationship is seen with y and 1/x^2 and not with 1/x.
To help you plan your year 11 maths lesson on: Abstract inverse 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 inverse 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
Lesson video
Loading...
Prior knowledge starter quiz
6 Questions
Q1.Two variables are proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.
Q2.Pair up the reciprocals with the following numbers.
3 -
$$\frac{1}{3}$$
5 -
$$\frac{1}{5}$$
$$\frac{3}{2}$$ -
$$\frac{2}{3}$$
2 -
$$\frac{1}{2}$$
12 -
$$\frac{1}{12}$$
$$\frac{5}{9}$$ -
$$\frac{9}{5}$$
Q3.What is the single multiplier that connects 9 to 54?
Q4.What is the single multiplier that connects 15 to 10?
Q5.What is the single multiplier that connects 24 to 9.6?
Q6.$$y\propto \sqrt{x}$$, when $$x=64, y=6$$. Work out the value of $$y$$ when $$x=400$$.
Assessment exit quiz
6 Questions
Q1.Match the equations with the correct proportions.
$$y\propto\frac{1}{x^2}$$ -
$$y=\frac{3}{x^2}$$
$$y\propto\frac{1}{\sqrt{x}}$$ -
$$y=\frac{10}{\sqrt{x}}$$
$$y\propto\frac{1}{\sqrt[3]{x}}$$ -
$$y=\frac{3}{4\sqrt[3]{x}}$$
$$y\propto\frac{1}{x}$$ -
$$y=\frac{\sqrt{2}}{x}$$
$$y\propto x^2$$ -
$$y= 9x^2$$
$$y\propto \sqrt{x}$$ -
$$y= 5\sqrt{x}$$
Q2.Which of the following are examples of inverse proportion?
Q3.$$p\propto \frac{1}{q}$$, match the correct values for A, B and C.
A -
20
B -
1000
C -
62.5
Q4.It takes 10 workers 6 hours to build a wall. They all work at the same rate. Firstly, all workers build for 2 hours, then 6 workers leave. How many hours will it take the 4 workers to finish the wall?
Q5.$$y\propto \frac{1}{\sqrt{x}}$$, when $$x=25, y=16$$. Work out the value of $$y$$ when $$x=400$$.
Q6.$$y\propto \frac{1}{\sqrt[3]{x}}$$, when $$x=125, y=0.15$$. Work out the value of $$y$$ when $$x=0.008$$.