Myths about teaching can hold you back
- Year 11•
- Higher
Finding the constant of proportionality for directly proportional relationships
I can use the general form for the directly proportional relationship y = kx^n to find k.
- Year 11•
- Higher
Finding the constant of proportionality for directly proportional relationships
I can use the general form for the directly proportional relationship y = kx^n to find k.
These resources were made for remote use during the pandemic, not classroom teaching.
Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
Lesson details
Key learning points
- y can be directly proportional to x^n
- This is because x^n could be written as a different variable.
Keywords
Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship
Common misconception
Setting up the initial proportion statement and hence the general form of the equation the wrong way around.
Pay particularly attention to the language used. Give pupils the opportunity to verbalise what different proportion statements mean. E.g. y ∝ x^2, 'read this aloud using the correct mathematical vocabulary'.
To help you plan your year 11 maths lesson on: Finding the constant of proportionality for directly proportional relationships, 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 directly proportional relationships, 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.What letter is used to represent the constant of proportionality?
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 $$k$$.
$$y={\sqrt4{x}}$$ -
$${\sqrt4}$$
$$y={3x\over4}$$ -
$$3\over4$$
$$y={\sqrt3{x}}$$ -
$${\sqrt3}$$
$$y={x\over4}$$ -
$$1\over4$$
$$y={5x\over6}$$ -
$$5\over6$$
Q4.$$y$$ is directly proportional to $$x$$. When $$x$$ = 70, $$y$$ = 245. Write an equation connecting $$x$$ and $$y$$.
Q5.$$y$$ is directly proportional to $$x$$. When $$x$$ = 8, $$y$$ = 13.2. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 35.
Q6.$$y$$ is directly proportional to $$x$$. When $$x$$ = 8, $$y$$ = 13.2. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$x$$ when $$y$$ = 66.
Assessment exit quiz
6 Questions
Q1.Which of the following equations represent $$y$$ being directly proportional to $$x$$ or a power of $$x$$ in some way?
Q2.Match each equation to its correct value of $$k$$.
$$a=5{b}^2$$ -
5
$$a=2{b}^3$$ -
2
$$a=3{\sqrt[3]{b}}$$ -
3
$$a=\sqrt{3}{\sqrt{b}}$$ -
$$\sqrt{3}$$
Q3.Match the following:
$$a\propto{b}$$ -
$$a$$ is directly proportional to $$b$$
$$a\propto{b}^3$$ -
$$a$$ is directly proportional to $${b}^3$$
$$a\propto{\sqrt[3]{b}}$$ -
$$a$$ is directly proportional to $${\sqrt[3]{b}}$$
$$a\propto{\sqrt{b}}$$ -
$$a$$ is directly proportional to $${\sqrt{b}}$$
$$a\propto{b}^2$$ -
$$a$$ is directly proportional to $${b}^2$$
Q4.$$y$$ is directly proportional to $$x^2$$. When $$x$$ = 6, $$y$$ = 108. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 11.
Q5.$$y$$ is directly proportional to $${\sqrt[3]{x}}$$. When $$x$$ = 64, $$y$$ = 20. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 343.
Q6.$$y$$ is directly proportional to $${\sqrt[3]{x}}$$. When $$x$$ = 64, $$y$$ = 20. Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$x$$ when $$y$$ = 25.