Myths about teaching can hold you back
- Year 11•
- Higher
Multiplication with vectors
I can multiply with vectors.
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Lesson details
Key learning points
- Vectors can be multiplied by a scalar.
- Vectors cannot be multiplied by each other.
- Multiplication by a scalar can be done when the vectors are in column form.
- Multiplication by a scalar can be done when the vectors are drawn.
Keywords
Scalar - A scalar is a quantity that has magnitude but not direction.
Displacement - Displacement is the distance from the starting point when measured in a straight line.
Common misconception
A reflection of a vector in the x or y axis is not the reverse of a vector. This is often seen with equilateral triangles and vectors.
When multiplying the vectors by -1 this gives the opposite direction of the vector only. The magnitude remains the same. Investigate with pupils by drawing column vectors and multiply by -1 and compare.
To help you plan your year 11 maths lesson on: Multiplication with vectors, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Multiplication with vectors, 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 Vectors 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.Find the additive inverse of $$ -4 \choose 3$$.
Q2.Match each subtraction to its equivalent addition.
$${-3 \choose 2}-{1\choose 4}$$ -
$${-3 \choose 2}+{-1\choose -4}$$
$${-3 \choose 2}-{1\choose -4}$$ -
$${-3 \choose 2}+{-1\choose 4}$$
$${-3 \choose 2}-{-1\choose 4}$$ -
$${-3 \choose 2}+{1\choose -4}$$
$${-3 \choose 2}-{-1\choose -4}$$ -
$${-3 \choose 2}+{1\choose 4}$$
Q3.Match each subtraction to its resultant.
$${-3 \choose 2}-{1\choose 4}$$ -
$${-4\choose -2}$$
$${-3 \choose 2}-{1\choose -4}$$ -
$${-4 \choose 6}$$
$${-3 \choose 2}-{-1\choose 4}$$ -
$${-2 \choose -2}$$
$${-3 \choose 2}-{-1\choose -4}$$ -
$${-2 \choose 6}$$
Q4.You are given that $${2\choose3}- {a\choose-3} = {-3\choose6}$$. The value of $$a$$ is .
Q5.Which vector subtraction can be represented by this diagram?
Q6.You are given that $${7\choose3}- {a\choose3} - {-3\choose-2} = {5\choose2}$$. The value of $$a$$ is .
Assessment exit quiz
6 Questions
Q1.A is a quantity that has magnitude but not direction.
Q2.The vector $$k {1 \choose 2}$$ represents the displacement A to B. The value of $$k$$ is .
Q3.The diagram shows the vector a. Which of the following shows −0.25a?
Q4.Match each scalar and vector to the resultant vector.
$$3{8\choose6}$$ -
$$24\choose 18$$
$$-6{-4\choose3}$$ -
$$24\choose -18$$
$$2{-12\choose-9}$$ -
$$-24\choose -18$$
$$-3{8\choose-6}$$ -
$$-24\choose 18$$
Q5.You are given that $$3 {5 \choose -4}= {a \choose b}$$ . Find the value of $$a$$ and of $$b$$.
Q6.You are given that $$x {6 \choose y}={24 \choose -36}$$. Find the value of $$x$$ and of $$y$$.