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Year 7

Multiplicative relationships

I can calculate the multiplier for any two given numbers.

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New
New
Year 7

Multiplicative relationships

I can calculate the multiplier for any two given numbers.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Any value divided by itself is equal to one.
  2. One is the multiplicative identity.
  3. There exists a multiplier for any pair of values.

Keywords

  • Reciprocal - Reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Common misconception

Using additive strategies instead of multiplicative.

Emphasise that proportional relationships maintain a constant multiplier so we are looking for a multiplicative relationship.

Embed the understanding that there exists a multiplier for any pair of values. Randomly pick a pupil to say a number, then ask another pupil to give a number. Ask the class to find the multiplier. Repeat for all types of numbers.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
A ____________ is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its __________ is equal to 1
integer
Correct answer: reciprocal
common factor
proportion
ratio
Q2.
What is the additive relationship between the numbers shown?
An image in a quiz
Correct answer: add 15
subtract 15
multiply by 4
divide by 4
Q3.
Using the function machine, what is the multiplicative relationship between the numbers?
An image in a quiz
add 15
subtract 15
Correct answer: multiply by 4
divide by 4
Q4.
Match the numbers with their reciprocal.
Correct Answer:2,$$\frac{1}{2}$$

$$\frac{1}{2}$$

Correct Answer:3,$$\frac{1}{3}$$

$$\frac{1}{3}$$

Correct Answer:$$\frac{3}{2}$$,$$\frac{2}{3}$$

$$\frac{2}{3}$$

Correct Answer:-3,$$\left(-\frac{1}{3}\right)$$

$$\left(-\frac{1}{3}\right)$$

Correct Answer:-2,$$\left(-\frac{1}{2}\right)$$

$$\left(-\frac{1}{2}\right)$$

Correct Answer:$$\left(-\frac{5}{2}\right)$$,$$\left(-\frac{2}{5}\right)$$

$$\left(-\frac{2}{5}\right)$$

Q5.
Which of these operations could connect these two numbers?
An image in a quiz
Correct answer: plus 20
Correct answer: minus (-20)
plus (-20)
Correct answer: multiply by 3
Correct answer: divide by $$\frac{1}{3}
Q6.
Which of these would fit the multiplicative relationship?
An image in a quiz
Correct answer: 1 to 5
$$\frac{5}{3}$$ to $$\frac{25}{15}$$
Correct answer: 6 to 30
Correct answer: $$\frac{3}{10}$$ to $$\frac{3}{2}$$
Correct answer: $$\frac{1}{5}$$ to 1

Exit quiz

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6 Questions

Q1.
Only using one step, what is the additive relationship for the connection of these numbers?
An image in a quiz
add 2
Correct answer: add (-2)
add $$\frac{1}{2}$$
Q2.
What two steps can be applied here for the connection of these numbers?
An image in a quiz
Correct answer: subtract 10 then add 8
Correct answer: add (-10) then add 8
Correct answer: divide by 6 then multiply by 5
Correct answer: add 8 then subtract 10
divide by 5 then multiply by 6
Q3.
Using the function machine, what is the multiplicative relationship between the numbers?
An image in a quiz
There is none as it is division not multiplication
Multiply by 6
Add 6
Correct answer: Multiply by $$\frac{1}{6}$$
Subtract 6
Q4.
What is the single additive step that connects these numbers?
An image in a quiz
Correct answer: add 18
add (-18)
add 42
add (-42)
Q5.
Using the values in the table, match the following.
An image in a quiz
Correct Answer:The additive step from A to B,4

4

Correct Answer:The additive step from B to A,(-4)

(-4)

Correct Answer:The multiplier from A to B,$$\frac{3}{2}$$

$$\frac{3}{2}$$

Correct Answer:The multiplier from B to A,$$\frac{2}{3}$$

$$\frac{2}{3}$$

Q6.
What is the single multiplier?
An image in a quiz
Correct answer: $$\frac{7}{3}$$
$$\frac{6}{14}$$
$$\frac{3}{7}$$
2.5