Direct Proportion
High Performance Learning
10/01/24
LO: We are learning to recognise when values are in
set up equations for direct proportion and plot graphs.
Routes:
Starter
 I can find an equation relating two quantities
 I can apply my understanding to find missing values
 I can draw and analyse a graph to prove the
proportion.
Links to the UAE and real life:
Science – Making predictions
Shopping
Key vocabulary:
Proportion
Direct Proportion
quantity, relationship
Literacy and Oracy focus:
•
•
•
Underline Date and Title
Explain your answers using full sentences
Discussions
Research what the term direct proportion
means. Then answer the questions below:
Direct Proportion
Lesson Objective:
We are learning to
recognise when
values are in direct
proportion, set up
equations for direct
proportion and plot
graphs.
Success Criteria:
 I can find an
equation relating
two quantities
 I can apply my
understanding to
find missing values
using y=kx
 I can draw and
analyse a graph to
prove the quantities
are in direct
proportion.
Starter:
Research what the term direct proportion means. Then
answer the questions below:
Introduction:
Two quantities are said to be in direct proportion if they
increase and decrease at the same rate. That is, if the ratio
between the two quantities is always the same.
𝑦 is directly proportional to 𝑥
𝑘 is multiplied
by 𝑥
𝑦 = 𝑘𝑥
k stands for constant
Direct Proportion
Example:
Lesson Objective:
We are learning to
recognise when
values are in direct
proportion, set up
equations for direct
proportion and plot
graphs.
Success Criteria:
 I can find an
equation relating
two quantities
 I can apply my
understanding to
find missing values
using y=kx
 I can draw and
analyse a graph to
prove the quantities
are in direct
proportion.
𝑊 is directly proportional to 𝐹.
When 𝑊 = 24, 𝐹 = 6.
a. Find an equation linking W and F.
b. Find the value of 𝑊 when 𝐹 = 10.
𝑊 = 𝑘𝐹
Substitute
𝑊 = 24, 𝐹 = 6
24 = 6𝑘
4=𝑘
𝑊 = 4𝐹
𝑊 = 4𝐹
When 𝐹 = 10,
𝑊 = 4 × 10
𝑊 = 40
Direct Proportion
Your Turn:
Lesson Objective:
We are learning to
recognise when
values are in direct
proportion, set up
equations for direct
proportion and plot
graphs.
Success Criteria:
 I can find an
equation relating
two quantities
 I can apply my
understanding to
find missing values
using y=kx
 I can draw and
analyse a graph to
prove the quantities
are in direct
proportion.
𝐺 is directly proportional to 𝐻.
When 𝐺 = 18 and 𝐻 = 5.
a. Find an equation linking G and H.
b. Find the value of 𝐺 when H= 16.
𝐴 is directly proportional to 𝐵.
When 𝐴 = 28 and 𝐵 = 7.
a. Find an equation linking A and B.
b. Find the value of 𝐵 when 𝐴 = 10.
𝐺 = 𝑘𝐻
𝐺 = 3.6𝐻
𝐴 = 𝑘𝐵
𝐴 = 4𝐵
Substitute
𝐺 = 18, 𝐻 = 5
When H = 16,
Substitute
𝐴 = 28, B = 7
When A = 10,
18 = 𝑘 × 5
18 = 5𝑘
G = 3.6(16)
28 = 𝑘 × 7
10 = 4𝐵
10 ÷ 4 = 𝐵
2.5 = 𝐵
G = 57.6
3.6 = 𝑘
4=𝑘
𝐺 = 3.6𝐻
𝐴 = 4𝐵
Direct Proportion
Graphs
Lesson Objective:
Success Criteria:
 I can find an
equation relating
two quantities
 I can apply my
understanding to
find missing values
using y=kx
 I can draw and
analyse a graph to
prove the quantities
are in direct
proportion.
When two quantities are in direct
proportion, as one increases the other
does too.
We can display this relationship in a
graph. Two quantities that are in direct
proportion will always produce a
straight-line graph that passes through
the origin.
£1.50
£1.20
Cost
We are learning to
recognise when
values are in direct
proportion, set up
equations for direct
proportion and plot
graphs.
90p
𝑦 = 𝑘𝑥
60p
30p
0
1
2
3
4
Number of packets
5
AFL
Direct propotion
Are the two quantities in direct proportion?
No
Are the two quantities in direct proportion?
Yes
Are the two quantities in direct proportion?
Yes
Are the two quantities in direct proportion?
No
Are the two quantities in direct proportion?
No
Direct Proportion
Example:
Lesson Objective:
We are learning to
recognise when
values are in direct
proportion, set up
equations for direct
proportion and plot
graphs.
Success Criteria:
 I can find an
equation relating
two quantities
 I can apply my
understanding to
find missing values
using y=kx
 I can draw and
analyse a graph to
prove the quantities
are in direct
proportion.
Example:
Direct Proportion
Example:
Lesson Objective:
We are learning to
recognise when
values are in direct
proportion, set up
equations for direct
proportion and plot
graphs.
Success Criteria:
 I can find an
equation relating
two quantities
 I can apply my
understanding to
find missing values
using y=kx
 I can draw and
analyse a graph to
prove the quantities
are in direct
proportion.
Direct Proportion
20/02/2023
Task – Choose Red or Amber. Then complete the Green task
Lesson Objective:
Green Task:
We are learning to
recognise when
values are in direct
proportion, set up
equations for direct
proportion and plot
graphs.
Success Criteria:
 I can find an
equation relating
two quantities
 I can apply my
understanding to
find missing values
using y=kx
 I can draw and
analyse a graph to
prove the quantities
are in direct
proportion.
Collect a slip from my desk once you have
completed red or yellow
The values of p and x are in direct
proportion. Work out the missing
numbers a, b, c and d.
The values of p and x are in direct proportion.
Work out the missing numbers a, b, c and d.
𝒑
𝒙
8
25
12
𝒂
𝒃
50
𝒄
62.5
20
𝒅
The values of p and x are in direct proportion.
Work out the missing numbers a, b, c and d.
𝒑
𝒙
8
25
12
𝒂
𝒃
50
𝒄
62.5
20
𝒅