theory about math

1. Venn Diagrams – Complete Lesson
Preview the presentation to check ability-level, AFL questions,
and the animations during demonstrations.
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2. Starter
A task at the beginning of the lesson that reviews a skill required
for the learning.
Knowledge Check
Questions to assess students’ current understanding and to
consequently show progress.
Real-Life Example A ‘hook’ to raise interest and provide a concrete example.
Demonstration
Slides for a teacher to lead students – didactically or via
questioning – through a mathematical method.
AFL Questions
Assessment For Learning Questions, used to assess students’
competency for independent tasks/activities.
Plenary An opportunity for students to prove/evaluate their learning.

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4. 27
??
x3
+4
-15
+4 ÷2 x4 ÷3
+8
x8
÷7
14

5. How could we
categorise
(group)
these animals?
List 5 ways in your book.

6. How have they been organised?
Dangerous Not dangerous

7. How have they been organised?
4 legs 6 legs
No legs
2 legs

8. 06 November 2022
Venn Diagrams

10. KNOWLEDGE CHECK
A
A = Odd Numbers
ξ = Numbers below 20
B = Multiples of 3
ξ
Complete the Venn Diagram.
a) How many numbers are even?
b) How many numbers are odd and a multiple of 3?
c) How many numbers are not a multiple of 3 and even?
B

11. KNOWLEDGE CHECK
A
A = Odd Numbers
ξ = Numbers below 20
B = Multiples of 3
ξ
Complete the Venn Diagram.
a) How many numbers are even?
b) How many numbers are odd and a multiple of 3?
c) How many numbers are not a multiple of 3 and even?
B
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
17
18
19
9
3
6

12. Live in water
Live on land
Which group would these animals go into?

13. Live in water
Live on land
Live on land
and
in water

14. Live in water
Live on land
Live on land
and
in water
This is called a Venn diagram.
They help organise data and compare groups.
They are very useful when some things are in both groups
(like a hippo!)

15. What are the different groups in these Venn diagrams?
Fly
Hawk Ant
Seagull Spider
Insect
Flying Animal
Man U
Arsenal
Chelsea Tomato
Stop
Light
Everton
Football Teams Red
Real Animals Human-eaters
Lions
Sharks
Zombies
Werewolf
Cow
Goat
Dolphin
Food
Circular
Pizza
Wheel
Pie
Cup
Chicken
Chips

16. ξ Long hair Blonde hair
4 students were picked from Year 7
(Ksi)
This means the
total group.
ξ =
Anna Tom Mary Jack Beth
Jack doesn’t have long or blond hair.
But he’s still in the group.

17. ξ Long hair Blonde hair
4 students were picked from Year 7
ξ =
Anna Tom Mary Jack Beth
Anna Tom
Mary
Jack
Beth

18. ξ Odd Multiple of 3
ξ = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
1
2
3
4
6
7
8
9
10
5
We want to sort the numbers 1 to 10.

19. ξ
Classmates in a Venn Diagram
blonde hair, curly hair, straight hair, short hair, female, male,
has a sister, has a brother, wears glasses, right-handed, left-handed,
pet dog, pet cat, plays football, loves maths…
Possible
Categories:

21. What’s wrong with these
Venn Diagrams?
ξ Long hair Short hair
ξ Human Insect
ξ Boy Male
ξ Even Multiple of 4

22. ξ
ξ =
Complete the Venn diagram.
Boy Wears glasses
Anna Jess
Jo Tom May
Pete
Rob
ξ = ξ Multiple of 5 Odd
3, 4, 5, 7, 10, 12,
13, 15, 20, 24, 25

23. ξ
ξ =
Complete the Venn diagram.
Boy Wears glasses
Anna Jess
Jo Tom May
Pete
Rob
Jo
Anna
Jess
Tom
May
Pete
Rob
ξ = ξ Multiple of 5 Odd
3, 4, 5, 7, 10, 12,
13, 15, 20, 24, 25

24. ξ
ξ =
Complete the Venn diagram.
Boy Wears glasses
Anna Jess
Jo Tom May
Pete
Rob
Jo
Anna
Jess
Tom
May
Pete
Rob
ξ = ξ Multiple of 5 Odd
3, 4, 5, 7, 10, 12,
13, 15, 20, 24, 25 5
15
25
7
13
3
10
20
4
12
24

25. ξ
Venn Diagrams
A) ξ = 1 2 3
7 8 9
11 12 13
16 17 18
Complete each Venn Diagram
Odd Over 10
ξ
B) ξ = 34 14 15 28
21 70 20 13
1 25 7 16
6 35 18 41
Multiple of 7 Even
ξ
C) ξ =
Multiple of 3 Multiple of 4
ξ
D) Blonde Short
Numbers from
1 to 25
What fraction of the numbers
are not a multiple of 3 or 4?
10 students were surveyed
about their hair.
4 students had short blonde hair.
3 students didn’t have
blonde or short hair.
6 students had blonde hair.
Can you complete the diagram with the totals?
①

26. ξ
Venn Diagrams
A) ξ = 1 2 3
7 8 9
11 12 13
16 17 18
Complete each Venn Diagram
Odd Over 10
ξ
B) ξ = 34 14 15 28
21 70 20 13
1 25 7 16
6 35 18 41
Multiple of 7 Even
ξ
C) ξ =
Multiple of 3 Multiple of 4
ξ
D) Blonde Short
1
2
3
7
8
9
11 12
13 16
17 18
7 14
28
35
6
21
70
15
20
34
25
16
13
1
18
41
Numbers from
1 to 25
4
8
12
16
20
24
3
6
9
15
18
21
1
2
5
7
10
11
13
14 17 19 22 23 25
What fraction of the numbers
are not a multiple of 3 or 4?
10 students were surveyed
about their hair.
4 students had short blonde hair.
3 students didn’t have
blonde or short hair.
6 students had blonde hair.
Can you complete the diagram with the totals?
4
3
2 1
①
Answers
13
25

27. ξ
Venn Diagrams
A) ξ = 1 2 3
7 8 9
11 12 13
16 17 18
Complete each Venn Diagram
Odd Over 10
ξ
B) ξ = 34 14 15 28
21 70 20 13
1 25 7 16
6 35 18 41
Multiple of 7 Even
ξ
C) ξ =
Multiple of 3 Multiple of 4
ξ
D) Blonde Short
Numbers from
1 to 25
What fraction of the numbers
are not a multiple of 3 or 4?
10 students were surveyed
about their hair.
4 students had short blonde hair.
3 students didn’t have
blonde or short hair.
6 students had blonde hair.
Can you complete the diagram with the totals?
①
ξ
Venn Diagrams
A) ξ = 1 2 3
7 8 9
11 12 13
16 17 18
Complete each Venn Diagram
Odd Over 10
ξ
B) ξ = 34 14 15 28
21 70 20 13
1 25 7 16
6 35 18 41
Multiple of 7 Even
ξ
C) ξ =
Multiple of 3 Multiple of 4
ξ
D) Blonde Short
Numbers from
1 to 25
What fraction of the numbers
are not a multiple of 3 or 4?
10 students were surveyed
about their hair.
4 students had short blonde hair.
3 students didn’t have
blonde or short hair.
6 students had blonde hair.
Can you complete the diagram with the totals?
①

29. ξ
Venn Diagrams
A) ξ = 44 90 45 88
54 27 6 26
91 16 71 9
18 13 24 33
Complete each Venn Diagram
Even Multiple of 9
ξ
B) ξ = Multiple of 4 Multiple of 5
ξ
C) Blonde Short
10 students were surveyed
about their hair.
2 students had short blonde hair.
3 students didn’t have
blonde or short hair.
6 students had blonde hair.
Can you complete the diagram with the totals?
②
Even numbers from
10 to 40
What fraction of the numbers
are multiple of 4 and 5?
ξ
D) Dog Cat
50 students were surveyed
about the pets they had.
30 students owned a dog.
25 students owned a cat.
10 students didn’t own a dog or cat.
How can we complete the diagram
with the totals? (hint: how many student had both a dog and cat?

30. ξ
Venn Diagrams
A) ξ = 44 90 45 88
54 27 6 26
91 16 71 9
18 13 24 33
Complete each Venn Diagram
Even Multiple of 9
ξ
B) ξ = Multiple of 4 Multiple of 5
ξ
C) Blonde Short
18
10 students were surveyed
about their hair.
2 students had short blonde hair.
3 students didn’t have
blonde or short hair.
6 students had blonde hair.
Can you complete the diagram with the totals?
2
3
4 1
②
90
9
27
45
6
16
24 54
13
33
44
71
91
88
Even numbers from
10 to 40
10
20
30
40
12
16
24
28
32
36
14
18
22
26
34
38
What fraction of the numbers
are multiple of 4 and 5?
2
16
=
1
8
ξ
D) Dog Cat
50 students were surveyed
about the pets they had.
30 students owned a dog.
25 students owned a cat.
10 students didn’t own a dog or cat.
How can we complete the diagram
with the totals? (hint: how many student had both a dog and cat?
15
10
15 10
26
Answers

31. ξ
Venn Diagrams
A) ξ = 44 90 45 88
54 27 6 26
91 16 71 9
18 13 24 33
Complete each Venn Diagram
Even Multiple of 9
ξ
B) ξ = Multiple of 4 Multiple of 5
ξ
C) Blonde Short
10 students were surveyed
about their hair.
2 students had short blonde hair.
3 students didn’t have
blonde or short hair.
6 students had blonde hair.
Can you complete the diagram with the totals?
②
Even numbers from
10 to 40
What fraction of the numbers
are multiple of 4 and 5?
ξ
D) Dog Cat
50 students were surveyed
about the pets they had.
30 students owned a dog.
25 students owned a cat.
10 students didn’t own a dog or cat.
How can we complete the diagram
with the totals? (hint: how many student had both a dog and cat?
ξ
Venn Diagrams
A) ξ = 44 90 45 88
54 27 6 26
91 16 71 9
18 13 24 33
Complete each Venn Diagram
Even Multiple of 9
ξ
B) ξ = Multiple of 4 Multiple of 5
ξ
C) Blonde Short
10 students were surveyed
about their hair.
2 students had short blonde hair.
3 students didn’t have
blonde or short hair.
6 students had blonde hair.
Can you complete the diagram with the totals?
②
Even numbers from
10 to 40
What fraction of the numbers
are multiple of 4 and 5?
ξ
D) Dog Cat
50 students were surveyed
about the pets they had.
30 students owned a dog.
25 students owned a cat.
10 students didn’t own a dog or cat.
How can we complete the diagram
with the totals? (hint: how many student had both a dog and cat?

33. ξ Has a brother Has a sister
20 students were surveyed about whether they had a brother or a sister.
10 had a brother and sister.
5 didn’t have a brother or sister.
8 only had a brother.
3 only had a sister.
We will complete the
Venn Diagram
with the totals.
10
5
8 3

34. ξ Dog Cat
20 people were surveyed about whether they had a dog or a cat.
8 had a dog and a cat.
5 didn’t have a dog or a cat.
3 only had a dog. How many
only had a cat?
8
5
3 4
The numbers
must total 20.

35. ξ Apple Burger
30 people were surveyed about their lunch.
15 had an apple and a burger.
3 didn’t have a burger or an apple.
20 had a burger.
How many
had an apple?
15
3
7 5

36. ξ
Venn Diagrams with Totals.
10
Have a brother Have a sister
20 students were asked about their siblings.
10 didn’t have a brother or sister.
8 had a sister.
7 had a brother.
That’s impossible!
It totals more than 20!
2 5 3

37. ξ Pasta Fries
50 students were surveyed
about their lunch.
10 students had pasta and fries.
15 students only had fries.
20 students had pasta.
How many didn’t have pasta or fries?
ξ Dog Cat
30 students were surveyed
about their pets.
8 students had a dog and a cat.
10 students only had a dog.
7 students didn’t have a dog or a cat.
How many students only had a cat?
Complete the Venn diagram.

38. ξ Pasta Fries
50 students were surveyed
about their lunch.
10 students had pasta and fries.
15 students only had fries.
20 students had pasta.
How many didn’t have pasta or fries?
10
10 15
15
ξ Dog Cat
30 students were surveyed
about their pets.
8 students had a dog and a cat.
10 students only had a dog.
7 students didn’t have a dog or a cat.
How many students only had a cat?
8
10 5
7
Complete the Venn diagram. Answers

39. ξ
Venn Diagrams with Totals
A) The Venn diagram shows a school survey.
Boy Blonde
3
ξ
ξ
How many students were surveyed?
How many boys had blonde hair?
How many students had blonde hair?
12
5
5
B) The Venn diagram shows a survey of 30 people.
Complete the diagram: How many people
owned a motorbike and a car?
How many people only owned a motorbike?
Motorbike
Car
6
7
13
Drama
Art
C) Out of 50 students, 25 studied art,
20 studied drama and 15 didn’t study either.
Complete the Venn diagram.
Complete a Venn diagram for each question.
a) 50 people were surveyed about
their pets. 15 people had a dog
and a cat. 10 people had only
a dog. 15 people didn’t have a
dog or a cat.
d) 80 people were asked whether
they liked apples, bananas
or cherries.
10 only liked apples.
8 only liked bananas.
12 liked apples and bananas.
14 like bananas and cherries.
12 only liked cherries.
9 liked all three.
6 didn’t like any.
b) 70 people were surveyed.
24 people had long hair.
32 people had black hair.
30 people didn’t have long or
black hair.
c) 100 people were surveyed about
their lunch. 40 people bought an
apple and a soda. 60 people
bought an apple. 50 people
bought a soda.
How many bought neither?

40. ξ
Venn Diagrams with Totals
A) The Venn diagram shows a school survey.
Boy Blonde
3
ξ
ξ
How many students were surveyed?
How many boys had blonde hair?
How many students had blonde hair?
12
5
5
B) The Venn diagram shows a survey of 30 people.
Complete the diagram: How many people
owned a motorbike and a car?
How many people only owned a motorbike?
Motorbike
Car
4 6
7
13
Drama
Art
C) Out of 50 students, 25 studied art,
20 studied drama and 15 didn’t study either.
Complete the Venn diagram.
10 10
15
15
Complete a Venn diagram for each question.
a) 50 people were surveyed about
their pets. 15 people had a dog
and a cat. 10 people had only
a dog. 15 people didn’t have a
dog or a cat.
b) 70 people were surveyed.
24 people had long hair.
32 people had black hair.
30 people didn’t have long or
black hair.
ξ Cat
Dog
15 10
10
15
c) 100 people were surveyed about
their lunch. 40 people bought an
apple and a soda. 60 people
bought an apple. 50 people
bought a soda.
How many bought neither?
d) 80 people were asked whether
they liked apples, bananas
or cherries.
10 only liked apples.
8 only liked bananas.
12 liked apples and bananas.
14 like bananas and cherries.
12 only liked cherries.
9 liked all three.
6 didn’t like any.
ξ Black
Long
16 16
8
30
ξ Apple
Soda
40 20
10
30
ξ B
A
10
C
8
9
12
9 14
12
6
25
3
15
4
6
Answers

41. ξ
Venn Diagrams with Totals
A) The Venn diagram shows a school survey.
Boy Blonde
3
ξ
ξ
How many students were surveyed?
How many boys had blonde hair?
How many students had blonde hair?
12
5
5
B) The Venn diagram shows a survey of 30 people.
Complete the diagram: How many people
owned a motorbike and a car?
How many people only owned a motorbike?
Motorbike
Car
6
7
13
Drama
Art
C) Out of 50 students, 25 studied art,
20 studied drama and 15 didn’t study either.
Complete the Venn diagram.
Complete a Venn diagram for each question.
a) 50 people were surveyed about
their pets. 15 people had a dog
and a cat. 10 people had only
a dog. 15 people didn’t have a
dog or a cat.
d) 80 people were asked whether
they liked apples, bananas
or cherries.
10 only liked apples.
8 only liked bananas.
12 liked apples and bananas.
14 like bananas and cherries.
12 only liked cherries.
9 liked all three.
6 didn’t like any.
b) 70 people were surveyed.
24 people had long hair.
32 people had black hair.
30 people didn’t have long or
black hair.
c) 100 people were surveyed about
their lunch. 40 people bought an
apple and a soda. 60 people
bought an apple. 50 people
bought a soda.
How many bought neither?
ξ
Venn Diagrams with Totals
A) The Venn diagram shows a school survey.
Boy Blonde
3
ξ
ξ
How many students were surveyed?
How many boys had blonde hair?
How many students had blonde hair?
12
5
5
B) The Venn diagram shows a survey of 30 people.
Complete the diagram: How many people
owned a motorbike and a car?
How many people only owned a motorbike?
Motorbike
Car
6
7
13
Drama
Art
C) Out of 50 students, 25 studied art,
20 studied drama and 15 didn’t study either.
Complete the Venn diagram.
Complete a Venn diagram for each question.
a) 50 people were surveyed about
their pets. 15 people had a dog
and a cat. 10 people had only
a dog. 15 people didn’t have a
dog or a cat.
d) 80 people were asked whether
they liked apples, bananas
or cherries.
10 only liked apples.
8 only liked bananas.
12 liked apples and bananas.
14 like bananas and cherries.
12 only liked cherries.
9 liked all three.
6 didn’t like any.
b) 70 people were surveyed.
24 people had long hair.
32 people had black hair.
30 people didn’t have long or
black hair.
c) 100 people were surveyed about
their lunch. 40 people bought an
apple and a soda. 60 people
bought an apple. 50 people
bought a soda.
How many bought neither?

43. KNOWLEDGE CHECK
A
A = Odd Numbers
ξ = Numbers below 20
B = Multiples of 3
ξ
Complete the Venn Diagram.
a) How many numbers are even?
b) How many numbers are odd and a multiple of 3?
c) How many numbers are not a multiple of 3 and even?
B

44. KNOWLEDGE CHECK
A
A = Odd Numbers
ξ = Numbers below 20
B = Multiples of 3
ξ
Complete the Venn Diagram.
a) How many numbers are even?
b) How many numbers are odd and a multiple of 3?
c) How many numbers are not a multiple of 3 and even?
B
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
17
18
19
9
3
6

45. I can complete Venn diagrams with data.
I can complete Venn diagrams with totals.
I can calculate missing values in Venn diagrams.
Check your success!

46. I can complete Venn diagrams with data.
I can complete Venn diagrams with totals.
I can calculate missing values in Venn diagrams.
Check your success!

47. Write a text message to a friend describing…
What a
Venn diagram
shows.

48. Questions?
Comments?
Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to email:
tom@goteachmaths.co.uk