4. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
5. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get __.
6. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
7. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is/is not a rational number?
8. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
9. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
We say that rational
numbers are closed under
addition, if for any two
rational numbers a and b,
a + b is also a rational
number.
10. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
and check if
these numbers are closed under subtraction.
11. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
We say that rational
numbers are closed under
subtraction, if for any two
rational numbers a and b,
____ is also a rational
number.
12. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
We say that rational
numbers are closed under
subtraction, if for any two
rational numbers a and b,
a - b is also a rational
number.
13. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
and check if
these numbers are closed under multiplication.
14. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
We say that rational
numbers are closed under
_____________, if for any
two rational numbers a and
b, a x b is also a rational
number.
15. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
We say that rational
numbers are closed under
multiplication, if for any
two rational numbers a and
b, a x b is also a rational
number.
16. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
and check if
these numbers are closed under division.
17. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
We say that rational
numbers are closed under
division, if for any two
rational numbers a and b,
______ is also a rational
number.
18. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
We say that rational
numbers are closed under
division, if for any two
rational numbers a and b,
a ÷ b is also a rational
number.
19. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
If the two rational numbers
were a and 0, would the
closure property still hold?
20. Properties of Rational Numbers
The ‘Closure’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Now, we add them and get 43
35
.
43
35
is a rational number.
Thus, we say that 𝟒
𝟓
and 𝟑
𝟕
are closed under addition.
If the two rational numbers
were a and 0, would the
closure property still hold?
No! Because any number
divided by 0 is not defined.
21. To discuss the closure property
To discuss commutative property
To discuss associative property
Learning Outcomes
How confident do you feel?
22. To discuss the closure property
To discuss commutative property
To discuss associative property
Learning Outcomes
How confident do you feel?
24. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
25. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
Let’s do 4
5
+ 3
7
.
26. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
27. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
Now, let’s do 3
7
+ 4
5
.
28. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
We get, 3
7
+ 4
5
= 43
35
.
29. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
We get, 3
7
+ 4
5
= 43
35
.
We say that addition is
commutative for rational
numbers if for any two
rational numbers a and b,
a + b = b + a.
30. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s check if subtraction is commutative for rational
numbers using 4
5
and 3
7
.
31. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
We get, 3
7
+ 4
5
= 43
35
.
We can say that subtraction
is ______________ for
rational numbers.
32. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
We get, 3
7
+ 4
5
= 43
35
.
We can say that subtraction
is not commutative for
rational numbers.
33. Properties of Rational Numbers
The ‘commutative’ Property
Let’s check if multiplication is commutative for rational
numbers using 4
5
and 3
7
.
34. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
We get, 3
7
+ 4
5
= 43
35
.
We can say that
multiplication is
_____________ for rational
numbers.
35. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
We get, 3
7
+ 4
5
= 43
35
.
We can say that
multiplication is
commutative for rational
numbers.
36. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s check if division is commutative for rational
numbers using 4
5
and 3
7
.
37. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
We get, 3
7
+ 4
5
= 43
35
.
We can say that division is
_____________ for rational
numbers.
38. Properties of Rational Numbers
The ‘Commutative’ Property
Let’s take two rational numbers, 4
5
and 3
7
.
We get, 4
5
+ 3
7
= 43
35
.
We get, 3
7
+ 4
5
= 43
35
.
We can say that division is
not commutative for
rational numbers.
39. To discuss the closure property
To discuss commutative property
To discuss associative property
Learning Outcomes
How confident do you feel?
40. To discuss the closure property
To discuss commutative property
To discuss associative property
Learning Outcomes
How confident do you feel?
42. Properties of Rational Numbers
The ‘Associative’ Property
We shall take three rational numbers, 1
2
, 2
4
and 3
6
.
43. Properties of Rational Numbers
The ‘Associative’ Property
We shall take three rational numbers, 1
2
, 2
4
and 3
6
.
Let’s do 1
2
+ (2
4
+ 3
6
).
44. Properties of Rational Numbers
The ‘Associative’ Property
We shall take three rational numbers, 1
2
, 2
4
and 3
6
.
We get 1
2
+ (2
4
+ 3
6
) = 18
12
.
45. Properties of Rational Numbers
The ‘Associative’ Property
We shall take three rational numbers, 1
2
, 2
4
and 3
6
.
We get 1
2
+ (2
4
+ 3
6
) = 18
12
.
Now, let’s do (1
2
+ 2
4
) + 3
6
.
46. Properties of Rational Numbers
The ‘Associative’ Property
We shall take three rational numbers, 1
2
, 2
4
and 3
6
.
We get 1
2
+ (2
4
+ 3
6
) = 18
12
.
We get (1
2
+ 2
4
) + 3
6
= 18
12
.
47. To discuss the closure property
To discuss commutative property
To discuss associative property
Learning Outcomes
How confident do you feel?
48. To discuss the closure property
To discuss commutative property
To discuss associative property
Learning Outcomes
How confident do you feel?
50. Properties of Rational Numbers
Learning Activity
Check the closure, associative and commutative
properties with natural numbers, whole numbers and integers.
Editor's Notes
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Ask students to give the question a go and point out that, at the end of the lesson, they should be able to answer fully
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Make an activity of this slide:
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You may feel that the students do not need privacy to self-assess and in this instance, the chat box may be used
Polling must be used until you can fully assess their confidence to use the chat box and express honesty
If students self-assess as a 4/5, ensure that you are fully confident in their assessment
Ask questions
Ask for examples
Students to ask each other questions
If a few students self-assesses as a 3, but others as a 4/5, discretely ask the higher ones to give examples and to explain their achievement/understanding
If all students are a 3 or below, do not move on. Move to a blank page at the end of the presentation and use as a whiteboard to further explain
If students are ½, go back to the beginning
Always ask students what the gaps are and help them to identify these in order to promote metacognition
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As previously.
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An overview of the content of the lesson
Must be in the form of a question where appropriate
Students should be able to answer the question at the end - either fully, partly or in a way that demonstrates they understand what gaps in their knowledge they need to address
Verbs such as to understand / to know / to gain confidence / to learn
Ask students to give the question a go and point out that, at the end of the lesson, they should be able to answer fully
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
