Fractions and Decimals 20, Multiplication and Division 22_Overview of Learning Plan
(Year 5) ACMNA098, ACMNA101, ACMNA121 NSW MA3-6NA
Dividing by single-digit numbers, dividing the remainder to create a fraction.
THIS IS A SUMMARY OF THE LEARNING PLAN, DESCRIBING THE SEQUENCE OF LEARNING WHICH WILL OCCUR OVER MULTIPLE LESSONS. COMPLETE LEARNING PLAN STARTS ON THE NEXT PAGE.
Divide by 2,
dividing the
remainder 1
by 2 to
create a
half.
Divide by 6,
dividing the
remainder 5
by 6 to
5
create 6 .
Children:
 divide by 2, for example,
 divide the remainder 1 by 2 to
create a half, for example,
 divide by 6, for example,
 divide the remainder 5 by 6 to
5
create 6, for example,
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Children
 ask one another questions about dividing the remainder
to create a fraction, for example:

How could we divide by 2?

How could we divide our remainder 1 by 2?

What is 1 divided by 2?

What is half of 1?

How could we divide by 6?

How could we divide our remainder 5 by 6?

What is 5 divided by 6?

What is a sixth of 5?

What does the vinculum mean?
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Fractions and Decimals 20, Multiplication and Division 22_Explicit Learning Plan
(Year 5) ACMNA098, ACMNA101, ACMNA121 NSW MA3-6NA
THIS IS THE FULL LEARNING PLAN, WITH DETAILS OF ACTIONS AND QUESTIONS THAT MAY BE USED TO DEVELOP DEEP UNDERSTANDING OVER MULTIPLE LESSONS.
Dividing by single-digit numbers, dividing the remainder to create a fraction.
Resources: playing cards, strips of paper, pencil, paper
EXPLICIT LEARNING
What could we do?
What language could we use to explain and ask questions?
Focuses
Children think about, talk and listen to a friend about, then have the
children’s
opportunity to share what they already know.
thoughts on the
concept, exposing
current
understanding and
any
misconceptions.
Reviews
seeing division in
2 ways, as
‘groups of …’
and as ‘… equal
groups’.
(Multiplication
and Division 7)
Record, for example, ‘groups of’ and ‘equal groups’
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►
Today brings an investigation about division.
►
What do you know about division?
►
Talk about division with a friend.
►
Is anyone ready to share what they are thinking about
division?

We’ve investigated division.

And we found that there are 2 ways we can see division.

We found we could divide by making ‘groups of’.

And we found that we could divide by making ‘equal
groups’.

We found that seeing dividing by as making ‘equal
groups’ is more efficient when dividing larger numbers
because we are finding a fraction of the number.
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Reviews

We’ve investigated division and fractions.

And we found that dividing and finding a fraction are the
same thing.

We found that when we divide by 2, we are finding a
half.

We found that when we divide by 3, we are finding a
third.

We found that when we divide by 4, we are finding a
quarter.

We found that when we divide by 10, we are finding a
tenth.

We found that the denominator in the fraction tells us
the number we have divided by.
Record, for example, division by a number greater than 1 makes a
number a number of times smaller.

Record, for example,
quotient
We found that division by a number greater than 1
makes a number a number of times smaller.

And we began to call the answer to a division, a quotient.

We’ve investigated dividing numbers.

We found that if we don’t know a quotient when we
divide, we could partition the number then divide the
parts and add the quotients.

We found that when we divided a non-multiple, we had
a remainder.
dividing creates a
fraction of the
number.
(Multiplication
and Division 10 –
18, Patterns and
Algebra 17)
Record, for example, ÷ 2 =
Reviews
Record, for example, ÷ 4 =
the denominator
tells us the
number we are
dividing by.
(Fractions and
Decimals 7)
Reviews
dividing using
properties and
relationships,
recording
remainders as
remainders.
(Multiplication
and Division 10 –
18, Patterns and
Algebra 17)
Record, for example, ÷ 3 =
1
2
1
3
1
4
Record, for example, ÷ 10 =
1
10
Record, for example, 335 ÷ 2 =
1
2
of 335 =
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Introduces
dividing using
properties and
relationships with
the remainder
divided to get a
unit fraction.
Record, for example,
1
335 ÷ 2 =
2
Reviews
300 + 30 + 5
dividing by 2 is
halving.
(Multiplication
and Division 2, 10, Record, for example,
Patterns and
335 ÷ 2 =
Algebra 17)
300 + 30 + 5
Reviews
partitioning using
standard place
value to divide by
2 because every
tens number is
divisible by 2.
(Multiplication
and Division 10,
Patterns and
Algebra 17)
of 335 =
300 + 30 + 5
4 + 1

Today we’re going to investigate dividing the remainder as well.

Let’s divide an odd number by 2.

If we divide an odd number by 2, will we get a
remainder?

When we divide by 2, what fraction do we get?

Will we get a number that is half as big?

Let's record our number sentences as both divisions and
as fractions.

Let’s partition 335 into our preferred multiples of 2.

We know that we can partition numbers using standard
place value to divide by 2 because every tens number is a
multiple of 2.

Let’s partition 335 using place value.

Is 5 a multiple of 2?

5 is not a multiple of 2.

Let’s partition 5 into 4 and 1.

Because 1 is less than 2, we can’t partition it into a
multiple of 2.

What does 300 divided by 2 equal?

Does 300 divided by 2 equal 150?

What is half of 300?
Children partition as much as they need to.
Record, for example,
1
300 ÷ 2 = 150
Record, for example,
30 ÷ 2 = 15
2
1
2
of 300 = 150
of 30 = 15
Record, for example,
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Reviews
4÷2=2
1
2
of 4 = 2

Is half of 300, 150?

What does 30 divided by 2 equal?

Does 30 divided by 2 equal 15?

What is half of 30?

Is half of 30, 15?
1

What does 4 divided by 2 equal?
1

Does 4 divided by 2 equal 2?

What is half of 4?

Is half of 4, 2?

So we’ve divided our partitions by 2 and we’ve found
half of our partitions.

In Year 3 and 4 we would have just recorded the 1 as
remaining.

But could we divide the remaining 1 by 2? Let’s
investigate!

Let’s record our number sentences.

1 divided by 2.

And half of 1.

Let’s look at the number sentence 1 divided by 2 first.

So we want to divide 1 by 2.

Here we have 1 strip of paper.
dividing the parts
by 2.
Record, for example,
335 ÷ 2 =
300 + 30 + 5
300 ÷ 2 = 150
30 ÷ 2 = 15
Introduces
dividing the
remaining 1 to get
a fraction.
Record 1 ÷ 2 =
1
of 335 =
2
300 + 30 + 5
of 300 = 150
2
of 30 = 15
2
1
2
of 1 =
Display 1 strip of paper, for example,
Divide the 1 strip of paper into 2 equal parts, for example,
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Introduces 1
divided by 2
equals a half.
1
Record, for example, 1 ÷ 2 = 2
Reviews
a half of 1 is a
Divide the 1 strip of paper in half, for example,
half. (Fractions
and Decimals 1, 2)
1
1
Record, for example, 1 ÷ 2 = 2
2
1
of 1 = 2

Let’s divide it into 2 equal parts.

What fraction did we get?

Did we get a half?

Does 1 divided by 2 equal a half?

Let’s look at the number sentence half of 1 now.

So we want to find a half of 1.

Here we have 1 strip of paper.

Let’s fold it in half.

What fraction did we get?

Did we get a half?

Is half of 1, a half?

Is that why it is called a half?

So we’ve divided all of our partitions by 2, and we’ve
found a half of all our partitions.

Let’s add all of the quotients together.

What does 150 plus 15 plus 2 plus a half equal?

Does 150 plus 15 plus 2 plus a half equal 167 and a half?

So does 335 divided by 2 equal 167 and a half?

Is half of 335, 167 and a half?

Does that make sense?

If we make 335 half as big, would it be about 167 and a
half?
Record, for example,
1
335 ÷ 2 =
Reviews
adding the
quotients.
of 335 =
2
300 + 30 + 5
300 ÷ 2 = 150
300 + 30 + 5
of 300 = 150
2
1
1
30 ÷ 2 = 15
of 30 = 15
2
1
4÷2=2
1÷2=
of 4 = 2
2
1
1
2
2
1
1
150 + 15 + 2 + 2 = 167 2
of 1 =
1
2
1
1
150 + 15 + 2 + 2 = 167 2
1
Record, for example, 335 ÷ 2 = 167 2
1
1
of 335 = 167 2
2
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Reviews
the vinculum
means divided by.
(Fractions and
Decimals 19)
1
Point to the number sentence 1 ÷ 2 = 2
1
Circle the 1 on both sides of the equal sign, for example, 1 ÷ 2 = 2
1
Circle the 6 on both sides of the equal sign, for example, 1 ÷ 2 = 2
Point to the 1 divided by 2 on the left side, for example,
1÷2=
1

Let’s look closely at our number sentence, 1 divided by 2
equals a half.

What does the equals sign mean?

Does the equals sign mean that both sides are equal?

We have a 1 on both sides.

We have a 2 on both sides.

The only other things we have is the division sign on one
side and a vinculum on the other side.

What must the vinculum mean?

Must the vinculum mean divided by?

Does the left side say ‘1 divided by 2’?

Does the right side say ‘1 divided by 2?

Does the fraction a half, mean ‘1 divided by 2’?
2
1 divided by 2
Point to the 1 divided by 2 on the left side, for example,
1
1÷2=2
1 divided by 2
Allow children time now to engage in guided and independent investigation of
dividing numbers using properties and relationships, dividing remainder of 1 to
create unit fractions.
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Introduces
dividing using
properties and
relationships with
the remainder
divided to get a
non-unit fraction.
Introduces
dividing a number
by 6 with
remainder 5
divided as a
fraction.
Record, for example,
77 ÷ 6 =
Record, for example, 77 ÷ 6 =
1
6
of 77 =
Reviews dividing
by 6 makes a
sixth.
(Multiplication
and Division 15,
Patterns and
Algebra 17)
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
Let’s divided by 6.

Let’s divide a non-multiple of 6, by 6.

Is 77 a multiple of 6?

We know that 78 is a multiple of 6, so 78 cannot be a
multiple of 6.

When we divide by 6, what fraction do we get?

Will we get a number that is a sixth as big?

Will we get a sixth of the number?

How could we record this in a number sentence?

Let's record our number sentence as both a division and
as a fraction.

Do both of these number sentences say the same thing?

When we divide by 6, are we finding a sixth?

How could we divide 77 by 6?

Could we partition 77 using standard place value?

Is 10 a multiple of 6?

No, 10 is not a multiple of 6.

Because 10 is not a multiple of 6, not every tens number
will be a multiple of 6.
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Reviews
partitioning using
standard place
value to divide by
6 is not always
efficient because
not every tens
number is
divisible by 6.
(Multiplication
and Division 15,
Patterns and
Algebra 17)

So partitioning a number using place value will not
always be efficient.

Is 60 a multiple of 6?

Because 77 is higher than 60, could we partition 77 into
60?

If we partition 77 into 60, how many will be in the other
part? Will we have 17 in the other part?

Let's partition 77 into 60 and 17.

Did we partition 77 using non-standard place value?

Is 17 a multiple of 6?

No, 17 is not a multiple of 6.
of 77 =

How could we partition 17 into multiples of 6?
60 + 17

Could we partition 17 into 12 and 5?

Because 5 is less than 6, we won’t be able to partition it
into multiples of 6.

Now that we have our preferred multiples of 6, could we
start dividing by 6 using these multiples?

What does 60 divided by 6 equal?

Does 60 divided by 6 equal 10?

What is a sixth of 60?

Is a sixth of 60, 10?
Record, for example,
1
77 ÷ 6 =
of 77 =
6
60 + 17
60 + 17
Record, for example,
1
77 ÷ 6 =
6
60 + 17
12 + 5
12 + 5
Reviews
dividing the parts
by 6.
Record, for
example,
60 ÷ 6 = 10
1
6
of 60 = 10
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Record, for example,
12 ÷ 6 = 2
1
6
of 12 = 2
Introduces
dividing the
remaining 5 to
get a fraction.
Record 5 ÷ 6 =
1
6
5 divided by 6
5
equals 6.
What does 12 divided by 6 equal?

Does 12 divided by 6 equal 2?

What is a sixth of 12?

Is a sixth of 12, 2?

So we’ve divided our partitions by 6 and we’ve found a
sixth of our partitions.

In Year 3 and 4 we would have just recorded the 5 as
remaining.

But could we divide the remaining 5 by 6? Let’s
investigate!

Let’s record our number sentences.

5 divided by 6 and a sixth of 5.

Let’s look at the number sentence 5 divided by 6 first.

So we want to find 5 divided by 6.

Here we have 5 strips of paper.

Let’s divide each strip into six parts.
of 5 =
Display 5 strips of paper, for
example,
Introduces

Divide each of the 5 strips of paper
into 6 equal parts, for example,
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Here we have 1 divided by 6 equals 6

Here we have 2 divided by 6 equals 6

Here we have 3 divided by 6 equals 6

Here we have 4 divided by 6 equals 6

Here we have 5 divided by 6 equals 6

So what does 5 divided by 6 equal?

Does 5 divided by 6 equal five-sixths?

Let’s look at the number sentence a sixth of 5 now.

So we want to find a sixth of 5.

Here we have 5 strips of paper.

Let’s fold each strip in sixths.

Now we don’t want a sixth of 1, we want a sixth of 5.

Here we have a sixth of 1.

Here we have a sixth of 2.

Here we have a sixth of 3.

Here we have a sixth of 4.

Here we have a sixth of 5.
1
Point to 1 divided by 6 = 6 , 2
2
divided by 6 = 6 , 3 divided by 6 =
3
6
4
, 4 divided by 6 = 6 , 5 divided
5
by 6 = 6 , for example,
Divide each of the 5 strips of paper
into 6 equal parts, for example,
Introduces
1
6
5
of 5 = 6.
Point to a sixth of 1, a sixth of 2, a
sixth of 3, a sixth of 4 and a sixth
of 5, for example,
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
2
3
4
5
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Record, for example,
Introduces
5 divided by 6
5
1
equals and
6
5
5÷6=
Display 5 strips of paper, for
example,
1
6
of 5 =
5
6

How many sixths in a sixth of 5?

Are there 5 sixths in a sixth of 5?

Does a sixth of 5 equal 5 sixths?

Let’s look at the number sentences in a different way.

So we want to divide 5 by 6 and we want to find a sixth
of 5.

Here we have 5 strips of paper.

Let’s divide the 5 strips of paper into 6 equal parts.

Have we divided the 5 strips into 6 equal parts?

Here is 1 equal part.

Here are 2 equal parts.

Here are 3 equal parts.

Here are 4 equal parts.

Here are 5 equal parts.
6
of 5 = 6.
Divide each of the 5 strips of
paper into 6 equal parts, for
example,
Point to 1 equal part, 2 equal
parts, 3 equal parts, 4 equal
parts, 5 equal parts, 6 equal
parts, for example,
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
Then if we join these 5 parts together we have another
equal part - 6 equal parts.

Have we divided 5 into 6 equal parts?

What is the size of each part?

Is each part, 5 sixths?

What fraction do we get when we divide 5 by 6?

Do we get 5 sixths?

Does 5 divided by 6 equal 5 sixths?

Can we see 5 divided by 6, and a sixth of 5 in more than
one way?

Which way makes more sense to you?

Let’s look closely at our number sentence, 5 divided by 6
equals 5 sixths.

What does the equals sign mean?

Does the equals sign mean that both sides are equal?
Circle the 5 on both sides of the equals sign, for example, 5 ÷ 6 = 6
5

We have a 5 on both sides.
5

We have a 6 on both sides.

The only other things we have is the division sign on one
side and a vinculum on the other side.

What must the vinculum mean?

Must the vinculum mean divided by?
Describe the size of each part,
for example,
Record, for example,
Reviews
Record, for example,
the vinculum
means divided by.
(Fractions and
Decimals 19)
5÷6=
5÷6=
5
1
6
6
5
1
6
6
5
of 5 = 6
5
of 5 = 6
Circle the 6 on both sides of the equals sign, for example, 5 ÷ 6 = 6
5
Circle the division sign and the vinculum, for example, 5 ÷ 6 = 6
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Point to the 5 divided by 6 on the left side, for example,

Does the left side say ‘5 divided by 6’?

Does the right side say ‘5 divided by 6?

Does the fraction 5 sixths, mean ‘5 divided by 6’?
5
5÷6=6
5 divided by 6
Point to the 1 divided by 2 on the left side, for example,
5
5÷6=6

5 divided by 6
Reviews
adding the
quotients.
(Multiplication
and Division 10 –
17, Patterns and
Algebra 17)

Record, for example,
77 ÷ 6 =
1
6
60 + 17
12 + 5
of 60 = 10
6
1
1
12 ÷ 6 = 2
6
1
5
5
of 77 =
60 + 17
12 + 5
60 ÷ 6 = 10
5÷6=6
So we’ve divided all of our partitions by 6, and we’ve
found a sixth of all our partitions.
5
10 + 2 + 6 = 12 6
6
of 12 = 2
5
of 5 = 6
5
5
10 + 2 + 6 = 12 6
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5
Record, for example, 77 ÷ 6 = 12 6
1
6
5
of 77 = 12 6

Let’s add all of the quotients together.

What does 10 plus 2 plus 5 sixths equal?

Does 10 plus 2 plus 5 sixths equal 12 and 5 sixths?

So does 77 divided by 6 equal 12 and 5 sixths?

Is a sixth of 77, 12 and 5 sixths?

Does that make sense?

If we make 77 a sixth as big, would it be about 12 and 5
sixths?
Allow children time now to engage in guided and independent investigation of
dividing numbers using properties and relationships, dividing remainder other
than 1 to create non-unit fractions.
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