MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
ESSENTIAL PRIOR, RELATED AND NEXT LEARNING
Identify students’ current levels of understanding using tracking data, and formative embedded or separate assessment for this concept, and for the essential prior learning.
Essential Prior Learning
Differentiate learning by
including the segment of each
Teaching Plan that children
demonstrate they are ready to
investigate.
Multiplication and Division 1 and 2 - Dividing in 2 ways – by dividing into ‘(2) equal
groups’ and by dividing into ‘groups of (2)’
Fractions and Decimals 2, Patterns and Algebra 9 - Halves of shapes and groups,
linked to odd and even numbers
Multiplication and Division 4 - Divide into groups, skip/rhythmic count
Multiplication and Division 5 – Divide into arrays, describe in 2 ways using division
Essential Next Learning
Multiplication and Division 8,
Fractions and Decimals 4 Dividing by 4 linked to
quartering groups
Use assessment data to select the levels of this concept, or essential related concepts, and the segments of each explicit teaching plan, to teach.
TEACHING VIDEOS, EXPLICIT TEACHING PLAN, INVESTIGATION, REFLECTION, PROBLEM SOLVING
The videos and the explicit teaching plan are divided into the same segments of the concept.
TEACHING SEGMENT and VIDEO 1: Dividing in 2 ways – by dividing into ‘… equal groups’ and counting groups, linked to halving, and by making
‘groups of …’ and counting number in each group, recording the same number sentence for each division,
identifying related division, and any remainders
VIEW the videos before teaching, to develop YOUR understanding and metalanguage, then teach the concept using YOUR understanding and metalanguage and the Explicit
Teaching PowerPoint, and/or SHOW the video to the whole class / groups of children / individual children to develop THEIR understanding and metalanguage.
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
MULTIPLICATION AND DIVISION 7_OVERVIEW OF TEACHING PLAN
(Year 2) ACMNA026, ACMNA031, NSW MA1-6NA MA1-8NA
Divide into ‘groups of …’ and count groups, and into ‘… equal groups’ and count counters in each group, identifying related divisions and remainders.
THIS IS A SUMMARY OF THE EXPLICIT TEACHING PLAN, DESCRIBING THE SEQUENCE WHICH WILL OCCUR OVER MULTIPLE LESSONS. THE COMPLETE EXPLICIT TEACHING PLAN STARTS ON PAGE 3.
SEGMENT 1: Children:
 divide counters into groups of 2, for example,
Divide into
 record a number sentence to describe what
‘groups
they did, for example, 8 ÷ 2 = 4
of …’ and
into ‘… equal  divide counters into 2 equal groups, for example,
groups’,
 record a number sentence to describe what they did,
recording the
for example, 8 ÷ 2 = 4
same division
 identify half
number
sentence.
 explain that the same number sentences describes both ways of
dividing
Identify
fractions.
Identify
related
divisions.
Identify
remainders.
Children
 ask one another questions about dividing in 2 ways, for
example:
 How could divide these counters into groups of …?
 How could we record a number sentence to describe
how we divided?
 How could divide these counters into … equal groups?
 How could we record a number sentence to describe
how we divided?
 Did we record the same number sentence for both ways
to divide?
 explain other ways to see the division, for example, 8 divided into
groups of 2 = 4 is the same as 8 divided into 4 equal groups = 2 so 8
÷ 2 = 4 and 8 ÷ 4 = 2 are related divisions.
 How could we pick up a fraction of our counters?
 divide a non-multiple number of counters, describing a number
sentence describing what they did, and the part remaining
 Do we have any counters remaining?
 How else could we see how we divided?
 divide by other numbers, for example, 3, 4 and 5
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
MULTIPLICATION AND DIVISION 7_EXPLICIT TEACHING PLAN
(Year 2) ACMNA026, ACMNA031, NSW MA1-6NA MA1-8NA
FULL EXPLICIT TEACHING PLAN, EMBEDDING THE INVESTIGATIONS, REFLECTIONS AND PROBLEMS THAT MAY BE USED TO DEVELOP DEEP UNDERSTANDING OVER MULTIPLE LESSONS.
Resources: counters, playing cards, pencil, paper
What could we do?
What language could we use to explain and ask questions?
Children think about, talk and listen to a friend about, then have the
Focuses
opportunity to share what they already know.
children’s
thoughts on the
concept, exposing
current
understanding and
any
misconceptions
Reviews
seeing dividing in
2 ways – as
Record, for example, groups of
‘groups of …’
and as ‘equal
groups …’,
Record, for example, equal groups
arrays, and the
division symbol.
(Multiplication
and Division 2, 5) Record the division symbol, for example,
÷
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►
Today brings an investigation about dividing.
►
What do you know about dividing?
►
Talk about dividing with a friend.
►
Is anyone ready to share what they are thinking about
dividing?
►
We’ve investigated dividing.
►
And we found that we could see dividing in 2 ways.
►
We found that we could see dividing as ‘groups of …’
►
And we found that we could see dividing as ‘… equal
groups’
►
We’ve divided into arrays of equal rows.
►
And we’ve investigated the symbol the means we
divided.
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Introduces
Children sit in a circle so you can see what every child is doing.
assessing
whether children Distribute 8 counters to each child.
can see division in
2 ways.
Allow children to divide their counters by 2 by making either
‘groups of’ 2, for example,
or 2 ‘equal groups’, for example.
Allow children to pick up one of their groups – either 2 counters (if
they made groups of 2) or 4 counters (if they made 2 equal groups)
Record, for example, groups of 2
Record, for example, 2 equal groups
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►
Today we’re going to continue this investigation of how
we can divide counters into groups.
►
Please get 8 counters.
►
How many counters do you have?
►
Are there 8 counters?
►
How could you divide your group of 8 counters by 2?
►
There is more than one way to do this, so don’t copy
anyone else.
►
If you’re doing it a different way to someone else, that’s
great!
►
Who made groups?
►
Did everyone make groups?
►
Please pick up one of your groups.
►
Who picked up 2 counters?
►
How did you divide by 2?
►
Did you divide by 2 by making groups of 2?
►
Who picked up 4 counters?
►
How did you divide by 2?
►
Did you divide by 2 by making 2 equal groups?
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Children place their counters back together in 1 group
►
Please put your counters back together in one group
Allow children to try to divide their counters by 2 in the other way
►
– if they made ‘groups of’ 2 the first
time, watch to see if they can also
make 2 ‘equal groups’, for example,
This time when you divide your counters by 2, I want
you to try to do it the other way.
►
Please divide your counters by 2.
►
Who made groups?
►
Did everyone make groups?
►
Please pick up one of your groups.
►
Who picked up 2 counters?
►
You divided by 2 by making groups of 2.
►
Who picked up 4 counters?
►
You divided by 2 by making 2 equal groups
►
Who picked up the same number of counters both
times?
►
Who picked up a different number of counters each
time?
– if they made 2 ‘equal groups’ the
first time, watch to see if they can
also make ‘groups of’ 2, for example.
NB: Most children will not automatically
be able to divide by 2 in both ways.
It is fine if children repeat the same way
to divide by 2 at this stage.
Allow children to pick up one of their groups – either 2 counters (if
they made groups of 2) or 4 counters (if they made 2 equal groups)
Point to where you recorded, for example, groups of 2
Point to where you recorded, for example, 2 equal groups
Note any children who can divide by 2 in both ways.
Note any children who cannot divide by 2 in both ways.
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Introduces
dividing a multiple
of 2 (an even
number) by 2 by
making groups of
2, then counting
Children divide their counters by 2
the number of
by making groups of 2, for example,
groups. top
Record the groups, for example,
Record, for example, ‘groups of 2’
Introduces
recording a
number sentence
to describe what
we did.
Record, for example, 8
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►
Please put your counters back together into 1 group
again.
►
Please listen to the way I want you to divide your
counters by 2.
►
Please divide your counters by 2 by making groups of 2.
►
Let’s record our groups.
►
How could we describe our groups?
►
Do we have groups of 2?
►
Let’s record a number sentence to describe what we
did.
►
We know that a number sentence is just like a word
sentence. It tells the story of what we did.
►
How many counters did we start with?
►
Did we start with 8 counters?
►
Let’s record that we started with 8 counters.
►
What did we do to the 8 counters?
►
Did we divide the 8 counters?
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Reviews
the division
symbol.
(Multiplication
and Division 5)
Record, for example, 8 ÷
►
Let’s record that we divided the counters.
►
How did we divide the counters?
►
Did we divide the counters into groups of 2?
►
Let’s record that we divided the counters into groups of
2.
►
How many groups did that equal?
►
Did that equal 4 groups?
Record, for example, 8 ÷ 2 = 4
►
Let’s record that that equalled 4 groups.
Point to the parts of the number sentence as children read it, for
►
Let’s read our number sentence – 8 divided by 2 equals
4.
►
How did we divide by 2?
►
Did we divide by 2 by making groups of 2?
►
When we divide by making groups of 2, what did we
count?
►
Did we count the number of groups?
Record, for example, 8 ÷ 2
example, 8
÷ 2 = 4
8 divided by 2 equals 4
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Introduces
Children place the counters into 1 group, for example,
dividing a multiple
of 2 (an even
number) by 2 by
making 2 equal
groups, then
Children divide their counters by 2 by making 2 equal groups, for
counting the
example,
number of
counters in each
group.
Record the groups, for example,
Record, for example, ‘2 equal groups’
►
Please put your counters back together into 1 group
again.
►
Please listen to the way I want you to divide your
counters by 2.
►
Please divide your counters by 2 by making 2 equal
groups
►
Let’s record our groups.
►
How could we describe our groups?
►
Do we have 2 equal groups?
►
Let’s record a sentence to describe what we did.
►
We know that a number sentence is just like a word
sentence. It tells the story of what we did.
►
How many counters did we start with?
►
Did we start with 8 counters?
►
Let’s record that we started with 8 counters.
►
What did we do to the 8 counters?
►
Did we divide the 8 counters?
►
Let’s record that we divided the counters.
►
How did we divide the counters?
Introduces
recording a
number sentence
to describe what
we did.
Record, for example, 8
Record, for example, 8 ÷
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
►
Did we divide the counters into 2 equal groups?
►
Let’s record that we divided the counters into 2 equal
groups.
►
How many counters did that equal in each group?
►
Did that equal 4 counters in each group?
Record, for example, 8 ÷ 2 = 4
►
Let’s record that that equalled 4 counters in each group.
Point to the parts of the number sentence as children read it, for
►
What does our number sentence say?
example, 8
►
Does our number sentence say ‘8 divided by 2 equals 4’?
►
You can choose whether you record your number
sentences with the words ‘divided by’ or with the
symbol that says ‘divided by’.
►
How did we divide by 2?
►
Did we divide by 2 by making 2 equal groups?
►
When we divide by making 2 equal groups, what did we
count?
►
Did we count the number of counters in each group?
Point to both number sentences, for example, 8÷2=4 and 8÷2=4
►
Did we record the same number sentence for both way
of dividing?
Point to 8 counters divided into groups of
2, for example,
►
We divided 8 counters into groups of 2.
Record, for example, 8 ÷ 2
÷ 2 = 4
8 divided by 2 equals 4
Introduces
the same number
sentence may
describe 2 ways
to divide.
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Point to the parts of the number sentence as children read it, for
example,
►
And our number sentence says we started with 8, and
we divided into groups of 2 and now we have 4 groups.
►
We divided 8 counters into 2 equal groups.
►
And our number sentence say we started with 8, and we
divided into 2 equal groups and now we have 4 in each
group?
►
Did we record the same number sentence to describe
how we divided 8 by 2?
►
Are there 2 ways to divide 8 by 2?
►
Do you think there are 2 ways to divide every number by
2?
►
When we divide by 2, by making 2 equal groups, can we
pick up half our counters?
►
Please pick up half of your counters?
►
What is half of 8?
►
Is 4, half of 8?
►
Do we have a symbol that says half?
8 ÷ 2 = 4
8 divided into groups of 2 equals 4 in each group
Children divided 8 counters into 2 equal groups, for example,
Point to the parts of the number sentence as children read it, for
example,
8 ÷ 2 = 4
8 divided into 2 equal groups equals 4 groups
Children pick up half of their counters.
Record, for example, half of 8 = 4
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Introduces
1
Record, for example, 2 of 8 = 4
dividing a multiple
of 2 (an even
number) by 2 by
making 2 equal Point to the parts of the number sentence as children read it, for
1
groups creates example,
of 8 = 4
2
halves.
half of 8 equals 4
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►
Let’s use that symbol so everyone can read our number
sentence!
►
What does our number sentence say?
►
Does our number sentence say half of 8 equals 4?
►
Is dividing into 2 equal groups, and halving the same
thing?
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Introduces
finding related
divisions.
Children divided 8 counters into groups
of 2, for example,
Record, for example,
8÷4=2
Children divided 8 counters into 2 equal groups,
for example,
Record, for
example, 8 ÷ 4 = 2
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►
Let’s look at our counters when we divided them into
groups of 2.
►
How else could we describe how we have divided?
►
Could we say that we have divided into 4 equal groups?
►
When we divided 8 into groups of 2, does it look like we
divided into 4 equal groups?
►
Could we describe what we did as 8 divided into 4 equal
groups equals 2 in each group?
►
Let’s look at our counters when we divided them into 2
equal groups.
►
How else could we describe how we have divided?
►
Could we say that we have divided into groups of 4?
►
When we divided 8 into 2 equal groups, does it look like
we divided into groups of 4?
►
Could we describe what we did as 8 divided into groups
of 4 equals 2 groups?
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Introduces
dividing a nonmultiple of 2 (an
odd number) by 2
by making groups
of 2, then
counting the
number of groups Children divide a number of counters that is not divisible by 2s by 2 by making groups of 2, for example,
and remaining
counters.
Record the groups, for example,
Record, for example, ‘groups of 2’
Record, for example, 9 ÷ 2 = 4 and 1 remaining
Record, for example, 9 ÷ 2 = 4 r1
Children read the number sentence, for example, 9
÷ 2 = 4 r1
9 divided by 2 equals 4 with 1 remaining
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Children divide their counters by 2 by making 2 equal groups, for example,
Record the groups, for example,
Record, for example, ‘2 equal groups’
Record, for example, 9 ÷ 2 = 4 and 1 remaining
Record, for example, 9 ÷ 2 = 4 r1
Children read the number sentence, for example, 9
÷ 2 = 4 r1
9 divided by 2 equals 4 with 1 remaining
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Introduces
dividing by other
single-digit
numbers in 2
ways.
Divide a multiple of 3 by 3 by making groups of 3, for example,
Record what they did in a number sentence, for example, 12 ÷ 3 = 4
Relate their division to 12 ÷ 4 = 3
Divide a multiple of 3 by 3 by making 3 equal groups, for example,
Record what they did in a number sentence, for example, 12 ÷ 3 = 4
Relate their division to 12 ÷ 4 = 3
Divide a non-multiple of 3 by 3 by making groups of 3, for example,
Record what they did in a number sentence, for example, 13 ÷ 3 = 4r1
Relate their division to 13 ÷ 4 = 3r1
Divide a non-multiple of 3 by 3 by making 3 equal groups, for example,
Record what they did in a number sentence, for example, 13 ÷ 3 = 4r1
Relate their division to 13 ÷ 4 = 3r1
Divide by 4 and by 5 in the same way.
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MULTIPLICATION AND DIVISION 7 – TEACHING DIVISION IN 2 WAYS, BY DIVIDING INTO ‘… EQUAL GROUPS’, AND DIVIDING INTO ‘GROUPS OF…’
Introduces
the investigation,
reflection and
problem solving
related to this
segment of the
concept.
Need a 10 fra m
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