Patterns and Algebra 13, Multiplication and Division 5 _Explicit Learning Plan
(Year 2) ACMNA026, ACMNA031, NSW MA1-6NA MA1-8NA
Divide into equal rows (array) with no remainder, then describe using multiplication.
Find total using skip counting, and by number of rows and number in each row
Record multiplication and division as repeated addition and subtraction on a number line
Explain even numbers as counters divided into an array of 2 equal rows
Resources: counters, playing cards, pencil, paper
EXPLICIT LEARNING
What could we do?
Focuses
children’s
Children think about, talk and listen to a friend about, then have the
thoughts on the opportunity to share what they already know.
concept, exposing
current
understanding and
any
misconceptions
Reviews 2 ways
to divide
Display 12 counters that are all the same size, for example,
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What language could we use to explain and ask questions?
►
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 there are 2 ways to divide.
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1
Divide the counters by 2 by making groups of 2, for example,
►
We found that we could divide counters by 2 by making
‘groups of 2’.
Count the groups, for example, 1 2 3 4 5 6
►
And we found that we counted the number of groups.
Record, for example, 12
►
We recorded a number sentence that said that we
started with 12 counters.
Record, for example, 12 divided by 2
►
And that we divided the counters.
Record, for example, 12 divided by 2 = 6
►
And we divided the 12 counters into groups of 2.
►
And that equalled 6 groups.
►
We found that we could record our number sentence
using a symbol that says we divided so that everyone
around the world could read our number sentence.
Record, for example 12 ÷ 2 = 6
►
And our number sentence says 12 divided by 2 equals 6.
Divide the counters by 2 by making 2 equal groups, for example,
►
We found that we could divide counters by 2 by making
‘2 equal groups’.
Count the groups, for example, 1 2 3 4 5 6
►
And we found that we counted the number of counters
in each group.
►
We recorded a number sentence that said that we
started with 12 counters.
Record, for example, 12 divided by
Record, for example, 12
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2
Record, for example, 12 divided by
►
And that we divided the counters.
Record, for example, 12 divided by 2
►
And we divided the 12 counters into 2 equal groups.
Record, for example, 12 divided by 2 = 6
►
And that equalled 6 counters in each group.
►
We found that we could record our number sentence
using a symbol that says we divided so that everyone
around the world could read our number sentence.
►
And our number sentence says 12 divided by 2 equals 6.
►
Today we’re going to investigate how we could arrange
the counters in the groups so that we can tell without
counting whether the groups are equal.
►
Are these groups equal?
►
How could we check?
►
Can we tell if these groups are equal just by looking or do
we need to count to check?
►
How could we arrange the counters so that we can tell
that the groups are equal just by looking, without having
to count?
►
What if we placed the counters into rows?
►
Would we be able to tell just by looking of each row was
equal without counting? Let's investigate!
►
Are the rows equal?
►
How can we tell that the rows are equal?
Record, for example 12 ÷ 2 = 6
Introduces
dividing into equal
rows
Divide the counters by 2 by making 2 equal groups, with one group
spread out more than the other so that it is not immediately obvious
that they are equal, for example,
Place the counters that are all the same size into 2 equal rows, for
example,
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3
►
Are the rows the same length?
►
When we place counters in rows, can we tell by looking,
without counting whether the rows are equal?
►
What name do you think we call a pattern of equal rows?
Record, for example, 'array'
►
We call a pattern of equal rows, an array.
Record the array, for example,
►
Let’s record our array.
Giving children 1 square centimetre
grid paper to record their arrays
allows them to make their rows
equal length.
►
How could we record a number sentence to describe this
array?
►
We know that a number sentence is just like a word
sentence.
►
Our number sentence is going to tell the story of what
we did to create this array.
►
How many counters did we start with?
►
Did we start with 12 counters?
►
What does our number sentence say so far?
►
Does our number sentence say, 12?
►
What did we do to the counters?
►
Did we divide the counters?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by?
►
How many rows did we divide the counters into?
►
Did we divide the counters into 2 rows?
Introduces arrays
as equal rows
Reviews recording
the way we
divided in a
number sentence
(Multiplication and
Division 1)
Record, for example, 12
Record, for example, 12 ÷
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4
Record, for example, 12 ÷ 2
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by 2?
►
How many counters did that equal in each row?
►
Did that equal 6 counters in each row?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by 2 equals 6?
►
Could we describe this array as 12 divided by 2 equals 6?
►
Could we divide the counters into a different array?
►
Could we try to divide the counters into 3 equal rows?
►
Are the rows equal?
►
How can we tell that the rows are equal?
►
Are the rows the same length?
►
When we place counters in rows, can we tell by looking,
without counting whether the rows are equal?
►
What name do we call a pattern of equal rows?
►
Do we call a pattern of equal rows, an array?
Record, for example, 'array'
►
Let’s record our array.
Record the array, for example,
►
How could we record a number sentence to describe this
array?
►
We know that a number sentence is just like a word
sentence.
Record, for example, 12 ÷ 2 = 6
Divide the counters that are all the same size into a different array,
for example,
Giving children 1 square centimetre grid paper to record their arrays
allows them to make their rows equal length.
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5
Record, for example, 12
Record, for example, 12 ÷
Record, for example, 12 ÷ 3
Record, for example, 12 ÷ 3 = 4
►
Our number sentence is going to tell the story of what
we did to create this array.
►
How many counters did we start with?
►
Did we start with 12 counters?
►
What does our number sentence say so far?
►
Does our number sentence say, 12?
►
What did we do to the counters?
►
Did we divide the counters?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by?
►
How many rows did we divide the counters into?
►
Did we divide the counters into 3 rows?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by 3?
►
How many counters did that equal in each row?
►
Did that equal 6 counters in each row?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by 3 equals 4?
►
Could we describe this array as 12 divided by 3 equals 4?
Allow children time now to engage in guided and independent investigation of
dividing counters into arrays of equal rows, describing how the array was created
in a number sentence.
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6
Children think about, talk and listen to a friend about, then have the
Introduces
dividing into equal opportunity to share what they already know.
rows and
recording 2
division number
sentences to
describe how the
array was created
Record, for example, array
Divide the counters that are all the same size into an array, for
example,
►
Today brings an investigation about arrays.
►
What do you know about arrays?
►
Talk about arrays with a friend.
►
Is anyone ready to share what they are thinking about
arrays?
►
We’ve investigated arrays.
►
And we found that an array is equal rows.
►
We found that we can divide counters into arrays of
equal rows.
►
And the array allowed us to see if the rows were equal
without counting.
►
We found that we could record a number sentence to
describe how we created the array.
►
We found that this number sentence says that we
started with 12 counters and we divided them into 3
equal rows and that equalled 4 in each row.
►
Today we’re going to investigate how we could describe
the array in different ways.
►
How could we divide these counters on this piece of
paper?
Record, for example, 12 ÷ 3 = 4
Display 12 counters that are all the same size, for example,
Display a piece of paper, for example,
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7
Divide the counters into an array of 2
equal rows on a piece of paper to allow
for easy rotation later, for example,
Record the array, for example,
►
Are the rows equal?
►
How can we tell that the rows are equal?
►
Are the rows the same length?
►
Let's record the array.
►
How could we record a number sentence to describe this
array?
►
We know that a number sentence is just like a word
sentence.
►
Our number sentence is going to tell the story of what
we did to create this array.
►
How many counters did we start with?
►
Did we start with 12 counters?
►
What does our number sentence say so far?
►
Does our number sentence say, 12?
►
What did we do to the counters?
►
Did we divide the counters?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by?
►
How many rows did we divide the counters into?
►
Did we divide the counters into 2 rows?
►
What does our number sentence say so far?
Giving children 1 square centimetre grid paper to record their arrays
allows them to make their rows equal length.
Record, for example, 12
Record, for example, 12 ÷
Record, for example, 12 ÷ 2
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8
Record, for example, 12 ÷ 2 = 6
Turn the array, for example,
Record, for example, 12
Record, for example, 12 ÷
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►
Does our number sentence say, 12 divided by 2?
►
How many counters did that equal in each row?
►
Did that equal 6 counters in each row?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by 2 equals 6?
►
Could we describe this array as 12 divided by 2 equals 6?
►
Is this the only way we could describe this array?
►
What if we turn the array?
►
How could we record a number sentence to describe this
array?
►
We know that a number sentence is just like a word
sentence.
►
Our number sentence is going to tell the story of what
we did to create this array.
►
How many counters did we start with?
►
Did we start with 12 counters?
►
What does our number sentence say so far?
►
Does our number sentence say, 12?
►
What did we do to the counters?
►
Did we divide the counters?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by?
►
How many rows did we divide the counters into?
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9
►
This time did we divide the counters into 6 rows?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by 6?
►
How many counters did that equal in each row?
►
Did that equal 6 counters in each row?
►
What does our number sentence say so far?
►
Does our number sentence say, 12 divided by 6 equals 2?
►
Could we describe this array as 12 divided by 6 equals 2?
►
Can we describe the array in 2 ways?
►
Can we describe this array as 12 divided into 2 equal
rows equals 6 in each row?
Turn the array, for example,
►
Does our number sentence say 12 divided by 2 equals 6?
Display, for example, 12 ÷ 6 = 2
►
Can we describe the array as 12 divided into 6 equal
rows equals 2 in each row?
Allow children time now to engage in guided and independent investigation of
dividing counters into arrays of equal rows, describing how the array was created
in 2 number sentences.
►
Does our number sentence say 12 divided by 6 equals 2?
Record, for example, 12 ÷ 6
Record, for example, 12 ÷ 6 = 2
Display the array, for example,
Display, for example, 12 ÷ 2 = 6
A child who has not demonstrated understanding of dividing counters
into arrays of equal rows, describing how the array was created in 1
number sentence will continue to investigate this.
A child could be sitting next to a child who is investigating at a
different level. They will explain their current levels of understanding
to one another as they investigate. This is a research-based way to
accelerate learning for children at all levels.
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10
Children think about, talk and listen to a friend about, then have the
Introduces
dividing into equal opportunity to share what they already know.
rows and
recording 2
multiplication
number sentences
to describe the
array
Record, for example, array
►
Today brings an investigation about arrays.
►
What do you know about arrays?
►
Talk about arrays with a friend.
►
Is anyone ready to share what they are thinking about
arrays?
►
We’ve investigated arrays.
►
And we found that an array is equal rows.
►
We found that we can divide counters into arrays of
equal rows.
►
And the array allowed us to see if the rows were equal
without counting.
►
We found that we could record number sentences to
describe how we created the array.
►
We found that this number sentence says that we
started with 12 counters and we divided them into 2
equal rows and that equalled 6 in each row.
►
And we found that this number sentence says that we
started with 12 counters and we divided them into 6
equal rows and that equalled 2 in each row.
Display the array, for example,
Display, for example, 12 ÷ 2 = 6
Turn the array, for example,
Display, for example, 12 ÷ 6 = 2
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11
Display 12 counters that are all the same size, for example,
►
Today we’re going to investigate how we can describe
arrays using multiplication.
►
How could we divide these counters on this piece of
paper?
►
How could we record the array?
►
How could we record a division number sentence to
describe how we created the array?
►
How many counters did we start with?
►
What did we do to the counters?
►
How many rows did we divide the counters into?
►
How many counters did that equal is each row?
►
What does our number sentence say?
►
Does our number sentence say 12 divided by 2 equals 6?
►
How else could we record a division number sentence to
describe how we created the array?
Display a piece of paper, for example,
Divide the counters into an array of 2
equal rows on a piece of paper to allow
for easy rotation later, for example,
Record the array, for example,
Giving children 1 square centimetre grid paper to record their arrays
allows them to make their rows equal length.
Record, for example, 12
Record, for example, 12 ÷
Record, for example, 12 ÷ 2
Record, for example, 12 ÷ 2 = 6
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12
Record, for example, 12
►
How many counters did we start with?
Record, for example, 12 ÷
►
What did we do to the counters?
Record, for example, 12 ÷ 6
►
How many rows did we divide the counters into?
Record, for example, 12 ÷ 6 = 2
►
How many counters did that equal is each row?
►
What does our number sentence say?
►
Does our number sentence say 12 divided by 6 equals 2?
►
How could we describe our array using multiplication?
►
How many rows?
►
Are there 2 rows?
►
How many in each row?
►
Are there 6 in each row?
►
How many does that equal altogether?
►
Does that equal 12 counters altogether?
►
Do we have symbol that says we have equal groups or
equal rows so that everyone around the whole world can
read our number sentence?
Record, for example, x
►
The symbol looks like this.
Record, for example, 2 x 6 = 12
►
Let’s record our number sentence using the symbol.
►
Let’s read our number sentence: It says 2 times 6 equals
12.
►
Why does the symbol say ‘times’?
►
How many times do we have 6?
Record, for example, 2 rows
Record, for example, 2 rows of 6
Record, for example, 2 rows of 6 = 12
Reviews the
multiplication
symbol says
‘times’
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13
Display the array, for example,
►
Do we have 6, 1 time?
►
Do we have 6, 2 times?
►
Do we have 2 times 6?
►
Does the number sentence say we have 2 times 6 and
that equals 12?
►
How else could we describe our array using
multiplication?
►
Could we turn the array?
►
How many rows?
►
Are there 6 rows?
►
How many in each row?
►
Are there 2 in each row?
►
How many does that equal altogether?
►
Does that equal 12 counters altogether?
►
Could we record our number sentence using the symbol
that says we have equal groups or equal rows so that
everyone around the whole world can read our number
sentence?
Point to 6, 1 time, for example,
Point to 6, 2 times, for example,
Display, for example, 2 x 6 = 12
Turn the array, for example,
Record, for example, 6 rows
Record, for example, 6 rows of 2
Record, for example, 6 rows of 2 = 12
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14
Introduces finding Record, for example, 2 x 6 = 12
the total using the
number of rows
and the number in
each row
►
Let’s record our number sentence using the symbol.
►
Let’s read our number sentence: It says 6 times 2 equals
12.
►
Why does the symbol say ‘times’?
Display the array, for example,
►
How many times do we have 2?
Point to 2, 1 time, for example,
►
Do we have 2, 1 time?
Point to 2, 2 times, for example,
►
Do we have 2, 2 times?
►
Do we have 2, 3 times?
►
Do we have 2, 4 times?
►
Do we have 2, 5 times?
►
Do we have 2, 6 times?
Point to 2, 3 times, for example,
Point to 2, 4 times, for example,
Point to 2, 5 times, for example,
Point to 2, 6 times, for example,
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15
Display, for example, 6 x 2 = 12
Reviews
differentiating the
investigation for
children as they
demonstrate
understanding
►
Do we have 6 times 2?
►
Does the number sentence say we have 6 times 2 and
that equals 12?
►
Did we describe the array in 4 number sentences?
Record, for example, 12 ÷ 2 = 6
►
Did we describe the array as 12 divided by 2 equals 6?
Record, for example, 12 ÷ 6 = 2
►
Did we describe the array as 12 divided by 6 equals 2?
Record, for example, 2 x 6 = 12
►
Did we describe the array as 2 times 6 equals 12?
Record, for example, 6 x 2 = 12
►
Did we describe the array as 6 times 2 equals 12?
Allow children time now to engage in guided and independent investigation of
dividing counters into arrays of equal rows, describing how the array was created
in 2 division number sentences and describing the array in 2 multiplication
number sentences.
A child who has not demonstrated understanding of dividing counters
into arrays of equal rows, describing how the array was created in 2
division number sentences will continue to investigate this.
A child who has not demonstrated understanding of dividing counters
into arrays of equal rows, describing how the array was created in 1
number sentence will continue to investigate this.
Introduces even
numbers as
counters divided
into an array of 2
equal rows
A child could be sitting next to a child who is investigating at a
different level. They will explain their current levels of understanding
to one another as they investigate. This is a research-based way to
accelerate learning for children at all levels.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
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16
Children think about, talk and listen to a friend about, then have the
opportunity to share what they already know.
Display an even number of counters that are all the same size, for
example, 12
Divide the counters into an array of
2 equal rows, for example,
Record, for example, 12 ÷ 2 = 6
►
Today brings an investigation about arrays.
►
What do you know about arrays?
►
Talk about arrays with a friend.
►
Is anyone ready to share what they are thinking about
arrays?
►
We’ve investigated arrays.
►
And we found that an array is equal rows.
►
We divided counters into arrays of 2 equal rows.
►
Can all numbers of counters be divided into 2 equal
rows? Let’s investigate!
►
How many counters do we have?
►
Do we have 12 counters?
►
Could we divide these 12 counters into an array of 2
equal rows?
►
Did we divide the counters into an array of 2 equal rows?
►
Did we have any counters remaining?
►
How could we record this in a division number sentence?
►
Could we record, 12 divided by 2 equals 6?
►
So when we divided 12 counters into an array of 2 equal
rows, we have no counters remaining.
►
We call numbers that can be divided into an array of 2
equal rows, even numbers.
►
Is 12 an even number?
Record, for example, even
Record, for example, 12 is an even number
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17
Display an odd number of counters that are all the same size, for
example, 15
Divide the counters into an array of
2 equal rows, for example,
Record, for example, 15 ÷ 2 = 7r1
Allow children time now to engage in guided and independent investigation of
identifying even numbers as counters paired in 2 equal rows.
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►
Let’s try to divide these counters into an array of 2 equal
rows.
►
How many counters do we have?
►
Do we have 15 counters?
►
Could we divide these 15 counters into an array of 2
equal rows?
►
Did we divide the counters into an array of 2 equal rows?
►
Did we have any counters remaining?
►
Do we have 1 counter remaining?
►
How could we record this in a division number sentence?
►
Could we record, 15 divided by 2 equals 7 and 1
remaining?
►
So when we divided 15 counters into an array of 2 equal
rows, we have 1 counter remaining.
►
Can 15 be divided into an array of 2 equal rows without
any counters remaining?
►
We call numbers that cannot be divided into an array of
2 equal rows, odd numbers.
►
Is 15 an odd number?
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18
Introduces
arranging
counters in an
array then skip
counting to find
the total
Children think about, talk and listen to a friend about, then have the
opportunity to share what they already know.
►
Today brings an investigation about arrays.
►
What do you know about arrays?
►
Talk about arrays with a friend.
►
Is anyone ready to share what they are thinking about
arrays?
►
We’ve investigated arrays.
►
And we found that an array is equal rows.
►
We found that we can divide counters into arrays of
equal rows.
►
And the array allowed us to see if the rows were equal
without counting.
►
We found that we could record number sentences to
describe the array.
►
We found we could describe arrays in 2 ways using
division.
►
And we found that we could describe arrays in 2 ways
using multiplication.
►
Today, we’re going to investigate making arrays to help
us to count counters.
►
How many counters?
►
How could we count these counters?
►
Because they are just in one large group, we’d probably
count them by ones.
Display an array, for example,
Record, for example, 12 ÷ 2 = 6
Record, for example, 12 ÷ 6 = 2
Record, for example, 2 x 6 = 12
Record, for example, 6 x 2 = 12
Display some counters that are all the same size, for example, 15
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19
►
Let's make an array using these counters to investigate
how we could then count the counters.
►
Could we make an array of 2 equal rows?
►
We have 1 counter remaining.
►
If we have 1 counter remaining when we divide the
counters into an array of 2 equal rows, what kind of
number is this?
►
Is this an odd number?
►
So we can’t make an array of 2 equal rows with these
counters because it is an odd number.
►
Could we make an array of 3 equal rows?
►
Did we make an array of 3 equal rows?
►
Now that the counters are arranged in an array of 3
equal rows, how could we count the counters?
►
Could we count the counters by skip or rhythmic
counting?
►
Let’s record the array.
Children attempt to make an array of 2 equal rows, for example,
Reviews odd
numbers
Children attempt to make an array of 3 equal rows, for example,
Point to the 3 equal rows, for example,
Record the array, for example,
Rhythmic count the counters, for example,
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12345
6 7 8 9 10
11 12 13 14 15
►
Let’s count the counters using rhythmic counting.
►
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
►
How could we record our rhythmic count?
►
Could we skip count the counters?
►
How many counters in each row?
►
Are there 5 counters in each row?
►
Could we skip count by 5s?
►
5 10 15
►
When we skip count by 5s, are we saying the multiples of
5?
►
Let’s say the multiples of 5, 5 10 15
►
How could we record our skip count?
►
Could we circle the last number we said each time we
rhythmic counted?
►
How many counters altogether?
►
Are there 15 counters altogether?
►
How did we count the counters?
Record the rhythmic count of the counters, for example,
12345
6 7 8 9 10
11 12 13 14 15
Skip count the counters, for example,
5
10
15
Reviews multiples
Record, for example, multiples
(Multiplication and
Division 3)
Record the rhythmic count of the counters, for example,
12345
6 7 8 9 10
11 12 13 14 15
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Introduces seeing
rows in an array
from any
perspective
►
Did we make an array?
►
Did we rhythmic or skip count the counters in rows?
►
When we skip counted by 5s, did we say the multiples of
5?
►
Let’s look at the array in a different way.
►
Could we see this array as 5 equal rows?
►
Now that we see an array of 5 equal rows, how could we
count the counters?
►
Could we still count the counters by skip or rhythmic
counting?
12345
►
Let’s count the counters using rhythmic counting.
6 7 8 9 10
►
1 2 3 4 5 6 7 8 9 10 11 12
Point to the 5 equal rows, for example,
Vertical rows are sometimes unnecessarily called columns. To make
the inconsistent distinction between rows and columns adds
irrelevant complexity to the concept of an array being able to be read
from any perspective. Rows (and columns) go vertically and
horizontally.
Rhythmic count the counters, for example,
13 14 15
11 12 13 14 15
1 4 7 10 13
2 5 8 11 14
3 6 9 12 15
Record the rhythmic count of the counters, for example,
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12345
►
How could we record our rhythmic count?
5
►
Could we skip count the counters?
10
►
How many counters in each row?
15
►
Are there 3 counters in each row?
►
Could we skip count by 3s?
►
3 6 9 12 15
►
When we skip count by 3s, are we saying the multiples of
3?
12345
►
How could we record our skip count?
6 7 8 9 10
►
Could we circle the last number we said each time we
rhythmic counted?
►
How many counters altogether?
►
Are there 15 counters altogether?
►
How did we count the counters?
►
Did we make an array?
6 7 8 9 10
11 12 13 14 15
1 4 7 10 13
2 5 8 11 14
3 6 9 12 15
Skip count the counters, for example,
Reviews multiples
3 6 9 12 15
(Multiplication and
Division 3)
Record the skip count of the counters, for example,
11 12 13 14 15
1 4 7 10 13
2 5 8 11 14
3 6 9 12 15
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►
Did we rhythmic or skip count the counters in rows?
►
When we skip counted, did we say multiples?
Allow children time now to engage in guided and independent investigation of
rhythmic or skip counting counters after making an array.
Children think about, talk and listen to a friend about, then have the
opportunity to share what they already know.
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Introduces
recording
multiplication as
repeated addition
on a number line
►
Today brings an investigation about arrays.
►
What do you know about arrays?
►
Talk about arrays with a friend.
►
Is anyone ready to share what they are thinking about
arrays?
►
We’ve investigated arrays.
►
And we found that an array is equal rows.
►
We found that we could divide counters into arrays of
equal rows.
►
We found we could record number sentences to
describe arrays in 2 ways using division.
►
And we found that we could record number sentences to
describe arrays in 2 ways using multiplication.
►
And we found that we could skip and rhythmic count the
counters in rows in 2 ways.
►
We could see the array as 3 rows of 5, and skip count by
5s.
►
Or we could see the array as 5 rows of 3, and skip count
by 3s.
►
When we skip count 3 rows of 5, are finding out what 3
times 5 equals?
►
When we skip count 5 rows of 3, are finding out what 5
times 3 equals?
►
Let’s investigate by recording the skip count on a number
line.
Display an array, for example,
Record, for example, 15 ÷ 3 = 5 and
15 ÷ 5 = 3
Record, for example, 5 x 3 = 15 and
3 x 5 = 15
Skip and rhythmic count of the counters, for example,
12345
6 7 8 9 10
11 12 13 14 15
1 4 7 10 13
2 5 8 11 14
3 6 9 12 15
Record, for example, 3 x 5 =
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Draw an open empty number line, for example,
Indicate left and right on the number line.
►
Let’s record an open empty number line.
►
If we skip counting forwards by 5s, are we going to get
bigger or smaller?
►
Will we get bigger?
►
If we’re going to get bigger, which end of the number will
we start from?
►
In which direction do the numbers get larger on a
number line – to the left or to the right?
►
Do the numbers get larger as we move to right on a
number line?
►
Will we start from the left end of the number line so we
can get bigger as we move towards the right?
►
Let’s place a mark on the left end of the number line.
►
Let's record zero under the mark.
►
The first number in our skip count is 5.
►
Let’s record a mark on the number line and record 5
under it.
Record a mark on the left end of the number line, for example,
Record 0 under the mark, for example,
0
Record a mark on the number line and record 5 under the mark, for
example,
0
5
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Record a jump forwards on the number line from the 0 to the 5, for
example,
0
►
Let’s record a jump forwards from the zero to the 5.
►
If we jump from zero to 5, how many have we added?
►
Have we added 5?
►
Let’s record that we added 5 above the jump.
►
The second number in our skip count is 10.
►
Let’s record a mark on the number line and record 10
under it.
►
Let’s record a jump forwards from the 5 to the 10.
►
If we jump from 5 to 10, how many have we added?
►
Have we added 5?
5
Record + 5 above the jump, for example,
+5
0
5
Record a mark on the number line and record 10 under the mark, for
example,
+5
0
5
10
Record a jump forwards on the number line from the 5 to the 10, for
example,
+5
0
5
10
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Record + 5 above the jump, for example,
+5
0
+5
The second number in our skip count is 15.
►
Let’s record a mark on the number line and record 15
under it.
►
Let’s record a jump forwards from the 10 to the 15.
►
If we jump from 10 to 15, how many have we added?
►
Have we added 5?
►
Let’s record that we added 5 above the jump.
+5
5
10
15
Record a jump forwards on the number line from the 10 to the 15, for
example,
+5
+5
5
10
15
Record + 5 above the jump, for example,
+5
0
►
10
Record a mark on the number line and record 15 under the mark, for
example,
0
Let’s record that we added 5 above the jump.
+5
5
0
►
+5
5
+5
10
15
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Reviews number
patterns
(Multiplication and
Division 3 Patterns
and Algebra 8)
►
We’ve investigated number patterns.
►
We found that a number pattern is a series of numbers
that repeat in the same way.
►
Is this a number pattern?
►
If this is a number pattern, there must be something that
happens repeatedly.
►
Is something happening repeatedly?
►
Is something happening over and over and over again?
►
Are we repeatedly adding 5?
►
Are we adding 5, over and over again?
►
Are we counting forwards by 5?
►
When we count forwards by 5, how many are we adding
each time?
►
Are we adding 5 each time?
►
How many times did we add 5?
►
Did we add 5, 3 times?
►
When we added 5, 3 times, how many did we have?
►
When we added 5, 3 times, did we have 15?
Record, for example, 3 x 5 = 15
►
When we have 3 times 5, did we have 15?
Allow children time now to engage in guided and independent investigation of
recording multiplication on a number line as repeated addition.
►
Could we say that 3 times 5 equals 15?
►
What does this number sentence say?
►
Does the number sentence say, 3 times 5 equal 15?
►
Did we multiply by 5 on a number line?
Point to the number line, for example,
+5
0
+5
5
+5
10
15
Point to repeatedly adding 5, for example,
+5
0
+5
5
+5
10
15
Point to the 3 times we added 5, for example,
+5
0
+5
5
+5
10
15
Children think about, talk and listen to a friend about, then have the
opportunity to share what they already know.
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Introduces
recording division
as repeated
subtraction on a
number line
►
Today brings an investigation about arrays.
►
What do you know about arrays?
►
Talk about arrays with a friend.
►
Is anyone ready to share what they are thinking about
arrays?
►
We’ve investigated arrays.
►
And we found that an array is equal rows.
Display an array, for example,
Record, for example, 15 ÷ 3 = 5 and
15 ÷ 5 = 3
►
We found that we could divide counters into arrays of
equal rows.
Record, for example, 5 x 3 = 15 and
3 x 5 = 15
►
We found we could record number sentences to
describe arrays in 2 ways using division.
►
And we found that we could record number sentences to
describe arrays in 2 ways using multiplication.
►
And we found that we could skip and rhythmic count the
counters in rows.
►
We found that we could see the array as 3 rows of 5, and
skip count by 5s.
►
We skip counted the 3 rows of 5 on a number line and
found that we are repeatedly adding 5.
Skip and rhythmic count of the counters, for example,
12345
6 7 8 9 10
11 12 13 14 15
Point to the 3 times we added 5, for example,
+5
0
+5
5
+5
10
15
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Record, for example, 3 x 5 = 15
►
We counted the number of times we added 5, to record
that 3 times 5 equals 15.
Display 15 counters, for example,
►
Today we’re going to investigate recording division on a
number line.
►
How many counters do we have?
►
Do we have 15 counters?
►
Let’s divide the counters into rows of 5.
►
Let’s make 1 row of 5.
►
Did we take away 5 of the counters to make a row of 5?
►
Let’s make another row of 5.
►
Did we take away another 5 of the counters to make
another row of 5?
►
Let’s make another row of 5.
►
Did we take away another 5 of the counters to make
another row of 5?
►
Did we divide the 15 counters into rows of 5 by making
repeatedly subtracting 5?
►
What does our number sentence say?
Make 1 row of 5, for example,
Make another row of 5, for example,
Make another row of 5, for example,
Record, for example, 15 ÷ 5 = 3
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Draw an open empty number line, for example,
►
Does our number sentence say, 15 divided into rows of 5
equals 3 rows?
►
Could we record 15 divided by 5 on a number line by
repeatedly subtracting 5? Let’s investigate!
►
Let’s record an open empty number line.
►
If we are going to repeatedly subtract 5 on the number
line, are we going to get bigger or smaller?
►
Will we get smaller?
►
If we’re going to get smaller, which end of the number
will we start from?
►
In which direction do the numbers get smaller on a
number line – to the left or to the right?
►
Do the numbers get smaller as we move to left on a
number line?
►
Will we start from the right end of the number line so we
can get smaller as we move towards the left?
►
Let’s place a mark on the right end of the number line.
►
How many counters did we start with?
►
Did we start with 15 counters?
►
Let's record 15 under the mark.
Indicate left and right on the number line.
Record a mark on the right end of the number line, for example,
Record 15 under the mark, for example,
15
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Record a jump backwards on the number line from the 15 and record
– 5 above the jump, for example,
►
Let’s record a jump backwards from the 15 and record
that we subtracting 5 above the jump.
►
If we start from 15 and subtract 5, how many will we
have left?
►
Will we have 10 left?
►
Let’s record a mark where the jump lands and record 10
under the mark.
►
Let’s record a jump backwards from the 10 and record
that we subtracting 5 above the jump.
►
If we start from 10 and subtract 5, how many will we
have left?
►
Will we have 5 left?
►
Let’s record a mark where the jump lands and record 5
under the mark.
-5
15
Record a mark where the jump lands and record 10 under the mark,
for example,
-5
10
15
Record a jump backwards on the number line from the 10 and record
– 5 above the jump, for example,
-5
-5
10
15
Record a mark where the jump lands and record 5 under the mark,
for example,
-5
5
-5
10
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Record a jump backwards on the number line from the 5 and record
– 5 above the jump, for example,
-5
-5
5
0
10
-5
5
Let’s record a jump backwards from the 5 and record
that we subtracting 5 above the jump.
►
If we start from 10 and subtract 5, how many will we
have left?
►
Will we have zero left?
►
Let’s record a mark where the jump lands and record 0
under the mark.
►
We’ve investigated number patterns.
►
We found that a number pattern is a series of numbers
that repeat in the same way.
►
Is this a number pattern?
►
If this is a number pattern, there must be something that
happens repeatedly.
►
Is something happening repeatedly?
►
Is something happening over and over and over again?
►
Are we repeatedly subtracting 5?
►
Are we subtracting 5, over and over again?
►
Are we counting backwards by 5?
-5
15
Record a mark where the jump lands and record 0 under the mark,
for example,
-5
►
-5
10
15
Reviews number
patterns
(Multiplication and
Division 3 Patterns
and Algebra 8)
Point to the number line, for example,
-5
0
-5
5
-5
10
15
Point to repeatedly subtracting 5, for example,
-5
-5
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0
5
10
15
►
When we count backwards by 5, how many are we
subtracting each time?
►
Are we subtracting 5 each time?
►
When we record dividing by 5 on a number line, how are
we seeing dividing by 5?
►
Are we seeing dividing by 5 as making ‘groups of 5’?
►
How many times did we subtract a group of 5?
►
Did we subtract a group of 5, 3 times?
►
How many groups of 5 did we subtract?
►
Did we subtract three groups of 5?
►
If we subtracted three groups of 5, how many groups of
5 are there in 15?
►
Are there three groups of 5 in 15?
►
So what is 15 divided into groups of 5?
►
Is 15 divided groups of 5, 3?
►
What does this number sentence say?
►
Does it say we divided 15 into groups of 5 and that
equalled 3 groups?
►
Does it say 15 divided by 5 equals 3?
►
Did we divide by 5 on a number line?
Point to the 3 times we subtracted 5, for example,
-5
0
-5
5
-5
10
15
Record, for example, 15 ÷ 5 = 3
Allow children time now to engage in guided and independent investigation of
recording division on a number line as repeated subtraction.
Need a 10 fra m
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