Addition Subtraction 30, Fractions Decimals 32, Place Value 32_Overview of Learning Plan
(Year 6) ACMNA128, NSW MA3-7NA
Add and subtract decimals using place value and compensation.
Resources: cards, pencil, paper
Add decimals Children:
 add decimals using place value, for example,
using place
value and
using
compensation.
 add decimals using compensation, for example,
Subtract
decimals
using place
value and
using
compensation.
 subtract decimals using place value, for example,
 subtract decimals using compensation,
for example,
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
Children
 ask one another questions about adding and subtracting
decimals, for example:

How could we add these numbers using place value?

Are either of these numbers close to a place value?

Because this number is close to a place value, how could
we add these numbers using compensation?

How is adding decimals the same as adding whole
numbers?

How could we subtract these numbers using place
value?

Are either of these numbers close to a place value?

Because this number is close to a place value, how could
we subtract these numbers using compensation?

How is subtracting decimals the same as subtracting
whole numbers?
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
1
Addition Subtraction 30, Fractions Decimals 32, Place Value 32_Explicit Learning Plan
(Year 6) ACMNA128, NSW MA3-7NA
Add and subtract decimals using place value and compensation.
Resources: cards, counters, pencil, paper
EXPLICIT LEARNING
What could we do?
Focuses
children’s
thoughts on the
Children think about, talk and listen to a friend about, then have the
concept, exposing
opportunity to share what they already know.
current
understanding and
any
misconceptions
Record, for example, 6825 + 5897 =
Reviews adding
whole numbers
using properties
and relationships
(Addition and
Subtraction 24)
What language could we use to explain and ask questions?
►
Today brings an investigation about addition.
►
What do you know about addition?
►
Talk about addition with a friend.
►
Is anyone ready to share what they are thinking about
addition?
►
We've investigated adding whole numbers using friends
of 10, partitioning and place value
►
We partitioned using friends of 10
►
And used place value to add
Record, for example,
6825 + 5 8 9 7 =
5000+800+90+7
4000+1000 200+600 80+10 5+2
Record jumps as you add place values, partitioned using friends of 10,
for example,
+4000
6825
+1000
10 825
+200
11 825 12 025
+600
+80 +10
+5 +2
12 625 12 705 12 715 12 720 12 722
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Record, for example, 6825 + 5897 =
►
We also investigated how compensation could be used.
►
Let's try something fun! Let's place a decimal point into each of
the numbers to change their values.
►
Now let's investigate how we can add two numbers with
decimals using friends of 10, partitioning and place value.
►
First let's look at the numbers. How big is 682.5? Is 682.5
more than 680? Is it closer to 680 or 690?
►
How big is 58.97?
►
Is 58.97 more than 50?
►
Is it closer to 60?
►
Let's record a number line.
►
Which end of the line will the 682.5 go on?
►
Will we get larger or smaller?
►
In which direction do the numbers get larger on a
number line?
►
If we're going to get larger, will we start on the left so we
can move to the right as we add?
►
How could we partition 58.97 to add it to 682.5?
►
Could we partition 5897 using place value?
Record, for example, 6825 + 6000 = 12 825
Record, for example, 12 825 - 103 = 12 722
Record, for example, 6825 + 5897 = 12 722
Introduces adding
decimals using
properties and
relationships. top
Record, for example, 682.5 + 58.97 =
Record a number line with the start number at the left hand end, for
Reviews recording example,
on a number line.
(Addition and
682.5
Subtraction 24)
Reviews
partitioning using
place value.
(Addition and
Subtraction 24)
Record, for example,
682.5 + 5 8 . 9 7 =
50 + 8+ .9 +.07
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
Reviews adding
using friends of
10. (Addition and
Subtraction 24)
►
How could we add the 50?
►
How many tens are we adding?
►
Are we adding 5 tens?
►
How many tens do we have?
►
Do we have 8 tens?
►
Is 100, 10 tens?
►
How many tens will we need to add to 8 tens to get to 10
tens?
►
What is 8's friend of 10?
►
Is 8’s friend of 10, 2?
►
Will we need to add 2 tens?
►
If we add 2 tens, will we have another hundred?
►
If we add 20, will we have 702.5?
►
How did we partition the 50?
►
We've added 20.
682.5 + 5 8 . 9 7 =
►
Did we partition 50 into 20 and 30?
50 + 8 + .9 + .07
►
Do we have another 30 to add?
►
How could we use place value to add the 30 to 702.5?
►
If we have 7 hundred and 2 ones and 5 tenths and we
add 30, which digit will change?
►
Will the tens digit change?
Record a jump, record +20 above it and record 702.5 where the jump
lands, for example,
+20
682.5 702.5
Partition 58.97 using place value, for example,
Reviews adding
using place value.
(Addition and
Subtraction 24)
20 +30
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
4
Record a jump, record +30 above it and record 732.5 where the jump
lands, for example,
+20
+30
682.5 702.5
►
682.5 702.5
+30
732.5
+8
682.5 702.5
Will we have 732.5?
+30
►
We’ve added the tens, let’s add the ones.
►
How could we add the 8?
►
How many ones do we have?
►
Do we have 2 ones?
►
If we add 8 ones, will we have another ten?
►
If we add 8, will we have 740.5?
►
We’ve added the tens and ones. Let’s add the tenths.
►
How could we add the 9 tenths?
►
How many tenths do we have?
►
Do we have 5 tenths?
►
How could we use friends of 10 to get the next one?
►
What is 5's friend of 10?
►
If we add 5 tenths, will we have another one?
►
If we add 5 tenths, will we have 741?
740.5
Record a jump, record +0.5 above it and record 741 where the jump
lands, for example,
+20
Will we have 7 hundred and 3 tens and 2 ones and 5
tenths
732.5
Record a jump, record +8 above it and record 740.5 where the jump
lands, for example,
+20
►
+8
+0.5
732.5 740.5 741
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
5
Record, for example,
►
How did we partition the 0.9?
682.5 + 5 8 . 9 7 =
►
We've added 0.5.
50 + 8+ .9 +.07
►
Did we partition 0.9 into 0.5 and 0.4?
►
How could we use place value to add the 4 tenths to
741?
►
If we have 741 and we add 4 tenths, will we have 741
and 4 tenths?
►
Will we have 741.4?
►
How could we use place value to add the 7 hundredths
to 741.4?
►
If we have 741 and 4 tenths and we add 7 hundredths,
will we have 741 and 4 tenths and 7 hundredths?
►
If we have 741.4 and we add 0.07, will we have 741.47?
20 +30
0.5 +0.4
Record a jump, record +0.4 above it and record 741.4 where the jump
lands, for example,
+20
682.5 702.5
+30
+8
+0.5 +0.4
732.5 740.5 741
741.4
Record a jump, record +0.07 above it and record 741.47 where the
jump lands, for example,
+20
682.5
702.5
+30
732.5
+8
+0.5 +0.4 +0.07
740.5 741 741.4 741.47
Record, for example, 682.5 + 58.97 = 741.47
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
6
Reviews adding
using
compensation.
(Addition and
Subtraction 24)
Record, for example, 682.5 + 58.97 =
Record, for example, 682.5 + 60 = 742.5
Introduces adding
decimals is the
same as adding
whole numbers
►
That was a lot of calculation!
►
I wonder if we could have used compensation.
►
Let’s look at our numbers, 682.5 plus 58.97.
►
Is 58.97 almost 60?
►
Is 58.97, 1.03 less than 60?
►
Could we add 60, then subtract 1.03? Let’s investigate!
►
Let's record what 682.5 plus 58.97 equals
►
Let's look at our answer, 741.47.
►
Does it make sense that if we add almost 680 to almost
60, we'll get close to 740?
►
Is adding numbers with decimals just the same as adding
whole numbers?
Record, for example, 742.5 – 1.03 = 741.47
Record, for example, 682.5 + 58.97 = 741.47
Allow children time now to engage in guided and independent investigation of
adding decimals using mental strategies.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
7
Reviews
subtracting whole
numbers using
properties and
relationships.
(Addition and
Subtraction 24)
Record, for example, 12 722 ̶ 5897 =
►
We've investigated subtracting whole numbers using
place value, partitioning and friends of 10.
►
We partitioned using place value.
►
And used friends of 10 and place value to subtract.
►
We also investigated how compensation could be used.
Record, for example,
12 722 ̶ 5 8 9 7 =
5000+800+90+7
4000+1000 200+600 80+10 5+2
Record jumps as you add place values, for example,
-4000
6825
-1000
10 825
-200
11 825 12 025
-600
-80
-10
-5
-2
12 625 12 705 12 715 12 720 12 722
Record, for example, 12 722 - 5897 = 6825
Record, for example, 12 722 - 5897 =
Record, for example, 12 722 - 6000 = 6722
Record, for example, 6722 + 103 = 6825
Record, for example, 12 722 - 5897 = 6825
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
8
Introduces
subtracting
decimals using
properties and
relationships. top
►
Let's try something fun! Let's place a decimal point into each of
the numbers to change their values.
►
Let's investigate how we can use place value, partitioning
and friends of 10 to subtract decimals.
►
First let's look at the numbers.
►
How big is 1272.2?
►
Is 1272.2 just over 1270?
►
How big is 58.97?
►
Is 58.97 almost 60?
►
If we subtract about 6 from about 1270, how big a
number do we estimate we will have?
►
Does it make sense that almost 1270 minus almost 60
would equal almost 1210?
►
Which end of the number line will we start on?
►
In which direction do the numbers get smaller?
►
If the numbers get smaller as we move to the left on the
number line, will we start at the right end of the number
line so we can get smaller as we subtract?
Record, for example, 1272.2 ̶ 58.97 =
Reviews recording Record a number line with the start number at the right hand end, for
on a number line. example,
(Addition and
Subtraction 24)
1272.2
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
9
Reviews
partitioning using
place value.
(Addition and
Subtraction 24)
Partition 58.97 using place value, for example,
1272.2 - 5 8 . 9 7 =
►
How could we partition 58.97 to subtract it from 1272.2?
►
Could we partition 58.97 using place value?
►
How could we subtract the tens using place value?
►
How many tens do we have?
►
Do we have 7 tens?
►
How many tens are we subtracting?
►
Are we subtracting 5 tens?
►
If we subtract 5 tens, how many tens will we have left?
►
Will we have 2 tens left?
►
What is 1272.2 minus 50?
►
Does 1272.2 minus 50 equal 1222.2?
►
How could we subtract the ones using place value?
►
How many ones do we have?
►
We have 2 ones and we need to subtract 8 ones.
►
How can we use place value to work out how many ones
we could subtract first to get back to a tens number?
►
Could we subtract 2 ones?
►
If we subtract 2 ones from 1222.2, will we have 1220.2?
►
How did we use place value to subtract 2 from 1222.2?
50 + 8 +.9 + .07
Reviews
subtracting using
place value.
(Addition and
Subtraction 24)
Record a jump, record -50 above it and record 1222.2 where the
jump lands, for example,
-50
1222.2 1272.2
Record a jump, record -2 above it and record 1220.2 where the jump
lands, for example,
-2
-50
1220.2 1222.2
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
1272.2
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
10
Record, for example,
1272.2 - 5 8 . 9 7 =
50 + 8 +.9 + .07
►
How did we partition the 8?
►
We've subtracted 2.
►
Did we partition 8 into 2 and 6?
►
Do have 6 more ones to subtract?
►
We have 20 and we want to subtract 6.
►
How can we describe 20 flexibly using place value?
►
Is 20, 2 tens? Is 20, 20 ones?
►
How could we use 6's friend of 10 to subtract 6 ones
from 20 ones?
►
Will we have 14 ones?
►
What is 1220.2 minus 6?
►
How could we subtract the tenths using place value?
►
How many tenths do we have?
►
Do we have 2 tenths?
►
How many tenths do we need to subtract?
►
Do we need to subtract 9 tenths?
►
How could we use place value to work out how many
tenths we could subtract first to get back to a ones
number?
2+ 6
Reviews
subtracting using
friends of 10.
(Addition and
Subtraction 24)
Record a jump, record -6 above it and record 1214.2 where the jump
lands, for example,
-6
-2
-50
1214.2 1220.2 1222.2
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
1272.2
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
11
Record a jump, record -0.2 above it and record 1214 where the jump
lands, for example,
-0.2
-6
-2
-50
►
Could we subtract the 2 tenths?
►
What number will we have if we subtract 2 tenths from
1214 and 2 tenths?
►
Will we have 1214?
►
How did we use place value to subtract 2 tenths from
1214.2?
►
How did we partition the 0.9?
►
We've subtracted 2 tenths.
►
Have we partitioned 0.9 into 0.2 and 0.7?
►
Do we have 7 more tenths to subtract?
►
How can we describe 1 using non-standard place value?
►
Is 1, 1 one? Is 1, 10 tenths?
►
What is 10 tenths minus 7 tenths?
►
How can we use 7's friend of 10 to subtract 7 tenths
from 10 tenths?
►
Will we have 3 tenths left?
►
What is 1214 minus 7 tenths?
►
Does 1214 minus 7 tenths equal 1213.3?
1214 1214.2 1220.2 1222.2 1272.2
Record, for example,
1272.2 - 5 8 . 9 7 =
50 + 8 +.9 + .07
2+6 0.2+0.7
Record a jump, record -0.8 above it and record 1213.3 where the
jump lands, for example,
-0.7 -0.2
-6
-2
-50
1213.3 1214 1214.2 1220.2 1222.2 1272.2
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
12
►
How did we use friends of 10 and place value to subtract
7 tenths from 1214?
►
How could we subtract the hundredths using place
value?
►
How many hundredths do we have?
►
How can we describe 3 tenths using non-standard place
value?
►
Introduces
subtracting
decimals is the
same as
subtracting whole
numbers.
Record a jump, record -0.07 above it and record 1213.23 where the
jump lands, for example,
-0.07 -0.7 -0.21
-6
-2
-50
1213.23 1213.3 1214 1214.1 1220.1 1222.1
Is 3 tenths, 3 tenths?
►
Is 3 tenths, 30 hundredths?
►
So we have 30 hundredths?
►
What is 30 hundredths minus 7 hundredths?
►
How can we use 7's friend of 10 to subtract 7 hundredths
from 30 hundredths?
►
Would we have 23 hundredths?
►
What is 1213.3 minus 0.07?
►
Does 1213.3 minus 7 hundredths equal 1213.23?
►
How did we use friends of 10 and place value to subtract
7 hundredths from 1213.3?
1272.1
Record, for example, 1272.2 - 58.97 = 1213.23
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
13
Introduces
subtracting
decimals using
compensation.
►
That was a lot of calculation!
►
I wonder if we could have used compensation.
►
Let’s look at our numbers 1272.2 minus 58.97.
Record, for example, 1272.2 - 58.97 =
►
Is 58.97 almost 60?
Record, for example,1272.2 - 60 = 1212.2
►
Is 58.97, 1.03 less than 60?
Record, for example,1212.2 + 1.03 = 1213.23
►
Could we subtract 60, then add 1.03? Let’s investigate!
►
Let's record what 1272.2 minus 58.97 equals
►
Let's look at our answer, 1213.23
►
Does it make sense that almost 1270 minus almost 60
would equal almost 1210?
►
So can we subtract numbers with decimals in the same
way as we can subtract whole numbers?
Record, for example,1272.2 - 58.97 = 1213.23
Introduces
subtracting
decimals is the
same as
subtracting whole
numbers
Allow children time now to engage in guided and independent investigation of
subtracting decimals using mental strategies.
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
14