Multiplication and Division 28, Fractions, Decimals and Percentages 27D, Place Value, Friends of 10,
Partitioning 30PV
Record remainders as fractions and decimals when dividing by 10
Resources: Playing cards, pencil, paper
EXPLICIT LEARNING
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
multiplicative
place value
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►
Today brings an investigation about dividing by 10.
►
What do you know about dividing by 10?
►
Talk about dividing by 10 with a friend.
►
Is anyone ready to share what they are thinking about
dividing by 10?
►
We’ve investigated dividing by 10.
►
We found we could use multiplicative place value to
divide numbers by 10 by moving the digits into the
column on the right.
►
We found that this is because the column on the right is
10 times lower than the column on the left.
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Children draw a multiplicative place value chart, from visualising one
(or copying one if necessary), for example,
►
Please draw a multiplicative place value chart.
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Let’s select 2 cards to place in the tens column and the
ones column.
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What digits have we selected?
►
Have we selected, a 5 and a 2?
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Let’s place the 5 in the tens column and the 2 in the ones
column.
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What is the value of the 5?
►
Is the value of the 5, 5 tens?
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Is the value of the 5, 50?
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What is the value of the 2?
►
Is the value of the 2, 2 ones?
(NB: Children investigate Multiplicative Place Value to numbers of
any size by multiplying and dividing by 10, 100 and 1000 in Place
Value, Friends of 10, Partitioning 28, 29 Fractions, Decimals and
Percentages 25 and 26, Multiplication and Division 27)
Reviews
dividing a twodigit whole
number by 10
Select 2 cards to place in the tens column and the
ones column, for example,
Place the 5 in the tens column and the 2 in the ones column, for
example,
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►
Is the value of the 2, 2?
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What is the value of our number?
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Is the value of our number, 52?
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Let’s record our division number sentence, 52 divided by
10 equals.
►
How could we use the place value chart to divide 52 by
10?
►
If we divide the 52 by 10, what column will the digit 2
move to?
►
Will the 2 move to the column to the right?
►
Is the column to the right, 10 times less than the column
on the left?
►
What is the value of the 2 now it’s been divided by 10?
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Is the value of the 2 now, 2 tenths?
►
If we divide the 52 by 10, what column will the digit 5
move to?
►
Will the 5 move to the column to the right?
►
Is the column to the right, 10 times less than the column
on the left?
►
Let’s move the 5 to the column to the right.
►
What is the value of the 5 now it’s been divided by 10?
►
Is the value of the 5 now, 5 ones?
►
Is the value of the 5 now, 5?
Record the number sentence, for example, 52 ÷ 10 =
Move the 2 to the tenths column the place value chart, for example,
Move the 5 to the tens column in the place value chart, for example,
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Reviews
recording
tenths as
fractions and
as decimals
2
Record, for example, 52 ÷ 10 = 5 10
Record, for example, 52 ÷ 10 = 5.2
Reviews
Select 3 cards to place in the hundreds column, the
dividing by
tens column and the ones column, for example,
using
multiplicative
place value
without a place
value chart
Reviews
standard place
value
Record the number sentence, for example, 752 ÷ 10 =
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►
So what is 52 divided by 10?
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Does 52 divided by 10 equal 5 and 2 tenths?
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How could we record the 2 tenths as a fraction?
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Could we record 5 and 2 tenths using the fraction
symbol?
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How could we record the 2 tenths as a decimal?
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Could we record 5 point 2?
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Do both of these number sentences say the same thing?
►
Is 2 tenths and .2 the same fraction?
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Let’s try one without drawing the place value chart!
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Let’s select 3 cards to place in the hundreds column, the
tens column and the ones column.
►
What digits have we selected?
►
Have we selected, a 7, a 5 and a 2?
►
What three-digit whole number have we made?
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Have we made 752?
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How could we describe 752 using standard place value?
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Is 752, 7 hundreds plus 5 tens plus 2 ones?
►
Let’s record our division number sentence, 752 divided
by 10 equals.
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Reviews
recording
tenths as
fractions and
as decimals
Reviews
differentiating
the
investigation
for children as
they
demonstrate
understanding
Record, for example, 752 ÷ 10 = 75.2
2
►
If we divide the 752 by 10, what column will each digit
move to?
►
Will each digit move to the column to the right?
►
Is the column to the right, 10 times less than the column
on the left?
►
Let’s move each digit to the column to the right.
►
What is the value of 752 now it has been divided by 10?
►
Is the value now7 tens plus 5 ones plus 2 tenths?
►
How could we record the 2 tenths as a decimal?
►
Could we record 75 point 2?
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How could we record the 2 tenths as a fraction?
►
Could we record 5 and 2 tenths using the fraction
symbol?
►
Do both of these number sentences say the same thing?
►
Is 2 tenths and .2 the same fraction?
Record, for example, 752 ÷ 10 = 75 10
Allow children time now to engage in guided and independent
investigation (at the end of this teaching plan) of dividing numbers
by 10 using multiplicative place value, recording remainders as
fractions and as decimals.
A child who has not demonstrated understanding of dividing
numbers by 10, using multiplicative place value, recording
remainders will continue at this level, before moving to dividing
numbers by 10 using multiplicative place value, recording remainders
as fractions and as decimals.
Children move to Guided and Independent Investigation now to investigate the concept at increasing levels of understanding over many learning sessions
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GUIDED INVESTIGATION
INDEPENDENT INVESTIGATION
REFLECTION
Resources: Playing cards, pencil, paper
What could we do?
Children:
1. sit in pairs
2. record and explain a
multiplicative place
value chart
3. select cards to numbers
as guided by the teacher
4. divide their number by
10 with or without the
place value chart
5. record their number
sentence
6. record remainders as
fractions and as decimals
What language could we
use to ask questions and
explain?
 How could you draw
and explain a
multiplicative place value
chart?
 What number did you
make?
 How could you divide
your number by 10 using
multiplicative place
value?
 How could you record
your remainder as a
fraction and as a
decimal?
What could we do?
Children:
1. sit in pairs
2. record a multiplicative
place value chart
3. select cards to numbers
as guided by the teacher
4. divide their number by 10
with or without the place
value chart
5. record their number
sentence
6. record remainders as
fractions and as decimals
What language could we
use to explain?
 I recorded a
multiplicative place value
chart.
 My multiplicative place
value chart means …
 My number is …
 I divided my number by
10 using multiplicative
place value by …
 I recorded the
remainder as a fraction
as … and as a decimal
as …
What questions could
children discuss and record a
response to?
What is multiplication?
What is division?
What is multiplicative place
value?
How could we use
multiplicative place value to
divide by 10?
Why can we record
remainders as fractions and
as decimals when dividing by
10?
Children may be investigating concepts at a level that varies from other children. In one class, there may be children investigating the concept at Level 1 while
another child is investigating the concept at Level 4, Level 12 or even higher.
Regardless of the child's current grade, children need to investigate concepts at the level of their current understanding. This means that a child in a given
grade, who has current understanding at Level 5, will investigate at Level 6, then Level 7 etc.
If this makes you worried that they are investigating at a level much lower than their grade level, consider this: If the child is made to try to investigate at a
higher level than their current level of understanding, they will be building on an unstable knowledge base with gaps, and will continue to use inefficient strategies
often based on misconceptions, guaranteeing that their level of understanding will be the same at the end of the year as it was at the beginning of the year. If the
child is allowed to investigate the concept at their current level of understanding, they will correct misconceptions, fill gaps in their understanding and build a firm
knowledge base, as they move through the levels, investigating at a higher level by the end of the year.
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CONGRUENT LEARNING
MULTIPLICATION AND DIVISION 28 FRACTIONS, DECIMALS AND PERCENTAGES 27
PLACE VALUE, FRIENDS OF 10, PARTITIONING 30 RECORD REMAINDERS AS FRACTIONS AND DECIMALS WHEN DIVIDING BY 10
These learning activities allow children to investigate and explain the concept in new and varied situations. ‘Doing’ mathematics is
simply not enough and is not a good indicator of understanding. As Einstein said, ‘If you can’t explain it simply, you don’t
understand it’! Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
at their current level of understanding. Differentiate learning for children working at all levels of the concept, including those
requiring extension, and allow children to differentiate their own learning, by varying the range and size of numbers investigated.
 Children sit with a friend. They individually select:
 2 cards to make a two-digit number they feel ready to divide by 10, recording remainders as both fractions and decimals
 3 cards to make a three-digit number they feel ready to divide by 10, recording remainders as both fractions and decimals
 3 cards to make a four-digit number they feel ready to divide by 10, recording remainders as both fractions and decimals
They explain to their friend how they used multiplicative place value to divide the number by 10.
 Children use a calculator to divide numbers as described above by 10, then check using their own strategy. Children explain
their strategy to a friend.
 In pairs, children play ‘guess my number’. They take it in turns to describe a number after it has been divided by 10. For
example, they may say, ‘when my number is divided by 10, it is 4.3 or 4 and three-tenths’. The other child works out what the
number is.
 In pairs, children lay out 12 cards in a 3 by 4 array. They take turns select a single card or 2 cards or 3 cards to make a singledigit, two-digit or three-digit number to divide by 10. They divide the number by 10, explaining how they used multiplicative
place value, and if correct, they keep the cards.
 In pairs, children convert between millimetres, centimetres, metres and kilometres by multiplying and dividing by 10 (100 and
1000) using multiplicative place value. (Links to Measurement and Geometry 51)
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PROBLEM SOLVING
MULTIPLICATION AND DIVISION 28 FRACTIONS, DECIMALS AND PERCENTAGES 27
PLACE VALUE, FRIENDS OF 10, PARTITIONING 30 RECORD REMAINDERS AS FRACTIONS AND DECIMALS WHEN DIVIDING BY 10
Problems allow children to investigate concepts in new and varied situations. Any problem worth solving takes time and effort –
that’s why they’re called problems! Problems are designed to develop and use higher order thinking. Allowing children to grapple
with problems, providing minimal support by asking strategic questions, is key. Differentiating problems allows children to solve
simpler problems, before solving more complex problems on a concept. Problems may not always be solved the first time they are
presented. Returning to a problem after further learning, develops both resilience and increased confidence as children take the
necessary time and input the necessary effort. As Einstein said, ‘It’s not that I’m so smart – I just stay with problems longer’. The
problem solving steps may be followed to solve problems.

What might the missing numbers be? __ 4 ÷ 10 = __.__

I bought 8 pizzas for 10 children. How much pizza have I allowed for each child?

10 children paid to see a show. Altogether the group paid $72. How much did each child pay?

Cupcakes are sold in boxes of 10. Jemima wants to give one cupcake to each of her 28 classmates. What is the least number
of boxes that Jemima needs?

Roland is paid the same amount for each lawn he mows. He gets paid $86 for mowing 10 lawns. How much does he get paid
per lawn?

Toni bought 10 drinks. Altogether the drinks cost 15.70 How much for one drink?

There are 2 number cards.

A goanna is about 48 cm long. A garden lizard is about 10 times shorter than the goanna. About how long is a garden lizard?

Jenna has 2 cards.

A child has 54 crayons. There are 2 crayons in each small packet. There are 10 crayons in each large packet. The child has 2
small packets. How many large packets does the child have?

See also problems in Place Value, Friends Of 10, Partitioning 25, 26, Fractions, Decimals And Percentages 25, 26,
Multiplication And Division 27
2
3
3
1
__ __ 4 ÷ 10 = __
Use the number cards to make this number sentence true:
÷ 10 = 3.1
She makes a two-digit number and divides it by 10. What quotients could Jenna make?
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Problem Solving Steps (back to Problems)
1. Read
2. Understand
3. Choose a strategy
Read the part that is
asking you to find out.
Read the information you
need to find it out.
Think about what you
could do to work it out.
4. Work it out
5. Check
6. Share
Use your strategy to work
it out.
Read the part that asked
you to find out.
Share and compare your
strategy and answer with a
friend’s strategy and
answer.
Did you find it out?
Need a 10 frame
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