PLACE VALUE 20, FRACTIONS DECIMALS 11_ INVESTIGATION and REFLECTION
(Year 4) ACMNA072, ACMNA073, ACMNA079, NSW MA2-4NA, MA2 7NA
Explain multiplicative, standard and non-standard place value of decimals to tenths.
GUIDED AND INDEPENDENT INVESTIGATIONS and REFLECTION
These investigations allow children to investigate and explain the concept in new and varied situations, providing formative
assessment data for both the child and the teacher. ‘Doing’ mathematics is not enough and is not a good indicator of
understanding.
Children investigate and explain independently over many lessons at just beyond their current level of understanding, informing
both themselves and the teacher of their current level of understanding. It is during independent investigation that deep understanding and
metalanguage develops.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop
resilience and deep understanding, If children knew what it was they were doing, it wouldn’t be called learning!
GUIDE children through the INVESTIGATION process until they are ready to investigate INDEPENDENTly.
Children DISCUSS then RECORD their response to the REFLECTION question.
These investigations and reflections are directly linked to Explicit Teaching, and also appear on the Explicit Teaching Plan. Instructions for students
appear on this PDF, on the corresponding Video and on the Explicit Teaching PowerPoint.
Teaching Segment and Video 1:
Multiplicative place value chart,
including tenths.

At least once a week, children draw a multiplicative place value chart to tenths from memory and then explain
multiplying by 10 to get the value of the column on the left and dividing by 10 to get the value of the column to
the right to a friend. Reflection: Why is the value of the column to the right of the ones column, tenths?
Teaching Segment and Video 2:
Investigate points, identifying
when they are decimal.

Children gather examples of points (dots) and investigate if they are decimal points. For example, in time, the
colon is sometimes recorded as a point. But it is not a decimal point because we are not dividing and multiplying
by 10, we are dividing and multiplying by 60. (Therefore it is a sexagesimal point!) However the point dividing
dollars and cents, and the seconds from the fractions of seconds when timing races are decimal points! In AFL,
scores the points are not decimal points either. Reflection: What is a decimal point?
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Teaching Segment and Video 3:
Zero ones.

Children draw a multiplicative place value chart to tenths. They select a card and place it in the tenths column,
4
for example,
. They record the number as 0.4 and as .4, explaining that the value is still 4 tenths or 10 .
Reflection: Why can we record a zero in the ones place when we record tenths?
Teaching Segment and Video 4:
1, 10 and 100 as tenths.

Children draw a multiplicative place value chart to tenths. They select a card and place it in the ones place. They
describe their number of ones using standard and non-standard place value as a number of ones and as a
number of tenths. They place their card in the tens place. They describe their number of tens using standard and
non-standard place value as a number of tens and as a number of tenths. They place their card in the hundreds
place. They describe their number of hundreds using standard and non-standard place value as a number of
hundreds and as a number of tenths. Reflection: How can we describe ones, tens and hundreds as tenths?
Teaching Segment and Video 5:
Standard, non-standard ones and
tenths.

Children draw a multiplicative place value chart to tenths. They select cards to make a number with ones and
tenths. They describe their number using standard and non-standard place value. They record their tenths as
decimals and fractions. Reflection: How can we describe numbers with tenths using standard and non-standard
place value?
Teaching Segment and Video 6:
Standard, non-standard tens,
ones and tenths.

Children draw a multiplicative place value chart to tenths. They select cards to make a number with tens, ones
and tenths. They describe their number using standard and non-standard place value. They record their tenths
as decimals and fractions. Reflection: How can we describe numbers with tenths using standard and nonstandard place value?
Teaching Segment and Video 7:
Multiply and divide numbers to
tenths by 10.

Children draw a multiplicative place value chart. They select cards to use as digits and place them in columns of
the place value chart. They move the digit/s to the left, explaining that they are multiplying by 10 and the new
value is 10 times larger than the original value. They move the digit/s to the right, explaining that they are
dividing by 10 and the new value is 10 times lower than the original value. Reflection: Why do digits move to the
left when we multiply by 10 and to the right when we divide by 10?
More investigations
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.
Order numbers to tenths.

In pairs, children each select cards to make a number with tenths. They place their numbers in order, explaining
their order using place value. Each child makes a number with tenths that would come between their numbers.
Reflection: How did you use place value to order your numbers?
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Place value game.

In pairs, children take turns to take a card and place it in either the tenths place or the ones place or the tens
place. Once placed it cannot be changed. Children read their number out loud and explain their number using
standard place value. They each place their number on the same number line, explaining their placements. The
child who creates the highest / lowest number takes all cards. Reflection: How did you use place value to decide
the values of your numbers?
Order numbers to tenths on a
number line.

In pairs, children take turns to flip 2 or 3 cards and each make a number with tenths. Children read their
numbers out loud. Each child places their number on the same number line. Each child suggests a number that
would come between the 2 numbers, using place value to explain how they know. Reflection: How did you use
place value to find a number between your numbers?
Make a target number to tenths.

In pairs, 2 or 3 cards are selected to be a target number with tenths. Each child flips 2 or 3 cards to make a
number with tenths. The child who makes a number closest to the target number wins. Reflection: How did you
use place value to find make a number close to the target number?
Tenths in metric length
measurement.

Children measure lengths in millimetres Measure lengths in millimetres. Convert to centimetres and millimetres,
then to centimetres and a fraction of a centimetre, then to centimetres and a decimal fraction of a centimetre,
1
for example, 45 mm = 4 cm + 5 mm = 42 cm = 4.5 cm. (Links to Measurement and Geometry 39) Reflection: How are
multiplicative place value and metric measurement related?
Place value slide.

In pairs, children make a place value slide. They take a sheet of paper and
cut slits into which they thread a strip of paper, for example,
They record a number onto the strip and move it between place value
columns, explaining they are multiplying or dividing by 10, and the digit’s
old and new value. Reflection: Why are we multiplying by 10 when we
move digits to the left and dividing by 10 when we move digits to the
right?
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PROBLEM SOLVING directly linked to videos, explicit learning, investigations and reflections
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 – or at all. The focus of problem solving is the development
of problem solving understanding and capacity – not mastery! Returning to a problem after further learning, develops both
resilience and increased confidence as children take the necessary time and input the necessary effort.
After solving problems, children also create their own problems.
Create 3 levels of a problem. GUIDE children through the first level using the problem solving steps. Allow children to investigate the second level
with friends, with minimal guidance. Allow children to investigate the third level INDEPENDENTly. Children create their own problem.
These problems are directly linked to Explicit Teaching, are embedded in the Explicit Teaching Plan, and appear on the Explicit Teaching PowerPoint.
These, and more problems, appear as blackline masters on the Problem Solving PDF and are differentiated on the Problem Solving PowerPoint.

What number is missing from this place value chart?
(10)
Teaching Segments and Video 2:
Decimal Points

Is this dot a decimal point? $5.25 (10) Why? (We are multiplying and dividing by 10.)
Teaching Segment and Video 3:
Zero Ones

Jill recorded a number as 0·7 and Jerry recorded a number as ·7 Do both numbers have the same value? (yes)
7
What is the value? (7 tenths or 10 )
Teaching Segment and Video 4:
1, 10, 100 as tenths

Alex recorded a number as 5 tens. Mike recorded a number as 500 tenths. Did they both record the same
number? (Yes, 5 tens = 500 tenths.)
Teaching Segments and Video 1:
Place Value chart
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Teaching Segment and Video 5:
Standard and non-standard ones
and tenths

7.3 is equal to:
(a) 7 tenths and 3 ones (b) 7 ones and 3 tenths (c) 73 ones (b)

7.3 is equal to:
7
3
(a) 3 10 (b) 7 10 (c) 73 (b)

6.8 is equal to:
(a) 68 tens (b) 68 ones (c) 68 tenths (c)
Teaching Segment and Video 6:
Standard and non-standard tens,
ones and tenths

47.3 is equal to:
(a) 4 tens and 7 tenths and 3 ones (b) 4 tens and 7 ones and 3 tenths (c) 473 ones (b)

47.3 is equal to:
7
3
(a) 43 10 (b) 47 10 (c) 473 (b)

46.8 is equal to:
(a) 468 tens (b) 468 ones (c) 468 tenths (c)
Teaching Segment and Video 7:
Multiply and divide numbers to
tenths by 10

Alex placed a digit in the tenths column. He multiplied it
by 10. Which column is the digit in now? (ones) What is
the value of the digit now? (8)

Alex placed a digit in the ones column. He divided it by 10.
Which column is the digit in now? (tenths) What is the
8
value of the digit now? (8 tenths or 10 )
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Email: [email protected]
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Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
At least once a week, draw a multiplicative place value chart to tenths from
memory.
Explain to a friend that you are multiplying by 10 to get the value of the column on
the left.
Explain to a friend that you are dividing by 10 to get the value of the column to the
right.
Reflection: Why is the value of the column to the right of the ones column, tenths?
Problem Solving
What number is missing from this place value chart?
Hint: Change the missing number in the multiplicative place value chart, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Gather examples of points (dots).
Investigate if they are decimal points.
For example,
 in time, the colon is sometimes recorded as a dot. Is the dot a decimal point?
Are we multiplying and dividing by 10?
 the dot dividing the seconds from the fractions of seconds when timing races.
Is the dot a decimal point? Are we multiplying and dividing by 10?
 in AFL, scores are recorded using a dot. Is the dot a decimal point? Are we
multiplying and dividing by 10?
 the dot between the dollars and cents. Is the dot a decimal point? Are we
multiplying and dividing by 10?
Reflection: What is a decimal point?
Problem Solving
Is this dot a decimal point? $5.25 Why?
Hint: Change the dot sample, and allow children to solve again!
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Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Draw a multiplicative place value chart to tenths.
Select a card and place it in the tenths column.
Record the number with and without the zero in the ones place.
Explain that the number’s value is still ‘tenths’.
For example, select
Record the number as 0·4 and as ·4, explaining that the value is still 4 tenths or
4
10
Reflection: Why can we record a zero in the ones place when we record tenths?
Problem Solving
Jill recorded a number as 0·7 and Jerry recorded a number as ·7
Do both numbers have the same value? What is the value?
Hint: Change the digit, and allow children to solve again!
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.
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Draw a multiplicative place value chart to tenths.
Select a card and place it in the ones place.
Describe your number of ones using standard and non-standard place value as a
number of ones and as a number of tenths.
Place your card in the tens place.
Describe your number of tens using standard and non-standard place value as a
number of tens and as a number of tenths.
Place your card in the hundreds place.
Describe your number of hundreds using standard and non-standard place value as
a number of hundreds and as a number of tenths.
For example, select
Place it in the ones column and describe as 4 ones and as 40 tenths.
Place it in the tens column and describe as 4 tens and as 40 ones and as 400 tenths.
Place it in the hundreds column and describe as 4 hundreds and as 40 tens and as
400 ones and as 4000 tenths.
Reflection: How can we describe ones, tens and hundreds as tenths?
Problem Solving
Alex recorded a number as 5 tens.
Mike recorded a number as 500 tenths.
Did they both record the same number?
Hint: Change the digit, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Draw a multiplicative place value chart to tenths.
Select cards to make a number with ones and tenths.
Describe your number using standard and non-standard place value.
Record tenths as both fractions and decimals.
For example,
3.2 = 3 ones + 2 tenths, 3.2 = 3
3.2 = 32 tenths, 3.2 =
2
10
32
10
Reflection: How can we describe numbers with tenths using standard and nonstandard place value?
Problem Solving
7.3 is equal to:
(a) 7 tenths and 3 ones (b) 7 ones and 3 tenths (c) 73 ones
Hint: Change the number, and allow children to solve again!
Problem Solving
7.3 is equal to:
7
3
(a) 3 10 (b) 7 10 (c) 73
Hint: Change the number, and allow children to solve again!
Problem Solving
6.8 is equal to:
(a) 68 tens (b) 68 ones (c) 68 tenths
Hint: Change the number, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Draw a multiplicative place value chart to tenths.
Select cards to make a number with tens, ones and tenths.
Describe your number using standard and non-standard place value.
Record tenths as both fractions and decimals.
For example,
53.2 = 5 tens + 3 ones + 2 tenths
53.2 = 53 ones + 2 tenths
53.2 = 532 tenths
53.2 = 3 tens + 12 ones + 12 tenths
Reflection: How can we describe numbers with tenths using standard and nonstandard place value?
Problem Solving
47.3 is equal to:
(a) 4 tens and 7 tenths and 3 ones (b) 4 tens and 7 ones and 3 tenths (c) 473 ones
Hint: Change the number, and allow children to solve again!
Problem Solving
47.3 is equal to:
7
3
(a) 43 10 (b) 47 10 (c) 473
Hint: Change the number, and allow children to solve again!
Problem Solving
46.8 is equal to:
(a) 468 tens (b) 468 ones (c) 468 tenths
Hint: Change the number, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Draw a multiplicative place value chart to tenths.
Place cards in columns to make a number.
Record the number.
Multiply the number by 10 by moving the digits one place to left.
Divide the number by 10 by moving the digits one place to the right.
Reflection: Why do digits move to the left when we multiply by 10 and to the right
when we divide by 10?
Problem Solving
Alex placed a digit in the tenths column.
He multiplied it by 10.
Which column is the digit in now?
What is the value of the digit now?
Hint: Change the number, and allow children to solve again!
Problem Solving
Alex placed a digit in the ones column.
He divided it by 10.
Which column is the digit in now?
What is the value of the digit now?
Hint: Change the number, and allow children to solve again!
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Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Sit with a friend.
Each select cards to make a number with tenths.
Place your numbers in order.
Explain your order using place value.
Each of you make a number with tenths that would come between your
numbers.
For example,
Reflection: How did you use place value to order your numbers?
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Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Sit with a friend.
Take turns to take a card and place it in either the tenths place or the ones place or
the tens place.
Once placed it cannot be changed.
Read your number out loud.
The child who creates the highest / lowest number takes all cards.
Explain your number using standard place value.
Each place your number on the same number line, explaining your placement.
Reflection: How did you use place value to decide the values of your numbers?
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Sit with a friend.
Take turns to flip 2 or 3 cards and each make a number with tenths.
Read your numbers out loud.
Each place your number on the same number line.
Each suggest a number that would come between the 2 numbers, using place value
to explain how you know.
Reflection: How did you use place value to find a number between your numbers?
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Sit with a friend.
2 or 3 cards are selected to be a target number with tenths.
Each of you flip 2 or 3 cards to make a number with tenths.
The child who makes a number closest to the target number wins.
Reflection: How did you use place value to find make a number close to the target
number?
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Measure lengths in millimetres.
Convert to centimetres and millimetres, then to centimetres and a fraction of a
centimetre, then to centimetres and a decimal fraction of a centimetre.
For example,
1
45 mm = 4 cm + 5 mm = 4 cm = 4.5 cm.
2
Reflection: How are multiplicative place value and metric measurement related?
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Tenths.
Place Value 20, Fractions Decimals 11 Explain multiplicative, standard and non-standard place value of decimals to tenths.
Sit with a friend.
Make a place value slide:
Take a sheet of paper and cut
slits into which you thread a
strip of paper, for example,
Record a number onto the strip,
for example,
Record the number’s value.
Move it between place value columns,
for example,
Record the number’s new value.
What number did you multiply or divide by?
Reflection: Why are we multiplying by 10 when we move digits to the left and
dividing by 10 when we move digits to the right?
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