PLACE VALUE 21, FRACTIONS AND DECIMALS 12_GUIDED AND INDEPENDENT INVESTIGATIONS
(Year 4) ACMNA072, ACMNA073, ACMNA079, NSW MA2-4NA, MA2 7NA
Explain multiplicative, standard and non-standard place value of decimals to hundredths.
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:
Record and explain a
multiplicative place value chart,
including hundredths.

At least once a week, children draw a multiplicative place value chart to hundredths 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 tenths column,
hundredths?
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1
Teaching Segment and Video 2:
Standard and non-standard place
value of tenths, ones and tens.

Children draw a multiplicative place value chart to hundredths. 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 and as a number of hundredths. 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 and
as a number of hundredths. 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 and
as a number of hundredths. Reflection: How can we describe tenths, ones and tens as hundredths?
Teaching Segment and Video 3:
Standard and non-standard place
value of numbers to hundredths.

Children draw a multiplicative place value chart to hundredths. They select cards to make a number with
hundredths. They describe their number using standard and non-standard place value. They record their
hundredths as decimals and fractions. Check by adding the values on a calculator. Reflection: How can we
describe numbers with hundredths using standard and non-standard place value?
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 hundredths.

In pairs, children each select cards to make a number with hundredths. They place their numbers in order,
explaining their order using place value. Reflection: How did you use place value to order your numbers?
Place numbers in place values.

In pairs, children take turns to take a card and place it in either the hundredths place, 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 make the highest / lowest number?
Order numbers to hundredths on
a number line.

In pairs, children take turns to flip 2 or 3 or 4 cards and each make a number with hundredths. 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 record numbers between your numbers?
Make a target number to
hundredths.

In pairs, 2, 3 or 4 cards are selected to be a target number with hundredths. Each child flips 2, 3 or 4 cards to
make a number with hundredths. The child who makes a number closest to the target number wins. Reflection:
How did you use place value to make a number close to the target number?

Children measure lengths in centimetres. Convert to metres and centimetres, then to metres and a fraction of a
1
metre, then to metres and a decimal fraction of a metre, for example, 425 cm = 4 m + 25 cm = 44 m = 4.25 m.
(Links to Measurement and Geometry 39) Reflection: How did you use place value convert between centimetres
and metres?
Hundredths in metric length
measurement.
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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 Segment and Video 2:
1 tenth, 1, 10 as hundredths

Alex recorded a number as 5 ones. Mike recorded a number as 500 hundredths. Did they both record the same
number? (Yes, 5 tones = 500 hundredths.)
Teaching Segment and Video 3:
Standard and non-standard ones
and hundredths

7.36 is equal to:
Teaching Segments and Video 1:
Place Value chart
(a) 7 tenths and 3 ones and 6 hundredths (b) 7 ones and 3 tenths and 6 hundredths (c) 736 ones (b)

7.36 is equal to:
(a) 3 +
7
10
3
+ 100 (b) 7 +
3
10
3
+ 100 (c) 73 (b)
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Email: [email protected]
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YouTube: A Learning Place A Teaching Place
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3

6.83 is equal to:
(a) 683 ones (b) 683 tenths (c) 683 hundredths (c)

47.38 is equal to:
(a) 4 tens and 7 tenths and 3 ones and 8 hundredths (b) 4 tens and 7 ones and 3 tenths and 8 hundredths (c)
4738 ones (b)

47.38 is equal to:
(a) 43

78
100
(b) 47
38
100
(c) 4738 (b)
46.82 is equal to:
(a) 4682 ones (b) 4682 tenths (c) 4682 hundredths (c)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
4
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Hundredths.
Place Value 21, Fractions and Decimals 12 Explain multiplicative, standard and non-standard place value of decimals to hundredths.
At least once a week, draw a multiplicative place value chart to hundredths 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 tenths column,
hundredths?
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 Hundredths.
Place Value 21, Fractions and Decimals 12 Explain multiplicative, standard and non-standard place value of decimals to hundredths.
Draw a multiplicative place value chart to hundredths.
Select a card and place it in the tenths place.
Describe your number of tenths using standard and non-standard place value as a
number of tenths and as a number of hundredths.
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, as a number of tenths and as a number of hundredths.
Place your card in the tens place.
Describe your number of tens using standard and non-standard place value as a
number of tens, as a number of ones, as a number of tenths and as a number of
hundredths.
For example, select
Place it in the tenths column and describe as 4 tenths and as 40 hundredths.
Place it in the ones column and describe as 4 ones and as 40 tenths and as 400
hundredths.
Place it in the tens column and describe as 4 tens and as 40 ones and as 400 tenths
and as 4000 hundredths.
Reflection: How can we describe tenths, ones and tens as hundredths?
Problem Solving
Alex recorded a number as 5 ones.
Mike recorded a number as 500 hundredths.
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 Hundredths.
Place Value 21, Fractions and Decimals 12 Explain multiplicative, standard and non-standard place value of decimals to hundredths.
Draw a multiplicative place value chart to hundredths.
Select cards to make a number with whole numbers, tenths and hundredths.
Describe your number using standard and non-standard place value.
Record hundredths as both fractions and decimals.
Reflection: How can we describe numbers with hundredths using standard and nonstandard place value?
Problem Solving
7.36 is equal to:
(a) 7 tenths and 3 ones and 6 hundredths (b) 7 ones and 3 tenths and 6 hundredths (c) 736 ones
Hint: Change the number, and allow children to solve again!
Problem Solving
7.36 is equal to:
7
3
(a) 3 + 10 + 100 (b) 7 +
3
10
+
3
100
(c) 73
Hint: Change the number, and allow children to solve again!
Problem Solving
6.83 is equal to:
(a) 683 ones (b) 683 tenths (c) 683
hundredths
Hint: Change the number, and allow children to solve again!
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
47.38 is equal to:
78
38
(a) 43 100 (b) 47 100 (c) 4738
Hint: Change the number, and allow children to solve again!
Problem Solving
46.82 is equal to:
(a) 4682 ones (b) 4682 tenths (c) 4682 hundredths
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 Hundredths.
Place Value 21, Fractions and Decimals 12 Explain multiplicative, standard and non-standard place value of decimals to hundredths.
Sit with a friend.
Each select cards to make a number with hundredths.
Place your numbers in order.
Explain your order using place value.
Reflection: How did you use place value to order your numbers?
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Hundredths.
Place Value 21, Fractions and Decimals 12 Explain multiplicative, standard and non-standard place value of decimals to hundredths.
Sit with a friend.
Take turns to take a card and place it in either the hundredths place or 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 make the highest / lowest number?
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Hundredths.
Place Value 21, Fractions and Decimals 12 Explain multiplicative, standard and non-standard place value of decimals to hundredths.
Sit with a friend.
Take turns to flip 2, 3 or 4 cards and each make a number with hundredths.
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 record numbers between your numbers?
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Hundredths.
Place Value 21, Fractions and Decimals 12 Explain multiplicative, standard and non-standard place value of decimals to hundredths.
Sit with a friend.
2, 3 or 4 cards are selected to be a target number with hundredths.
Each of you flip 2, 3 or 4 cards to make a number with hundredths.
The child who makes a number closest to the target number wins.
Reflection: How did you use place value to make a number close to the target
number?
http://www.alearningplace.com.au
Investigating Multiplicative, Standard and Non-standard Place Value of Numbers
to Hundredths.
Place Value 21, Fractions and Decimals 12 Explain multiplicative, standard and non-standard place value of decimals to hundredths.
Measure lengths in centimetres.
Convert to metres and centimetres, then to metres and a fraction of a metre, then
to metres and a decimal fraction of a metre.
1
For example, 425 cm = 4 m + 25 cm = 4 m = 4.25 m
4
Reflection: How did you use place value convert between centimetres and metres?
http://www.alearningplace.com.au