FRACTIONS AND DECIMALS 21, PLACE VALUE 25_ INVESTIGATION and REFLECTION
(Year 5) ACMNA104 NSW MA3 7NA
Multiplicative and standard and non-standard place value of decimals to thousandths, expressing decimals to thousandths as both fractions and decimals.
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.
Teaching Segment and Video 1:
Multiply and divide numbers to
thousandths by 100 and 1000
using multiplicative place value.
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.

Children record a multiplicative place value chart to thousandths, demonstrating multiplication and division by
10 and 100 and 1000, and explain it to their friend. Doing this often will deepen understanding. Children select
cards to make numbers to multiply and divide by 100 and by 1000 using multiplicative place value. They record
the original number in a place value chart. They multiply or divide the number by 100 by moving the digits 2
places to the right or left, and by 1000 by moving the digits 3 places to the left or right. They record the new
number. They read their original and new number to a friend. The numbers of cards may follow this
developmental sequence:
►
1 card to place in a column
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1
►
►
►
►
►
►
Teaching Segment and Video 2:
Standard and non-standard place
value of numbers with whole
numbers, tenths, hundredths and
thousandths.
More investigations.
2 cards to place in consecutive columns
2 cards to place in non-consecutive columns
3 cards to place in consecutive columns
3 cards to place in non-consecutive columns
4 cards to place in consecutive columns
4 cards to place in non-consecutive columns
Reflection: How can we multiply and divide by 100 and by 1000 using multiplicative place value?

Children draw a multiplicative place value chart to thousandths. They select cards to make a number with
thousandths. They describe their number using standard and non-standard place value. They record their tenths,
hundredths and thousandths as decimals and fractions. They check by adding the values on a calculator.
Reflection: How can we describe numbers with thousandths using standard and non-standard place value?
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.

Children make a video of themselves explaining how to multiply or divide numbers to thousandths by 100 or
1000 using multiplicative place value.
Order numbers to thousandths.

In pairs, children each select cards to make a number with thousandths. 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 thousandths place, 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 thousandths
on a number line.

In pairs, children take turns to flip 2 or 3 or 4 or 5 cards and each make a number with thousandths. 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
thousandths.

In pairs, 2, 3, 4 or 5 cards are selected to be a target number with thousandths. Each child flips 2, 3, 4 or 5 cards
to make a number with thousandths. 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?
Video
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Email: [email protected]
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2
Thousandths in metric length
measurement.

Children convert between kilometres, metres, centimetres and millimetres, using multiplicative place value. For
example, 15 mm = 1.5 cm (15 ÷ 10 = 1.5) and 1.5 cm = 15 mm (1.5 x 10 = 15), 135 cm = 1.35 m (135 ÷ 100 = 1.35)
and 1.35 m = 135 cm (1.35 x 100 = 135), 1350 m = 1.35 km (1350 ÷ 1000 = 1.35), 1.35 km = 1350 m (1.35 x 1000
= 1350), 29.356 km = 29 356 m (29.356 x 1000 = 29 356), 5865 m = 5.865 km (5865 ÷ 1000 = 5.865) (Links to
Measurement and Geometry 51) Reflection: How did you use multiplicative place value convert between metric
units of measurement of length?
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.
Teaching Segments and Video 1:
Multiply and divide by 100 and
1000

What is missing from this place value chart?
(a = x 1000 b = x 10 c = ÷ 100)
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Teaching Segment and Video 2:
Standard and non-standard to
hundredths

7.368 is equal to:
(a) 7 tenths and 3 ones and 6 hundredths and 8 thousands
(b) 7 ones and 3 tenths and 6 hundredths and 8 thousandths
(c) 7368 ones (b)

7.368 is equal to:
(a) 3 +
7
10
3
+ 100 +
8
1000
(b) 7 +
3
10
6
+ 100 +
8
1000
(c) 7368 (b)

6.837 is equal to:
(a) 6837 ones (b) 6837 tenths (c) 6837 hundredths (d) 6837 thousandths (d)

47.385 is equal to:
(a) 4 tens and 7 tenths and 3 ones and 8 hundredths and 5 thousands (b) 4 tens and 7 ones and 3 tenths and 8
hundredths and 5 thousandths (c) 47 385 ones (b)

47.385 is equal to:
(a) 43

785
100
(b) 47
385
1000
(c) 47 385 (b)
46.825 is equal to:
(a) 46 825 ones (b) 46 825 tenths (c) 46 825 hundredths (d) 46 825 thousandths (d)
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 and additive place value of decimals to thousandths.
Place Value 25, Fractions and Decimals 21 Multiplicative and additive place value of decimals to thousandths.
Draw a multiplicative place value chart, including thousandths, demonstrating
multiplication and division by 10 and 100 and 1000.
Explain it to a friend.
Select cards to make numbers to multiply and divide by 100 and by 1000 using
multiplicative place value.
Record the original number in a place value chart.
Multiply or divide the number by 100 by moving the digits 2 places to the right or
left and by 1000 by moving the digit 3 places to the left or right.
Record the new number.
Read your original and new number to a friend.
The numbers of cards may follow this developmental sequence:
o 1 card to place in a column
o 2 cards to place in consecutive columns
o 2 cards to place in non-consecutive columns
o 3 cards to place in consecutive columns
o 3 cards to place in non-consecutive columns
o 4 cards to place in consecutive columns
o 4 cards to place in non-consecutive columns
Reflection: How can we multiply and divide by 100 and by 1000 using multiplicative
place value?
Problem Solving
What is missing from this place value chart?
Hint: Change the missing numbers and operations in the multiplicative place value chart, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Multiplicative and additive place value of decimals to thousandths.
Place Value 25, Fractions and Decimals 21 Multiplicative and additive place value of decimals to thousandths.
Draw a multiplicative place value chart, including thousandths, demonstrating
multiplication and division by 10 and 100 and 1000.
Explain it to a friend.
Select cards to make a number with thousandths.
Describe your number using standard and non-standard place value.
Record your tenths and hundredths and thousandths as both decimals and fractions.
Check by adding the values on a calculator.
Reflection: How can we describe numbers with thousandths using standard and
non-standard place value?
Problem Solving
7.368 is equal to:
(a) 7 tenths and 3 ones and 6 hundredths and 8 thousands (b) 7 ones and 3 tenths and 6 hundredths
and 8 thousandths (c) 7368 ones
Hint: Change the number, and allow children to solve again!
Problem Solving
7.368 is equal to:
7
3
(a) 3 + 10 + 100 +
8
1000
(b) 7 +
3
10
6
+ 100 +
8
1000
(c) 7368
Hint: Change the number, and allow children to solve again!
Problem Solving
6.837 is equal to:
(a) 6837 ones (b) 6837 tenths (c) 6837
hundredths (d) 6837 thousandths
Hint: Change the number, and allow children to solve again!
hundredths
Problem Solving
47.385 is equal to:
(a) 4 tens and 7 tenths and 3 ones and 8 hundredths and 5 thousands (b) 4 tens and 7 ones
and 3 tenths and 8 hundredths and 5 thousandths (c) 47 385 ones
Hint: Change the number, and allow children to solve again!
Problem Solving
47.385 is equal to:
785
385
(a) 43 100 (b) 47 1000 (c) 47
385
Hint:
Change the number, and allow children to solve again!
Problem Solving
46.825 is equal to:
(a) 46 825 ones (b) 46 825 tenths (c) 46 825 hundredths (d) 46 825 thousandths
Hint: Change the number, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Multiplicative and additive place value of decimals to thousandths.
Place Value 25, Fractions and Decimals 21 Multiplicative and additive place value of decimals to thousandths.
Make a video of yourself explaining how you use multiplicative place value to
multiply and divide numbers to thousandths by 10, 100 and 1000.
http://www.alearningplace.com.au
Investigating Multiplicative and additive place value of decimals to thousandths.
Place Value 25, Fractions and Decimals 21 Multiplicative and additive place value of decimals to thousandths.
Sit with a friend.
Each select cards to make a number with thousandths.
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 and additive place value of decimals to thousandths.
Place Value 25, Fractions and Decimals 21 Multiplicative and additive place value of decimals to thousandths.
Sit with a friend.
Take turns to take a card and place it in either the thousandths place or 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 and additive place value of decimals to thousandths.
Place Value 25, Fractions and Decimals 21 Multiplicative and additive place value of decimals to thousandths.
Sit with a friend.
Take turns to flip 2, 3, 4 or 5 cards and each make a number with thousandths.
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 and additive place value of decimals to thousandths.
Place Value 25, Fractions and Decimals 21 Multiplicative and additive place value of decimals to thousandths.
Sit with a friend.
2, 3, 4 or 5 cards are selected to be a target number with thousandths.
Each of you flip 2, 3, 4 or 5 cards to make a number with thousandths.
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 and additive place value of decimals to thousandths.
Place Value 25, Fractions and Decimals 21 Multiplicative and additive place value of decimals to thousandths.
Measure and record lengths in millimetres, centimetres, metres and kilometres.
Convert between millimetres, centimetres, metres and kilometres, using
multiplicative place value to multiply and divide by 10 and 100 and 1000.
For example,
15 mm = 1.5 cm (15 ÷ 10 = 1.5) and 1.5 cm = 15 mm (1.5 x 10 = 15)
135 cm = 1.35 m (135 ÷ 100 = 1.35) and 1.35 m = 135 cm (1.35 x 100 = 135)
29.356 km = 29 356 m (29.356 x 1000 = 29 356) and 5865 m = 5.865 km (5865 ÷
1000 = 5.865)
Reflection: How did you use multiplicative place value convert between metric units
of measurement of length?
http://www.alearningplace.com.au