PLACE VALUE 25, FRACTIONS AND DECIMALS 21_PROBLEM SOLVING
(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.
PROBLEM SOLVING
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 and appear on this PDF, are embedded in the Explicit Teaching Plan, appear on the
Investigation PDF and the Explicit Teaching PowerPoint, and are differentiated into 3 levels on the Problem Solving PowerPoint.
Teaching Segments and Video 1:
Multiply and divide by 100

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
thousandths 1

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)
Standard and non-standard to
thousandths 2

7.368 is equal to:
7
(a) 3 +
10
3
+ 100 +
8
1000
(b) 7 +
3
10
6
+ 100 +
8
1000
(c) 7368 (b)
Standard and non-standard to
thousandths 3

6.837 is equal to:
(a) 6837 ones (b) 6837 tenths (c) 6837 hundredths (d) 6837 thousandths (d)
Standard and non-standard to
thousandths 4

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)
Standard and non-standard
thousandths 5

47.385 is equal to:
Standard and non-standard to
thousandths 6
More Problems
(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)
These problems are not directly linked to Explicit Teaching and appear here and are differentiated into 3 levels on the Problem Solving
PowerPoint.
Digits move 1

When Joan multiplies 53.248 by 1000, will the digits move 3 places to the left or right? Why? (left – multiply by
1000 to get value of column 3 to the left)
Measurement

Which measurement is equal to 1537 centimetres? 0.1537 m 1.537 m 15.37 m 153.7 m (15.37 m)
Digits move 2

When Ally divides 53.2 by 100, will the digits move 2 places to the left or the right? Why? (right – divide by 100
to get value of column 2 to the right)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
Cardboard sheets

A stack of cardboard sheets is 3.5 centimetres thick. Each sheet of cardboard is 0.035 centimetres thick. How
many sheets of cardboard are in the stack? (100, 0.03 cm x 100 = 3 cm)
x10 x100 x1000

What is 6.666 x 10? What is 6.666 x 100? What is 6.666 x 1000? (66.66, 666.6, 6666)
÷10 ÷100 ÷1000

What is 524 ÷ 10? What is 524 ÷ 100? What is 524 ÷ 1000? (52.4, 5.24, 0.524)
Multiplied by 1000

A number multiplied by 1000 is 56. What is the number? (0.056, 0.056 x 1000 = 56)
Brick wall

Dan is building a brick wall. The length of a brick is 0.255 metres. How many bricks will he need to make a row
of bricks 25.5 metres long? (100, 0.255 m x 100 = 25.5 m)
Litres of petrol

Sally used 4.95 litres of petrol for every 100 kilometres she drove. How much petrol does she use for every 10
kilometres? (0.495 L, 4.95 L ÷ 10 = 0.495 L)
Number sentence 1

What number makes this number sentence correct? 1.652 ×
= 1652 (1000)
Number sentence 2

What number makes this number sentence correct? 16.5 ÷
= 0.165 (100)
Number sentence 3

What operation makes this number sentence correct? 16.3
100 = 0.163 (÷)
Lengths of wood

Brian had 100 lengths of wood each 1.257 metres in length. What was the total length of the wood? (125.7,
1.257 x 100 = 125.7)
Calculator

Helen’s calculator showed 63.258. Then it showed 63 258. What did Helen do to make her calculator change
from 63.258 to 63 258? (multiply by 1000, 63.258 x 1000 = 63 258)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
What number 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!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
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!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
7.368 is equal to:
7
3
(a) 3 +
+
+
10
3
100
6
(b) 7 +
+
+
10
100
(c) 7368
8
1000
8
1000
Hint: Change the number, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
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!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
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!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
47.385 is equal to:
(a) 43
(b) 47
785
100
385
1000
(c) 47 385
Hint: Change the number, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
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!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
When Joan multiplies 53.248 by 1000, will the digits
move 3 places to the left or right?
Why?
Hint: Change the missing number in the multiplicative
place value chart, and allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
Which measurement is equal to 1537 centimetres?
0.1537 m 1.537 m 15.37 m 153.7 m
Hint: Change the number of centimetres, and allow
children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
When Ally divides 53.2 by 100, will the digits move
2 places to the left or the right?
Why?
Hint: Change the number, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
A stack of cardboard sheets is 3.5 centimetres thick.
Each sheet of cardboard is 0.035 centimetres thick.
How many sheets of cardboard are in the stack?
Hint: Change the thickness, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
What is 6.666 x 10?
What is 6.666 x 100?
What is 6.666 x 1000?
Hint: Change the number, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 25, Fractions and Decimals 21 Multiplicative and standard and non-standard place value of decimals to thousandths,
expressing decimals to thousandths as both fractions and decimals.
What is 524 ÷ 10?
What is 524 ÷ 100?
What is 524 ÷ 1000?
Hint: Change the number, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 24 Fractions and Decimals 18 Multiplicative and standard and non-standard place value of decimals to thousandths, expressing
decimals to thousandths as both fractions and decimals.
A number multiplied by 1000 is 56.
What is the number?
Hint: Change the number, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 24 Fractions and Decimals 18 Multiplicative and standard and non-standard place value of decimals to thousandths, expressing
decimals to thousandths as both fractions and decimals.
Dan is building a brick wall.
The length of a brick is 0.255 metres.
How many bricks will he need to make a row
of bricks 25.5 metres long?
Hint: Change the lengths, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 24 Fractions and Decimals 18 Multiplicative and standard and non-standard place value of decimals to thousandths, expressing
decimals to thousandths as both fractions and decimals.
Sally used 4.95 litres of petrol for every 100
kilometres she drove.
How much petrol does she use for every 10 kilometres?
Hint: Change the number of litres of petrol used, and
allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 24 Fractions and Decimals 18 Multiplicative and standard and non-standard place value of decimals to thousandths, expressing
decimals to thousandths as both fractions and decimals.
What number makes this number sentence correct?
1.652 ×
= 1652
Hint: Change the numbers, and allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 24 Fractions and Decimals 18 Multiplicative and standard and non-standard place value of decimals to thousandths, expressing
decimals to thousandths as both fractions and decimals.
What number makes this number sentence correct?
16.5 ÷
= 0.165
Hint: Change the number, and allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 24 Fractions and Decimals 18 Multiplicative and standard and non-standard place value of decimals to thousandths, expressing
decimals to thousandths as both fractions and decimals.
What operation makes this number sentence correct?
16.3
100 = 0.163
Hint: Change the number, and allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
Problem Solving
Place Value 24 Fractions and Decimals 18 Multiplicative and standard and non-standard place value of decimals to thousandths, expressing
decimals to thousandths as both fractions and decimals.
Brian had 100 lengths of wood each 1.257 metres in
length.
What was the total length of the wood?
Hint: Change the length, and allow children to solve
again!
Make up your own problem!
http://www.alearningplace.com.au
http://www.alearningplace.com.au
Problem Solving
Place Value 24 Fractions and Decimals 18 Multiplicative and standard and non-standard place value of decimals to thousandths, expressing
decimals to thousandths as both fractions and decimals.
Helen’s calculator showed 63.258.
Then it showed 63 258.
What did Helen do to make her calculator change
from 63.258 to 63258?
Hint: Change the number, and allow children to solve again!
Make up your own problem!
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
http://www.alearningplace.com.au
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place