Place Value 24, Fractions and Decimals 18_Guided and Independent Investigations
(Year 5) ACMNA104, ACMNA105, NSW MA3-4NA
Multiplicative place value of numbers to hundredths by multiplying and dividing by 10, 100 and 1000.
INDEPENDENT INVESTIGATION
GUIDED INVESTIGATION
Children investigate and explain independently over many lessons at their current
Children learn how to investigate the concept by following teacher’s instructions until
level of understanding informing both themselves and the teacher of their current level of
understanding
they are ready to investigate the concept independently.
Resources: cards, pencil, paper
What could we do?
Children:
1. sit in pairs
2. select cards to make a number as
guided by the teacher
3. record the number in a place value
chart
4. multiply their number by 10 or 100 or
1000 using multiplicative place value
by moving the digits two or three
places to the left
5. divide their number by 10 or 100 or
1000 using multiplicative place value
by moving the digits two or three
places to the right
What language could we use to ask
questions and explain?
 What number did you select?
 How could you record your
number in a place value chart?
 How could you multiply your
number by 100?
 How could you multiply your
number by 1000?
 How could you divide your number
by 100?
 How could you divide your number
by 1000?
REFLECTION Before, during and after lessons, children discuss
then record responses to reflection questions to inform themselves
and the teacher of their current level of understanding.
What could we do?
Children:
1. sit in pairs
2. select cards to make a number that is
neither too easy nor too challenging
3. multiply their number by 10 or 100 or
1000 using multiplicative place value
by moving the digits two or three
places to the left
4. divide their number by 10 or 100 or
1000 using multiplicative place value
by moving the digits two or three
places to the right
What language could we use to explain?
 The number I selected is ...
 I recorded my number in a place
value chart ...
 I multiplied my number by 100 by
moving the digits 2 places to the left
because …
 I multiplied my number by 1000 by
moving the digits 3 places to the left
because ….
 I divided my number by 100 by
moving the digits 2 places to the right
because ….
 I divided my number by 1000 by
moving the digits 3 places to the right
because ….
What is multiplicative place value?
How can we use multiplicative place value to multiply by 100?
How can we use multiplicative place value to multiply by 1000?
How can we use multiplicative place value to divide by 100?
How can we use multiplicative place value to divide by 1000?
Why do digits move 2 columns when they are multiplied or divided by 100?
Why do digits move 3 columns when they are multiplied or divided by 1000?
Website: http://www.alearningplace.com.au
Email: [email protected]
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1
CONGRUENT INVESTIGATIONS
If you can’t explain it
simply, you don’t
understand it well enough.
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.
Anyone who has
Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
never made a
at their current level of understanding.
mistake has never
tried anything new.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop
resilience and deep understanding,
Record multiplicative
place value to
hundredths.

Children record a multiplicative place value chart with hundredths and explain it to their friend. Doing this often will
deepen understanding.

In pairs, children select cards to make numbers to multiply and divide by 10, 100 and 1000 using multiplicative place
value. Record the original number in a place value chart. Multiply or divide the number by moving the digits 1, 2, or 3
places to the right or left. Record the new number. Read your original and new number to a friend. The numbers of
cards may follow this developmental sequence:
►
1 card to place in a column
►
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
In pairs, one child selects cards and places them in a place value chart to make a number. Their friend makes a number
10, 100 or 1000 times greater or smaller. Each reads their number aloud.
Multiply and divide by
10, 100, 1000 using
multiplicative place
value.
Partner multiply and
divide by 10, 100, 1000.

Video explaining.

Convert km / m / cm /
m, Multiply and divide
by 10, 100, 1000.

In pairs, children could make a video of themselves explaining how they use multiplicative place value to multiply and
divide by 10, 100 and 1000.
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.)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Investigating Multiplying and Dividing by 10, 100, 1000 using Multiplicative Place
Value.
Place Value 24, Fractions and Decimals 18 Multiplying and dividing by 10, 100, 1000 using multiplicative place value by
moving digits 1, 2, or 3 places to the right or left.
Draw a multiplicative place value chart, including hundredths.
Explain what it means to a friend.
http://www.alearningplace.com.au
Investigating Multiplying and Dividing by 10, 100, 1000 using Multiplicative Place
Value.
Place Value 24, Fractions and Decimals 18 Multiplying and dividing by 10, 100, 1000 using multiplicative place value by
moving digits 1, 2, or 3 places to the right or left.
Select cards to make numbers to multiply and divide by 10, 100 and 1000 using
multiplicative place value. Record the original number in a place value chart.
Multiply or divide the number by moving the digits 1, 2, or 3 places to the right or
left. 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
http://www.alearningplace.com.au
Investigating Multiplying and Dividing by 10, 100, 1000 using Multiplicative Place
Value.
Place Value 24, Fractions and Decimals 18 Multiplying and dividing by 10, 100, 1000 using multiplicative place value by
moving digits 1, 2, or 3 places to the right or left.
Sit with a friend.
One of you select cards and place them in a place value chart to make a number.
Your friend makes a number 10, 100 or 1000 times greater or smaller.
Each of you read your number aloud.
http://www.alearningplace.com.au
Investigating Multiplying and Dividing by 10, 100, 1000 using Multiplicative Place
Value.
Place Value 24, Fractions and Decimals 18 Multiplying and dividing by 10, 100, 1000 using multiplicative place value by
moving digits 1, 2, or 3 places to the right or left.
Make a video of yourself explaining how you use multiplicative place value to
multiply and divide by 10, 100 and 1000.
http://www.alearningplace.com.au
Investigating Multiplying and Dividing by 10, 100, 1000 using Multiplicative Place
Value.
Place Value 24, Fractions and Decimals 18 Multiplying and dividing by 10, 100, 1000 using multiplicative place value by
moving digits 1, 2, or 3 places to the right or left.
Convert between millimetres, centimetres, metres and kilometres by multiplying
and dividing by 10, 100 and 1000 using multiplicative place value.
http://www.alearningplace.com.au