Multiplication and Division 26, Fractions and Decimals 26, Place Value 29_Guided and Independent Investigations
(Year 6) ACMNA129, ACMNA130 NSW MA3-6NA, MA3 7NA
Multiply and divide decimals to thousandths by whole numbers and powers of 10, recording remainders as fractions and decimals.
INDEPENDENT INVESTIGATION
GUIDED INVESTIGATION
Children investigate and explain independently over many lessons at their
Children learn how to investigate the concept by following teacher’s instructions until
they are ready to investigate the concept independently.
current level of understanding informing both themselves and the teacher of their
current level of understanding
Resources: cards, pencil, paper
What could we do?
Children:
1. sit in pairs
2. select cards to make a decimal
and a whole number as guided
by the teacher
3. record their number sentence
4. multiply or divide the numbers
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 language could we use to ask
questions and explain?
 What numbers did you select?
 How could you record the
number sentence?
 How could you multiply / divide
the numbers?
 How could you record your
solution strategy?
What could we do?
Children:
1. sit in pairs
2. select cards to make a decimal
and a whole number that are
neither too easy nor to
challenging
3. record their number sentence
4. multiply or divide the numbers
What language could we use to explain?
 The numbers I selected are ...
 I recorded my number sentence
by ...
 I multiplied / divided by ...
 I recorded my strategy as ...
What is multiplication?
What is division?
How are multiplication and division related?
How are division and fractions related?
How can we use properties and relationships to multiply and divide whole number and decimals?
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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,
Multiply a decimal by a
whole number.

Children select cards to make whole numbers and decimals that they are ready to multiply. They multiply the decimal
by the whole number by either:
►
keeping the decimal as a decimal and multiplying, or
►
multiplying the decimal by powers of 10 to make a whole number, multiplying the whole numbers, then dividing
the product by the power of 10.
Children explain their strategy to a friend.
Divide a decimal by a
whole number.

Children select cards to make whole numbers and decimals that they are ready to divide. They divide the whole
number by the decimal by either:
►
keeping the decimal as a decimal and dividing, or
►
multiplying the decimal by powers of 10 to make a whole number, dividing by the whole number, then dividing
the product by the power of 10.
Children explain their strategy to a friend.
Calculator multiplication.

Children use a calculator to multiply a decimal by a whole number, then check using their own strategy. Children
explain their strategy to a friend.
Calculator division.

Decimal target number
through multiplication or
division.
Children use a calculator to divide a decimal by a whole number, then check using their own strategy. Children explain
their strategy to a friend.

In pairs, children have a decimal target number. They make their calculator show the target number using multiplication
or division. For example, the target number 12.36 may be made by multiplying 6.18 by 2, 3.09 by 4 or by dividing 24.72
by 2, or 49.44 by 4 etc.
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 Decimals to Thousandths by Whole
Numbers.
Fractions and Decimals 26 Multiply and divide decimals to thousandths by whole numbers.
Select cards to make whole numbers and decimals that you are ready to multiply.
Multiply the decimal by the whole number by either:


keeping the decimal as a decimal and multiplying, or
multiplying the decimal by powers of 10 to make a whole number, multiplying
the whole numbers, then dividing the product by the power of 10.
Explain your strategy to a friend.
http://www.alearningplace.com.au
Investigating Multiplying and Dividing Decimals to Thousandths by Whole
Numbers.
Fractions and Decimals 26 Multiply and divide decimals to thousandths by whole numbers.
Select cards to make whole numbers and decimals that you are ready to divide.
Multiply the decimal by the whole number by either:


keeping the decimal as a decimal and dividing, or
multiplying the decimal by powers of 10 to make a whole number, dividing
the whole numbers, then dividing the product by the power of 10.
Explain your strategy to a friend.
http://www.alearningplace.com.au
Investigating Multiplying and Dividing Decimals to Thousandths by Whole
Numbers.
Fractions and Decimals 26 Multiply and divide decimals to thousandths by whole numbers.
Use a calculator to multiply a decimal by a whole number.
Check using your own strategy.
Explain their strategy to a friend.
http://www.alearningplace.com.au
Investigating Multiplying and Dividing Decimals to Thousandths by Whole
Numbers.
Fractions and Decimals 26 Multiply and divide decimals to thousandths by whole numbers.
Use a calculator to divide a decimal by a whole number.
Check using your own strategy.
Explain their strategy to a friend.
http://www.alearningplace.com.au
Investigating Multiplying and Dividing Decimals to Thousandths by Whole
Numbers.
Fractions and Decimals 26 Multiply and divide decimals to thousandths by whole numbers.
Sit with a friend.
Have a decimal target number.
Make your calculator show the target number using multiplication or division.
For example, the target number 12.36 may be made by multiplying 6.18 by 2, 3.09
by 4 or by dividing 24.72 by 2, or 49.44 by 4 etc.
http://www.alearningplace.com.au