PLACE VALUE 28, FRACTIONS AND DECIMALS 25_INVESTIGATION AND REFLECTION
(Year 6) ACMNA131 NSW MA3 7NA
Multiplicative place value of numbers of any size.
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:
Place value numbers any size.
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 numbers of any size and explain it to their friend. Doing this
often will deepen understanding. Reflection: How does grouping digits in 3s help us to read large numbers?
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1
More investigations.
Place Value App
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.
 A really great app named simply ‘really big numbers’ is freely available on the Internet here children input a
number and the program writes it out using place value. (Simply Google ‘really big numbers’ and it’s the first hit.)
Reflection: How does grouping digits in 3s help us to read large numbers?

To ensure children understand the size of 1 million, children work out how long it would take them to count
aloud to 1 million. For example, the first numbers could be counted at a rate of 1 per second, but as the
numbers gets higher, it may take up to 4 or 5 seconds (test how long it takes to say 5 hundred and 74 thousand,
3 hundred and 89!) So if we say 3 seconds per number as an average, it would take 3 million seconds to count to
1 million. 3 million seconds divided by 60 = 50 000 minutes divided by 60 = 833 hours divided by 24 = 34.7
days!!!! Don’t tell the children, guide them to work it out to develop deep understanding of the size of the
number. (A radio station once began a competition to have people count to a million, then had to abandon the
idea when they ‘did the maths’ to work out how long it would take!) Reflection: How big is a million?

Children could work out how long it would take them to earn $1 million if they earned, say $50 000 per year or
$100 000. Reflection: How big is a million?

Children could investigate the amount of money actors are paid to make 1 movie, then work out how long it
would take a person on $50 000 per year to earn the same amount. For example, it would take 300 years for a
person earning $50 000 per year to earn $15 million! Reflection: How big is a million?
Count to a million
Earn a million
Movie star millions
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
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:
Fractions increase

Alan recorded this place value chart.
What is the value of the column to the left of the 100 billions column? Why? (1 trillion. Because ones, tens and hundreds
of trillions come after ones, tens and hundreds of billions)
What is the value of the column to the right of the 100 thousandths column? Why? (1 millionth. Because ones, tens and
hundreds of millionths come after ones, tens and hundreds of thousandths)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
Investigating Place Value of Number of Any Size.
Place Value 28, Fractions and Decimals 25 Place value of numbers of any size.
Draw a multiplicative place value chart, including as much information as you can.
Explain what it means to a friend.
Reflection: How does grouping digits in 3s help us to read large numbers?
Problem Solving
Alan recorded this place value chart.
What is the value of the column to the left of the 100 billions column? Why?
What is the value of the column to the right of the 100 thousandths column? Why?
Hint: Change the end values in the place value chart, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Place Value of Numbers of Any Size.
Place Value 28, Fractions and Decimals 25 Place value of numbers of any size.
A really great app named simply ‘really big numbers’ is freely available on the
Internet.
Input a number and the program writes it out using place value.
(Simply Google ‘really big numbers’ and it’s the first hit.)
Reflection: How does grouping digits in 3s help us to read large numbers?
http://www.alearningplace.com.au
Investigating Place Value of Numbers of Any Size.
Place Value 28, Fractions and Decimals 25 Place value of numbers of any size.
To ensure you understand the size of 1 million, work out how long it would take you
to count aloud to 1 million.
Reflection: How big is a million?
http://www.alearningplace.com.au
Investigating Place Value of Numbers of Any Size.
Place Value 28, Fractions and Decimals 25 Place value of numbers of any size.
Work out how long it would take a person to earn $1 million if they earned, $50 000
per year.
Reflection: How big is a million?
http://www.alearningplace.com.au
Investigating Place Value of Numbers of Any Size.
Place Value 28, Fractions and Decimals 25 Place value of numbers of any size.
Investigate the amount of money actors are paid to make 1 movie.
Work out how long it would take a person on $50 000 per year to earn the same
amount.
Reflection: How big is a million?
http://www.alearningplace.com.au