FRACTIONS AND DECIMALS 29_INVESTIGATION AND REFLECTION
(Year 6) ACMNA131, ACMNA132 NSW MA3 7NA
Explain percentages as hundredths, related to 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:
Hundredths as fractions, decimals
and percentages.
This investigation and reflection is directly linked to Explicit Teaching, and also appears on the Explicit Teaching Plan. Instructions for students
appear on this PDF, on the corresponding Video and on the Explicit Teaching PowerPoint.

In pairs, children select cards to create a hundredth. They record their hundredth as a fraction. They record
their hundredth as a decimal. They record their hundredth as a percentage. They draw a number line and
place their hundredth as a fractions, decimal and percentage on the number line. Reflection: How can we
express hundredths as fractions, decimals and percentages?
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1
PROBLEM SOLVING directly linked to explicit teaching, 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 Segment and Video 1:
Percentages.

Jane got 86 out of a hundred for a test. What percentage did she get? (86% )

Alice sat for a test. If she gets in the top 10%, she’ll get an A. If she gets in the next 10% she’ll get a B. If she gets
in the next 10% she’ll get a C. Alice got 85%. What grade will she get? (B)

Jon got 67 questions right out of 100. What percentage is this? (67% )

Mary was recording some fractions, decimals and percentages. What percentage makes this number sentence
25
true?
= 0.25 = ___ % (25% )
100

What number could be in the blank space on this number line?

Where would 20% go on this number line?
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Email: [email protected]
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YouTube: A Learning Place A Teaching Place
(37% )
(b)
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2
Investigating Hundredths as Fractions, Decimals and Percentages
Fractions and Decimals 29 Explain percentages as hundredths, related to fractions and decimals
Select cards to create a hundredth.
Record your hundredth as a fraction.
Record your hundredth as a decimal.
Record your hundredth as a percentage.
Draw a number line and place your hundredth as a fraction, decimal and percentage
on the number line.
Reflection: How can we express hundredths as fractions, decimals and percentages?
Problem Solving
Problem Solving
Jane got 86 out of a hundred for a test.
What percentage did she get?
Alice sat for a test.
If she gets in the top 10%, she’ll get an A.
If she gets in the next 10% she’ll get a B.
If she gets in the next 10% she’ll get a C.
Alice got 85%. What grade will she get?
Hint: Change the mark, and allow children to solve again!
Problem Solving
Jon got 67 questions right out of 100.
What percentage is this?
Hint: Change the percentage, and allow children to solve again!
Hint: Change the number of questions, and allow children to solve again!
Problem Solving
Mary was recording some fractions, decimals and
percentages.
What percentage makes this number sentence true?
25
= 0.25 = ___ %
100
Hint: Change the fraction and decimal, and allow children to solve again!
Problem Solving
What number could be in the blank space on this number line?
Hint: Change the mark, and allow children to solve again!
Problem Solving
Where would 20% go on this number line?
Hint: Change the percentage, and allow children to solve again!
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