ADDITION AND SUBTRACTION 30, FRACTIONS AND DECIMALS 33_INVESTIGATION AND REFLECTION
(Year 6) ACMNA126, NSW MA3-7NA
Add and subtract fractions and mixed numerals with related denominators.
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:
Add fractions and with
related denominators
using place value.
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.

In pairs, children select cards to make fractions and mixed numerals with related denominators (halves, quarters, thirds,
fifths, sixths, eighths, tenths and twelfths). They add their fractions and mixed numerals using place value. Reflection:
How can we add fractions and mixed numerals using place value?
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1
Teaching Segment and
Video 2:
Subtract fractions with
related denominators
using place value.

In pairs, children select cards to make fractions and mixed numerals with related denominators (halves, quarters, thirds,
fifths, sixths, eighths, tenths and twelfths). They subtract their fraction and mixed numerals using place value. Reflection:
How can we subtract fractions and mixed numerals using place value?
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.
More investigations.
Name the fraction needed
to make 1.

In pairs, children use playing cards to make a unit fraction (halves, quarters, thirds, fifths, sixths, eighths, tenths and
twelfths). They name the fraction needed to make 1. They name an equivalent fraction needed to make 1.
Name the fraction needed
to add to get to the
nearest whole number.

In pairs, children use playing cards to make a mixed numeral (halves, quarters, thirds, fifths, sixths, eighths, tenths and
twelfths). They name the fraction needed to add to get to the nearest whole number. They name an equivalent fraction
needed to make the nearest whole number.
Join fractions with
related denominators
together to make a circle.

In pairs, children are given paper circles. They each divide 1 circle in halves, 1 circle in quarters, 1 circle in eighths, 1
circle in thirds, 1 circle in sixths, 1 circle in twelfths, 1 circle in fifths and 1 circle in tenths. They use their understanding
of measuring and constructing angles with a protractor and the number of degrees in a circle (revolution). They join
fractions with related denominators together to make a circle, for example, 1 half, 1 quarter and 2 eighths. They record
the number sentence and prove that the fractions do add up to 1. Extension: Children make 1 and half circles, 2 circles,
etc.
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Email: [email protected]
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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.
Teaching Segment and Video 1:
Adding fractions
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.

3
1
Sarah was paving a path. She used 4 of a bag of sand on Saturday, and 1 2 bags of sand on Sunday. How much
3
1
1
sand did she use altogether? (4 + 1 2 = 2 4 )
Teaching Segment and Video 2:
Subtracting fractions

3
1
Sarah is paving 2 paths. She has 2 bags of sand. She needs 4 of a bag of sand for the first path and 1 2 bags of sand
3
1
1
1
for the second path. How much more sand will she need? (4 + 1 2 = 2 4 , she’ll need 4 bag more)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
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Investigating Adding and Subtracting Fractions and Mixed Numerals with Related
Denominators
ADDITION AND SUBTRACTION 30, FRACTIONS AND DECIMALS 33 Add and subtract fractions and mixed numerals with related
denominators.
Select cards to make 2 fractions or mixed numerals with related denominators that
are neither too easy nor too challenging to add.
Record the fractions in an addition number sentence.
Add the fractions using place value.
Reflection: How can we add fractions and mixed numerals using place value?
3
Sarah was paving a path. She used 4 of a bag of
1
sand on Saturday, and 1 2 bags of sand on Sunday.
How much sand did she use altogether?
Hint: Change the fractions, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Adding and Subtracting Fractions and Mixed Numerals with Related
Denominators
ADDITION AND SUBTRACTION 30, FRACTIONS AND DECIMALS 33 Add and subtract fractions and mixed numerals with related
denominators.
Select cards to make 2 fractions or mixed numerals with related denominators that
are neither too easy nor too challenging to subtract.
Record the fractions in a subtraction number sentence.
Subtract the fractions, using place value.
Reflection: How can we subtract fractions and mixed numerals using place value?
Sarah is paving 2 paths.
She has 2 bags of sand.
3
She needs 4 of a bag of sand for the first path and
1
1 2 bags of sand for the second path.
How much more sand will they need?
Hint: Change the fractions, and allow children to solve again!
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Investigating Adding and Subtracting Fractions and Mixed Numerals with Related
Denominators
ADDITION AND SUBTRACTION 30, FRACTIONS AND DECIMALS 33 Add and subtract fractions and mixed numerals with related
denominators.
Use playing cards to make non-unit fractions (fractions where the numerator is not
2
1, for example, ) that is neither too easy nor too challenging.
3
Name the fraction needed to make 1.
Name an equivalent fraction needed to make 1.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Fractions and Mixed Numerals with Related
Denominators
ADDITION AND SUBTRACTION 30, FRACTIONS AND DECIMALS 33 Add and subtract fractions and mixed numerals with related
denominators.
Use playing cards to make a mixed numeral.
Name the fraction needed to add to get to the nearest whole number.
Name an equivalent fraction needed to make the next whole number.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Fractions and Mixed Numerals with Related
Denominators
ADDITION AND SUBTRACTION 30, FRACTIONS AND DECIMALS 33 Add and subtract fractions and mixed numerals with related
denominators.
Sit with a friend.
Have some paper circles.
Each of you divide 1 circle in halves.
Each of you divide 1 circle in quarters.
Each of you divide 1 circle in eighths.
Each of you divide 1 circle in thirds.
Each of you divide 1 circle in sixths.
Each of you divide 1 circle in twelfths.
Each of you divide 1 circle in fifths.
Each of you divide 1 circle in tenths.
Use your understanding of measuring and constructing angles with a protractor and
the number of degrees in a circle (revolution).
Using both sets of fractions, join fractions with the same denominators together.
Record in an addition number sentence.
For example, join 3 fifths with 4 fifths, and record
3
5
+
4
5
=
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