FRACTIONS AND DECIMALS 13_INVESTIGATION AND REFLECTION
(Year 4) ACMNA077, NSW MA2 7NA
Equivalent unit and non-unit fractions with concrete material and the relationship between numerator and denominator.
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:
Find fractions equivalent to unit
fractions on a fraction wall,
identifying the relationship between
numerator and denominator.
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.

1 1 1 1 1
1
1
In pairs, children have a commercially available fraction wall. They select a unit fraction (2 , 4 , 8 , 3 , 6 , 12 , 5 ,
1
) and then build a fraction wall under it to identify equivalent fractions. Children record the equivalent
fractions in a number sentence. Children identify the relationship between the numerator and denominator
in the equivalent fractions. Children use the relationship to create other equivalent fractions not on the
fraction wall. Reflection: How do we know if fractions are equivalent?
10
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1
Find fractions equivalent to non-unit
fractions on a fraction wall,
identifying the relationship between
numerator and denominator.
More investigations.

2 3
In pairs, children have a commercially available fraction wall. They select a non-unit fraction (4 , 4 ,
6 7
2
8 8
3
, ,
,
2
,
3
,
4
,
5
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10 11 2 3 4
,
, , , ,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
2 3 4 5
, , , ,
8 8 8 8
) and then build
a fraction wall under it to identify equivalent fractions. Children record the equivalent fractions in a number
sentence. Children identify the relationship between the numerator and denominator in the equivalent
fractions. Children use the relationship to create other equivalent fractions not on the fraction wall.
Reflection: How do we know if fractions are equivalent?
6
6
6
6 12
12 12 12 12 12 12 12 12 12 5 5 5 10 10 10 10 10 10 10
10
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.
Identify fractions equivalent to unit
fractions.

Children have a pack of playing cards. They select cards to make a unit fraction. They identify the relationship
between the numerator and denominator. They use the relationship between the numerator and
denominator to create equivalent fractions. Reflection: How do we know if fractions are equivalent?
Identify fractions equivalent to nonunit fractions.

Children have a pack of playing cards. They select cards to make a non- unit fraction. They identify the
relationship between the numerator and denominator. They use the relationship between the numerator
and denominator to create equivalent fractions. Reflection: How do we know if fractions are equivalent?
Equivalent fraction cards.

Children have a set of fraction cards. They group the fractions into groups of equivalent fractions. They
explain how they know the fractions are equivalent. Reflection: How do we know if fractions are equivalent?
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Email: [email protected]
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2
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:
Equivalent fractions – unit
fractions

Mary recorded some fractions equivalent to

What are the missing numbers?
Equivalent fractions – non-unit
fractions

Tony recorded some fractions equivalent to

What are the missing numbers?
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Twitter: @learn4teach
1
2
2
5
=
=
6
15
=
=
1
3
5
22
6
8
. What fractions could she have recorded? (6 or 10 or 44 etc)
2
=
12
2
5
7
3
6
7
(6 = 12 = 14 etc)
4
. What fractions could he have recorded? (10 or 15 or 20 etc)
30
=
10
2
(5 =
6
15
=
12
30
10
= 25 etc)
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3
Fraction Cards
Back
1
2
3
3
4
4
4
5
2
2
1
4
1
5
5
5
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
1
3
2
4
2
5
1
6
YouTube: A Learning Place A Teaching Place
2
3
3
4
3
5
2
6
Facebook: A Learning Place
4
3
6
1
8
5
8
1
10
4
6
2
8
6
8
2
10
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
5
6
3
8
7
8
3
10
YouTube: A Learning Place A Teaching Place
6
6
4
8
8
8
4
10
Facebook: A Learning Place
5
5
10
9
10
3
12
7
12
11
12
6
10
10
10
4
12
8
12
12
12
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
7
10
1
12
5
12
9
12
8
10
2
12
6
12
10
12
0
1
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
6
Fraction Wall
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
7
Investigating Equivalent Fractions on Fraction Wall and Using the Relationship
between the Numerator and Denominator
FRACTIONS AND DECIMALS 13 Equivalent fractions with concrete material and the relationship between numerator and denominator
Have a fraction wall.
1 1 1 1 1
Select a unit fraction ( , , , , ,
1
1
, ,
1
)
2 4 8 3 6 12 5 10
Build a fraction wall under the unit fraction to identify equivalent fractions.
Record the equivalent fractions in a number sentence.
Identify the relationship between the numerator and denominator in the equivalent
fractions.
Use the relationship to create other equivalent fractions not on the fraction wall.
Reflection: How do we know if fractions are equivalent?
Problem Solving
Mary recorded some fractions equivalent to
1
2
.
What fractions could she have recorded?
Hint: Change the fraction, and allow children to solve again!
Problem Solving
What are the missing numbers?
1
2
=
6
=
12
=
7
Hint: Change the fractions, numerators and denominators, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Equivalent Fractions on Fraction Wall and Using the Relationship
between the Numerator and Denominator
FRACTIONS AND DECIMALS 13 Equivalent fractions with concrete material and the relationship between numerator and denominator
Have a fraction wall (either a commercially available one or the one on the page
below).
2 3
2 3 4 5 6 7
2
4 4 8 8 8 8 8 8
10 11 2 3 4 2
3
3
4
Select a non-unit fraction ( , ,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
,
, , , , , ,
, , , ,
,
,
2
,
,
,
3
,
4
,
5
,
2
,
6 6 6 6 12
5
6
7
8
9
,
,
,
12 12 12 12 12 12 12 12 12 5 5 5 10 10 10 10 10 10 10
,
)
10
Build a fraction wall under it to identify equivalent fractions.
Record the equivalent fractions in a number sentence.
Identify the relationship between the numerator and denominator in the equivalent
fractions.
Use the relationship to create other equivalent fractions not on the fraction wall.
Problem Solving
Mary recorded some fractions equivalent to
2
5
.
What fractions could she have recorded?
Hint: Change the fraction, and allow children to solve again!
Problem Solving
What are the missing numbers?
2
5
=
15
=
30
=
10
Hint: Change the fractions, numerators and denominators, and allow children to solve again!
http://www.alearningplace.com.au
Investigating Equivalent Fractions on Fraction Wall and Using the Relationship
between the Numerator and Denominator
FRACTIONS AND DECIMALS 13 Equivalent fractions with concrete material and the relationship between numerator and denominator
Have a pack of playing cards.
Select cards to make a unit fraction.
Identify the relationship between the numerator and denominator.
Use the relationship between the numerator and denominator to create equivalent
fractions.
Reflection: How do we know if fractions are equivalent?
http://www.alearningplace.com.au
Investigating Equivalent Fractions on Fraction Wall and Using the Relationship
between the Numerator and Denominator
FRACTIONS AND DECIMALS 13 Equivalent fractions with concrete material and the relationship between numerator and denominator
Have a pack of playing cards.
Select cards to make a non-unit fraction.
Identify the relationship between the numerator and denominator.
Use the relationship between the numerator and denominator to create equivalent
fractions.
Reflection: How do we know if fractions are equivalent?
http://www.alearningplace.com.au
Investigating Equivalent Fractions on Fraction Wall and Using the Relationship
between the Numerator and Denominator
FRACTIONS AND DECIMALS 13 Equivalent fractions with concrete material and the relationship between numerator and denominator
Have a set of fraction cards.
Group the fractions into groups of equivalent fractions.
Explain how you know the fractions are equivalent.
Reflection: How do we know if fractions are equivalent?
http://www.alearningplace.com.au