ADDITION AND SUBTRACTION 22, PATTERNS AND ALGEBRA 19_INVESTIGATION AND REFLECTION
(Year 3) ACMNA054, ACMNA055, NSW MA2-5NA
Solve missing and equivalent number sentences, explaining equality and the relationship between addition and subtraction.
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:
Relationship between addition
and subtraction, and missing
and equivalent number
sentences.
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 an addition number sentence, for example, 63 + 27 = 90, They record 2 subtraction number
sentences from the addition number sentence, for example, 90 – 63 = 27 and 90 – 27 = 63. Reflection: How can
we create subtraction number sentences from addition number sentences?

Children are given one side of an equals sign, for example, 63 + 27 =. They come up some many different ways to
make the number sentence true. For example, they could record, 63 + 27 = 73 + 17, 63 + 27 = 80 + 10, 63 + 27 =
100 – 10, 63 + 27 = 97 – 7, etc. Reflection: What does the equals sign mean? How can we use the meaning of the
equals sign to help us to solve missing and equivalent number sentences?
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1
More investigations.
Expressions to create
equivalent number sentences.
Missing and equivalent number
sentences.
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.

In pairs, each child records expressions that equal a given number, for example, 74. They place their expressions
on either side of the equals sign and record the number sentence. For example, child A records 91 - 17 and child B
records 58 + 16. They place their expressions on either side of the equals sign and record 91 - 17 = 58 + 16.
Reflection: What does the equals sign mean? How can we use the meaning of the equals sign to help us to solve
missing and equivalent number sentences?

In pairs, children select or create missing number sentences, for example,
___ + ___ = ___ + ___
___ + ___ = ___ - ___
___ - ___ = ___ + ___
___ - ___ = ___ - ___
Reflection: What does the equals sign mean? How can we use the meaning of the equals sign to help us to solve
missing and equivalent number sentences?
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Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
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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:
Missing and equivalent number
sentences
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.

Gerry said that this number sentence is true: 85 + 27 = 141 – 29. Is he right? Why? (yes, both sides equal 112)

What number makes this number sentence true? 153 – 87 = 38 + ____ (202, both sides equal 140)

79 + 43 has the same value as 43 + ____ (79)

What number is missing from all of these number sentences? 56 + ___ = 64, 64 - ___ = 56, 64 – 56 = ___ (8)
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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Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
Record an addition number sentence, for example, 63 + 27 = 90
Record 2 subtraction number sentences from the addition number sentence, for
example, 90 – 63 = 27 and 90 – 27 = 63
Record one side of an equals sign, for example, 63 + 27 =
Work out what the left side of the equals sign equals, for example, 90
Come up with some different ways to make the number sentence true.
For example, you could record,
63 + 27 = 73 + 17,
63 + 27 = 80 + 10
63 + 27 = 100 – 10
63 + 27 = 97 – 7, etc.
Reflection: How can we create subtraction number sentences from addition number
sentences? What does the equals sign mean? How can we use the meaning of the
equals sign to help us to solve missing and equivalent number sentences?
Problem Solving
Gerry said that this number sentence is true:
85 + 27 = 141 – 29.
Is he right? Why?
Hint: Change the number sentence, and allow children to solve again!
Problem Solving
What number makes this number sentence true?
153 – 87 = 38 + ____
Hint: Change the number sentence, and allow children to solve again!
Problem Solving
79 + 43 has the same value as 43 + ____
Hint: Change the number sentence, and allow children to solve again!
Problem Solving
What number is missing from all of these number sentences?
56 + ___ = 64, 64 - ___ = 56, 64 – 56 = ___
Hint: Change the number sentence, and allow children to solve again!
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Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
Sit with a friend.
Each of you record an expression that equals a given number, for example,
74, one of you records 91 - 17 and your friend records 58 + 16.
Place your expressions on either side of the equals sign 58 + 16and record the
number sentence, for example, 91 - 17 = 58 + 16.
Reflection: What does the equals sign mean? How can we use the meaning of the
equals sign to help us to solve missing and equivalent number sentences?
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Solve missing and equivalent number sentences, explaining equality and
the relationship between addition and subtraction.
Create missing number sentences, for example,
___ + ___ = ___ + ___
___ + ___ = ___ - ___
___ - ___ = ___ + ___
___ - ___ = ___ - ___
Reflection: What does the equals sign mean? How can we use the meaning of the
equals sign to help us to solve missing and equivalent number sentences?
http://www.alearningplace.com.au