Addition and Subtraction 22, Patterns and Algebra 19_Guided and Independent Investigations
(Year 3) ACMNA054, ACMNA055, NSW MA2-5NA
Solve missing and equivalent number sentences, explaining equality and the relationship between addition and subtraction.
INDEPENDENT INVESTIGATION
Children investigate and explain independently over many lessons at their current level of
understanding informing both themselves and the teacher of their current level of
understanding
GUIDED INVESTIGATION
Children learn how to investigate the concept by following teacher’s
instructions until they are ready to investigate the concept independently.
Resources: Playing cards, card with equals sign, pencil, paper
What could we do?
Children:
1. sit in pairs
2. create equivalent number
sentences as guided by the
teacher
3. select cards to place either
side of the equals sign as
guided by the teacher
4. record their number sentence
5. identify of their number
sentence is true using the
meaning of the equals sign as
equality
What language could we use to ask
questions and explain?
 What numbers could we
use to create a number
sentence?
 How could we create a
number sentence using these
cards?
 What does your number
sentence say?
 Is your number sentence
true?
 How could you make your
number sentence true?
REFLECTION Before, during and after lessons, children discuss then record responses to
reflection questions to inform themselves and the teacher of their current level of
understanding
What could we do?
What language could we use to explain?
Children:
1. sit in pairs
2. create equivalent number sentences
that are neither too easy nor too
challenging
3. select 2 cards to place either side of
the equals sign that are neither too
easy nor too challenging
4. record their number sentence
5. identify of their number sentence is
true using the meaning of the
equals sign as equality
 The numbers I used to create a
number sentence are …
 I created a number sentence using
cards by …
 My number sentence says ...
 My number sentence is / is not true
because both sides are / are not
equal.
 I made my number sentence true
by adding / subtracting …
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What is addition?
What is subtraction?
What does the equals sign mean?
How can we make both sides of the equals sign equal?
What is the relationship between addition and subtraction?
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1
CONGRUENT INVESTIGATIONS
If you can’t explain it
simply, you don’t
understand it well enough.
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.
Anyone who has
Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
never made a
at their current level of understanding.
mistake has never
tried anything new.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop
resilience and deep understanding,

Children are given one side of an equals sign, for example, 63 + 27 =. They come up with as many different ways as they can
to make the number sentence true. For example, they could record, 63 + 27 = 73 + 17, 63 + 27 = 80 + 10 etc.

In pairs, each child selects 2 cards to make a two-digit number. They work out how many they need to add or subtract from
their card to make their friend’s number. Each child records a number sentence. For example, child A has 46 and child B has
73. Child A adds 27 to his number and record 46 + 27 = 73. Child B subtract 26 from his number and records, 73 – 27 = 46.

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.

In small groups, children each record an expression that equals a given number, for example, 74. They place the expressions
in the centre pf the table and record as many equivalent number sentences as they can. For example, 4 children may record,
91 – 17, 58 + 16, 123 – 49 and 18 + 56. The equivalent number sentences include 91 – 17 = 58 + 16, 123 – 49 = 18 + 56, 91 –
17 = 123 – 49, 58 + 16 = 18 + 56 etc.

In pairs, children select or create missing number sentences, for example,
___ + ___ = ___ + ___
___ + ___ = ___ - ___
___ - ___ = ___ + ___
___ - ___ = ___ - ___
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Email: [email protected]
Twitter: @learn4teach
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2

Display a missing number sentence, for example, ____ + ____ = 126 - 58. Children record numbers to make the number
sentence true.

Display a missing number sentence, for example, ____ - ____ = 357 + 86. Children record numbers to make the number
sentence true.

Display 2 missing number sentences, for example, 47 + ____ = 121 and 121 - ____ = 47. Children complete each number
sentence and explain to a friend how the number sentences are related.

Children select 4 cards to make 2 two-digit numbers to be used in missing number sentences For example, the numbers 4, 8,
6 and 3 may be used in 43 + 68 = ____,
68 + 43 = _____, 68 - 43 = _____,
____ - 68 = 43,
____ + 43 = 68 etc
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Record one side of an equals sign, for example, 63 + 27 =
Come up with as many different ways as you can to make the number sentence
true. For example, you could record, 63 + 27 = 73 + 17, 63 + 27 = 80 + 10 etc.
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Sit with a friend.
Each of you select 2 cards to make a two-digit number.
Work out how many you need to add or subtract from your number to make your
friend’s number.
Each of you record a number sentence.
For example, child A has 46 and child B has 73. Child A adds 27 to his number and
record 46 + 27 = 73. Child B subtract 26 from his number and records, 73 – 27 = 46.
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Sit with a friend.
Each of you record an expression that equals a given number, for example, 74.
Place your 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.
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Sit in a small group.
Each of you record an expression that equals a given number, for example, 74.
Place the expressions in the centre pf the table.
Record as many equivalent number sentences as the you can.
For example, 4 children may record, 91 – 17, 58 + 16, 123 – 49 and 18 + 56.
The equivalent number sentences include
91 – 17 = 58 + 16,
123 – 49 = 18 + 56,
91 – 17 = 123 – 49,
58 + 16 = 18 + 56 etc.
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Select or create missing number sentences, for example,
___ + ___ = ___ + ___
___ + ___ = ___ - ___
___ - ___ = ___ + ___
___ - ___ = ___ - ___
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Record a missing number sentence, for example, ____ + ____ = 126 - 58.
Record numbers to make the number sentence true.
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Record a missing number sentence, for example, ____ - ____ = 357 + 86.
Children record numbers to make the number sentence true.
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Record 2 missing number sentences, for example, 47 + ____ = 121 and 121 - ____ =
47.
Complete each number sentence.
Explain to a friend how the number sentences are related.
http://www.alearningplace.com.au
Missing and Equivalent Number Sentences, Describing the Equals Sign as Equality
ADDITION AND SUBTRACTION 22 PATTERNS AND ALGEBRA 19 Investigate missing and equivalent number sentences involving addition
and subtraction, describing the equals sign as equality
Select 4 cards to make 2 two-digit numbers to be used in missing number sentences
For example, the numbers 4, 8, 6 and 3 may be used in
43 + 68 = ____,
68 + 43 = _____,
68 - 43 = _____,
____ - 68 = 43,
____ + 43 = 68 etc
http://www.alearningplace.com.au