Addition and Subtraction 34, Multiplication and Division 30, Patterns and Algebra 31 _Guided and Independent Investigations
(Year 6) ACMNA134, NSW MA3-6NA
Create and solve missing and equivalent number sentences using order of operations and grouping symbols.
.
INDEPENDENT INVESTIGATION
GUIDED INVESTIGATION
Children learn how to investigate the concept by following teacher’s instructions until
they are ready to investigate the concept independently.
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
Resources: Playing cards, pencil, paper
What could we do?
Children:
1. sit in pairs
2. solve number sentences that contain more
than one operation using the order of
operations and grouping symbols as guided
by the teacher
3. select cards to create and solve missing
number sentences using order of
operations and grouping symbols as guided
by the teacher
4. select cards to create and solve equivalent
number sentences using order of
operations and grouping symbols as guided
by the teacher
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 language could we use to ask
questions and explain?
 What does your number
sentence say?
 How could you solve it using
order of operations?
 How could you solve it using
grouping symbols?
 Did you get the same answer
each time? Why?
 What missing number sentence
did you create and solve?
 What equivalent number
sentence did you create and
solve?
Children:
1. sit in pairs
2. solve number sentences that contain more than
one operation using the order of operations
and grouping symbols as guided by the teacher
3. select cards to create and solve missing number
sentences using order of operations and
grouping symbols as guided by the teacher
4. select cards to create and solve equivalent
number sentences using order of operations
and grouping symbols as guided by the teacher
What are the order of operations?
Why did people make up the order of operations?
How do the order of operations make sure that we all get
the same answer?
What are grouping symbols?
Why did people make up the grouping symbols?
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What language could we use to
explain?
What could we do?
 My number sentence is ...
 I solved the number
sentence using order of
operations by …
 I solved the number
sentence using grouping
symbols by …
 I created and solved a
missing number sentence
by …
 I created and solved an
equivalent number sentence
by …
How do grouping symbols ensure that we all get the
same answer?
What does the equals symbol mean?
How does knowing what the equals sign means, order
of operations and grouping symbols help us to create
and solve missing / equivalent number sentences?
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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,
 In pairs, children select or create missing number sentences, for example,
►
___ x ___ + ___ - ___ = ___
►
___ x ___ ÷ ___ - ___ = ___
►
___ + ___ x ___ - ___ = ___
►
___ - ___ + ___ x ___ = ___
 In pairs, children select or create missing number sentences with grouping symbols, for example,
►
___ x ( ___ + ___ ) - ___ = ___
►
___ x ___ ÷ ( ___ - ___ ) = ___
►
( ___ + ___ ) x ___ - ___ = ___
►
( ___ - ___ ) + ___ x ___ = ___
 In pairs, children select or create equivalent number sentences, for example,
►
___ x ___ = ___ + ___ x ___
►
___ ÷ ___ = ___ + ___ x ___
►
___ - ___ = ___ + ___ ÷ ___
►
___ + ___ ÷ ___ = ___ + ___
 In pairs, children select or create missing number sentences with grouping symbols, for example,
►
___ x ___ = ( ___ + ___ ) x ___
►
___ ÷ ___ = ( ___ + ___ ) x ___
►
___ - ___ = ( ___ + ___ ) ÷ ___
►
( ___ + ___ ) ÷ ___ = ___ + ___
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
2
Investigating Order of Operations and Grouping Symbols
ADDITION AND SUBTRACTION 34 MULTIPLICATION AND DIVISION 30 PATTERNS AND ALGEBRA 31 Create and solve missing and
equivalent number sentences using order of operations and grouping symbols
Create or select a missing number sentence, for example,
___ x ___ + ___ - ___ = ___
___ x ___ ÷ ___ - ___ = ___
___ + ___ x ___ - ___ = ___
___ - ___ + ___ x ___ = ___
Select 4 cards as the numbers to place in the missing number sentence.
Solve the missing number sentence.
http://www.alearningplace.com.au
Investigating Order of Operations and Grouping Symbols
ADDITION AND SUBTRACTION 34 MULTIPLICATION AND DIVISION 30 PATTERNS AND ALGEBRA 31 Create and solve missing and
equivalent number sentences using order of operations and grouping symbols
Create or select a missing number sentence, for example,
___ x ( ___ + ___ ) - ___ = ___
___ x ___ ÷ ( ___ - ___ ) = ___
( ___ + ___ ) x ___ - ___ = ___
( ___ - ___ ) + ___ x ___ = ___
Select 4 cards as the numbers to place in the missing number sentence.
Solve the missing number sentence.
http://www.alearningplace.com.au
Investigating Order of Operations and Grouping Symbols
ADDITION AND SUBTRACTION 34 MULTIPLICATION AND DIVISION 30 PATTERNS AND ALGEBRA 31 Create and solve missing and
equivalent number sentences using order of operations and grouping symbols
Create or select an equivalent number sentence, for example,
___ x ___ = ___ + ___ x ___
___ ÷ ___ = ___ + ___ x ___
___ - ___ = ___ + ___ ÷ ___
___ + ___ ÷ ___ = ___ + ___
Record numbers to make the equivalent number sentence true.
http://www.alearningplace.com.au
Investigating Order of Operations and Grouping Symbols
ADDITION AND SUBTRACTION 34 MULTIPLICATION AND DIVISION 30 PATTERNS AND ALGEBRA 31 Create and solve missing and
equivalent number sentences using order of operations and grouping symbols
Create or select an equivalent number sentence, for example,
___ x ___ = ( ___ + ___ ) x ___
___ ÷ ___ = ( ___ + ___ ) x ___
___ - ___ = ( ___ + ___ ) ÷ ___
( ___ + ___ ) ÷ ___ = ___ + ___
Record numbers to make the equivalent number sentence true.
http://www.alearningplace.com.au