Addition and Subtraction 25, Patterns and Algebra 21_ Guided and Independent Investigations
(Year 4) ACMNA071, NSW MA1-5NA
Add and subtract combinations of even and odd numbers, using the relationships to check calculations.
GUIDED INVESTIGATION
Children learn how to investigate the concept by following teacher’s
instructions until they are ready to investigate the concept independently.
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
Resources: cards, pencil, paper
What could we do?
Children:
1. select cards to make
combinations of odd and
even numbers to add and
subtract 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 numbers did you add /
subtract?
 Were your numbers odd or
even?
 Was your answer odd or
even?
 How can we use these
relationships to check
calculations?
What could we do?
Children:
1. sit in pairs
2. select cards to make
combinations of odd and even
numbers to add and subtract
that are neither too easy nor too
challenging
What language could we use to explain?





I added / subtracted ... even numbers.
My answers were even
I added / subtracted ... odd numbers.
My answers were …
I added / subtracted ... odd and ... even
number.
 My answers were …
 I used these relationships to check
calculations by …
How do you know if a number is odd?
How do you know if a number is even?
What relationships are there when we add combinations of odd and even numbers? How do you know?
How can we use the relationships to check calculations?
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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,
Add combinations
of odd and even
numbers.
Subtract
combinations of
odd and even
numbers.


Children select cards to make combinations of odd and even numbers to add,
identifying and explaining relationships including
2 even numbers
2 odd numbers
3 even numbers
3 odd numbers
1 odd and 1 even
2 odd and 1 even
2 even and 1 odd
Children select cards to make combinations of odd and even numbers to subtract,
identifying and explaining relationships including
an even number from an even number
an odd number from an odd number
an even number from an odd number
an odd number from an even number
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Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
The size of the
numbers will
depend on
current level of
understanding.
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2
Odd and even
number patterns.

Children make number patterns that repeat by adding even numbers or adding odd numbers. They record them, identifying
relationships. For example, when starting with an even number and repeatedly adding even numbers, all numbers will be
even, when starting with an odd number and repeatedly adding even numbers, all numbers will be odd, when repeatedly
adding odd numbers, we’ll have alternating odd and even numbers regardless of whether we started with an odd or an even
numbers.
Predict odd or
even addition.

In pairs, one child selects odd and their friend selects even. Each child flips a card and adds the numbers. If the sum is odd,
the ‘odd’ child takes the cards. If the sum is even, the ‘even’ child takes the cards. NB: Children could make two-, three-, four-,
five-digit numbers.
Predict odd or
even subtraction.

In pairs, one child selects odd and their friend selects even. Each child flips a card and subtracts the numbers. If the difference
is odd, the ‘odd’ child takes the cards. If the difference is even, the ‘even’ child takes the cards. NB: Children could make two-,
three-, four-, five-digit numbers.
Friends of 10 odd
or even.

Children investigate friends of 10 using their understanding of adding and subtracting combinations of odd and even
numbers. For example, 1 and 9, 3 and 7 and 5 and 5 are all odd, and 2 and 8, 4 and 6 and 10 and 0 are all even!
Odd and even 2
partitions.

Children investigate partitioning numbers into 2 parts, then check their calculations using the relationships when adding odd
and even numbers. For example, partitioning 82 into 79 + 3 (2 odd = even), 65 + 17 (2 odd = even) 60 + 22 (2 even = even).
Odd and even 3
partitions.

Children investigate partitioning numbers into 3 parts, then check their calculations using the relationships when adding odd
and even numbers. For example, partitioning 482 into 400 + 79 + 3 (2 odd and 1 even = even), 400 and 80 + 2 (3 even = even)
180 + 300 + 2 (3 even = even) (Links to Place Value Friends of 10 Partitioning 19 Patterns and Algebra 19)
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
3
Investigating Adding and Subtracting Combination of Odd and Even Numbers
ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21 Add and subtract combinations of even and odd
numbers, using the relationships to check calculations.
Select cards to make combinations of odd and even numbers to add.
2 even numbers
2 odd numbers
You can select
the size of your
numbers.
3 even numbers
3 odd numbers
1 odd and 1 even
2 odd and 1 even
2 even and 1 odd
Identify and explain whether the combination results in odd or even numbers.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Combination of Odd and Even Numbers
ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21 Add and subtract combinations of even and odd
numbers, using the relationships to check calculations.
Select cards to make combinations of odd and even numbers to subtract.
an even number from an even number
an odd number from an odd number
an even number from an odd number
an odd number from an even number
You can select
the size of your
numbers.
Identify and explain whether the combination results in odd or even numbers.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Combination of Odd and Even Numbers
ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21 Add and subtract combinations of even and odd
numbers, using the relationships to check calculations.
Make number patterns that repeat by adding or subtracting even numbers or
adding odd numbers.
Record them, identifying relationships.
For example,
Start with an even number and repeatedly add or subtract an even number.
Start with an odd number and repeatedly add or subtract an odd number.
Start with an even number and repeatedly add or subtract an odd number.
Start with an odd number and repeatedly add or subtract an even number.
Repeatedly alternate between adding or subtracting an odd and an even
number.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Combination of Odd and Even Numbers
ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21 Add and subtract combinations of even and odd
numbers, using the relationships to check calculations.
Sit with a friend.
One of you select odd and the other select even.
Each of you flip a card and add the numbers.
If the sum is odd, the ‘odd’ child takes the cards.
If the sum is even, the ‘even’ child takes the cards.
You could make two-, three-, four-, five-digit numbers.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Combination of Odd and Even Numbers
ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21 Add and subtract combinations of even and odd
numbers, using the relationships to check calculations.
Sit with a friend.
One of you select odd and the other select even.
Each of you flip a card and subtract the numbers.
If the answer is odd, the ‘odd’ child takes the cards.
If the answer is even, the ‘even’ child takes the cards.
You could make two-, three-, four-, five-digit numbers.
http://www.alearningplace.com.au
Investigating Adding and Subtracting Combination of Odd and Even Numbers
ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21 Add and subtract combinations of even and odd
numbers, using the relationships to check calculations.
Investigate friends of 10 using your understanding of adding and subtracting
combinations of odd and even numbers.
For example, are both numbers in friends of 10 even or odd?
http://www.alearningplace.com.au
Investigating Adding and Subtracting Combination of Odd and Even Numbers
ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21 Add and subtract combinations of even and odd
numbers, using the relationships to check calculations.
Investigate partitioning numbers into 2 parts.
Check your calculations using the relationships when adding odd and even
numbers.
For example,
When you partition an even number into 2 parts, are both partitions odd,
even or a combination of odd and even?
When you partition an odd number into 2 parts, are both partitions odd, even
or a combination of odd and even?
http://www.alearningplace.com.au
Investigating Adding and Subtracting Combination of Odd and Even Numbers
ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21 Add and subtract combinations of even and odd
numbers, using the relationships to check calculations.
Investigate partitioning numbers into 3 parts.
Check your calculations using the relationships when adding odd and even
numbers.
For example,
When you partition an even number into 3 parts, are all partitions odd, even
or a combination of odd and even?
When you partition an odd number into 3 parts, are all partitions odd, even or
a combination of odd and even?
http://www.alearningplace.com.au