ADDITION AND SUBTRACTION 25, PATTERNS AND ALGEBRA 21_INVESTIGATION AND REFLECTION
(Year 4) ACMNA071, NSW MA1-5NA
Add and subtract combinations of even and odd numbers, using the relationships to check calculations.
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:
Add and subtract combinations
of odd and even numbers.
This investigation and reflection is directly linked to Explicit Teaching, and also appears on the Explicit Teaching Plan. Instructions for students appear on
this PDF, on the corresponding Video and on the Explicit Teaching PowerPoint.

Children select cards to make combinations of odd and even numbers to
add and subtract, 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
Reflection: What happens when we add and subtract combinations of odd and even numbers?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
1
These investigations are not directly linked to Explicit Teaching. Instructions for students appear here and on the Explicit Teaching PowerPoint.
More investigations.
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. Reflection: What happens when we add and
subtract combinations of odd and even numbers?
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). Reflection: What happens when we add and subtract combinations of odd and even
numbers?
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) Reflection: What happens when we add and subtract combinations of odd and even
numbers?
Website: http://www.alearningplace.com.au
Email: [email protected]
Twitter: @learn4teach
YouTube: A Learning Place A Teaching Place
Facebook: A Learning Place
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.
Teaching Segment and Video 1:
Add and subtract odd and even
numbers
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.

Lola said that 12 365 + 85 268 equals 97 633. Could she be right? (yes, odd plus even equals an odd)

Billy said that 18 654 – 13 827 equals 4828. Could he be right? (no, an even minus an odd equals an odd)

Helen said she partitioned 835 into 3 odd numbers. Could she be right? (yes, odd + odd + odd equals an odd number)
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 and subtract.
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
Explain which combination result in odd numbers and which combinations result in
even numbers.
Reflection: What happens when we add and subtract combinations of odd and even
numbers?
Problem Solving
Lola said that 12 365 + 85 268 equals 97 633.
Could she be right?
Hint: Change the numbers, and allow children to solve again!
Problem Solving
Billy said that 18 654 – 13 827 equals 4828.
Could he be right?
Hint: Change the numbers, and allow children to solve again!
Problem Solving
Helen said she partitioned 835 into 3 odd numbers.
Could she be right?
Hint: Change the numbers, and allow children to solve again!
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.
Reflection: What happens when we add and subtract combinations of odd and 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.
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?
Reflection: What happens when we add and subtract combinations of odd and
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.
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?
Reflection: What happens when we add and subtract combinations of odd and even
numbers?
http://www.alearningplace.com.au