2. MATHS PD AIMS:
We aim to improve our students enjoyment and
achievement in Maths by:
• increasing the use of concrete materials within lessons
• becoming more familiar with the maths continuum and
the scope and sequence of skills
• Setting tasks and problems worth solving in an
increasingly open ended way
• using Mathletics to support our planning and
teaching, as well as to increase student practice and
engagement.
3. Addition and Subtraction PD Intentions
PD Intentions:
• Investigate Mental and Written Addition and
Subtraction concepts
• Examine scope and sequence for Addition and
Subtraction
• Determine how we can use Concrete Materials to
assist us in successfully teaching Addition and
Subtraction
• Continue to explore the use of Open Ended Rich
Tasks to develop mathematical problem solving
5. Addition and Subtraction
Addition and subtraction are
connected:
•Addition names the whole in
terms of the parts.
•Subtraction names a missing
part.
7. Addition and Subtraction
To summarise the research, effective
teaching of addition and subtraction will
be:
-Learned from direct modelling first
-Embedded within a story or context
-Children should be given the chance to
develop their own methods for solving
addition and subtraction problems first
8. Addition and Subtraction
At early stages allow children to invent their
own methods to solve addition and
subtraction problems.
Children’s struggles with the invention of
their own methods of computation will both
enhance their understanding of place value
and provide a firm foundation for flexible
methods of computation.
9. Addition and Subtraction
To summarise the research, effective
teaching of addition and subtraction will
be:
-A range of strategies (mental and written)
should be taught
-We should DELAY teaching the traditional
algorithm for addition and subtraction
We should teach the traditional algorithm
through direct modelling.
10. Addition and Subtraction
As a part of students development of
Whole Number Place-Value
concepts, students should begin to work
at putting numbers together and taking
them apart in a wide variety of ways as
they solve addition and subtraction
problems with two or three digit
numbers.
11. Direct Modelling
Direct Modelling strategies are thinking tools
to help students understand what is
happening in the problem and a means of
keeping track of the numbers and solving the
problem.
Students may use blocks, counters, base ten
blocks and number lines during direct
modelling.
12. Mental Computation
A mental computation strategy is simply
any invented strategy that is done
mentally.
What may be a mental strategy for one
student may require written support by
another.
13. Mental Computation
Mental Computation strategies:
Complements to Ten (friends of ten, number
bonds to ten)
Jump Strategy (jump and hop, hop and
jump, empty number line)
Split Strategy
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16. The Split Strategy
Try calculating these in your head:
There are 233 girls that attend RPPS and 262 boys.
How many students attend RPPS altogether?
MHPS has a roll of 595 students and RPPS has 495.
How many students attend both schools in total?
Tip: work in place value from left to right.
17. Written Computation
Jump Strategy (using an empty number line)
Split Strategy
Traditional Algorithm: DELAY TEACHING!
Focus on Place Value first
-Bridging methods using direct modelling
-Bridging methods moving from left to right
-Move to traditional method which focuses
on value of digits (as opposed to place value)
18. The Empty Number Line
An extremely versatile tool with so many
potential applications for all four operations.
Further Reading:
http://www.k-5mathteachingresources.com/empty-
number-line.html
21. Key to Success?
The key to successful use of all computation
strategies is a focus on HOW and WHY the strategy
works. Each strategy is just another tool to be added
to the toolkit for solving problems. Getting a student
able to explain why each tool works is as much the
goal as being able to use the strategy.
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28. Programme:
• Open Ended Task: Jennah
• Learning Intentions
• AUSVELS Scope and Sequence Scavenger Hunt
• Summary of what ‘experts’ say about teaching
addition and subtraction
• Introduce Mental Strategies for Addition and
Subtraction
• Introduce Written Strategies for Addition and
Subtraction: Using Concrete Materials
• End with Open Ended Task: Donna
