12-06-2013

ADDITION &

SUBTRACTION

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.

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

Booker:

Chapter 4 pp188-236

Van Der Walle:

Chapters 9-12

REFERENCES FOR PLANNING

Addition and Subtraction

Addition and subtraction are connected: •Addition names the whole in terms of the parts. •Subtraction names a missing part.

Addition and Subtraction

Developmental sequence:

Direct modelling.

Mental methods of computation.

Written methods of computation.

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

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.

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 subtractionWe should teach the traditional algorithm through direct modelling.

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.

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.

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.

Mental ComputationMental 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

The Split StrategyTry 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.

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)

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

ADDITION

SUBTRACTION

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.

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