MATHS PD AIMS:We aim to improve our students enjoyment andachievement in Maths by:• increasing the use of concrete materials within lessons• becoming more familiar with the maths continuum andthe scope and sequence of skills• Setting tasks and problems worth solving in anincreasingly open ended way• using Mathletics to support our planning andteaching, as well as to increase student practice andengagement.
Addition and Subtraction PD IntentionsPD Intentions:• Investigate Mental and Written Addition andSubtraction concepts• Examine scope and sequence for Addition andSubtraction• Determine how we can use Concrete Materials toassist us in successfully teaching Addition andSubtraction• Continue to explore the use of Open Ended RichTasks to develop mathematical problem solving
Booker:Chapter 4 pp188-236Van Der Walle:Chapters 9-12REFERENCES FOR PLANNING
Addition and SubtractionAddition and subtraction areconnected:•Addition names the whole interms of the parts.•Subtraction names a missingpart.
Addition and SubtractionDevelopmental sequence:Direct modelling.Mental methods of computation.Written methods of computation.
Addition and SubtractionTo summarise the research, effectiveteaching of addition and subtraction willbe:-Learned from direct modelling first-Embedded within a story or context-Children should be given the chance todevelop their own methods for solvingaddition and subtraction problems first
Addition and SubtractionAt early stages allow children to invent theirown methods to solve addition andsubtraction problems.Children’s struggles with the invention oftheir own methods of computation will bothenhance their understanding of place valueand provide a firm foundation for flexiblemethods of computation.
Addition and SubtractionTo summarise the research, effectiveteaching of addition and subtraction willbe:-A range of strategies (mental and written)should be taught-We should DELAY teaching the traditionalalgorithm for addition and subtractionWe should teach the traditional algorithmthrough direct modelling.
Addition and SubtractionAs a part of students development ofWhole Number Place-Valueconcepts, students should begin to workat putting numbers together and takingthem apart in a wide variety of ways asthey solve addition and subtractionproblems with two or three digitnumbers.
Direct ModellingDirect Modelling strategies are thinking toolsto help students understand what ishappening in the problem and a means ofkeeping track of the numbers and solving theproblem.Students may use blocks, counters, base tenblocks and number lines during directmodelling.
Mental ComputationA mental computation strategy is simplyany invented strategy that is donementally.What may be a mental strategy for onestudent may require written support byanother.
Mental ComputationMental Computation strategies:Complements to Ten (friends of ten, numberbonds to ten)Jump Strategy (jump and hop, hop andjump, 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 ComputationJump Strategy (using an empty number line)Split StrategyTraditional 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 focuseson value of digits (as opposed to place value)
The Empty Number LineAn extremely versatile tool with so manypotential applications for all four operations.Further Reading:http://www.k-5mathteachingresources.com/empty-number-line.html
Key to Success?The key to successful use of all computationstrategies is a focus on HOW and WHY the strategyworks. Each strategy is just another tool to be addedto the toolkit for solving problems. Getting a studentable to explain why each tool works is as much thegoal 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 teachingaddition and subtraction• Introduce Mental Strategies for Addition andSubtraction• Introduce Written Strategies for Addition andSubtraction: Using Concrete Materials• End with Open Ended Task: Donna