Building Fluency with Addition and Subtraction

Building Fluency with Addition and SubtractionRegion 10 RSS Mini ConferenceRaphaella ArchieJune 26-27Pictures, drawings.The math work students are doing at school may look very different to the kind of sums you remember. This is because children are encouraged to work mentally, where possible, using personal jottings to help support their thinking.Formal calculations are introduced from Year 3 onwards. Children are then encouraged to use these methods for calculations they cannot solve in their heads.

Whats your strategy?

ResourcesMastering the Basic Math Facts in Addition and Subtraction by Susan OConnell and John SanGiovanni

Developing Thinking Strategies for Addition Facts by Larry P. Leutzinger

What does that mean?Strategy Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another.

Algorithm- A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly

Fluency is based on strategies that make sense to students and that help build visual images for the brain to connect to and build upon (not timed tests of basic facts).

Fluency with a strategy or fluency with an algorithm

KindergartenKindergarten students are just beginning to understand the concepts of putting small collections together, or taking a small amount from a collection. Fluently add and subtract within 5(counting on, counting back, doubling, facts)Models/RepresentationsConcrete manipulativeNumber LineNumber CubesFive/Ten FramesFirst GradeKnow combinations to 10 fluentlyStrategiesCounting on/backMaking TenDecomposingUsing Known Facts/Related FactsModels, RepresentationsNumber LineTens FramesBase Ten PiecesHundreds GridHundred ChartEquation

Second Grade It is critically important that students have may experiences using mental strategies for addition and subtraction to build fluency and connect conceptual understanding with the ability to retrieve the information. Relying solely on rote memorization limits the ability to recall and apply knowledge and skills.Mental Strategies Doubles, Doubles + 1Making TensBenchmark numbersAddition/Subtraction Relationships CompensationModels and Representations Number line (Methods for recording strategy)Hundred chart and gridsRectangular Array (Repeated Addition)Third Grade Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtractionStrategiesPartial Sums Adding up and Subtracting Back (Chunks)Benchmark NumbersCompatible numbers (sums to make 50, 100)

Fourth GradeFluently add multi-digit whole numbers using the standard algorithmFluently subtract multi-digit whole numbers using the standard algorithmExplain why the algorithm (based on place value, properties)

Situation TableAdd to Take FromPut Together/Take ApartCompare

The Number Line

In grades 1, 2, and 3 there is no room for the standard algorithms( J.M. Fernadez)

Contexts for Column Addition and Subtraction, May 2011

What Happen?

Left to Right or Right to Left?

ActivitiesAddition BagAddition PlateMake TenTen-Frame FillGreat RaceFour in a Row with Near Doubles3-Digit Subtraction Split

4-digits a Mental Calculation?