Building Fluency with Addition and Subtraction

1. Building Fluency with Addition and Subtraction Region 10 RSS Mini Conference Raphaella Archie June 26-27

2. Pictures, 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.

3. What’s your strategy?

4. Resources • Mastering the Basic Math Facts in Addition and Subtraction by Susan O’Connell and John SanGiovanni • Developing Thinking Strategies for Addition Facts by Larry P. Leutzinger

5. 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

6. Kindergarten • Kindergarten 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/Representations • Concrete manipulative • Number Line • Number Cubes • Five/Ten Frames

7. First Grade • Know combinations to 10 fluently • Strategies • Counting on/back • Making Ten • Decomposing • Using Known Facts/Related Facts • Models, Representations • Number Line • Tens Frames • Base Ten Pieces • Hundreds Grid • Hundred Chart • Equation

8. 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 + 1 • Making Tens • Benchmark numbers • Addition/Subtraction Relationships • Compensation • Models and Representations • Number line (Methods for recording strategy) • Hundred chart and grids • Rectangular Array (Repeated Addition)

9. 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 subtraction • Strategies • Partial Sums • Adding up and Subtracting Back (Chunks) • Benchmark Numbers • Compatible numbers (sums to make 50, 100)

10. Fourth Grade • Fluently add multi-digit whole numbers using the standard algorithm • Fluently subtract multi-digit whole numbers using the standard algorithm • Explain why the algorithm (based on place value, properties)

12. Situation Table • Add to • Take From • Put Together/Take Apart • Compare

14. The Number Line

22. 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

36. What Happen?

38. Left to Right or Right to Left?

39. Activities • Addition Bag • Addition Plate • Make Ten • Ten-Frame Fill • Great Race • Four in a Row with Near Doubles • 3-Digit Subtraction Split

42. 4-digits a Mental Calculation?