Mastering the Facts (K-5) Moving from counting to strategies to recall. Summer 2011 Flex Day Math Workshop Amber Myers, Cindy Campbell, Janis Mason, Yvonne Wentz

The Problem 4th and 5th graders are not fluent with addition and subtraction. Middle schoolers are not fluent with multiplication. Mastery relies on how well students have constructed relationships about numbers and how well they understand the operations. It is dependent on development of reasoning strategies.

Computational Fluency… Means that students have strategies to solve a problem. Those strategies include mental strategies, a combination of intermediate written steps and mental calculation, and complete written solutions. Students should be flexible in their choice of algorithm or procedure, and they can use one method to check another.

The Standard- NCTM NCTM Focal Points: Knowing basic number combinations- single digit addition and multiplication pairs and their counterparts for subtraction and division- is essential. NCTM Focal Points: 1st grade: Addition & Subtraction concepts learned 2nd grade: Addition & Subtraction mastery/quick recall 3rd grade: Multiplication & Division concepts learned 4th grade: Multiplication & Division concepts mastery and quick recall

The Need We need much more than flashcards and timed tests to teach our students. Quick and accurate recall with basic facts is a developmental process. The Approach Memorize facts in isolation Teach Strategies Guide student generated strategies Are there limitations with these?

Limitations to Memorizing: Inefficient- there are so many- overwhelming! Inappropriate applications- misapply facts and don’t check work Inflexibility- strategies aren’t flexible to other sums. Ineffective for struggling learners, causing anxiety, decreasing interest, and confidence

Limitations to teaching strategies: Focus on memorizing a strategy and which facts work with that strategy doesn’t always work. Students memorize strategies that don’t make sense to them and they are likely to misapply them. When students don’t memorize well, they resort to counting.

What about Guiding Strategies? Tasks and problems must be designed to promote invention of effective strategies. Strategies must be clearly articulated. Strategies must be shared and highlighted. Create lots of opportunities to highlight and share them.

So what do we do? Plan experiences to help movement from counting to strategies to recall. Teach reasoning strategies. Use story problems to provide context. Use many exposures. One is not enough to learn a strategy. COUNTING-STRATEGIES-RECALL

Investigations Fluency with the Facts

Grade Level Fluency Grade 1- addition combinations that make 10 (practiced & assessed) Grade 2 – addition combinations to 10 + 10 (practiced & assessed) Grade 3 – subtraction facts (practiced & assessed) Multiplication facts (to product of 50 Grade 4 – Multiplication facts (to 12 x 12) Grade 5 – Division facts practiced &assessed.

Facts Practice in Investigations: Routines and 10-Minute Math Games and Activities HW/Practice Pages Sorting Cards

Fluency Assessment in Investigations: K-2: Individual and small groups 3-5: Ongoing assessments 30 problems in 3 min. to determine facts to “work on” 2nd Grade: Unit 8 (session 4.5) 26 addition problems with student checklist to assess fluency per student 3rd Grade: Unit 1 (session 2.5) 33 addition problems in 5 min. Unit 8 (session 1.4) 30 multiplication problems in 3 min. to determine facts “to work on”. 4th Grade: Unit 1 (session 2.5) 30 multiplication problems in 5 min. Unit 3 (session 3.4) 30 multiplication problems in 5 min. 5th Grade: Unit 3 (session 3.1) 30 division facts in 5 min.

Connecting with Parents Parent Letters

Focus Points & Benchmarks: What’s the difference? Focus Points- what you teach Benchmarks- what you assess

Unit Benchmark Benchmark Benchmark Focus points ongoing Summative: Formative: ongoing

Assessing the Benchmarks (p. 15 in teacher’s manual)

Summative vs. Formative Assessments

Focus Walls Pearson has a blue ribbon school in Riverside, CA with helpful materials. Here is a link with pictures of math walls: http://k6math.rusd.k12.ca.us/focus_walls.htm

Focus Walls