Computational Fluency What is Computational Fluency Adding It

Computational Fluency

What is Computational Fluency?

Adding It Up The National Academies Press “Procedural Fluency- -skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. ”

Priorities in Mathematics Grade K– 2 3– 5 6 7 8 Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding Addition and subtraction, measurement using whole number quantities Multiplication and division of whole numbers and fractions Ratios and proportional reasoning; early expressions and equations Ratios and proportional reasoning; arithmetic of rational numbers Linear algebra

Key Fluencies Grade K 1 Required Fluency Add/subtract within 5 Add/subtract within 10 Add/subtract within 20 (using mental strategies) 2 (by end of Grade 2, know from memory all sums of two one-digit numbers) Add/subtract within 100 (pencil and paper) (using strategies based on place value, properties of operations and/or the relationship between addition and subtraction) Multiply/divide within 100 (using strategies such as the relationship between multiplication and division (e. g. , knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations) 3 (by the end of Grade 3, know from memory all products of two one-digit numbers) Add/subtract within 1000 (using strategies and algorithms based on place value, properties of operations and/or the relationship between addition and subtraction) 4 5 Add/subtract within 1, 000 (using the standard algorithm) Multi-digit multiplication (using standard algorithm)

Key Fluencies (6 -8) 6 Multi-digit division (using standards algorithm) Multi-digit decimal operations (add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation) 7 Solve px + q = r, p(x + q) = r 8 Solve simple 2 2 systems by inspection

Fourth Grade • M. 4. OA. 4 fluently add and subtract multi-digit whole numbers using the standard algorithm.

Developing Fluency 1. Help children develop a strong understanding of number relationships within the operations. 2. Develop efficient strategies for fact retrieval through practice. 3. Then provide drill in the use and selection of those strategies once they have been developed. John A. Van de Walle & Lou. Ann H. Lovin

From Memory ≠ Memorize Develop Understanding Meaningful Practice Fluency M. 2. OA. 2 fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. M. 3. OA. 7 fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e. g. , knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations and by the end of Grade 3, know from memory all products of two one-digit numbers.

Fifth Grade • M. 5. NBT. 5 fluently multiply multi-digit whole numbers using the standard algorithm.

Number Talks http: //books. google. com/books? id=p 4 B 9 F 1 u 2 T 4 k. C&printsec=fro ntcover&dq=number+talks&hl=en&sa=X&ei=6 EPXT_v 4 Nsbx 0 g. Gsx 8 Ck. Aw&ved=0 CDUQ 6 AEw. AA#v=onepage&q=number%2 0 talks&f=false

Number Talks • Number talks are short conversations centered around purposefully crafted computation problems.

Strategies Addition Subtraction Multiplication Division Counting All/Counting On Adding Up Repeated Addition or Skip Counting Repeated Subtraction or Sharing/Dealing Out Doubles/Near-doubles Removal or counting Back Making Landmark or Friendly Numbers Partial Quotients Making Tens Place Value and Negative Numbers Partial Products Multiplying Up Making Landmark or Friendly Numbers Adjusting One Number to Create an Easier Problem Doubling and Halving Proportional Reasoning Breaking Each Number into Its Place Value Keeping a Constant Difference Breaking Factors into Smaller Factors Compensation Adding Up in Chunks

Key Components Number Talks • • • Classroom environment and community Classroom discussions The teacher’s role The role of mental math Purposeful computation problems

Classroom Environment Quiet Thumbs Up Me Too Strategy—Quiet Thumbs Up Me Too!

Number Talks in Action • Select several problems for the participants complete as a number talk.

Create Number Talks • Create Number Talks for the first week of school. • Practice with a partner.

Teaching Basic Facts What to do--- What NOT to do--- • Ask students to selfmonitor • Focus on self-improvement • Drill in short time segments • Work on facts over time • Involve families • Make drill enjoyable • Use technology • Emphasize the importance of quick recall of facts • • • Don’t use lengthy timed tests Don’t use public comparisons of mastery Don’t proceed through all facts all at once Don’t move to memorization to soon Don’t use facts as a barrier to good mathematics Don’t use fact mastery as a prerequisite for calculator use