Focused on Understanding and Fluency

Transcription

1 Math Expressions: A Fresh Approach To Standards-Based Instruction Focused on Understanding and Fluency K Consumable workbooks K-4 Homework & Remembering K-5 Hardback book gr. 5 Consumable Student activity book

2 Welcome Parents! Stillwater Math Program (based on MN standards) K-5 5 Math Expressions Gr.. 6 Holt Course 2 (leading into Holt JH and HS) Expectations: at least K 60 minutes daily, Gr at least 70 minutes daily You will see homework and remembering books K-5K K-4 4 will be using the teacher-created created math assessments throughout the year Math report cards will be standards-based Math Enrichment options (ALEKS, differentiation strategies, MX components) Math intervention programs: Mathletics Number Worlds

3 The Next Generation NSF Program Dr. Karen Fuson Introduction Math Chapters Research Summary Whole Numbers Study Committee

4 The Math Expressions Difference Only NSF program to be published post Principles and Standards for School Mathematics (NCTM, 2000) Incorporates the best of reform and traditional mathematics instruction Uses accessible algorithms that relate to common (traditional) methods Focus on Math Talk and representations Differentiated Instruction for each lesson to meet a broad range of student needs

5 The Five Learning and Teaching Structures in Math Expressions Building Concepts Math Talk Student Leaders Math Drawings Quick Practice Helping Community

6 Building Concepts Focuses on KEY concepts at each grade level Does NOT spiral. Numbers Concepts and Word Problems is a K-5 5 strand! Manipulatives in the early grades and in the early stages of development of a concept at the upper grades.

7 Math Talk Math Talk Solve Manipulatives Math Drawings Symbols Explain Math Drawings Language Symbols Question Language Justify Proof Pictures Language Symbols

8 Quick Practice Brief, structured, whole class/individual/ partner practice that facilitates fluency. Some quick practice routines build prerequisites others follow concept building.

9 Helping Community * Everyone is a teacher and a learner, creating a secure base for learning. * Teachers help students learn to help each other at the board, in pairs or groups, or when working individually.

10 Helping Community Quick Summary of the Supporting Research Math Talk Quick Practice Student Leaders

11 Manipulative options to meet different classroom needs!

12 Student Leader and Quick Practice Model Activity With Hidden n Code Cards

13 Five Important Qualities of Algorithms An algorithm consists of a precisely specified sequence of steps that will lead to a complete solution for a certain class of problems. Accuracy (or reliability) Does it always lead to a right answer if you do it right? Generality For what kinds of numbers does this work? (The larger the set of numbers the better.) Efficiency (or complexity) How quick is it relative to the task? Do students persist? Ease of accurate use (versus error proneness) Does it minimize errors? Transparency (versus opacity) Can you SEE the mathematical ideas behind the algorithm? Hyman Bass. Computational Fluency, Algorithms, and Mathematical Proficiency: One Mathematician s Perspective. Teaching Children Mathematics. February, 2003.

14 Addition algorithm- left to right or right to left QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

15 Show All Totals can also be called: Add the hundreds ( ) Add the tens ( ) 70 Add the ones (5 + 6) Add the partial sums ( )

16 Addition Algorithm- keeps the teens together QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

17 Subtraction Algorithm- Break apart the numbers QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

18 Students complete all regrouping before doing the subtraction. This can be done from left to right (or right to left). In this case, we need to regroup a 100 into 10 tens. The 7 hundreds is now 6 hundreds and the 2 tens is now 12 tens. Next, we need to regroup a 10 into 10 ones. The 12 tens is now 11 tens and the 3 ones is now 13 ones Now, we complete the subtraction. We have 6 hundreds minus 4 hundreds, 11 tens minus 5 tens, and 13 ones minus 9 ones.

19 Subtract the hundreds ( ) Subtract the tens (30 40) Subtract the ones (6 5) Add the partial differences (500 + (-10) + 1)

20 A Geometrical Representation of Partial Products (Area Model) 52 46

21 Multiplication: break numbers apart QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

22 Multiplication algorithm QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

23 19 R Add the partial Students begin quotients, and by choosing record the partial quotients quotient along that they with the recognize! remainder

24 Division Algorithm: QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture.

25 E-Glossary E-Manipulatives E-Games

26 HOLT COURSE II- Gr. 6 Reasons for choosing Holt course II Online text: My.hrw.com Math plan

27 Students will Learn math concepts at their level Prepare for state tests and focus on state standards Have a consistent amount of math across the district Have access to intervention and enrichment options Work with highly trained teachers and paras Think and grow mathematically Be challenged and inspired mathematicians

28 Thank you!! Feel free to contact: Amy Jones (K-5) Kate Pechacek (6-12) Look for a math family night in the spring!!!!