Middle School Mathematics

Arnall Middle School

August 11, 2015

Math Manipulatives A Bridge to Abstract Ideas

Coweta Committed to Student Success

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We believe as a learning community, we must continually improve.

Area of Focus

We believe that we are responsible for the success of each student.

Curriculum/instruction/assessment update

Georgia Standards of Excellence

Resources for middle school math

Georgia Milestones

Hands-on lessons with Carolyn Cutts, ETA Hand2Mind

Upcoming professional learning opportunities

Wrap-up

Agenda

We believe we must see students as volunteers in their learning.

ELA and math standards revised and renamed using “GSE” instead of “CC”

Math frameworks updated

Georgia Standards of Excellence

We believe that we are responsible for the success of each student.

Revised math standards

Grade 6 Grade 7 Grade 8

6.NS.1

6.NS.4

6.EE.9

6.RP.3

6.RP.3c

6.RP.3d

6.SP.5

6.G.1

6.G.2

7.NS.1a

7.NS.1b

7.EE.2

7.EE.3

7.EE.4c

7.RP.3

7.SP.3

7.SP.6

7.SP.7

7.SP.8c

7.G.2

7.G.3

7.G.4

8.NS.2

8.EE.2

8.EE.3

8.EE.4

8.EE.8

8.SP.4

8.G.1

8.G.9

We believe as a learning community, we must continually improve.

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q in which p and q are rational numbers.

Standard added: 7.EE.4c

We believe that we are responsible for the success of each student.

Mean Absolute Deviation has been removed from 6th and 7th grade Statistics and Probability standards.

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We believe we must see students as volunteers in their learning.

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We believe, as a learning community, we must continually improve.

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http://curriculum.cowetaschools.org/http://curriculum.cowetaschools.org/

Curriculum webpage

Intranet

Shared drive (\\mushu\middlemath\)

Foundations of Algebra materials (https://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspx)

2015-2016 MS Math Professional Learning folder in Google

Resources

We believe we must provide challenging, interesting, and satisfying work for students.

file://mushu/middlemath/file://mushu/middlemath/file://mushu/middlemath/file://mushu/middlemath/file://mushu/middlemath/file://mushu/middlemath/https://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://www.georgiastandards.org/Georgia-Standards/Pages/Math-9-12.aspxhttps://drive.google.com/a/cowetaschools.net/folderview?id=0B7zs-qLM0eK3fjdJYktKQUlYbGpETThVODU1d3lzNVhQQTBPOXBEUlptOEVNYVpHY2ppeGs&usp=sharing

Scores will be issued in October

Scores will consist of the following:

• Scale Scores

• Achievement Levels designating proficiency

• For ELA, grade level reading determination and writing rubric scores

• For other content areas, domain mastery signals

• For embedded norm-referenced items, national percentile ranks

Georgia Milestones

Note: It is anticipated that scoring and reporting will occur approximately two

weeks after receipt of student responses/answer documents beginning in 2015-2016.

Our vision is to ensure the success of each student.

Beginning Learners do not yet demonstrate proficiency in the knowledge and skills necessary at this grade level/course of learning, as specified in Georgia’s content standards. The students need substantial academic support to be prepared for the next grade level or course and to be on track for college and career readiness.

Developing Learners demonstrate partial proficiency in the knowledge and skills necessary at this grade level/course of learning, as specified by in Georgia’s content standards. The students need additional academic support to be prepared for the next grade level or course and to be on track for college and career readiness.

Proficient Learners demonstrate proficiency in the knowledge and skills necessary at this grade level/course of learning, as specified in Georgia’s content standards. The students are prepared for the next grade level or course and are on track for college and career readiness.

Distinguished Learners demonstrate advanced proficiency in the knowledge and skills necessary at this grade level/course of learning, as specified in Georgia’s content standards. The students are well prepared for the next grade level or course and are well prepared for college and career readiness.

Achievement levels

We will provide high-level, engaging work for all learners and leaders.

Carolyn Cutts ETA Hand2Mind

Coweta Committed to Student Success

Warm-Up Activity - Last Survivor

from The Super Source

1. How did you decide what moves to make?

2. Did you find strategies that worked?

3. Did it matter who went first?

4. What would happen if you changed the number of starting tiles?

5. Using pictures and words, show a strategy for winning Last Survivor.

Last Survivor –

Discussion Questions

Carolyn Cutts @CarolynCutts

ccutts@hand2mind.com

404-308-2174

@ETAhand2mind

Hands-on

Learning

…in order to develop every student’s

mathematical proficiency, leaders and

teachers must systematically integrate

the use of concrete and virtual

manipulatives into classroom instruction

at all grade levels.

NCSM Position Statement

Research shows that the systematic use of visual representations and manipulatives may lead to statistically significant or substantively important positive gains in math achievement. (PAGES 30-31)

The evidence indicates, in short, that manipulatives can provide valuable support for student learning when teachers interact over time with the students to help them build links between the object, the symbol, and the mathematical idea both represent. (PAGE 354)

Research Summary

When students are exposed to hands-on learning on a weekly rather than a monthly basis, they prove to be 72% of a grade level ahead in mathematics (PAGE 27)

Impact on Student Performance

Virtual Manipulatives

Virtual manipulatives are important tools for

teacher modeling and demonstration….

…virtual manipulatives do not replace the

power of physical objects in the hands of

learners.

NCSM Position Statement

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Concrete

Abstract

Representational

Hands-On Learning Instructional Cycle

Multiplication as Repeated Addition

Multiplying Two-digit Numbers

Punnett Square & Partial Products

Important Beyond Elementary School

1. How did you go about building the

tables?

2. What patterns did you discover in the

numbers you recorded?

3. Why do you think each number grows the

way it does?

We are usually convinced more easily by

reasons we have found ourselves than by

those which have occurred to others.

Blaise Pascal

With thanks to Dr. Sherry Parrish for introducing this quote to me

Instructional Shifts

for Mathematics

Conceptual Understanding

Application Procedural

Fluency

Focus

Coherence

Rigor

NOTE: The 6, 8, and 9 tiles have directionality dots. The dot

goes at the bottom of the tile.

When students are exposed to hands-on learning on a weekly rather than a monthly basis, they prove to be 72% of a grade level ahead in mathematics (PAGE 27)

Impact on Student Performance

We learn best by doing…

Carolyn Cutts @CarolynCutts

ccutts@hand2mind.com

404-308-2174

@ETAhand2mind

Workshop: Math Talks

August 31 @ 4 p.m. SD1, Werz

Additional district-wide meetings

October 13 East Coweta

November 10 Evans

December 1 Lee

January 19 Madras

February 23 Smokey Road

Professional learning

We believe as a learning community, we must continually improve.

Wrap-up

We believe we must see students as volunteers in their learning.

National Council of Supervisors of Mathematics (2013). Improving student achievement in mathematics by using manipulatives with classroom instruction. Denver, CO: Author.

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Research Council (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

Moore, S. D. (2013, Fall). Teaching with manipulatives: Strategies for effective instruction. Colorado Mathematics Teacher. Retrieved from http://www.cctmath.org/cmtjournal/

Van de Walle, J.A., Karp, K.S., & Bay Williams, J.M. (2013). Elementary and middle school mathematics: Teaching developmentally. 8th Edition. Boston: Pearson.

References