Common+Core+Standards

**__Grade 7 Math__**

**Unit 1: Ratios and Proportions** Weeks 1-3 Use proportional relationships to solve multistep ratio and percent problems. This unit focuses on solving both contemporary and historical real-life problems that involve applying percents. The expectations include finding the percent of a number, solving problems using the percent proportion, finding the percent of increase or decrease, calculating simple interest, solving problems involving sales tax and discount.
 * __Description__**

Throughout the unit there will be an emphasis on taking the knowledge obtained in the classroom and applying these learned skills in everyday life situations. This will be achieved through problem solving, the use of technology, and real-life applications. Real world problems will include sales markups/markdowns, tips, commissions, fees, and percent error.


 * __Big Ideas__**

-Percents are used in the world all around us.

-Percentage is often used as a method of measuring increases and decreases in numbers.


 * __Essential Questions__**

-Where are percents used in the real world?

-How do we use percents to solve problems?

-How do we find the percent of a number?


 * __Overarching Common Core Standard__**


 * CC.7RP.3** Use proportional relationships to solve multistep ratio and percent problems.


 * __Learning Expectations w/Blooms Taxonomy__**

B1-__Define__ percent as “out of a hundred”.

B1-__Match__ percents with corresponding benchmark fractions and decimals.

B2-__Represent__ percents as their corresponding fractions and decimals.

B3-__Use__ proportional relationships.

B4-__Solve__ multistep ratio and percent problems.

B5-__Evaluate__ the strategies that will be necessary to solve problems involving money amounts.

B6-__Create__ a circle graph from survey data.

B6-__Construct__ a price and percent off problem from a coupon cut out from a sales flyer.

B6-__Develop__ percent increase/decrease problems from historical data.
 * __Significant Tasks__**

1. Students will calculate simple interest of a mock bank savings account with a 4% interest rate. Students will evaluate how different starting balances affect the accumulation of interest and the account balance over the period of one year. Students will graph their results. Students will predict the amount of money they need to save now in order to accumulate interest so that they can afford to pay for college when they graduate high school. Students will research college tuition fees and predict what those fees will be in the future. Simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

2. Students will solve problems involving sales tax and discount. For example, students will realize that a 6% sales tax represents a 6% increase in cost and a 10% discount represents a 10% decrease in cost. Students will discuss the factors that lead to their purchasing decisions. In groups of their peers, students will visit 4 stations throughout the room. Each station will have a relevant item (e.g., iPod, concert tickets, sneakers). Each item will be posted with a price and there will be two options for purchasing the item. One option will have a lower discount with a higher sales tax and the other will a higher discount with a lower sales tax. Students will determine which option will get them the lowest overall price for the item.

3. Students will find the percent of increase or decrease in a range of contemporary and historical problems/scenarios based on the topics they are currently studying in Social Studies. Students will collect the data from text and from graphical representations. Students will synthesize their findings into a written document in which they explain the problem presented by the scenario and the percent increase/decrease that they determined and also the relevance of their findings

4. Students will be given the results of an archeological dig which contain the measurements of a skull and a tooth of a Tyrannosaurus Rex. Using their knowledge of scale, measurement, and ratios, the students will write a paragraph to help someone younger than them understand how the size of a T-Rex compares with a human, which will include a ratio and a proportion problem in order to help explain the relationship.
 * __Supporting Learning Activites__**

Investigation 1.1: Taxing Tapes-Sales tax computations on purchases. Use calculators for computation. Represent $1.00 as 100 pennies on the hundredths grid in order to visualize percentages.Investigation 1.2: Computing Tips-Restaurant exercise where students are provided with a menu then must calculate tips and sales tax. Use hundredths grid paper to represent pennies per dollar. Investigation 1.3: Finding Bargains-Price and discount exercise. Use benchmarks to estimate answers. Use calculators to do final computations. Use actual coupons to determine final prices.Investigation 1.4: Spending Money-Students calculate cost for a night out, including sales tax. Use benchmarks and rounding strategies to estimate answers. Use calculators to do final computations. Use context to help reason about the problem.Investigations 2.1 and 2.2: Finding Percents-Converting ratios into percents. Use context to reason about problem and estimate answers. Investigation 2.3: Clipping Coupons-Percent discounts. Convert percentages into fractions and decimals to help estimate answers.Investigation 2.4: Making CircleGraphs-Converting percentage survey results. Convert percentages into fraction benchmarks to visualize circle graph picture.
 * __Resources/Suggested Texts__**

Connected Math Series: Bits & Pieces II: Using Rational Numbers Publishers:Pearson/Prentice Hall

Ratio: The Simple Codes Behind the Craft of Everyday Cooking by [|__Michael Ruhlman__]
 * __Assessments__**

Solve 1-step problems involving percents.

Solve problems involving percents and proportions in context.

Solve multistep problems involving ratio or proportion, and explain how the solution was determined.

Coupon Clipping Project

Survey Project


 * __Extension Activities__**

Survey Project: Take a survey of classmates and put results into circle graphs using percentages.

Cooking with Ratios: Make and share posters explaining how cooking with ratios is different than cooking according to a recipe, explaining why. Stock Market Game: Following stocks and determining percent profit and loss. Food and Fractions party – inquiry activity in small groups involving food, fractions and open-ended response and student-created video explanations of meaning of fractions/real-life application of fractions
 * __Common Misconceptions__**

Proportional thinking is a skill that needs to be solved on paper. In reality, many proportional reasoning can be done using estimation.

Often students are able to determine how to find the percent of a number, but fail to understand the meaning of percentages.


 * __Grade 7 Math__**
 * Unit 2: Operations with Rational Numbers**

Weeks 4-5

Apply properties of operations as strategies to add and subtract rational numbers.
 * __Description__**

-Sometimes we have to combine numbers that are less than one. Why do we work with numbers that are less than one?
 * __Big Ideas__**
 * __Essential Questions__**

How do you combine numbers that are less than one?

How do we find the difference between two fractions? CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
 * __Overarching Common Core Standards__**
 * __Learning Expectations w/Blooms Taxonomy__**


 * __Significant Tasks__**

Connected Math Series: Bits & Pieces II: Using Rational Numbers Publishers:Pearson/Prentice Hall Add and subtract fractions and mixed numbers with reasonable and appropriate denominators. Cooking with Ratios: Make and share posters explaining how cooking with ratios is different than cooking according to a recipe, explaining why.
 * __Supporting Learning Activities__**
 * __Resources/Suggested Texts__**
 * __Assessments__**
 * __Extension Activities__**

Stock Market Game: Following stocks and determining percent profit and loss.

Food and Fractions party – inquiry activity in small groups involving food, fractions and open-ended response and student-created video explanations of meaning of fractions/real-life application of fractions Fractions are added and subtracted by simply adding or subtracting the numerators and denominators.
 * __Common Misconceptions__**


 * Unit 3: Operations with Rational Numbers**

Weeks 6-8

Apply properties of operations as strategies to multiply and divide rational numbers.
 * __Description__**

Sometimes we have to use numbers that are less than one
 * __Big Ideas__**

Why do we work with numbers that are less than one?How do you combine numbers that are less than one?How do we find the product of two fractions?
 * __Essential Questions__**

CC7.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.
 * __Overarching Common Core Standards__**


 * __Learning Expectations w/Blooms Taxonomy__**


 * __Significant Tasks__**


 * __Supporting Learning Activities__**

Connected Math Series: Bits & Pieces II: Using Rational Numbers Publishers:Pearson/Prentice Hall
 * __Resources/Suggested Texts__**

Multiply and divide fractions and mixed numbers with reasonable and appropriate denominators.
 * __Assessments__**

Cooking with Ratios: Make and share posters explaining how cooking with ratios is different than cooking according to a recipe, explaining why.
 * __Extension Activities__**

Stock Market Game: Following stocks and determining percent profit and loss.

Food and Fractions party – inquiry activity in small groups involving food, fractions and open-ended response and student-created video explanations of meaning of fractions/real-life application of fractions
 * __Common Misconceptions__**

Fractions need to have the same denominator before you multiply or divide them.

** Grade 6 Math **
 * Ratio, rate, rational numbers, dividing fractions, expressions, equations, statistical thinking **

(1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.


 * Resources/Suggested Texts **


 * 1) Fractions -- Concepts **

// YouTube—Fractions with Music // // [] //

// YouTube—Introduction to Fractions, Pt. 2 // // [] //

// *One Hundred Hungry Ants // by [|Elinor J Pinczes], [|Bonnie MacKain] , [|Elinor Pinczes]

// * //// Each Orange Had 8 Slices // by Paul Giganti

*//The Hershey's Milk Chocolate Bar Fractions Book// by Jerry Pallotta


 * __ 2) Ratios – Concepts & Vocabulary __**

// * Ratio: The Simple Codes Behind the Craft of Everyday Cooking // by [|Michael Ruhlman]

* ** YouTube: Ratio and Proportion word problem solving, similar triangles and equivalent fractions ** []

* ** YouTube: Using Ratio and Proportion 1 ** []

[]
 * * Real Life Application of Ratio and Proportion: **


 * 3) Statistical Thinking – Concepts and Resources **


 * YouTube – Statistics, The Average **
 * [] **


 * YouTube – Raw Data, Dot Plots and Stem Plots **
 * [] **

Sports Illustrated: The College Football Book [|Editors of Sports Illustrated]

ESPN: The Mighty Book of Sports Knowledge [Hardcover] [|Steve Wulf]

Statistical Thinking in Sports [Hardcover] [|Jim Albert] (Editor),

The Everything Kids' Baseball Book: From baseball history to player stats - with lots of homerun fun in between! (Everything (Sports & Fitness)) [Paperback] [|Greg Jacobs] (Author)

NFL Record & Fact Book 2010 [Paperback] [|Editors at the NFL] (Author)

The Basketball Hall of Fame's Hoop Facts and Stats [Paperback] [|Alex Sachare]

Soccer Statistics Foundation []

World Karate Foundation http://www.karaterec.com/en/stats.php

WEBSITES (math, general)

* multi-skill, interactive [|http://www.aaamath.com/]
 * Math Websites—multi-topic **

*game-like, multi-skill, multi-genre [|http://www.funbrain.com/math/]

**Extension Activities/Real-Life Connections**

* Food and Fractions party – inquiry activity in small groups involving food, fractions and open-ended response and student-created video explanations of meaning of fractions/real-life application of fractions

* Cooking with Ratios – make food and enjoy; make and share posters explaining how cooking with ratios is different than cooking according to a recipe, explaining why

* Statistics and Sports – inquiry activity, small groups; uncover and present to class how statistics are used in sports and why this is important to sports fans and sports history

GRADE 7 MATH UNIT 1 RESOURCES/DIFFERENTIATION ACTIVITIES

Friday Group Math Common Core Standards Grade 7


 * __ Resources and Activities __**

Mathematics | Grade 7 In Grade 7, instructional time should focus on four critical areas:

(1) developing understanding of and applying proportional relationships;

(2) developing understanding of operations with rational numbers and working with expressions and linear equations;

(3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and

(4) drawing inferences about populations based on samples.

Resources/Activities Grade 7—all 4 Common Core Math Standards []

Interactive Math Website – global math skills []

Professional Development Resource—all 4 core standards []

(1) developing understanding of and applying proportional relationships;

Students or teachers can click on each highlighted substandard and be instantly linked to an online practice activity (applies to all of grade 7 math in this area) []
 * __ Online Interactive Site Connected with Each Sub-Standard __**


 * __ Professional Development Resource/Trinity University __**

[|http://digitalcommons.trinity.edu/cgi/viewcontent.cgi?article=1104&context=educ_understandings&sei-redir=1&referer=http%3A%2F%2Fwww.google.com%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Dapplying%2520proportional%2520relationships%2520grade%25207%26source%3Dweb%26cd%3D3%26ved%3D0CC0QFjAC%26url%3Dhttp%253A%252F%252Fdigitalcommons.trinity.edu%252Fcgi%252Fviewcontent.cgi%253Farticle%253D1104%2526context%253Deduc_understandings%26ei%3DJwniTtnUIoL40gGKo6nlBQ%26usg%3DAFQjCNGzcZKT9_S613_n3h4Ss8pmv3UhMQ%26sig2%3DA8jJ_oHXERwey_2O19MedA#search=%22applying%20proportional%20relationships%20grade%207%22]

(2) developing understanding of operations with rational numbers and working with expressions and linear equations;

[]
 * __ Understanding Linear Equations __**

(3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and

Interactive Website []

(4) drawing inferences about populations based on samples.

Main Idea: []

Interactive []


 * __ Activities for Differentiation/Cross-Disciplinary Work __**

* population/statistics – project with Social Studies * students make bulletin board displays with posters using the 5 W’s to explain and inform each sub-standard; include graphics (advanced students write a 5 paragraph essay on real-life applications) * video gamers or chess players can have a tournament and do a multi-media report explaining their statistical analysis of this

GRADE 8 Unit ONE Resources and activities

Friday Group Math Common Core Standards Grade 8


 * __ Resources and Activities __**

Mathematics | Grade 8

In Grade 8, instructional time should focus on three critical areas:

(1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations

(2) grasping the concept of a function and using functions to describe quantitative relationships

(3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem

interactive website activities []
 * __ Uni- and Bi- variate data: __**

Activity: work with partners; inquiry activity – what other words in the world start with UNI- BI- and TRI? What do these prefixes mean? How do they help you as a reader and as a math student?

[]
 * Graphing Linear Equations: **

Activity: use glossary (left hand menu) on this site work in small groups to make a meaningful poem (rhyming or free verse) using this math vocabulary. Differentiation: put high functioning and struggling students together. Add djembes for performance. (speaking and listening as part of literacy)

Patterns, Functions and Algebra: Teacher Resource site: []
 * Using Functions: **

Interactive Student Practice: Algebra, graphs, patterns []

Activity: write out algorithm steps in words (expository essay), then teach peers using words to see if the numbers match the word description

[]
 * Using distance, angle, similarity, and congruence, and…. **

high school level with videos: []


 * Pythagorean Theorem **

Grades 6-9 []

Instructional Video YouTube, Grades 5-8 []

Book: What’s Your Angle, Pythagoras? Julie Ellis []

Activity: Work with Grade 6 Social Studies teacher to do a multi-age, multi-level, hands-on project that is interdisciplinary. (Ancient Greece, contemporary US, meaning of history, cause and effect of one person on society, practical application of math

12/23/11

As I wait for someone to tell me how to revise what I have sent, I will do word problems, K-5 foundation in hands-on algebraic thinking, real-life applications, biography of mathematicians, and robotics related.




 * • The K‐5 standards build on the best state standards to provide detailed guidance to teachers on how to navigate their way through knotty topics such as //fractions, negative numbers, and geometry//, and do so by maintaining a continuous progression from grade to grade. **
 * • The standards stress not only procedural skill but also conceptual understanding, to make sure students are learning and absorbing the critical information they need to succeed at higher levels ‐ rather than the current practices by which many students learn enough to get by on the next test, but forget it shortly thereafter, only to review again the following year. **
 * • Having built a strong foundation K‐5, students can do //hands on learning// in geometry, algebra and probability and statistics. Students who have completed 7th grade and mastered the content and skills through the 7th grade will be //well‐ prepared for algebra// in grade 8. **

From CCStandards pdf – main points about math

Since algebraic thinking is stressed from K on, students at Trailblazers who are behind or ahead need more algebraic resources…..


 * __ 1) WORD PROBLEMS __**

[|**Amusement Park Word Problems Starring Pre-Algebra (Math Word Problems Solved)**] by [|Rebecca Wingard-Nelson] (Mar 2009)

Painless Math Word Problems (Barron's Painless) [Paperback] [|Marcie Abramson B.S. Ed.M.] (Author)

Comic-Strip Math: 40 Reproducible Cartoons with Dozens of Funny Story Problems That Build Essential Skills, Grades 3-6 [Paperback] [|Dan Greenberg] (Author)
 * __ 2) Algebraic Thinking __**

Practical Algebra: A Self-Teaching Guide, Second Edition [Paperback] [|Peter H. Selby] (Author), [|Steve Slavin] (Author)

Algebra Survival Guide: A Conversational Guide for the Thoroughly Befuddled [Paperback] [|Josh Rappaport] (Author), [|Sally Blakemore] (Illustrator)

Algebra Survival Guide Workbook: Thousands of Problems to Sharpen Skills and Enhance Understanding [Paperback] [|Josh Rappaport] (Author)

How to Solve Word Problems in Algebra, (Proven Techniques from an Expert) [Kindle Edition] [|Mildred Johnson] (Author), [|Tim Johnson] (Author) , [|Linus Johnson]  (Author) , [|Dean McRaine]  (Author) , [|Sheralyn Johnson]  (Author)


 * __ 3) Professional Development Resources __**

Young Mathematicians at Work: Constructing Algebra [Paperback] [|Catherine Twomey Fosnot] (Author), [|Bill Jacob]

Hands on approach, geared towards elementary students, therefore foundational for our students who are behind and/or need extra practice with hands on materials.

Connecting Arithmetic to Algebra (Professional Book): Strategies for Building Algebraic Thinking in the Elementary Grades [Paperback] [|Susan Jo Russell] (Author), [|Deborah Schifter] (Author), [|Virginia Bastable] (Author)

Algebra readiness: it's a topic of concern that seems to pervade every school district. How can we better prepare elementary students for algebra? More importantly, how can we help //all// children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Both the NCTM Principles & Standards and the new Common Core State Standards (CCSS) for Mathematics call for providing elementary students with a strong mathematics foundation through algebraic thinking. //Connecting Arithmetic to Algebra// invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators **Susan Jo Russell, Deborah Schifter**, and **Virginia Bastable** and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true. Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies. Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning

Algebra and the Elementary Classroom: Transforming Thinking, Transforming Practice [Paperback] [|Maria Blanton] (Author)

This basic algebra lesson will introduce you to five types of word problems that are applications of linear equations.
 * __ 4) Amazon instant video series, linear equations, word problems, algebra: __**
 * 140 Solving Word Problems Using Linear Equations Part I**
 * Directed by:** Math Made Simple Inc.
 * Runtime:** 1 hour 17 minutes
 * Studio:** Math Made Simple Inc.

This basic algebra lesson follows on from 135 Solving Linear Equations Part I to help you solve more difficult linear equations.
 * 145 Solving Linear Equations Part II & Word Problems**
 * Directed by:** Math Made Simple Inc.
 * Runtime:** 1 hour 15 minutes
 * Studio:** Math Made Simple Inc.

This 56 minute basic algebra lesson is for the beginning algebra student or for anyone who has not recently studied algebra.
 * 110 Basic Algebra Part I**
 * Directed by:** Math Made Simple Inc.
 * Runtime:** 57 minutes
 * Studio:** Math Made Simple Inc.


 * __ 5) Real Life Applications __**

Life by the Numbers [Paperback] [|Keith Devlin] (Author)

From uncanny movie dinosaurs to the loopy physics of the triple axel, Keith Devlin's vibrantly illustrated book illuminates the mathematics inherent in every human endeavor.

The Number Devil: A Mathematical Adventure [Paperback] [|Hans Magnus Enzensberger] (Author), [|Rotraut Susanne Berner] (Author), [|Michael Henry Heim] (Author) Age Level: ** 10 and up ** | Grade Level: ** 5 and up ** The international best-seller that makes mathematics a thrilling exploration. In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone-from those who fumble over fractions to those who solve complex equations in their heads-winds up marveling at what numbers can do.

Math Trek: Adventures in the Math Zone [Paperback] [|Ivars Peterson] (Author), [|Nancy Henderson] (Author)

Age Level: ** 10 and up ** | Grade Level: ** 5 and up ** There s a new amusement park in town. Come on in and find out all the exciting ways you can have fun with math in everyday life. Wander through the fractal forest, take a ride on the Mobius-strip roller coaster, and get dizzy learning about how math makes the Tilt-A-Whirl possible. The more activities you try, the more you ll learn how cool it can be to see the world through the eyes of a mathematician.

The Man Who Counted: A Collection of Mathematical Adventures [Paperback] [|Malba Tahan] (Author), [|Patricia Reid Baquero] (Illustrator), [|Leslie Clark] (Translator), [|Alastair Reid] (Translator)

Malba Tahan is the creation of a celebrated Brazilian mathematician who was looking for a way to bring some of the mysteries and delights of mathematics to a wider public. He turned out to be a born storyteller.

The adventures of Beremiz Samir, //The Man Who Counted//, take the reader on an exotic journey in which, time and again, he summons his extraordinary mathematical powers to settle disputes, give wise advice, overcome dangerous enemies, and win for himself fame and fortune. as we accompany him, we learn much of the history of famous mathematicisns who preceded him; we undergo a series of trials at the hands of the wise men of the day; and we come to admire the warm wisdom and patience that earn him the respect and affection of those whose problems he resolves so astutely. In the grace of their telling, these stories hold unusual delights for the reader.

The Adventures of Penrose the Mathematical Cat [Paperback] [|Theoni Pappas] (Author) // …useful as motivational stories…and extensions of their lessons. … //

Fractals, Googols, and Other Mathematical Tales [Paperback] [|Theoni Pappas] (Author)

// "…For those you love math, for those indifferent to it, and for those who absolutely dread and fear it, this is an entertaining way to explore the world of numbers regardless of age or background." —Bookpaper //

// "This book is a pleasant presentation of math subjects not generally made accessible to young children, as well as containing more conventional topics such as tangrams, the abacus, mazes, magic squares, and logic problems. The topics were greatly enhanced, in my son's opinion, by being couched in stories." // —Pat Willette, parent

Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians [Paperback] [|Luetta Reimer] (Author), [|Wilbert Reimer] (Author)

Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 2 [Paperback] [|Luetta Reimer] (Author), [|Wilbert Reimer] (Author)


 * __ 6) Robotics Related: __**

Lego Mindstorms Kits

[|**The LEGO MINDSTORMS NXT 2.0 Discovery Book: A Beginner's Guide to Building and Programming Robots**] by [|Laurens Valk] (May 10, 2010) [|Buy new]: $29.95 **$19.77**

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[|**The Unofficial LEGO MINDSTORMS NXT 2.0 Inventor's Guide**] by [|David J. Perdue] and [|Laurens Valk] (Dec 15, 2010) [|Buy new]: $29.95 **$18.80**

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[|**The Art of LEGO MINDSTORMS NXT-G Programming**] by [|Terry Griffin] (Sep 2, 2010) [|Buy new]: $29.95 **$19.08**

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1.
 * Results for "legos** mindstorms and **math" in** Books ([|See all 24 results])

[|**Winning Design!: LEGO MINDSTORMS NXT Design Patterns for Fun and Competition**] by James Jeffrey Trobaugh (Dec 15, 2010) [|Buy new]: $29.99 **$19.59**

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[|**Getting Started with LEGO Robotics: A Guide for K-12 Educators**] by [|Mark Gura] (Jul 15, 2011) [|Buy new]: $37.95 **$25.05**

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[|**Extreme Mindstorms: an Advanced Guide to Lego Mindstorms**] by Dave Baum, [|Michael Gasperi], Ralph Hempel and Luis Villa (Oct 2000) [|Buy new]: $29.95 **$24.01**

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Algebra Professional Development Resources: []
 * Integrating Picture Story Books into the Algebra I and Geometry classrooms **

VIRTUAL LIBRARIAN BIBLIOGRAPHY 1/3/12 ** MIDDLE SCHOOL MATH LITERATURE ** ** Shannon DeSantis ** Glazer, E., & McConnell, J. W. (2002). //Real-life math: Everyday use of mathematical concepts//. Westport, Conn: Greenwood Press. ISBN-10:0313361231 ISBN-13:978-0313361234 Summary: What does this have to do with real life? This is a question that every math teacher hears from students. This book makes connections to real life examples making it meaningful to students. Concepts include: algebra, trigonometry, geometry, analysis, probability, and statistics. Pappas, T. (1997). //The adventures of Penrose, the mathematical cat//. San Carlos, CA: Wide World Pub./Tetra. ISBN-10: 1884550142 ISBN-13: 978-1884550140 Summary: Penrose the cat explores and experiences different math concepts from fractals, infinity, and more.
 * General: **

Pappas, Theoni. (2004). //Further Adventures Of Penrose, The Mathmatical Cat//. Demco Media. ISBN-10: 0606313141 ISBN-13: 9780606313148 Summary: Penrose the cat is back to take readers on more math adventures including algebra, symmetry, and more.

Pappas, T. (1991). //Math talk: Mathematical ideas in poems for two voices//. San Carlos, CA: Wide World Pub. /Tetra. ISBN-10: 0933174748 ISBN-13: 9780933174740 Summary: A book of poetry about math concepts for two voices to read aloud. The poems include topics such as fractions, integers, triangles, and infinity.
 * Gifted/ Talented: **

Burns, M., & Weston, M. (1982). //Math for smarty pants//. Boston: Little, Brown.

ISBN-10: 0316117390 ISBN-13: 978-0316117395

Summary: Math concepts are portrayed through puzzles, tricks, and word puzzles. This book is for both the math enthusiast and struggling student alike. Clemens, M., Clemens, G., & Clemens, S. (2003). //The everything kids' math puzzles book: Brain teasers, games, and activities for hours of fun//. Avon, Mass: Adams Media. ISBN-10: 1580627730 ISBN-13: 1580627730 Summary: This book contains math puzzles, games, and riddles for every kind of math student! Skills include: reasoning, geometry, multiplication, division, and more.

Salvadori, M., & Wright, J. P. (1998). //Math games for middle school: Challenges and skill-builders for students at every level//. Chicago, Ill: Chicago Review Press. ISBN-10: 1556522886 ISBN-13: 978-1556522888 Summary: This book uses explanations, puzzles, word problems, and games to clarify middle school math concepts including measurements, geometry, probability, and more. = Stickels, T. // Math Puzzles and Games, Grades 6-8: Over 300 Reproducible Puzzles that Teach Math and Problem Solving //. = ISBN-10: 1556522886 ISBN-13: 978-1556522888 = Summary: This volume contains math puzzles and games. Concepts include: numbers and operations, geometry, measurement, reasoning, algebra, statistics, probability, and more. = **Lower-Level:** Long, Lynette, & Morehouse, Hank. (2008). //Painless Algebra//. Paw Prints. ISBN-10: 1439530920 ISBN-13:9781439530924 Summary: This book is a part of a series written for students who find the subject matter difficult or challenging. Using humor, puzzles, and games, the text tries to clear up student confusion and increase student interest in algebra.

Rappaport, J. (2011) //Pre-Algebra Blastoff: Understanding Positive and Negative Numbers, Grades 3-8//. Singing Turtle Press. ISBN-10: 0764147153 ISBN-13: 9780965911368 //Pre-Algebra Blastoff// is a guide for parents and educators to help teach students pre-algebra concepts including positive and negative numbers. This program has three stages. First, students read a comic book introducing how positive and negative numbers combine. During the second stage, students use foam manipulatives to solve problems and then learn to solve problems abstractly. In the third and final stage of the program, students play board games to review concepts. Strazzabosco, J. (2004). //Extreme temperatures: Learning about positive and negative numbers//. New York: PowerKid Press. ISBN-10: 0823989275 ISBN-13: 9780823989270 Summary: //Extreme Temperatures// explains positive and negative numbers, how to measure temperature, and explores places on Earth with extreme weather conditions.
 * Positives and Negatives: **


 * Ratio and Proportions/ Multiplication and Division **

Ellis, J., & Peacock, P. H. (2010). //Pythagoras and the ratios: A math adventure//. Watertown, MA: Charlesbridge. ISBN-10: 1570917752 ISBN-13: 9781570917769 Summary: A young boy in Ancient Greece teaches his cousins how to change the pitches of their pipes using ratios to make the pipes shorter or longer and affect the pitch of the instrument.

Caron, L., & St, J. P. M. (2012). //Percent and ratio smarts!//. Berkeley Heights, NJ: Enslow Publishers. ISBN-10: 9781598453171 ISBN-13: 1598453173 Summary: This book explains a variety of mathematical concepts related to percents and ratios including reducing ratios, finding equivalent ratios, as well as fractions, decimals, and probability. The text uses word problems and illustrations to teach readers.

Lasky, K., & Hawkes, K. (1994). //The librarian who measured the earth//. Boston: Joy Street Books. ISBN-10: 9780316515269 ISBN-13: 0316515264 Summary: This biography of Erastophanes, a famous geographer and astronomer, tells the story of a curious man who always wanted to learn life’s mysteries. This story focuses on how Erastophanes accurately measured the Earth’s circumference.

Calmenson, S., & Brunkus, D. (1989). //The principal's new clothes//. New York: Scholastic. ISBN-10: 0590447785 ISBN-13: 9780590447782 Summary: This story is a twist on the classic tale, The Emperor’s New Clothes. Principal Bundy is persuaded by two tricksters into wearing a suit that only intelligent people who are good at their jobs can see. Everyone around him is in for a surprise!

Collins, S. H. (1988). //Advanced fractions//. Eugene, OR: Garlic Press. ISBN-10: 0931993210 ISBN-13:978-0931993213 Summary: students who have mastered basic fraction skills can learn how to add, subtract, multiply, and divide using the methods in this book.


 * Expressions and Equations **

Demi,. (1997). //One grain of rice: A mathematical folktale//. New York: Scholastic Press. ISBN-10: 059093998X ISBN-13:978-0590939980 Summary: A girl bests a raja and turns one grain of rice into a feast for her people.

Anno, M. (1995). //Anno’s magic seeds//. New York: Philomel Books. ISBN-10: 0698116186 ISBN-13: 978-0698116184 Summary: A wizard gives a boy a gift which makes his fortunes grow by ones, twos, threes, and so on. The challenge is to keep track of the boy’s riches as the story develops.

McKellar, D. (2008). //Kiss my math: Showing pre-algebra who's boss//. New York: Hudson Street Press. ISBN-10: 1594630496 ISBN-13: 9781594630491 Summary: Danica McKellar, a well-known actress and excelling mathematician, wrote a book to help girls who are struggling with pre-algebra. Danica explains numbers, variables, x, exponents, and functions using step-by-step instructions, tips and tricks, and sample problems.
 * Algebra/ Low: **

McKellar, D. (2007). //Math doesn't suck: How to survive middle school math without losing your mind or breaking a nail//. New York: Hudson Street Press. ISBN-10: 0452289491 ISBN-13: 978-0452289499 Summary: Danica McKellar, a well-known actress and excelling mathematician, wrote this book for girls who are struggling in math. She takes the most challenging math concepts and applies them to real world applications for teenage girls. Danica gives instructions as well as tips and tricks to solve these problems. Each section contains practice problems and explanations for each concept covered. Concepts include: factors, prime numbers, complex fractions, decimals, and much more.

Albert, J., & Bennett, J. (2001). //Curve ball: Baseball, statistics, and the role of chance in the game//. New York: Copernicus Books. ISBN-10: 038700193X ISBN-13: 978-0387001937 Summary: Baseball revolves around the mathematical concepts of statistics and probability. This work presents a great deal of baseball statistics while discussing math concepts such as the box plot, five number summary, probability and baseball, batting averages, and more. This book would be great to pull real life math applications from for the average boy or baseball enthusiast.
 * Statistics **

Gonick, L., & Smith, W. (2008). //The cartoon guide to statistics//. New York, NY: Collins Reference. ISBN-10: 0062731025 ISBN-13: 978-0062731029 Summary: //The Cartoon Guide to Statistics// explains all of the main ideas of statistics using comics. Concepts include: probability in gambling, hypothesis testing, Central Limit Theorem, and much more. The illustrations are funny, simple, and easy to understand. Schwartz, D. M., & Warhola, J. (1999). //If you hopped like a frog//. New York: Scholastic Press. ISBN-10: 0590098578 ISBN-13: 978-0590098571 Summary: //If you hopped like a frog// teaches readers about ratios and proportions by comparing humans to animals. Find the answers to interesting problems like this: If a frog can jump twice the length of its body, how far could you jump if you were a frog? Each example has both zoological and mathematical explanations for the reader. Poskitt, K. (2011). //Murderous Maths Series Box Set.// Scholastic. Summary: //Murderous Maths// introduces all of the tips and tricks of algebra you won’t learn in school. The series uses entertaining characters to solve math problems and make math more relatable to students. This series includes: //Savage Shapes, The Perfect Sausage, Easy Questions, Evil Answers,// //The Phantom X, Essential Arithmetricks, Key to the Universe, Desperate Measures, Do You Feel Lucky, Guaranteed to Mash your Mind,// and //Guaranteed to Bend your Brain.// Concepts: // Murderous Maths: Do You Feel Lucky? // -proportions // Murderous Maths: Savage Shapes //- Surface area/ volume/ geometry //Murderous Maths- The Phantom X// -Rational numbers/ linear equations

Neuschwander, C., & Geehan, W. (2001). //Sir Cumference and the Great Knight of Angleland: A math adventure//. Watertown, Mass: Charlesbridge. ISBN-10: 0590098578 ISBN-13: 978-0590098571 Summary: Radius embarks on a journey to achieve his knighthood by finding a missing king. Readers will discover many facts about angles including right angles, straight lines, and how to use a protractor while reading this adventure.
 * Angles **

Ellis, J., & Peacock, P. H. (2004). //What's your angle, Pythagoras?: A math adventure//. Watertown, MA: Charlesbridge. ISBN-10: 1570911509 ISBN-13: 978-1570911507 Summary: A fictionalized account of how Pythagoras discovered his famous theorem. Pythagoras travels with his father and meets a man who introduces him to right triangles. He begins to experiment, observe, and note different mathematical ideas about triangles until he arrives at his theorem.

=HIGH AND LOW DIFFERENTIATION= =ROBOTICS and LEGOS= =LATIN and MATH= =Multi-CULTURAL history and math (muslim)= =many YouTube videos= =1/11/12= =from Ms. Avakian=


 * __ More Resources for math team re: differentiation both ends/multi-disciplinary activities __**


 * 1) LEGOS, common core math, science, engineering, robotics, social skills, poetry, music, video, website/wiki, outside community participation **

PD: $1800 for 10 teachers – LEGOS/ROBOTICS – verify first if aligned to Common Core []

WE HAVE SO MANY BUILDERS IN THIS SCHOOL!!!!!!!!!!

How cool would it be to have a Lego League (they have them in Stamford) and/or Robotics Club? We could combine this with poetry and music and video.

CHEAPER DATE: legos mindstorms robot building software $99.00 I believe

EVEN CHEAPER DATE: build robots out of junk lying around in the street

YouTube has a lot of videos such as WeDo Legos []


 * 2) Latin roots, prefixes, suffixes and math vocabulary – a fruitful area for literacy and math to combine forces, especially at TBA **

WONDERFUL list – origin of math terms (alphabetical, easy to skim) []

YouTube video of a kid’s take on metric words – we could better than this! []

Funny video by a kid of what the metric system is []

1:30 YouTube – infinity sign, mobius strip, Latin word []

Articles/websites/resources – Latin and math [] []

Muslim roots of algebra – could be research project/bulletin board/presentation for students needing an independent project
 * __ 3) Math, Science, History, Multiculutral __**

YouTube -- Hour Long video – Science and Islam Part 1 of 3 – subtitled, British accent “ Physicist Jim Al-Khalili travels through Syria, Iran, Tunisia and Spain to tell the story of the great leap in scientific knowledge that took place in the Islamic world between the 8th and 14th centuries.a Its legacy is tangible, with terms like algebra, algorithm and alkali all being Arabic in origin and at the very heart of modern science - there would be no modern mathematics or physics without algebra, no computers without algorithms and no chemistry without alkalis. For Baghdad-born Al-Khalili this is also a personal journey and on his travels he uncovers a diverse and outward-looking culture, fascinated by learning and obsessed with science. From the great mathematician Al-Khwarizmi, who did much to establish the mathematical tradition we now know as algebra, to Ibn Sina, a pioneer of early medicine whose Canon of Medicine was still in use as recently as the 19th century, he pieces together a remarkable story of the often-overlooked achievements of the early medieval Islamic scientists.”

[]

SHORT YouTube instructional math videos in a series with a cool, urban feel and simple, thoughtful explanations. “The Language of Math Series”
 * __ 4) __** **__ FOR THE STRUGGLING: __**

[]

[] [] []
 * __ 5) ROBOTICS CONCEPTS and EXAMPLES – real world, short videos, __** [|Bielefeld University]


 * __ 6) Singapore Math __** – ever hear of it? It was explained to me that the KIDS come up with the QUESTIONS by manipulating objects/data

Dobbs Ferry School in Westchester is using it. Sounds to me a lot like Connected Math?????

[]

This source only goes up to grade 6, but it may be a useful chart re: connecting Singapore Math concepts with Common Core:

[]

FRAYER MODEL GRAPHIC ORGANIZER -- vocab./concepts ELL differentiation
 * __ Math Concepts/Vocabulary __**
 * __ Common Core Standards, Grades 6-8 __**
 * __ Applicable to any topic/concept/word __**


 * __ FRAYER MODEL GRAPHIC ORGANIZER __**

Some more differentiation/extension activities-- Ideas I got from the ELL PD this last week:


 * For ELL/Struggling Readers or all students: **


 * Use the Frayer Model Graphic Organizer to re-teach/practice and review math vocabulary and concepts. **


 * (Note: I had better luck going in this order: Concept word in center, Examples, Non-examples, Facts, Definition). Students can have a binder of these graphic organizers and that will be of great aid to studying for tests, CMTs and finals. You could also morph work with the graphic organizer into a review game or inquiry game. **


 * Blank template: **


 * [] **


 * Template with an added box for an image: **


 * [] **

UNIT 4 IDEAS FROM Ms. Avakian GEOMETRY Mr. Dean –
 * Short explanation: **
 * [] **

Please see Mr. Green’s email for cylinders, cones, and spheres for ideas also….

7th grade: geometry, area, perimeter, boxes, column, cubes, cylinders, cones

__Area & Perimeter, etc.__

Something wacky would be fun ---OUT IN THE STREET


 * What about getting a mini-grant from the City of Stamford to ride the city bus and measure stuff out on the street near the Public Library?**


 * One group measures perimeter of several street objects of choice and videos what is happening, including problems they are running into – specific math concepts and vocabulary to use while speaking were discussed in advance and there is a rubric in hand**


 * The other group measures area of several street objects of choice and videos what is happening as above.**


 * Later, when you return to class, the students can watch and discuss the videos and self-reflect as to their OWN misconceptions, in addition to what you have listed**

__Extensions to differentiate for strugglers, learning styles, fast finishers:__
 * 1) a small group asks the Librarian for books and activities on this topic**
 * 2) a small group interviews patrons at Starbucks as to real world applications**
 * of this list of geometry concepts**
 * 3) a small group sits on the stairs outside the library and photographs the others working and writes a poem about what is happening making sure to use the math vocabulary list meaningfully**
 * 4) If grant $, then use $ to buy treats at Starbucks, but each team can only get treats if they can write in a paragraph using math vocabulary how the deserts, drinks, and food items there use the shapes**
 * 5) EXTEND activity into an initiation, conclusion, or significant task by adding in ALL THE SHAPES and a self-reflective essay using math vocabulary**



Sources for Robotics ideas:


 * []**
 * bioinformatics, biomedicine**
 * []**
 * online construction of robots using free program it looks like**
 * (students could have an inquiry project and then write/speak about what they discovered)**
 * []**
 * again, inquiry project perhaps with teacher assigning a particular menu item to a need the student may have**
 * []**
 * students research this website and others and make a short grant proposal to take upstairs in regard to starting a robotics club, Common Core Standards, real life application, college and career, private schools that have these programs, etc.**

__common misconceptions__


 * (in addition to what the students discover about themselves)**


 * 1) girls aren’t into robots**
 * 2) math is boring**
 * 3) math does not go with poetry**
 * 4) math does not go with field trips**
 * 5) middle school math has nothing to do with my future college and career**
 * 6) robots are just in science fiction movies and books**
 * 7) writing has nothing to do with math**
 * 8) using math vocabulary in my daily speech is not important**


 * For Mr. Greene: **
 * 6/19/12 **


 * volume of cylinders, cones and sphere, real world application **
 * references and tasks -- BRAINSTORM **

Playdoh—initiation/review


 * [] **
 * (includes use of playdoh, which addresses kinesthetic learning as well as review and practice….also, if you make the playdoh, you review fractions. **


 * the whole class could use playdoh for review/initiation or you could do this at the Guided Math table for the strugglers **


 * 3 constructed response items that can be morphed together into a larger project: **

Entrepeneurial focus – you own store/restaurant/ice cream shop 3 questions address the math source for 3 constructed response questions: []

ideas for differentiation for strugglers, and high achievers below

finale for all: ice cream! spheres in a cone with pictures and make bulletin board out of it—make sure everyone gets in the name of their business and explains in a short paragraph HOW they use math to be successful.


 * 1) Which is the better buy, oranges 7 cm in diameter that cost 20 cents each or oranges 9 cm in diameter that cost 30 cents each? Explain.


 * 1) A cylindrical glass 7 cm in diameter and 10 cm tall is filled with water to a height of 8 cm. If a ball 5 cm in diameter is dropped into the class and sinks to the bottom, will the water in the glass overflow? Explain and justify your response. What if the ball floats instead of sinks, will the water overflow? Explain.


 * 1) The Taste Good Ice Cream Shop is about to advertise giant spherical scoops of ice cream 8 cm in diameter! The owner of the shop wants to be sure there is enough ice cream and wonders how many scoops can be obtained from each cylindrical container of ice cream. The containers are 20 cm in diameter and 26 cm tall. How can the owner determine how many containers of ice cream to order?


 * differentiation of these for struggling students ** – hands-on items done at the guided math table WITH the teacher – one student has the job of typing up notes about what is being done/discussed. Essentially, the teacher guides the students through the 3 questions in a hands-on way FIRST, then gives them notes and 3 diagrams which are gone over together. THEN the strugglers do the constructed response and if students are reading grade level 3 or below, then a further modification would be to have the answers written out with words missing and the students fill in the blank using a word bank.


 * __ differentiation for high achievers __** (or whole class if you like) – choose one or more:

1) write a poem that teaches a Kindergartner about real world applications of cones, cylinders, and spheres

2) make a video with a friend(s) using Dr. E-P’s flip camera in which you become characters with a TV show – can be funny, scary, surreal, straight up – your goal is to teach real world applications of cylinders cones and spheres in a fun and mathematically informative way. Your audience are 6th graders. After videos are approved for success, you will show them to the 6th grade math class and they will grade your work based on rubric you create.

3) Use the Internet to figure out how to write to a real life engineer, astronaut or scientist and ask to interview him/her over Skype about their job and how they apply the math involved with cylinders, cones and spheres. Ask any other (respectful) questions you have. Make a poster out of the project to display in class.

4) Research the Internet to find out if cylinders, cones and spheres are used to make insect robots/nano-bots; then make your own 3-D prototype out of pipe cleaners and paper clips and washers and wire and old junk lying around.


 * DIFFERENTIATION for strugglers ** – ask Reading Specialist to find the sources and do a skimming lesson with strugglers at the guided math table and/or a vocabulary chart re: robotic vocabulary/concepts

5) Students interview the art teacher (at her convenience) for resources and ideas re: cylinders, cones and spheres in art appreciation, critique and 3-D construction. Then students try to make something based on interview.

Other resources:

1) manipulatives []

all of these ideas can be made for all ages to address kinesthetic and ADHD learners

2) SMART board games:

though billed as for 2nd graders, this is an extensive list for ideas or even actual games – scroll down to part C []

3) this easy to read site even has I-pad apps for this unit! You might be able to get a mini-grant from the city of Stamford to get an I-pad and use it as a carrot for good behavior

http://interactivemaths.wikispaces.com/3D