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CITY YEAR CHICAGO

CITY YEAR CHICAGO. CITY YEAR CHICAGO. CITY YEAR CHICAGO. Math 101 Session Developer: Mari Mermelstein City Year Chicago. Warm-Up. 5 Minute Free-Write Write down anything and everything you think about MATH. Write about your feelings

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CITY YEAR CHICAGO

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  1. CITY YEAR CHICAGO CITY YEAR CHICAGO CITY YEAR CHICAGO Math 101 Session Developer: Mari Mermelstein City Year Chicago

  2. Warm-Up 5 Minute Free-Write Write down anything and everything you think about MATH Write about your feelings Write about your experiences Write about all the things you wanted to say to your teachers but never did.

  3. Ultimate Goal • Re-frame your mindset and attitude towards Math

  4. Putting Idealism to Work PITW #134 - A Positive, “Can-Do” Attitude Is the First Qualification for Being a Part Of City Year. This must be true for both corps and staff. Inspiring others and maintaining an environment in which idealism can flourish depends on all of us maintaining positive attitudes. This does not mean always being “rah rah.” But it does mean that we must all remain positive, constructive and inspired, even when being critical.

  5. Agenda • “Know” Questions • Common Misconceptions • Foundational Skills • Math Anxiety and it’s causes • Common student struggles • 1st month strategies

  6. “Know” Questions • How to refute common misconceptions about mathematics • How the Common Core State Standards can help you help your students • How to identify common struggles that students have • Computational Strategies

  7. Misconceptions • Math is only about learning to compute • Math is about following rules to guarantee correct answers • Some people have the ability to do math and some don’t • Men are naturally better than women at math • Learning math isn’t important in the age of calculators and computers.

  8. Math is only about learning to compute • “It is a way of approaching new challenges through investigating, reasoning, visualizing and problem solving with the goal of communicating the relationships observed and problems solved to others.”1 • “Knowledge of mathematics and the ability to apply math skills to solve problems can be an empowering force for all students—both while in school and later in their lives.”1 1Illinois State Board of Education: http://www.isbe.state.il.us/ils/math/standards.htm

  9. Math is about following rules to guarantee correct answers • Some people do take comfort in the “black and whiteness” of Math, but NOT all. • About the sense-making process. • Learning to reason and understand why math “works” is just as important as finding the “right” answer.

  10. Some people have the ability to do math and some don’t • Which is a person more likely to admit: That they are Illiterate or Innumerate (math illiteracy)? • If a student comes across a word they don’t know, they don’t say they cannot read; but if a student comes across a problem they can’t solve, they say they cannot do math. • Why is it socially acceptable to be math illiterate, • but not verbally illiterate? • By allowing this mindset, we are saying it is OK • for our students to fail in Math

  11. Men are naturally better than women at math • Girls Sweep Google Science Fair: • “A contrast to when women were largely excluded from the science world.” Kenneth Chang • “It shows you that women are stepping up in science” Shree Bose, Age 17 (Best in Show) • “This is just a reminder that women are fully capable of doing the same or better quality work than men can.” Dr. Vint Cerf Chang, Kenneth. “First-Place Sweep by American Girls at First Google Science Fair,” July 18th, 2011

  12. Learning math isn’t important in the age of calculators and computers • Arithmetic vs Algebraic thinking • The emphasis now is getting people to be sophisticated algebraic thinkers. You cannot become good at algebra without a mastery of arithmetic, because arithmetic is the gateway to algebra. But arithmetic itself is no longer the ultimate goal.2 • Need to be smarter than the machine • Need to understand/be able to write the program that does the math for you • Need to be able to understand the information the technology gives you 2NPR Interview with Keith Devlin, “The Way You Learned Math Is So Old School” March 5th, 2011

  13. (Lacking) Foundational Skills Time to get up and move! Activity: Mental Math Strings

  14. Operations and Algebraic Thinking (including Functions)

  15. 1. Rewrite the expression 3(2x2 + 5x) - 7 - 3x + 1 - x2 Order of Operations: Multiplication and division should be solved before addition and subtraction. Always work from right to left. 2. Distribute 6x2 + 15x – 7 – 3x + 1 - x2 3. Gather like terms together 6x2 – x2 + 15x – 3x – 7 + 1 Ensures proper simplification Order of Operations: Addition and subtraction from left to right, do whichever operation appears first. 4. Simplify 5x2 + 12x – 6 Simplify 3(2x2 + 5x) - 7 - 3x + 1 - x2 Reason Steps Calculation

  16. Operations and Algebraic Thinking (including Functions) 3(2x2 + 5x) - 7 - 3x + 1 - x2 = 5x2 + 12x – 6

  17. Operations and Algebraic Thinking (including Functions)

  18. Number and Operations in Base Ten (including Fractions/Ratios/Proportions

  19. Geometry

  20. Measurement and Data/Statistics and Probability

  21. Weak Computational Skills Poor conversation or academic language skills Lack of Confidence Unable/Unwilling to write out complete solutions Weak Conceptual Understanding Poor test-taking skills Low Work Completion Rate Poor English Language Skills Math Anxiety

  22. Learning Differences • People learn in different ways. • Visual • Auditory • Kinesthetic • Combo • If the student’s learning style and the classroom teaching style are not compatible students may struggle

  23. Strategies for the 1st month • “Check List” - watch for the above listed struggles • Flash Cards • Multiplication strategy - Elizabethan Boxes • As a way to move toward the standard algorithm • Division strategy - Clustering • As a way to move toward the standard algorithm • Fractions/Decimals/Percentages • Order of Operations and Properties of Equalities

  24. Standard Multiplication Algorithm 156  72 312  1092 11,232

  25. Multiply each single digit pair Add along the diagonals Multiplication Strategy:Elizabethan Boxes (Lattice Method)*if student is struggling with the standard algorithm* Create the box grid Answer: 11,232

  26. Multiplication Strategy:Elizabethan Boxes Are useful for multiplying polynomials of any size: (5x2 - 3x + 2)(x2 + 3) Answer: 5x4 - 3x3 + 17x2 - 9x + 6

  27. Standard Division Algorithm Multiply, subtract, and repeat

  28. Division Strategy: Clustering*if student is struggling with the standard algorithm* Problem: 128  16 Example 1 Example 2 16 5 = 80 16 2 = 32 16 2 = 32 16 2 = 32 16 1 = 16 16 2 = 32 16 2 = 32 5 + 2 + 1 = 8 2 + 2 + 2 + 2 = 8 (Check: 80 + 32 + 16 = 128) (Check: 32 + 32 + 32 + 32 = 128) Guess: 5 Check: 128 - 80 = 48 48 remaining Guess: 2 Check: 48 - 32 = 16 16 remaining Guess: 1 Check: 16 - 16 = 0 Guess: 2 Check: 128 - 32 = 96 96 remaining Guess: 2 Check: 96 - 32 = 64 64 remaining Guess: 2 Check: 64 - 32 = 32 64 remaining Guess: 2 Check: 32- 32 = 0 

  29. Fractions, Decimals, and Percentages

  30. Order of Operations (fraction bar)

  31. Properties of Equality

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