The ABC’s of Algebra: Alignment, Buy-in, and Classroom Activities PRESENTED BY Leslie A. Texas November 16, 2007 1

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Session Objectives Participate in a variety of classroom activities that model best practice Determine how to design assignments that are engaging and require students to develop higher order thinking skills

Southern Regional Educational Board Visits in the last several years to well over 100 middle grades schools indicate that the schools’ goals and priorities often are unclear to teachers, students, and the community. States, like New Jersey, have set content and performance standards in mathematics, but these standards need to be translated into daily work in the classroom. Identifying readiness indicators for Algebra 1 is one way to translate middle school mathematics content standards for the classroom. It is also a way to guide high schools in planning and implementing catch-up courses in mathematics for incoming 9th graders.

Identifying Gaps and Overlaps Questions to address: Which readiness indicators are not being addressed (gaps)? Which readiness indicators are addressed by multiple grade levels (overlaps)?

Engaging Activity Traffic Jam 6

Questions: What process skills were required in the activity? What content knowledge was required? 7

Cooperative Learning Activity Match your puzzle-piece with other similar pieces to form a problem to solve. As a learning group team, select a strategy to solve the problem. Solve the problem as a team then submit a solution to the class. Your team must be able to justify the solution!!!

DGHEF (prime factorization of 13,090 or 2 · 5 · 7 · 11 · 17 ) Problem #5 Find a path through the maze of numbers, starting at “Enter” and ending at “Exit.” The value of the path is determined by multiplying each number along the path. You may move up, down, or right but not diagonally. You can only cross a number once. Try to find a path through the maze that results in 13,090. List the letters in order for each box you cross to reach the exit. An example, 7 x 13 x 2 would be DAB. 13 A 2 B 3 C 7 D 11 E 5 F Enter Exit 15 I 17 H 2 G DGHEF (prime factorization of 13,090 or 2 · 5 · 7 · 11 · 17 )

Problem #9 Which set of factors of the number 420 has the least possible sum? Which set of factors of the number 420 has the greatest possible sum? Be sure that the two sets of factors both have a product of 420. Answers: 19 and 421

32 + 4 2 x 8 – 5 + 12 4 =41 32 + 4 2 x (8 – 5) + 12 4 = 41 Problem #11 Place one set of parentheses on the left side of the equals sign to make the equation true. 32 + 4 2 x 8 – 5 + 12 4 =41 32 + 4 2 x (8 – 5) + 12 4 = 41

Answer: 184 > It is greater than 100. > It is less than 200. Problem #12 Find the greatest whole number that meets all of the following conditions: > It is greater than 100. > It is less than 200. > It is 20 greater when rounded to the nearest 100 than when rounded to the nearest 10. Answer: 184

Answer: 171 y = 3x + 3 Problem #13 - 2 - 3 1 6 3 12 7 24 17 54 56 ???? Robin uses a rule to create the input/output table shown. If Robin uses her rule with an input of 56, what will be her output? INPUT OUTPUT - 2 - 3 1 6 3 12 7 24 17 54 56 ???? 89 270 Answer: 171 y = 3x + 3

A Menu of Fun Math Problems Source: Mathematics Teaching in the Middle School (NCTM) February 2007 Issue

Possible Uses Pre-Assessment Exercise Introduce classroom procedures (cooperative learning, word problems, no “I don’t know’s accepted) Hook for new unit Review Exit Slip

Engaging Activity Are you a Solution? 16

Literacy Strategies and Assessment Practices Pg 21 17

Improving Student Vocabulary Write a math vocabulary word on one side of the index card. 18

Improving Student Vocabulary- Word Illustrations On the other side, illustrate the concept (meaning) of your word…using NO numbers or letters. 19

What Math Words are Illustrated Below? Subtraction, Common Denominators, Probability 20

Frayer Model Concept Essential Characteristics Non-Essential Characteristics Examples Non-Examples Concept 21

Parallelogram with 4 equal sides Frayer Model Essential Characteristics Is a four sided figure Four sides have equal length Opposite angles are equal Perimeter is 2(l + w) Area is b x b Non-Essential Characteristics Angles may or may not be right Length of sides can vary Diagonals may or may not be equal in length Examples Non-Examples RHOMBUS Trapezoid Triangle Square Parallelogram with 4 equal sides Rectangle 22

Frayer Model 23

R-A-F-T 24

Choose one item from each column RAFT Examples for Math Choose one item from each column Role Audience Format Topic Zero Whole Numbers Campaign Speech The importance of the number 0 Percent Student Tip Sheet Mental ways to calculate percents Prime Number Rational Numbers Instructions Rules for divisibility Parts of a Graph TV Show Audience Script How to read a graph Exponent Jury Instructions to the jury Laws of exponents Acute Triangle Obtuse Triangle Letter Explaining their differences Square Root Whole Number Love Letter Explain Relationship Repeating Decimal Set of Rational Numbers Petition Prove you belong to the set 25