Percent: From 7RP.3 through College and Career Readiness Jim Olsen, Ph.D. Western Illinois University W.I.U. Mini-Conference on Secondary Mathematics Teaching November 16, 2017 These slides may be accessed from Jim Olsen’s Home Page: http://faculty.wiu.edu/JR-Olsen/wiu/

Outline Ratios and Proportional relationships – 6.RP.3 and 7.RP.3 Percent Change Kahn Academy ‘Regular area’ SAT Prep area Exponential Functions Helping students understand percent needs to be ongoing from 6th through 12th grade....because to be College and Career Ready students need to understand percent. Some Usable Resources along the way.

RP Ratios and Proportional relationships 6.RP.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. “Percent of” problems – first of two general problem types ___% of ___ is ___ 30% of 80 is what number? 120% of what number is 48? What percent of 400 is 600?

Percent Visualization V2 app Link: https://ggbm.at/SUG4ay7J Description: Type in the Amount (“part”), Base (“whole”), and/or Percent Shows a visual representation of the percent. Note: Percents larger than 100% are possible!!

7.RP.3 Ratios and Proportional relationships 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How Important is Percent? Q: When and where are percentages used?

Percent is Pervasive Note from the back of the CCSSM: We’ll see that SAT agrees.

Percent: Important, pervasive, and profound 4 5 =.8=80% .5%=.005= 1 200 175%=1.75=1 3 4 When dealing with percentages, Conceptual Knowledge and Procedural Knowledge are both needed and they complement one another.

Percent Change - second of two general percent problem types 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. The Difficulty is there are four numbers: Original amount New amount Amount of change Percent change Usually, two are given.

Percent Change Infographic Link: http://math260.drjimo.net/pfd/infographic- making-sense-percent-change/ Description: This infographic, titled Making Sense of Percent Change, introduces a graphic organizer for keeping the numbers straight in percent change problems. It provides examples of the six (6) problem types.

(Portion of the Infographic) Two key formulas (tools) for percent change. Compliment one another. Done repeatedly, this is Exponential Growth/Decay.

7th Grade PARCC Sample Items (percent change) From: https://parcc.pearson.com/practice-tests/math/

7th Grade PARCC Sample Items (“percent of”) Quite similar to SAT items.

Connections between “percent of” and percent change problems. Percent of the Original amount = Amount of change. Percent Remaining method. If percent increase is 20%, then the percent remaining is 120% (1.2). If the percent decrease is 17%, then the percent remaining is 83% (0.83).

24 Percent Tweets Link: http://faculty.wiu.edu/JR- Olsen/wiu/BootCamp/24-percent-tweets.html Description: Twenty-four useful things to know about percent. Each is 140 characters or less. Slides and Quizlet (question) decks. [Tweets, 16, 18, 21, & 23 are on Percent Change.]

Kahn Academy “regular area” Link: https://www.khanacademy.org/ Description: Videos and practice (and some notes) on most of the K-12 math curriculum.

Kahn Academy “regular area” Three Icons: Triangle Star Page

Kahn Academy SAT Prep Area Link: https://www.khanacademy.org/sat Description: Practice (and videos and some notes) on the SAT Test.

Kahn Academy SAT Prep Area

Kahn Academy SAT Prep Area

The (New) SAT - my take-away The Heart of Algebra and the Problem Solving and Data Analysis sections (36 of 58 questions; 62% of the SAT) involve: Multi-step word problems from a real-world context based on middle school math.

Exponential Functions (and other places)

The Exponential Function

Kahn Academy SAT Prep Area (Next slide)

Kahn Academy SAT Prep Area

These slides may be accessed from Jim Olsen’s Home Page: Thank You. Questions. These slides may be accessed from Jim Olsen’s Home Page: http://faculty.wiu.edu/JR-Olsen/wiu/ Email: JR-Olsen@wiu.edu