WHAT’S BEHIND THE FORMULA? Improving Student Math Ability (and GED 2014 Performance) on Frequently-Missed GED 2014 Questions

INTRODUCTIONS Amy Vickers

MY CURRENT AREAS OF INTEREST  Mathematical Practice #7 and CCRS  How to support numeracy instruction for ELLs  The math classroom as a workshop for leadership development

WHAT BRINGS YOU TO THIS WORKSHOP?

INTRODUCTIONS 1.Learn the names of your colleagues at your table. Select a facilitator at your table. If no one volunteers, choose the person whose birthday is earliest in the year. 2.The job of the facilitator is to  Make sure that you are hearing from everyone at the table.  Communicate with Amy.

OBJECTIVES Participants will be able to…  Describe the Levels of Knowing Mathematics  Approach formulas from a Levels of Knowing Mathematics perspective  Create or modify existing classroom activities to incorporate all Levels of Knowing Mathematics

TOP SKILLS 2014 TEST-TAKERS ARE MISSING  Q.4.b Compute the area and circumference of circles. Find the radius or diameter of a circle when given the area or circumference.  Q.4.c Compute the perimeter and area of polygons. Find side lengths of a polygon when given the perimeter or area.  Compute the perimeter and area of two-dimensional composite shapes, which could include circles.  A.1.c Create linear expressions as part of word-to-symbol translations or to represent situations you have been given.  A.2.c Create one- or two-variable linear equations to represent situations you have been given.  A.3.d Create one-variable linear inequalities to represent situations you have been given.

PINATA ACTIVITY

Given what you have seen and heard, write one sentence that would instruct the children how to share the candy.

A formula is…

NOW WE CAN USE THE FORMULA SHEET

GED MATH FORMULA SHEET Mean: mean is equal to the total of the values of a data set, divided by the number of elements in the data set

THINK OF FORMULAS THAT YOU HAVE USED. In general, what additional skills are needed in order to work with formulas?

WHAT’S BEHIND THE FORMULA? Improving Student Math Ability (and GED 2014 Performance) on Frequently-Missed GED 2014 Questions

LEVELS OF KNOWING MATHEMATICS Intuitive Concrete Pictorial Abstract (formulas are here) Application Communication

IT’S TIME FOR GRADUATION! To decorate for the ceremony, one of the graduates offered to make a fancy table cloth for this reception table. The shorter front side is three feet long, while the longer side in back is five feet long. From front to back the table measures 2 ½ feet. The sewer will add one foot to each end of each of these measurements so that the tablecloth will hang down along each of the four sides. About how many square feet of cloth would you buy for the graduate to make this tablecloth?

DISCUSS THESE QUESTIONS AT YOUR TABLE – MAKE SURE THAT YOU HEAR FROM EVERYONE 1.What reflections do you have about the tablecloth activity? 2.How could you adapt this activity for use in your setting? 3.What other ways could you engage learners at the intuitive, concrete, and pictorial levels of knowing mathematics?

DISCUSS THESE QUESTIONS AT YOUR TABLE—DO NOT USE THE FORMULA SHEET 1.What is area? 2.What is a cylinder? Make your own with paper and tape. 3.Have you seen any cylinders today? What are other examples of cylinders? 4.What is surface area? 5.Describe each “face” of a cylinder. 6.Verbally create instructions for finding the surface area of a cylinder. 7.On poster paper, write a sentence and then a formula for finding the surface area of a cylinder based on your instructions. Be sure to define all variables.

WHICH OF THESE MATCH THE FORMULAS THAT WE CREATED? EXPLAIN.

ALGEBRAIC EXAMPLE: INEQUALITIES

ALGEBRAIC EXAMPLE: WORKING BACKWARD The number of steps in the Washington Monument is 27 less than 6 times the number of steps in the Statue of Liberty. If there are 2097 steps in the Washington Monument, how many are in the Statue of Liberty?

NOW YOU TRY!  Select one of the most missed skills on the GED test. If possible, choose one that involves a formula.  Complete the planning sheet and make sure to include intuitive, concrete, and pictorial activities.

MATHEMATICAL PRACTICE #2 Reason abstractly and quantitatively. Contextualize and decontextualize

THANK YOU! Amy Vickers