## Is Over Of

### Annette NixonSanta Rosa District Schools

#### Description

This lesson discusses an often used, but rarely seen in books, method of teaching percents. Former students report this is one of the most useful algorithms learned in class.

#### Objectives

The student solves real-world problems involving whole numbers, fractions, decimals, and common percents using one or two-step problems.

The student solves real-world problems involving decimals and fractions using two- or three-step problems.

The student solves real-world problems involving integers, ratios, proportions, numbers expressed as percents, decimals, and fractions in two- or three-step problems.

The student solves real-world problems involving percents including percents greater than 100% (for example percent of change, commission).

The student translates verbal expressions into algebraic expressions.

The student translates verbal expressions and sentences into algebraic expressions and equations.

The student translates verbal expressions and sentences into algebraic expressions, equations, and inequalities.

The student solves single- and multi-step linear equations and inequalities that represent real-world situations.

#### Materials

-Worksheet (attatched) or similar practice exercises within class text

#### Preparations

1. Familiarize self with the algorithm.
2. Copy one worksheet per student or select corresponding book exercises.

#### Procedures

1. Many books present 3 cases for learning percents: A) finding % of a number B) what % of a number another is C) a number is what % of another. Many present a different method for solving each of these. Students often become confused as to which method should be used, whether to move a decimal, whether to multiply or divide, and so on. Often there is trouble relating the case to a real-life problem.
2. Many veteran teachers use the -is over of- approach. Students should be familiar with solving proportions before going onto the percents.
3. Put up the proportion IS/OF = %/100. (Write it using horizontal bars.)
Offer no explanation yet, but put up an example such as: WHAT IS 80% OF 30? Again without explanation (yet), fill in the proportion: X/30 = 80/100 and solve. Leaving this up, try another example and ask the students to predict to themselves in which spots the numbers will go. 15 IS WHAT PERCENT OF 25? Fill in the proportion (go slowly, draw the two lines and the equal sign, next fill in the 100, and last fill in the other two numbers) and solve. Do one more on the overhead without much explanation, just setting it up slowly and in the same method each time. Example: 20% OF WHAT IS 15? This algorithm is being taught in the -discovery- method and hopefully by now each student has a -light bulb- going on. (Students seem to remember it much more effectively if they discover what was done instead of being told.) For those who don't -get it- yet, ask for a volunteer to explain what is happening.
4. Give a few more examples, one at a time, on the overhead for each student to work individually. Circulate throughout the class, correcting errors, offering suggestions, giving one-on-one time to those who are having trouble. Keep saying outloud -IS OVER OF = % OVER 100- to drill it into the students.
5. This algorithm also works well with real-world applications, but students must first re-word the problem to fit the -IS OVER OF = % OVER 100- format . This requires some practice but incorporates valuable problem solving skills. Practice re-wording and setting up proportions for some real-life applications on the overhead.
6. Provide some examples for students to do as you circulate and check volunteer's answers. Once students -get it- they will be begging to have their's checked.
Examples: A) IN A GROUP OF 60 TEENAGERS, 12 HAVE EARRINGS. WHAT PERCENT HAVE EARRINGS?
Re-worded: 12 IS WHAT % OF 60?

B) A CAR SALESMAN MAKES 5% COMMISSION ON ALL THAT HE SELLS. HOW MUCH DOES HE HAVE TO SELL TO MAKE \$1500?
Re-worded: 5% OF WHAT IS 1500?

C) A CD IS USUALLLY \$15. THERE IS A SALE FOR 20% OFF. HOW MUCH WILL YOU SAVE?
Re-worded: 20% OF 15 IS WHAT?

#### Assessments

Informally assess students by circulating as students work on overhead examples. Determine mastery of concept from score on worksheet. (4 pts each)