Beacon Lesson Plan Library
Is Over Of
Annette Nixon Santa 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 realworld problems involving whole numbers, fractions, decimals, and common percents using one or twostep problems.
The student solves realworld problems involving decimals and fractions using two or threestep problems.
The student solves realworld problems involving integers, ratios, proportions, numbers expressed as percents, decimals, and fractions in two or threestep problems.
The student solves realworld 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 multistep linear equations and inequalities that represent realworld situations.
Materials
Overhead projector or chalkboard
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 reallife 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 oneonone 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 realworld applications, but students must first reword the problem to fit the IS OVER OF = % OVER 100 format . This requires some practice but incorporates valuable problem solving skills. Practice rewording and setting up proportions for some reallife 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?
Reworded: 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?
Reworded: 5% OF WHAT IS 1500?
C) A CD IS USUALLLY $15. THERE IS A SALE FOR 20% OFF. HOW MUCH WILL YOU SAVE?
Reworded: 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)
