Ratios as Percentages

In teaching ratio, percentage is where the rubber meets the road! Students need to understand the concept of percent thoroughly, which is the objective of the first five resources here. Students also need practice in converting from fractions to decimals to percents, and in finding percentages. The last four resources offer practice in various scenarios, generally through a game format.

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Grid and Percent It http://illuminations.nctm.org/LessonDetail.aspx?id=L249

This lesson begins with a basic visual used in many textbooks: a 10 × 10 grid as a model for demonstrating percent as "parts per hundred." It goes on to extend the model to solve various percentage problems. Especially valuable are the illustration of each problem and the thorough explanation that accompanies it. This is an exceptional lesson plan!

Percentages http://nlvm.usu.edu/en/nav/frames_asid_160_g_4_t_1.html

In this interactive activity, students can enter any two of these three numbers: the whole, the part, and the percentage. The missing number is not only calculated but the relationship among the three is illustrated as a colored section of both a circle and a rectangle. The exercise is an excellent help to understanding the meaning of percentage. MSP full record

Majority Vote: What Percentage Does It Take to Win a Vote? http://www.figurethis.org/challenges/c36/challenge.htm

This problem challenges students' understanding of percentage. Two solutions are available, plus hints for getting started. Clicking on "Try these" leads to different but similar problems on percentage. Questions under "Did you know?" include "Can you have a percentage over 100?" and "When can you add, subtract, multiply, or divide percentages?" These questions can lead to interesting math conversations. MSP full record

Fraction Model III http://illuminations.nctm.org/ActivityDetail.aspx?ID=45

Using this applet, students create a fraction for which the denominator is 100 and then make the numerator any value they choose. A visual of the fraction is shown—either as a circle, a rectangle, or a model with the decimal and percent equivalents of the fraction. An excellent aid in understanding the basics of percentages!

Tight Weave: Geometry http://nlvm.usu.edu/en/nav/frames_asid_313_g_3_t_3.html

This is a fractal that can be used to give a visual of percentages. At each stage in the creation of the fractal, the middle one-ninth of each purple square area is transformed to gold. This gives progressively smaller similar patterns of gold and purple. At any stage of iteration, the percentage of gold is given. Interesting questions that your class might consider: At what stage will more than 50% of the area be gold? Or you could pick a stage, show it visually, and ask the students to estimate the percentage of the original purple square that has turned to gold. MSP full record

Dice Table http://www.shodor.org/interactivate/activities/dice/index.html

This activity shows the student the possible results of rolling two dice. It can become a game between several students who select various combinations of results, which appear on an interactive table. The players then figure the probability of winning the roll, giving the probabilities as fractions, decimals, and percentages. Good practice in converting from fractions to percents. MSP full record

Fraction Four http://www.shodor.org/interactivate/activities/fgame/index.html

A game for two players, this activity requires students to convert from fractions to percents, find percentages of a number, and more. Links go to game ideas and a brief discussion of the connection between fractions and percentages, presented as a talk between a student and a mentor. MSP full record

Snap Saloon http://www.bbc.co.uk/education/mathsfile/shockwave/games/saloonsnap.html

In this interactive online game, students practice matching fractions with decimals and percentages. Three levels of difficulty are available. This is one of 12 games from The Maths File Game Show. MSP full record

Perplexing Percentages: So How Much Does It Cost? http://www.math.nmsu.edu/breakingaway/Lessons/puzzle3pc/puzzle3pc.html

A problem straight from the mall! Here is a rack of clothing, originally on sale for 30% off the original price, but now discounted by an additional 50%. Is the new price actually 80% of the original price? Two complete solutions are set out, and several more problems in the shopping scenario are offered under "Try these." MSP full record

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Copyright June 2006 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.