Lesson 3.1.2Concept: Portions as Percents

1Vocabulary:

Portion -A part of something; a part of a whole. Sampling - A subset (group) of a given population with

the same characteristics as the whole population.

 In this lesson, you will find ways to describe the portion of raisins in a mix.  (A portion is a part of a whole.)  You will also learn more about ways to represent and describe portions as you investigate the connections between these representations.  As you work, keep these questions in mind: 

How many ways can we represent the portion?How can we compare estimates to tell which portion is greater?

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22. PRETTY PORTIONSExamine a jar filled with “raisins” and “peanuts.” What portion of the mix do you think is raisins?  First, make an estimate on your own.  Then discuss your ideas with your team.  Work together to agree on one estimate that you think best describes the portion of the mix that is made up of raisins. 

23. Compare the estimates by the different teams in your class.  Which estimate is greatest?  As a class, order the estimates from least to greatest. 

24.  One way you may have described the portion of raisins is as a percent.  A percent is a number that can be written as a fraction with a denominator of 100.  For example, 5 percent, written 5%, is equivalent to   . Or, you could say, “Five out of every one hundred.”a.Have you ever thought about why a percent is called a percent?  With your team, brainstorm ideas about what the prefix “per” means.  Give an example of where you have seen the word “per” used. b.Now brainstorm what the word “cent” means.  Give an example of where you have seen the word “cent” used. c.Explain why 32 percent is equivalent to   by using your answers to parts (a) and (b).

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25. If you were able to separate the raisins and peanuts and return them to the jar in layers, with the raisins on the bottom, what would that arrangement look like?  Use the problems below to help you answer this question.

a.Obtain a Lesson 3.1.2A Resource Page from your teacher.  The rectangle represents a side view of the mixture of raisins and peanuts in the jar.  Shade a portion to represent the layer that you think would be raisins.

b.After drawing this picture, do you want to change your estimate of what portion of the whole mix is made up of raisins?  Discuss this with your team and decide whether your original estimate is still the best.  Then decide how to name the portion that would be peanuts.  

c.Your teacher will use a “percent ruler” to help you estimate the percent of the mixture represented by the shaded part of your diagram.  Write down the measurement estimated using the percent ruler.  Does this change your estimate much? 

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26. PORTION OF A SAMPLE

Sometimes scientists need to make an estimate of a portion, such as a certain kind of bacteria in a pond or white blood cells in a human body.  The technique they use is called sampling.  They find the portion of the item in a smaller sample, such as a small part of the pond water or a vial of blood.  Then they assume that the same portion will exist in the whole pond or body.  

You will apply this technique to the mix of peanuts and raisins.  Your teacher will mix the jar well and then remove a sample (a smaller, randomly selected amount) of the mixture. 

a.Work with your class to count the raisins and peanuts in the sample.  Then represent the portion of raisins in the whole sample as a fraction. How could someone tell the size of the whole sample by looking at your fraction?  Explain.   b.Recall the definition of “percent” from problem 3-24.  Use a Giant One to change your fraction from part (a) to a percent. 

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27 - USING A PERCENT RULERIn part (b) of problem 3-26, you used a Giant One to determine what percent of the whole was made up of raisins.  Below, you will learn another method for calculating percents.

With your team, you will use the percent ruler shown above to examine a sample of 40 raisins and peanuts.

a.Copy the percent ruler onto your paper.  Then use it to determine how many raisins would make 50% of the sample.  How many raisins are in 10% of the sample? b.Use your percent ruler to calculate the percent of raisins in the sample your teacher collected in problem 3-26. c.Which method do you prefer, using a Giant One or a percent ruler?  Why? 

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28. How can the percent you found in problem 3-27 help you predict how many total raisins that might be in different amounts of mix?  Work with your team to draw a diagram to help you make sense of each of the following questions.  Be prepared to explain your thinking to the class.

a.What if your sample had contained a total of 100 peanuts and raisins?  How many raisins would you predict would have been in that sample? b.What if your sample had contained a total of 150 peanuts and raisins?  How many raisins would you predict would have been in that sample? c.What if your sample had contained a total of 82 peanuts and raisins?  How many raisins would you predict would have been in that sample?

29. Shown below are representations of peanut-and-raisin samples from teams in Ms. McGlotsky’s second-period class.  Order the samples from the least portion of raisins to the greatest portion of raisins.

Team A raisins

Team B13 out of 26 are

raisins.

Team C

 Team D

25% are peanuts.

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30. LEARNING LOGIn your Learning Log, write your own definition of the word “percent.”  Then describe at least one method to find a percent from a sample. 

Title this entry “Percents” and include today’s date. 

Tonight’s homework is… 3.1.2 Review & Preview, problems #31-35. (text page 110)

• Label your assignment with your name and Lesson number in the upper right hand corner of a piece of notebook paper. (Lesson 3.1.2)

•Show all work and justify your answers for full credit.

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