Concept 5 – Finding Percentages

How can I find a percentage?

Food labels tell you about what is in the food you eat.  The nutrition-facts label lists the percentages of macronutrients (protein, carbohydrates, and fat) as well as vitamins and minerals in each serving.  However, it often does not tell you exactly how much of each thing is in the food or how much you should have each day to be healthy.

If you know how much Vitamin C is in a serving, can you figure out how much is needed in a day?  To help you answer a question like that, in this section you will develop strategies for finding information about parts and wholes.

 

 

5-1. WHAT ARE YOU EATING?

The government has created guidelines for how much of various nutrients, vitamins, and minerals a person should eat or drink each day to be healthy.  These guidelines are then used to create labels like the one shown above to inform the public about the nutritional content of food.

According to the sample label above, one serving of Cheesy Mac macaroni and cheese contains 15% of the recommended daily amount of saturated fat that a person should eat.  Nutritionists recommend that a person should have no more than a certain amount of saturated fat each day.  One serving of Cheesy Mac has 3 grams (3g) of saturated fat.  How many grams of saturated fat should a person eat in one day?

Your Task: With your team, determine how many grams of saturated fat a person should eat each day.  Look for more than one way to solve the problem and be ready to explain your reasoning.

 

 

 

5-2. To help you represent the situation in problem 5-1, copy the number line below on your paper.

pic

a. With your team, decide how to partition the line (divide it into equal parts) so that 15% is shown.  Why did you choose to make that number of parts?  Is there another way that you could have divided the line?

b. The amount of saturated fat in one serving of Cheesy Mac is 3 grams.  Where should 3g be labeled on the number line?  Add this number to your diagram and justify your decision.

c. Use your diagram to help you decide how much saturated fat is in the recommended daily serving.  Record your thinking.

 

 

 

 

5-4. One granola bar contains 4g of dietary fiber.  The label says that 4g is 16% of the daily recommended amount.  Louis decided to draw a diagram like the one below to understand this situation.pic

a. Copy the diagram on your paper and add the label for 16%.

b. How many grams of fiber are recommended each day?  How can you show this with equal ratios?

c. What percent of fiber should Louis get from other foods?  Why is this percent equivalent to the ratio pic?

d. What other amounts are missing on the diagram?  Add labels for all parts, percents, and the whole.

e. Chris is eating cookies that contain 12g of dietary fiber, which he says is 48% of the recommended daily amount.  How can you use ratios and part (b) above to check that 12g is equivalent to 48%?

 

 


 

5-5. One large carrot contains approximately 6 mg of Vitamin C.  The recommended daily intake of Vitamin C is 60 mg.  Resa wanted to find out what percentage of her daily Vitamin C she gets from one carrot.  She started with a line divided into 10 parts.

pic

a. Why do you think she divided the line segment into 10 parts?

b. Copy the diagram on your paper and fill in the missing labels.

c. The ratio pic represents the portion of Vitamin C in one large carrot.  Work with your team to find this ratio in the diagram.  Where do you see each amount?  What other ratio could you write that would be equal to this?

e. Use the diagram to help you find and write at least two other ratios on the number line that are equal to each other. 

 

5-6. Resa was mixing blue and red paint to create purple paint.  She created the drawing below to show the portions of blue paint to red that she used.pic

a. What does the picture tell you about the paint mixture?  What statements can you make?

b. If you have not stated it yet, what percent of the paint is blue?  What percent of the paint is red?  Justify your answer.

 

5-7. Additional Challenge: Turner Middle School has 110 boys.  Fifty-six percent of the students in the school are girls.  How many students go to this school?

a. Create a model like Resa’s from problem 5-5.  Label the percentage of girls, the percentage of boys, and the number of boys on your drawing, as well as 0% and 100%.

b. How many students go to the school?  How do you know?

c. How many girls go to the school?  Explain your reasoning.

 

 

5-8. Additional Challenge: Maria is making paper flowers as decorations for the fall dance.  She has made 40 flowers so far, and she is 16% finished.  If she plans to finish making 70% of the total flowers needed by tonight, how many more will she need to make by then?  Show your work.

 

Assignment: 5.1.1 Homework

What is the percentage of the whole?

5-14. Miranda is always looking for a great deal while shopping.  She found a sale rack where all of the jeans are marked 40% off.  Her favorite jeans regularly cost $65.

a. To figure out if she has enough money to buy a pair of jeans, Miranda decides to estimate.  She thinks that the jeans will cost approximately $30.  Is her estimate reasonable?  Explain your thinking.

b. To find the exact answer, Miranda created the diagram below.  How could she add marks to partition the line evenly?  Partition the line and calculate the missing values. pic

c. How much money will Miranda save?  What is the price she will have to pay?

d. Miranda wants to check her answer from part (c).  How could she use ratios with the amount she saved and the original price to verify that she received a 40% discount?

 

5-15. At the same sale, Evelynn sees a shirt on sale for just $37.50.  It originally cost $50.

a. Estimate the percentage of the discount on the shirt.

b. Draw a diagram to represent this situation.  Label all parts.

c. What percent is the discount on Evelynn’s shirt?

d. What is the relationship between the discount, the sale price, and the original price?  Write a statement that shows the relationship between the sale price, discount, and original price.

 

5-16. So far in this section, you have used a linear model to represent percent problems in various contexts.

a. Obtain a Lesson 5.1.2 Resource Page and use the linear models to find parts and wholes when different types of information are provided on the diagrams.

b. For each diagram, write at least three statements describing how parts and percentages are related.  Some statements are started for you.

 

5-17. When Evelynn was about to pay for her clothes, she realized that she had forgotten to include an 8% sales tax.

a. The belt Evelynn wants to buy costs $15.  She does not have paper to draw a linear model.  To estimate tax, she figured that calculating 10% would be close enough.  Explain how Evelynn might find 10% of $15 without a linear model.

b. Calculate exactly how much the 8% sales tax will cost Evelynn.  What will be the total amount she will have to pay to the store?

 

Assignment: 5.1.2 Homework