# Gallery Problems ## Work Time

2. Review the rubric to check that you have included everything in your project.
3. Remember each project must contain:
• A written explanation that describes how you used ratios in your project
• At least one diagram or graph that shows how you used ratios in your project
• Accurate mathematical representations

# Equivalent Ratios

1. Which of these ratios are equivalent?
a. 2:5
b. 100:240
c. 40%
d. $\frac{5}{12}$
e. 1:2$\frac{1}{2}$
f. 0.4
g. $\frac{2}{5}$
h. 41.66666...%
i. 5:12$\frac{1}{2}$

2. Choose one of your sets of equivalent ratios in problem 1. Represent the set of equivalent ratios using one of these models:

• Tape diagram
• Ratio table
• Double number line
• Graph
3. Now choose another type of model to represent the same set of equivalent ratios you chose in problem 2.

4. Share your models for problems 2 and 3 with a partner. Develop or refine your models as needed together.

# Three Farmers

Together three farmers ( X, Y, and Z) buy seed for their farms and share it in the ratio 3:7:8.

1. If they buy 144 kilograms of seed, how many kilograms of seed does each farmer receive?
2. Show the problem solution using a tape diagram.

# The Dance

Two students are discussing the upcoming school dance.

Martin says: “There are 70 more girls than boys coming.”

Mia says: “Yes, I heard that the ratio of boys to girls is 3 to 4.”

1. Can both Martin and Mia be right? Use words and diagrams to justify your answer.
2. Think about the two ways of comparing quantities.

b. Think of situations in which each way of comparing quantities would be useful.

# Work Time

1. All adults at Martin Luther King Middle School are either teachers or non-teaching staff members. The ratio of teachers to non-teaching staff is 3:5.
a. What is the ratio of teachers to adults?
b. What is the ratio of non-teaching staff to adults?
c. What is the ratio of non-teaching staff to teachers?
d. What percent of adults is non-teaching staff?
2. Make a diagram to represent the ratio of teachers to non-teaching staff at Martin Luther King Middle School.

3. There are two types of ratios: part-part ratios and part-whole ratios. Explain why percents are always part-whole ratios. Refer to the tape diagram shown.

4. For each school listed in the table shown, give the comparison of teachers to non-teaching staff in the following forms: as a whole number ratio (a :b), as a decimal (rounded to hundredths), as a fraction in simplest form, and as a percent of the whole.

5. Suppose the ratio of teachers to non-teaching staff at a school is 1:r.
a. Express this ratio as a fraction.
b. What does the expression represent?
c. The teachers make up 40% of the adults at school. Calculate r.  # Sports Reporters

One of the most famous soccer stadiums in the world is the Estadio Azteca in Mexico City.

The stadium can host about 111,000 spectators. During one match, there are exactly 110,000 spectators. Of the spectators, 10,000 are women.

One reporter says the ratio of women spectators to total spectators is 10:100, which is exactly 10%.

Another reporter disagrees. He says the ratio 10 women to 100 men is not the same as saying that 10% of all spectators are women.

• Misunderstandings like this happen quite often. Who is right? Explain your reasoning.

# Screen Challenge

An aspect ratio compares width to height.

The following aspect ratios are used to describe the shape of different TV screens.

4:3       16 : 9       3:2

Movie screens have different formats. The two most common aspect ratios are 2.39:1 and 1.85:1.

1. Which TV aspect ratio gives a rectangle that is most like a square?

2. Write all three TV aspect ratios in the format 1 : __

3. The golden ratio is 1:0.6180… . This ratio is considered to create the most pleasing rectangle to the eye. Which of the three TV aspect ratios comes closest to the golden ratio?

4. The aspect ratio of movie screens used to be expressed in terms of the number of sprocket holes of the film. (Sprockets are the wheels that move the film.) Today, the number of pixels is used. Express the aspect ratio in lowest terms for a screen that is 640 pixels by 480 pixels (assuming square pixels).

5. Blu-ray discs commonly are 1,920 pixels by 800 pixels. Express this aspect ratio in lowest terms.  # Election Results

For a local election, the town newspaper reported the accompanying results for a bond measure.

1. Explain why there must be a misprint in the table.
2. Suggest a correction in one of the figures in the table that would make it consistent with the other three. # Birthday at the Movies

Mia’s family has invited her whole class to a movie to celebrate her birthday. Mia expects that most of the class will come. She made a ratio table to calculate the total cost for 28 to 32 students.

1. Complete the table and explain your strategy.
2. Make a graph to show the information in the table. HANDOUT: Birthday at the Movies

# Dinner Reservations

The ratio of tables to chairs in a restaurant is 1:4.

1. Sketch a tape diagram to represent this situation. Be sure to label your tape diagram accurately.
2. It’s graduation night, and the restaurant has a reservation for a party of 26 people. How many tables does the restaurant need for this party? (Assume the tables are not pushed together.)

# Birth Months

The data in the table represents the ratio of students in a class who have birthdays in each month.

1. What percent of the students were born in June?
2. What is the ratio of the number of students born in January to the number of students born in February?
3. What is the ratio of the number of students born in January to the total number of students in the class?
4. Look carefully at the numbers in the table. About how many students might be in the class? How can you tell? 