Lesson 2

In this activity, students review work with percentages and arithmetic from earlier units. It also gives them a framework for thinking about the next activity. Students have to decide how to treat a situation in which ratios are approximately equivalent (MP6). People can only be reported in whole number quantities, and students need to decide how to round numbers appropriately as a result.

Give students 5 minutes of quiet think time followed by a whole-class discussion. Provide access to four-function calculators.

For the third question, students may not recognize that the ratio of people from Africa to the world population is only approximately equal to the ratio of students in the class from Africa to the total number of students. Ask these students about how many people they think live in Africa.

Make sure that students recognize 12 students out of 30 as a benchmark percentage. Point out to them that the fraction \(\frac{12}{30}\) is equal to \(\frac{2}{5}\) (a benchmark fraction) and also to \(\frac{40}{100}\) (showing 40% explicitly).

For the third question, ask students if the ratio for the world population is equivalent to the population for people in the class. The answer is no. But 7.4 billion is only an approximate value of the population, so what we are looking for here is a value of people from Africa that gives a ratio close to 5 out of 30 (or equivalent). 

Students brainstorm quantitative questions about the world and submit their best ideas to the class. For the next classroom activity, compile all of the questions into one document, removing inappropriate questions. Either do the necessary research, provide resources that students can use to find the needed information, or let students do the research themselves, depending on time and internet access.

Note that some student ideas may be challenging to research (for example, how many people in the world have a car?). If there is no chance to gather data beforehand, encourage students to make some simplifying assumptions with the data that they do find.

Arrange students in groups of 2–4. “We are going to investigate the world population. Think about what you would like to know about all the people of the world!”

Invite students to share which questions they are most interested in investigating. Ask them how they might learn more about a given topic and how easy or hard it might be to find the information. The most likely resource is the Internet and some populations will be easier to investigate than others. For example, it is not difficult to find information about the number of cars in the world (more than 1 billion but well less than 2 billion). But this does not answer how many people own a car, and that data can be very difficult to find. Encourage students, in preparation for investigating these questions, to make some reasoned assumptions with the data that they can find to make their best estimate. For the car example, they might assume, for example, that 1 billion people in the world own a car. 

If students investigated the answers to their questions in the previous activity, they need access to their findings. They can either work with the questions generated by their group, or everyone can work from a master list of questions compiled by the teacher.

If students have access to a spreadsheet program, they can use it to find the results (MP5). Students need to communicate their findings clearly in graphical displays (MP6). They can choose to illustrate all or some of the questions in their graphical displays. Encourage the students to be creative with their displays. For example, if students are examining the question “How many people would live on each continent?” they might sketch the continents and place stick figures on the continents to represent the class. They might also draw a bar graph showing the same information in a different way.

Students work in same groups of 2–4 from previous activity. Provide access to four-function calculators. If students are doing their own research, provide access to internet-enabled devices. If conducting a gallery walk at the end, provide access to tools for making a visual display.

To give students a sense of the magnitude of the world versus the classroom, consider zooming in from Earth to North America, the United States, your state, your city, and finally your school. 

Invite students to work on the question or questions that are of most interest to them either from their own group work on from the compiled list. 

Students may struggle with the difficult numbers for the percent of the world population with different characteristics. For example, there are about 1.2 billion people living in Africa. Ask them  to calculate \(1.2 \div 7.4 \approx 0.162\). "What percent of the world population this is?" (16%). "If our class were the world, then about 16% of the class would live in Africa.  So how many students in our class would live in Africa?" (Since 16% of 25 is 4, that means that 4 students in our class would live in Africa.) 

In some cases, there might be two acceptable answers to how many students in our class have a certain characteristic. About 10% of the world population is in Europe. For our class, we could have 2 students (8%) or 3 students (12%) that are in Europe. Either one is an acceptable answer. Make sure that students understand that 2.5 (10% of 25) is not a reasonable answer.

Invite groups to share their displays. Consider doing a gallery walk and asking:

• Were you surprised by any of your findings?
• In what ways is the class actually representative of the world? (possibly gender distribution, religious adherence, etc.) 
• In what ways is it not? (age, place of residence, access to clean water, etc.)

Make sure to highlight the fact that having a small class limits the percentages that are possible. This can make deciding how many students in the class have a particular characteristic difficult. Consider asking:

• What percentages are possible for students in the class? (0, 4, 8, . . . multiples of 4 up to 100)
• There are 1 billion people living in the Americas. That’s a little more than 13.5% of the world population. If our class was the world, how many students in our class would be from the Americas? (3 students would be 12%, and 4 would be 16%. So 3 students is as close as we can get.)