Authentic Lessons for 21st Century Learning

If Our Classroom Were the World

Proportions

Amber Stokes, Kate Raymond | Published: December 6th, 2024 by K20 Center

  • Grade Level Grade Level 7th
  • Subject Subject Mathematics
  • Course Course Middle School Mathematics
  • Time Frame Time Frame 165–180 minutes
  • Duration More 4 class periods

Summary

This lesson challenges students to write and solve proportions comparing the characteristics of a larger community with the characteristics of a smaller community. Students begin the lesson by listening to a story about what the world would look like and sound like if it were represented by 100 people. Students then explore the definitions of proportions and rations before applying their knowledge to solve various proportions that compare different populations.

Essential Question(s)

How can we use proportions to understand our world?

Snapshot

Engage

Students demonstrate their prior knowledge of world populations in a Sticky Bars activity then listen to or read the book If the World Were a Village.

Explore

Students work in small groups and use proportions to determine what the classroom would look like if it were representative of the whole world.

Explain

Students share their approaches to solving proportions, then use their favorite approach to solve a problems.

Extend

Students solve proportions for a classroom representative of a given country and create a booklet to display their data.

Evaluate

Students take on the role of fact-checkers and verify the accuracy of their peers’ work.

Materials

  • Lesson Slides (attached)

  • Our Global Village handout (attached; one per student; print two-sided)

  • Our Global Village (Teacher Guide) document (attached)

  • Globally Minded handout (attached; one or two per class; print one-sided)

  • If the World Were a Village (book by David J. Smith; one per teacher)

  • Sticky notes (three per student)

  • Posters or large chart papers (optional; three per class)

  • Pencils

  • Paper

  • Student devices with internet access or the following materials:

    • Copy paper (optional; two sheets per student)

    • Coloring utensils (optional)

Engage

30 Minute(s)

Introduce the lesson using the attached Lesson Slides. Show slide 3 and display the essential question, “How can we use proportions to understand our world?” Show slide 4 and share the learning objectives. Review these with your class to the extent you feel necessary.

Display slide 5 and hand three sticky notes to each student. Preview the Sticky Bars strategy and guide students’ attention to the space you prepared for the activity. Preview the activity by explaining to students that they are going to write their response to the question on the sticky note along with a sentence that explains how they know the answer to each question on the sticky notes. Point out to students that the available options are listed along the bottom of the bar graph. Ask students the first question on the slide, “Most people live on which continent?”

Repeat this process for slides 6–7, asking students to respond to the following questions:

  • Around the world, which language is spoken by the most people?

  • What is the most popular religion in the world?

Once students have completed their sticky notes, remind students where to place their sticky notes above each answer choice to create a bar graph.

After each bar graph is complete, show slide 8. Give each student one copy of the attached Our Global World handout. Tell students that you’ll read aloud the book If the World Were a Village. Have them listen as you read and record as much mathematical information from the book as they can on their handouts. Let them know that it is okay if they can not record every numerical value, but that you would like them to do their best.

Read aloud the book If the World Were a Village by David J. Smith.

After reading the book, display slide 9 and redirect students’ attention to the results on the Sticky Bar graphs. Ask students what information they recorded from the book about the three questions on the slide. As students answer, record the information in a visible location. Refer to the attached Our Global Village (Teacher Guide) document for a list of the numerical information presented in the book.

Discuss with the class whether their answers from the Sticky Bars activity were correct and ask what things may influence our perceptions of the world.

Display slide 10. Explain to students that understanding mathematical concepts, like fractions, percentages (with which they should be familiar), and proportions (which they are about to explore) can help them make sense of the people and events in different parts of the world even if they do not have personal experience with those people and events.

Explore

45 Minute(s)

Show slide 11 and introduce the question, “What would our class look like and sound like if it represented the whole world?” Use the Think-Pair-Share instructional strategy to have students consider the prompt, share their ideas with a partner, then prepare to share their answers with the class.

If a student asks what the word “represented” means or if you notice the discussion coming to an end, display slide 12. If a student does not ask what “represented” means, pose the question to the class. Ask students what it means to “represent” the world. Students may answer that to represent the world you need the “right” or “same” number of people from each continent, language, etc. If they respond this way, ask them to define what they mean by “right” or “same.” Use these responses to begin to explore the definition of a proportion.

Show slide 13. Assist students in establishing the idea that the ratio (or fraction) of people with a given characteristic needs to be equal for the world and the class. Once students understand that fractions (or ratios) need to be equal, define “proportion” as an equation that sets two fractions (or ratios) as equal to each other.

Show slide 14 and ask students how a proportion could be used to decide what the class might look like or sound like if it represented the whole world. Guide students in a discussion about what this proportion may look like until they are able to write a proportion that includes an unknown value represented by a blank, a variable, or a question mark.

Once you have written the first proportion with students, show slide 15. Have students form small groups of 2–4 students then work together to create strategies for finding the number of students who would represent the population of Asia if the class were representative of the whole world.

Explain

20 Minute(s)

Display slide 16. Once most groups have found the value of x, or when groups grow too frustrated to be productive, lead a whole class discussion about the various approaches that different groups took.

Have students present their work and results to the class. After each group presents, ask the whole class what they liked and what they found challenging about the approach.

If students did not think of an approach involving inverse operations, ask guiding questions to have students consider this method. Use slide 17 to have students walk you through the process of solving a proportion using inverse operations similar to the example above. Have students consider the problem x/28 = 59/100. Ask students how they could use their knowledge of isolating variables to solve the problem. If students are unsure, ask them to read aloud the side with the variable, “x over 28” and ask what the operation “over” means. Once students read the side with the variable as “x divided by 28,” ask them which operation would be the opposite of dividing by 28, then have them apply that operation to solve for x. Once students have arrived at an answer to the above problem, lead them in a discussion of whether decimals are appropriate or not in this context, because of what the number represents.

After all groups have presented, ask students to choose one method that they would like to use to solve another proportion. Remind students that there are multiple accurate approaches to solving proportions. Show slide 18 and have students determine how people in the class would speak Chinese if the classroom were representative of the world.

Allow students time to try their chosen approaches, then discuss the final values students found. Discuss the various approaches different students used and guide students to find an approach that works best for them.

Extend

60 Minute(s)

Show slide 19 and introduce the activity. Tell students that they will create a children’s book modeled on the book read earlier in the lesson, If the World Were a Village. Tell students that they must create a book titled If ____ Were a Classroom which contains data about their assigned country. Explain that each person is expected to create a book in which they calculate data for a classroom that represents their given country.

Transition to slide 21 and give each student one half-page of the attached Globally Minded handout, so that each student has data from one country. Direct students to navigate to bit.ly/CountryBook, click the “Use template for new design” button, and log in to Canva. Students now have their own template necessary to create their ebook.

Display slide 22 and introduce the expectations for the cover of the books. Have students include their book titles, “If ____ Were a Classroom” by filling in the blank with their given country. Tell them to also include one image that represents that country and include the author’s name (their name).

Transition to slide 23 and explain to students how to use the tools in Canva to create the cover of their books. Consider opening the ebook template yourself and demonstrating how to use the tool, especially if this is the first time students are using Canva. If you created a sample book, this would be an ideal time share it with students.

Once students have accessed the ebook template, direct their attention to the left side of their screens and point out the “Elements” and “Text” tabs. Explain to students that they can use these tabs to add backgrounds, shapes, graphics, text boxes, and more. Tell them that they are able to use the search bar to find their preferred images, text, and other components.

Encourage students to create a visually appealing cover. Use the If the World Were a Village book to model what a visually appealing cover might look like. To save time, consider limiting students to 10 minutes to create their covers.

After students complete their covers, transition through slides 24–29 to show students the expectations for the interior pages in more detail.

Use slide 24 to explain to students that they should fill in the blank at the top of page 1 with the population of their given country and the top of page 2 with the classroom’s population.

Have students fill in the information about the religions practiced in their given country on the first page. Tell them to then calculate and fill in the corresponding information for the classroom on the second inside page. Have students show their work on a separate piece of scratch paper.

Continue through the slides and demonstrate to students that they must complete pages 3–4 using the information about languages spoken in their given countries and complete pages 5–6 using information from the “Other” section of the Globally Minded handout. Slides 25, 27, and 29 offer specific examples. The values on these slides are approximations from the 2024 edition of the CIA’s The World Factbook.

As you share each slide, point out to students that the same type of information is listed first on both pages. For example, slide 25 has the number of people that practice Buddhism listed at the top of both pages. Help students understand that they are placing equivalent information in two columns, one column on each page. Stress to students that they should organize the information like this on each inside page of their books.

As students begin working, transition to slide 30 to display a summary of the project requirements. Based on the needs of your students, check in with the whole class to gauge progress and answer questions.

Evaluate

20 Minute(s)

Once students complete the inside pages of their books, display slide 31 and direct students’ attention to the back cover of their books. Introduce the I Used to Think… But Now I Know strategy to have students reflect on their knowledge of proportions. Have them respond to the prompts on the back cover of their books.

Display slide 32 and share with students what a fact-checker is and what someone in that profession does. Transition to slide 33 and create a scenario in which students assume the role of an author. Tell students that they must have the information in their books verified by a fact-checker prior to publication. Explain that each student will take on the role of a fact-checker in addition to having their own books reviewed.

Have students trade books with a partner. You may have students trade physical books (if you chose to have them create books on paper) or you may have them share their ebooks by trading devices or sharing links. Show slide 34 and have students fact-check the statements on the second page by checking the proportion calculations. You may choose how many statements each student should fact-check based on your students’ needs or the amount of class time available.

Notify students that if they find any mistakes as a fact-checker they should tell the author of the book. As time allows, consider having the fact-checkers review pages 4 and 6.

Resources