## Solving Math Problems in the Real World

By Cooper-Hewitt National Design Museum, December 3, 2007

### Grade Level

- Middle School

### Category

- Design for the Other 90%

### Subject Area

- Language Arts
- Mathematics
- Social Studies

### Lesson Time

Two fifty-minute class periods

### Introduction

Solving Math Problems in the Real WorldCooper-Hewitt, National Design Museum’s exhibition

*Design for the Other 90%*explores a growing movement among designers to design low-cost solutions the 90% of the world’s population that have little or no access to most of the products and services many of us take for granted. In this lesson, students use information from the*Design for the Other 90%*website to create real-world mathematical word problems.### National Standards

**Common Core Literacy for Other Subjects**

**Strand Reading for Science and Technical Subjects**

**Grades 6-8**

**RST.6-8.2.**Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions.

**RST.6-8.3.**Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

**Strand Writing**

**Grades 6-8**

**WHST.6-8.9.**Draw evidence from informational texts to support analysis reflection, and research.

**Common Core English Language Arts**

**Strand Speaking and Listening**

**Grades 6-8**

**SL.6-8.1.**Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacherled) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly.

**Common Core Mathematics 6-8**

**Grade 6**

**Cluster Solve real-life and mathematical problems using numerical and algebraic expressions and equations.**

**Grade 7**

**Mathematics**

**Standard 1.**

**Uses a variety of strategies in the problem-solving process**

**Level III.**

**Benchmark**

**1.**Understands how to break a complex problem into simpler parts or use a similar problem type to solve a problem

**Benchmark 2.**Uses a variety of strategies to understand problem-solving situations and processes (e.g., considers different strategies and approaches to a problem, restates problem from various perspectives)

**Standard 2.**

**Understands and applies basic and advanced properties of the concepts of numbers**

**Level III. Benchmark 4.**Uses number theory concepts (e.g., divisibility and remainders, factors, multiples, prime, relatively prime) to solve problems

**Economics**

**Standard 1.**

**Understands that scarcity of productive resources requires choices that generate opportunity costs**

**Level III. Benchmark 1.**Understands that scarcity of resources necessitates choice at both the personal and the societal levels

**Language Arts - Writing**

**Standard 1.**

**Uses the general skills and strategies of the writing process**

**Level III. Benchmark 1.**Prewriting: Uses a variety of prewriting strategies (e.g., makes outlines, uses published pieces as writing models, constructs critical standards, brainstorms, builds background knowledge)

**Benchmark 11.**Writes compositions that address problems/solutions (e.g., identifies and defines a problem in a way appropriate to the intended audience, describes at least one solution, presents logical and well-supported reasons)

**Speaking and Listening - Writing**

**Standard 8.**

**Uses listening and speaking strategies for different purposes**

**Level III. Benchmark 1.**Plays a variety of roles in group discussions (e.g., active listener, discussion leader, facilitator)

**Reading**

**Standard 5.**

**Uses the general skills and strategies of the reading process**

**Level III. Benchmark 1.**Establishes and adjusts purposes for reading (e.g., to understand, interpret, enjoy, solve problems, predict outcomes, answer a specific question, form an opinion, skim for facts; to discover models for own writing)

### Objectives

Students will:

- explore design innovations
- learn about the applications of math in the real world
- discuss the benefits of new and productive innovations
- create a mathematical word problem with real-world applications

### Resources

- Cooper-Hewitt, National Design Museum:
*Design for the Other 90%*http://www.designother90.org/solutions/?exhibition=12 - "Solve my Problem!" handout (attached)

### Materials

Computer with internet access

### Procedures

**Building Background**

**Activity One: Math Is Everywhere**

*The purpose of this activity is to help students see that math is part of everyday life.*

- "Although he may not always recognize his bondage, modern man lives under a tyranny of numbers." Nicholas Eberstadt,
*The Tyranny of Numbers: Mismeasurement and Misrule*http://www.quotegarden.com/math.html - "Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub." Richard J. Trudeau,
*Dots and Lines*http://www.quotegarden.com/math.html - "From the time of Kepler to that of Newton, and from Newton to Hartley, not only all things in external nature, but the subtlest mysteries of life and organization, and even of the intellect and moral being, were conjured within the magic circle of mathematical formulae." Samuel Taylor Coleridge http://www.mathacademy.com/pr/quotes/index.asp?ACTION=TOP&VAL=history

- museum
- supermarket
- amusement park
- school
- bank
- sports arena
- movie theater

**Steps for Learning**

**Activity One: Learning Math Through a Variety of Topics**

*The purpose of this activity is for students to see that problems and situations from everyday life can be used to learn math.*Teacher Note: This lesson can be used to reinforce the current math topic in your classroom, and as such, can be reused with each new topic introduced. You can use the samples given in this lesson as a guideline, and add others that support your instructional goals.1. Tell the students that math is not just about numbers and their relationships to each other, but that it has real-world applications. Talk about some of the examples the students provided in the last activity. Lead a class discussion based on the following questions:

- How does applying mathematical ideas to the real world make math more meaningful?
- Does seeing how math is used in the real world help you to better understand math concepts? Does it make it more interesting for you?

**Teaching Topic: Percentages**Word Problem: The Museum of Natural History in New York City monitors the number of visitors each season. In 2006, there were a total of 10,355 visitors. Of this total, 3,003 visited in the spring, 4,349 visited in the summer, 2,175 visited in the fall and 828 visited in the winter. What percentage of total visitors came to the museum each season? Solution: 29%, 42%, 21%, and 8%, respectively Application: How can the museum use this information to improve the number of visits to the museum?

**Teaching Topic: Percentages**Word Problem: Of the 34 innovations described on the

*Design for the Other 90%*website, what percentage is used by countries in Asia? What percentage is used by countries in Europe? Solution: Asia, 47%; Europe, 12% Application: What conclusion could you draw about the needs of those living in Asia versus those living in Europe?

**Teaching Topic: Volume**Word Problem: The dimensions of the ceramic water filter are 3.5’ h x 2’ w x 2’ d. If the ship transporting the filters has 16,800 cubic feet of available space, how many filters can be shipped in this space? Solution: 1,200 filters Application: In what way can this information influence the decisions of those manufacturing the filters? How does it influence the decisions of those shipping them?

**Teaching Topic: Computation, Percentages**Word Problem: The use of the ceramic water filter has decreased the number of days lost due to illness in Nepal’s workforce by 45% each year. Before the use of the filter, the average number of days missed due to illness was 25 days per worker. With a work force of 6,500, how many less days of work are missed each year? Solution: 73,125 Application: Would it be cost-effective for employers in Nepal to purchase ceramic water filters for their workers? Discuss each problem, and clarify any questions students might have about how to construct word problems. 3. Divide the class into pairs. Ask each pair to generate three examples of word problems. Invite the students to share their word problems with their classmates. You may also choose to assign this as homework.

**Activity Two: Creating Word Problems**

*The purpose of this activity is for students to create mathematical word problems based on the information presented on Cooper-Hewitt’s*Design for the Other 90%

*website.*1. As a class, visit Cooper Hewitt’s

*Design for the Other 90%*website at http://www.designother90.org/solutions/?exhibition=12. Provide time for students to explore the different parts of the website. 2. Divide the class into small groups. Give each group a copy of the “Solve My Problem” handout. 3. Provide time for the students to share their presentations. Lead a class discussion using the following questions as guidelines:

- What did you learn from your classmates’ presentations?
- What were the most effective ways to design word problems?
- What kinds of design innovations were represented in the presentations?
- What did you learn about math in this activity?

### Assessment

Create a class rubric with your students that will help them understand the effectiveness of their work. Use the following guidelines to help create the rubric.

- Rate how well you understood the application of mathematical concepts to the real world.
- Rate how well you understood the concept behind the innovations on the
*Design for the Other 90%*website. - Rate the quality of the word problem made by your group.
- Rate the value of the real-world application of your group’s word problem.
- Rate your participation in the design of your group’s presentation.
- Rate how well your group was able to collaborate.

### Enrichment Extension Activities

**Differentiation for Elementary School:**

- Students can participate by writing simpler word problems related to the exhibition
*Design for the Other 90%,*along with the solution and real world application. For example:

Problem: How much longer can fruit stay fresh using the Pot-in-Pot Cooler design? Solution: 18 days. Application: How can this help the farmers of Nigeria who have to travel for 2 days to get to market?

**Differentiation for High School:**

- Have the students create a poster, blog post or PowerPoint presentation that includes and explains the information they gathered for the creation of the word problem.
- Ask the students to exchange word problems with another group and write an additional word problem to go along with the information included.
- Ask the students to provide an additional real-world application of the word problem and solution written by another group.

D. Assael said on January 2, 2014

Activity One is something that I think every math teacher could use multiple times in their classroom! Opening a new unit by solving a real world problem with the new skills to be developed in the unit is a wonderful way to gain student interest and intrigue in what they will be learning. Making connections for students to math in the real world is something that does need to be explicitly done from time to time so that students can develop their own strategies to find the true applications of mathematics.