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Is That a Plan? Problem-Solving: Using Diagrams and Models (Grades 5-6)

Master Teacher

Christi Sauls

Time Allotment

One 60-minute class period

Overview

This lesson concentrates on the problem-solving strategy of using diagrams and models. Students will be allowed to explore a variety of diagrams and models in order to solve problems. Students will also be able to create their own drawings to solve problems.

Subject Matter

Mathematics

Learning Objectives

Students will be able to:

use a flow chart to solve problems
solve real-world problems by using a diagram
or model
create their own diagrams for problem-solving

South Carolina Standards

Visit the South Carolina Department of Education for the South Carolina Mathematics Standards.

Mathematics—Grades 5_6

The student will solve multi-step consumer application problems, including those involving fractions and decimals, and present data and conclusions in paragraphs, tables, or graphs.

Media Components

Video

Math Works, Lesson 16: Using Diagrams and Models uses different diagrams to illustrate how to put things together. This is a very important part of problem-solving. The students will use this video to recognize how different problems were solved.

Web Site

Ask Dr. Math is a question and answer service for math students and their teachers. A searchable database is available by level and topic, as well as summaries of "Frequently Asked Questions."

Materials

Per student:

paper

pencil

Equipment

computers with Internet access

Prep for Teacher

Prior to teaching, bookmark the Web site used
in the lesson.
Cue the videotape to the appropriate starting point.
Make copies of the discussion and problem- solving questions
(Activity Sheets 1 and 2).
Create a complete flow chart drawn on a transparency to use in class. (Optional)

Introductory Activity: Setting the Stage

Step 1

The following activity will prepare your students to use a diagram or model to solve a problem. Write the problem on the board or overhead and have students solve the problem by drawing a diagram.

The Smiths moved into a new house and wanted to build a new back porch onto their house. They wanted the porch to be 23 feet long and 18 feet wide. Draw a diagram of the porch and determine the perimeter and area of the new back porch.

Step 2

After about five or ten minutes, have students present their solutions to the class. Students should explain how they drew the diagram and how they used the diagram to solve the problem.

Step 3

After the students present their work, you should give them an example of all the information that their answer should have. Explain to them that this is a problem-solving strategy that is used in everyday life. Tell them that today they will be exploring other diagrams and models to solve problems. Stress the explanation of their word problem, so that when they do their own, they will have a good explanation.

For example the students' solutions should include a drawing of the porch with the correct measurements in the correct place. The students should also show the computation of finding the area and the perimeter of the porch. After the computation, the students should write a four- or five-sentence paragraph describing the problem-solving strategy they used (draw a picture) and how they found the area and perimeter of the porch.

Learning Activity

Step 1

Focus for Media Interaction: Before watching the Math Works lesson, tell students to raise their hands when they see examples of different types of diagrams. START at the beginning of the tape where you will see two people putting together a swing set. STOP the videotape when the swing set is put together but it doesn't resemble a swing set. One of the characters convinces the other one to use the diagram and the results are much improved. Discuss with students what went wrong while they were putting together the swing set.

RESTART the video until the swing set is put together properly. Continue to watch the tape until you see Session 17. STOP the tape at this point.

Step 2

After viewing the video, use these discussion questions. You may want to have them on a handout for students (Activity Sheets 1), on the overhead, or orally discuss the answers with the class.

1. What specific things could Mark and Andy have learned from following the swing set's
assembly diagram from the beginning? (What the pieces are, how they are meant to fit
together, and the order in which the pieces should be put together. In general, diagrams
show how to do something, how something works, or the relationship between two or more things.)

2. Why are diagrams useful? (They can help identify problems, show possible solutions and help find the best solution.) Can you name some of the types of diagrams you saw in the program? Can you think of additional types?

3. If the girls at the theme park had made a diagram of the activities they had planned
for the day, what type of diagram would it have been? (a flow chart)

4. What are some of the different types of diagrams that NASA uses to manage the
space shuttle flights?

5. What type of model did Sammy, John, and Emily make to help figure out the carnival booth arrangement? (a floor plan)

Step 3

As a class, review the purpose of a flow chart. Emphasize that flow charts show a process step by step and can be used to simplify or clarify a complicated process. Then divide the class into groups of three or four students each. Each group should pick a topic from the list below. You may have a completed flow chart on the overhead.

Topics for Flow Charts

How to make a handcraft item
How to make a favorite dish
How to tie shoelaces
How to wash a car
How to perform a mathematics procedure
How to do a particular maneuver in a sport

Allow one student in the group to come to the front of the class and explain the group's flow chart.

Step 4

Another activity that can be done outside class is to have students draw floor plans. They can choose from the following topics:

A floor plan of your classroom with the furniture rearranged
A floor plan of the student's bedroom with the furniture rearranged
A plan of a vegetable or flower garden
A floor plan of an ideal student recreation center

Culmination Activity/Assessment

Distribute Activity Sheet 2 (a copy of the questions on page ?) and have the students use diagrams to help solve problems on the sheet. As problems occur, have them write down their questions. Ask students to log on to Ask Dr. Math.

Focus for Media Interaction: Allow Dr. Math to answer their questions.

1. During the month of March, Oliver will work three days and then have three days off. Eric will work two days and then have five days off. Eric will work on the 1^st and 2^nd of March and Oliver will work on the 1^st, 2^nd, and 3^rd. On the days they work together, they go to work together. On what days will they be able to go to work together during the 31 days of March? (1, 2, 8, 9, 15)

2. James has a vegetable and flower garden that is 7 meters by 5 meters. The vegetables are in the center of the garden, with a ½ meter flower border around the outside. Rabbits have been eating the vegetables, so James wants to put a fence around just the vegetable part of the garden. How long a fence will he need? Illustrate your answer. (20
meters)

3. Dick, Tom, Paula, Carol, Zev, Lucy, and Meg want to have a chess tournament in which everyone plays everyone else once. Who will play in each game and how many games will be played? Illustrate your answer. (21 games)

4. A magic plant grows 30 cm the first day and then gets 5 cm shorter that night. It continues this growth pattern until it reaches the height of 260 cm. At 260 cm, it stops growing and shrinking. How many days will it take the magic plant to reach 260 cm? Illustrate
your answer. (11 days)

Review students' work for accuracy. Have them explain the process for solving each problem. This is a good tool for assessing their comprehension of the problem-solving process.

Cross-Curricular Extensions

Social Studies: Use maps to solve problems with directions. To help students solve problems, obtain maps from the social studies teachers in your school.

Language Arts: The Writing Process—Students in an expository writing assignment will describe how to do something or give directions to their favorite place. Students may also describe how to put some-thing together. Students will need to use a web, rough draft, and final copy of their writing.

Community Connections

Contact NASA for copies of a flow chart that they may actually use.
Interview family members who use diagrams on their jobs.
Research and develop floor plans for a new
school. Involve the community and district
office staff in this process.