Real World Problems

Designed by:  Tammy B. Hester

Grade level:  8th       Subject:  Math  

1) Core Curriculum Objective:  Solve real  world problems using operations with whole numbers using a variety of strategies and tools. (ex.  Calculators, sketches,  computers, etc.)   This lesson plan can  be modified using, fractions, decimals, percents and integers.    (8NA1-1) [PACT I.A. 4]

Restatement:  Using the four-step plan, students will choose appropriate strategies for solving real world problems.

2) Overview:  Students will work in groups and independently to develop different strategies for solving real world problems.  Students will show their work and share their ideas.

3) Focus Question:   How do you solve problems?

4) Time Frame:  2  fifty minute class periods

5) Assessment:   10 Real world problems will be given for each student to solve.  Each student will incorporate the 4-step plan in their strategy to solve the real world problems.  Students can receive as many as 10 points for each question.  The teacher will look for the following: an estimate of the answer, a plan or strategy,  the work shown (plan carried out), the correct answer, and is the answer reasonable.

[See attachment I ,  labeled Assessment of Real World Problems]

6) Resources:  

Mathematics Applications and Connections, course 3, Glencoe, Macmillian/Mcgraw-Hill 1995,

Overhead transparency showing the  Four Step Plan for Problem Solving 

Computer with internet access

Website:  Word Problems for kids

http://juliet.stfx.ca/people/fac/pwang/mathpage/math1.html

CD Rom    How the West was One + three x  four , by Sunburst Communications , Lesson #4, Developing a Good Problem-Solving Strategy for West

Day One

Activity One

Give students the following problem to solve.

The committee for the Gibbes Middle School's spring dance has decided to decorate the ceiling of the cafeteria by covering it with balloons.  Their sponsor agreed, but said she needed to know how many balloons they needed.  If the room is 40 by 60 feet, what is the least number of balloons they will need if two balloons are put per square foot?

Explain that in mathematics, we have a plan to solve problems that involves four steps.  The four steps are Explore, Plan, Solve, and Examine.

The four step plan should be shown on an overhead transparency.

The Four Step Plan for Solving Problems

1.  Explore    Determine what information is given in the problems and what you need to find.  Do you have all the information you need to solve the problem? Is there too much information?

2.  Plan    Make an estimate of what you think the answer should be.  Then select a strategy for solving the problem. There may be any number of ideas or strategies that you can use.

3. Solve  Solve the problem by carrying out your plan.  If your plan doesn't work, try another, and maybe even another.

4.  Examine    Examine your answer carefully. See if its fits the facts given in the problem.  Compare it to your estimate.  If the answer is not reasonable, make a new plan.  You may also want to check your answer by solving the problem again in a different way.

 Allow them to work in groups of four. The teacher may want to choose the groups. The teacher should monitor the class to make sure all students are working.  The teacher should be available for questions.  Each group will then present their answers and strategies in a class discussion.

Activity Two

Groups will then be given 4 more problems to solve.   See attachment II.  Groups will record their work on transparencies.

Students should be reminded:

1. Estimate what you think the answer would be.

2. Devise a Strategy

3. Carry out your plan

4. Check to see if your answer is reasonable

5. Double check to see if your answer is correct

The teacher should circulate the room to monitor participation and understanding.

After the students have completed their assignment, they should pick a spokesperson to go to the overhead with a transparency of one of the solutions and explain to the rest of the class.

Activity Three

Students will write a paragraph in their journals explaining the purpose of each of the four steps in the problem-solving plan.

Activity Four

Homework  -   Each student should write one real world problem than can be solved.

Day Two

Activity One

Review the 4 Step-plan for solving problems.

Activity Two

Allow students to return to previous day groups and share the problems they wrote for homework .  Have the students to solve each problem. The teacher should visit each group to check if all students participated in the assignment.

Activity Three:

Each group will evaluate real world problems and devise a strategy for solving the problem. Students will work 5 problems from the website, "Word problems for kids."

http://juliet.stfx.ca/people/fac/pwang/mathpage/math1.html

 Groups will then share their most difficult problem with the rest of the class. A class discussion will provide students insight on how problems can be tackled in different ways.

Activity Four:  

Students will write in their journals how using different strategies to solve real world problems would carry over into areas other than math.

Additional Enrichment Activity

CD rom, How the West Was One + Three x Four , Lesson 4

If students know the order of operations rules, this lesson exposes students to a variety of problem formats that would encourage students to improve their problem solving strategies.

Attachment I

Assessment for Real World Problems

1. "Go Dogs, Go Dogs, Go, Go, Go,"  is a cheer for the bulldogs' basketball team.  If 15 cheerleaders yell the cheer 5 times , how many times is "go" said?

2. A can of orange juice concentrate holds 12 ounces.  If you mix it with 3 cans of water, how big a pitcher do you need to hold it all?

3. There will be 460 people at the sports award banquet.  If each table seats 8 people, how many tables are needed?

4. Kiko works Saturday mornings at the videotape store.  She bought ten videotapes on sale and used a $10 employee discount coupon to help pay for the tapes.   The tapes sale 5 for $49.95.  How much did she actually spend of her own money?

5. The sign read "Going out of business, Handbags----3 for $15."  If bought six handbags at the store.  How much did she spend for each bag?

6. Sid earned $40 working after school.  How much money will he have left if he buys a sweatshirt and four jigsaw puzzles?  Sweatshirts cost $9.95 each and jigsaw puzzles are 2 for $5.

7. Nine school buses serve Maplewood Middle School.  The buses travel a total of 4,482 miles in one school week.   How many miles does each bus travel weekly?

8. Phyllis joined speaker wires together so that the speakers to her stereo would reach into her living room.  She used pieces that were 22 feet, 17 feet, and 31 feet long.  Will the combined length reach 80 feet?

9. A bicyclist planning a 1,800-mile trip decides that he can ride 15 miles per hour for 6 hours each day.  How many days will it take for him to complete the trip?

10. Pat and Mei began work at the same time.  It took Mei 110 minutes to mow the lawn, while Pat took 1 3/4 hours to paint the fence.  Who finished first?

Attachment II

Name________________________________

Use the four-step plan.

1. The photography class needs to enlarge a 15-centimeter by 25-centimeter picture so that the shorter side is 30 centimeters long.  How long will the longer side be after the enlargement?

2. Geothermal energy is heat from inside the earth.  Underground temperatures generally increase 9 degrees C for every 300 feet of depth.  For the ground temperature to rise 90 degrees C, how deep would you have to dig?

3. A DC -11 jumbo jet carries 342 passengers with 36 in first class seating and the rest in coach class seating.  A first class ticket to fly from Los Angeles to Chicago  cost $750, and a coach class ticket costs $450.  What will be the ticket sales for the airline if the flight is full?

4. At the school bookstore, a ball point pen cost  $0.28 and a small tablet cost $0.23.  What could you by and spend exactly $0.74?