What you should learn

To explore problem situations

To translate verbal sentences and problems into equationsor formulas and vice versa

NCTM Curriculm Standards 2, 4, 6 - 10

 

 

Introduction: Bugs, bugs, everywhere! That could be the slogan for James Fujita, an avid bug collector. Fujita has been fascinated with bugs since he was bitten by a cricket at the age of three. His collection includes hundreds of buys - bettles, spiders, millipedes, scorpions, just to name a few - both living and dead.

Fujita has studied bugs as far away as Japan and Costa Rica, as well as in his own backyard in Oxnard, California. He has given bug presentations and workshops, donated some of his bugs to museums and zoos, and even appeared on a television talk show with some of his larger bugs.

You can explore problems about Fujita's bug collecting by asking and answering questions. In this text, we will use a four-step plan to solve problems.

Problem-Solving Plan

1. Explore the problem

2. Plan the solution

3. Solve the problem

4. Examine the solution

The first step in solving a problem is to read and explore it until you completely understand the relationships in the given information.

Step 1: Explore the Problem

To solve a verbal problem, first read the problme carefully and explore what the problme is about.

Identify what information is given

Idnetify what you are asked to find

Step 2 : Plan the Solution

One strategy you can use the solve a problem is to write an equation. Choose a variable to represent one of the unspecified numbers in the problem. This is called defining the variable. Then use the variable to write expressions for the other unspecified numbers in the probllem.

Step 3: Solve the Problem

Use the strategy you chose in Step 2 to solve the problem.

Step 4: Examine the Solution

Check your answer within the context of the original problem. Does your answer make sense? Does it fit the information in the problem?

Exercise 1: Gregory Arakelian of Herndon, Virginia, set a speed record for typingthe most words per minute, with no errors, on a personal computer in the KeyTronic World Invitational Type-Off on September 24, 1991. Suppose his closet competitor typed 10 fewer words per minute than Arakelian. If his closet competitor typed 148 words per minute, how many words did Arakelian type per minute?

Explore

How many words can Arakelian type in relation to his closet competitor? 10 more words

How many words per minute did his competitor type? 148 words

Plan

Write an equation to represent the situation. Let w represent the wrods per minute that Arakelian typed.

Solve

w - 10 = 148

w = 158

Arakelian typed 158 words per minute

Examine

The problem asks how many words Arakelian typed per minute. His competitor typed 10 fewer words per minute. Since 158 - 10 = 148, the answer makes sense.

 

 

When solving problems, many sentences can be written as equations. Use variables to represent the unspecified numbers or measures referred to in the sentence or problem. Then write the verbal expressions as algebraic expressions. Some verbal expressions that suggest the equals sign are listed below.

Exercise 2: Translate each sentence into an alebraic sentence.

a. Six times a number x is equal to 7 times the sum of z and y.

6x = 7 (z + y)

b. A number is less than or equal to 5.

 

 

Another strategy you can use to solve a problem is to write a formula. A formula is an equation that states a rule for the relationship between certain quantities. Sometimes you can develop a formula by makeing a model.

Exercise 3: Translate the sentence into a formula.

The area of a circle equals the product of and the square of the radius r.

 

 

You can also translate equations into verbal sentences or make up your own verbal problem if you are given an equation or two.

Example 4: Translate x + 6 = 39 into a verbal sentence.

Example 5: Write a problem based on the given information.

l = Lawana's height in inches

l + 5 = Tatewin's height in inches

2l + (l + 5) = 194

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 13 - 35 odd, 37 - 43

Alternative Homework: Enriched: 14 - 32 even, 33 - 43

Extra Practice: Students book page 761 Lesson 2-9

Extra Practice Worksheet: Click Here.

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