Word Problems: What a Problem for Most

Kelly Meeks and Connie SeibertTexas Adult Basic Education Mathematics Institute ConferenceOctober 15 & 16, 2010

Math is a Four-Letter Word!

Complete the following phrase using a four letter word:

Math is (a) ___________________

Getting Started

Word ProblemsWhat goes through your mind?What goes through your students’ minds?

Problem Solving Steps

Understand the QuestionFind the InformationMake a PlanSolve the ProblemCheck the Answer

George Polya, 1973, How to Solve It

Understand the Question

ReadRereadMake a guessRestate the problemRewrite the questionIs it a set-up problem?

Find the Information

Look at labelsFind “hidden” information

Numbers in word form1 week instead of 7 days

Extra informationNot enough information

Make a Plan

Choose the correct operation(s)Draw a pictureConstruct a table or graphUse a modelFind a patternWork backwardsUse a formula or equation

Solve the Problem

Write out workSolve an equationEstimating the answer

Check the Answer

Did you answer the question?Is the answer reasonable?Is the answer in the correct units?

Strategies for Word Problems

TablesWorking BackwardsPicturesRewriting ProblemSubstituting with real numbersProportionsFormula

Types of Algebra Word Problems Numbers

Relationships among numbers Find numbers given their sum and other

relationshipsConsecutive numbers: sums and

multiplesReal world number problems

Number Problem

One number is 2 less than another number. Three times the smaller number is 30 more than the larger number. What are the two numbers?

What strategies could we use to solve this problem?

One way to solve

Write expressions representing each description: x = the larger number

x – 2 = the smaller numberWrite an equation using the two

expressions: 3(x-2)=x+30Simplify the equation: 3x-6=x+30Group like terms: 2x=36Solve: x=18; x-2=16

Time, Motion and Travel

Travel Related Problems Trains (and other objects) moving

towards each other or in the same direction; meeting, catching up

Going and coming backGoing against (and with) wind and

current

Travel Problem

Two trains leave a station at the same time. One heads north at an average speed of 60 miles per hour, and the other heads south at an average speed of 75 miles per hour. How far apart will they be at the end of 2 hours?

What strategies?

Travel Solution

Draw a diagram to help you picture the movement of the trains.

Write an equation to describe the problem: 60 x 2+75 x 2 = d

Solve the equation: 120 + 150 = d

Linear Problems

Problems reducible to linear equations 2 apples and 3 oranges cost , 1 apple

and 2 oranges cost .

Linear equation problem

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

What strategies would you use?

Solution

number of adults: anumber of children: c

total number: a + c = 2200 total income: 4a + 1.5c = 5050

a = 2200 – c

4(2200 – c) + 1.5c = 5050

8800 – 4c + 1.5c = 5050

8800 – 2.5c = 5050

–2.5c = –3750

c = 1500

a = 2200 – (1500) = 700

There were 1500 children and 700 adults.

Age

Typical age-related problems Combined age Relation of ages now and some time ago

What strategies would you use?

Age Problem

Fred is 5 times as old as his grandson Joe. In 10 years, the sum of Fred’s age and Joe’s age will be 92. How old are Fred and Joe now?

Age solution

Age now Age in 10 years

Joe X X + 10

Fred 5 X 5X + 10

Fill in the diagram with the facts from the problem

Write an equation to describe the problem: x + 10 + 5x + 10 = 92

Solve the equation

Finance Problems

Typical finance-related problems Interest income Total amounts and partial investments

What strategies?

Money problem with tables

Donna earns twice as much money per month as Omar. Omar earns $200 more than Alex. Together the three workers earn $3320 per month. How much does Omar earn per month?

Alex Omar Donna

x

Geometry Problems

Triangles, rectangles, spheres etc

What strategies would you use?

Any questions?

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