1. Word Problems: What a Problem for Most Kelly Meeks and Connie Seibert Texas Adult Basic Education Mathematics Institute Conference October 15 & 16, 2010

2. Math is a Four-Letter Word! Complete the following phrase using a four letter word: Math is (a) ___________________

3. Getting Started Word Problems What goes through your mind? What goes through your students’ minds?

4. Problem Solving Steps Understand the Question Find the Information Make a Plan Solve the Problem Check the Answer George Polya, 1973, How to Solve It

5. Understand the Question Read Reread Make a guess Restate the problem Rewrite the question Is it a set-up problem?

6. Find the Information Look at labels Find “hidden” information Numbers in word form 1 week instead of 7 days Extra information Not enough information

7. Make a Plan Choose the correct operation(s) Draw a picture Construct a table or graph Use a model Find a pattern Work backwards Use a formula or equation

8. Solve the Problem Write out work Solve an equation Estimating the answer

9. Check the Answer Did you answer the question? Is the answer reasonable? Is the answer in the correct units?

10. Strategies for Word Problems Tables Working Backwards Pictures Rewriting Problem Substituting with real numbers Proportions Formula

11. Types of Algebra Word Problems Numbers Relationships among numbers Find numbers given their sum and other relationships Consecutive numbers: sums and multiples Real world number problems

12. 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?

13. One way to solve Write expressions representing each description: x = the larger number x – 2 = the smaller number Write an equation using the two expressions: 3(x-2)=x+30 Simplify the equation: 3x-6=x+30 Group like terms: 2x=36 Solve: x=18; x-2=16

14. 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 back Going against (and with) wind and current

15. 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?

16. 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

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

18. 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?

19. What strategies would you use?

20. Solution number of adults: a number of children: c total number: a + c = 2200 total income: 4a + 1.5c = 5050 a = 2200 – c

21. 4(2200 – c) + 1.5c = 5050 8800 – 4c + 1.5c = 5050 8800 – 2.5c = 5050 –2.5c = –3750 c = 1500

22. a = 2200 – (1500) = 700 There were 1500 children and 700 adults.

23. Age Typical age-related problems Combined age Relation of ages now and some time ago What strategies would you use?

24. 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?

25. Age solution Age nowAge in 10 years JoeXX + 10 Fred5 X5X + 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

26. Finance Problems Typical finance-related problems Interest income Total amounts and partial investments What strategies?

27. 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? AlexOmarDonna x

28. Geometry Problems Triangles, rectangles, spheres etc What strategies would you use?

29. Any questions?

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