Problem Solving Strategies

1. Making a Table

Process Problem 1

Holly checked a book out of the library and read this notice about fines: It a book is 1 day overdue, the fine is 1¢, 2 days overdue, 2¢, 3 days overdue, 4¢, and so on. It Holly's book is 7 days overdue, how much is her fine? (Hint: Complete this table.)

Day	1	2	3	4	5	6	7
Fine	1¢	2¢	4¢	8¢

Understanding the Problem

· How much is the fine for 1 day? (1 ¢)
· How much is the fine for 2 days? (2¢)
· How much is the fine for 3 days? (4¢)

Planning a Solution

· How much would the fine be for 4 days if we double the previous day? (8¢)
· How much is the fine for 5 days? (16¢)

Finding the Answer

Make a Table

Day	1	2	3	4	5	6	7
Fine	1¢	2¢	4¢	8¢	16¢	32¢	64¢

Holly's fine is 64¢.

 Process Problem 2

Seth and Bob each began reading a Hardy Boys book today. If Seth reads 8 pages each day and Bob reads 5 pages each day, what page will Bob be reading when Seth is reading page 56? (Hint: Complete the table.)

Day	Seth's Page	Bob's Page
1	8	5
2	16	10
3	24	15

Understanding the Problem

· How many pages does Seth read each day? (8) Bob? (5)
· Did they start reading their books on the same day? (yes)

Planning a Solution

· How many pages had Seth read at the end of the first day? (8) Bob? (5)
· When Seth has read 16 pages, how many pages will Bob have read?(10)
· Find the number of pages Seth read for the first 5 days. (8, 16, 24, 32, 40)

Finding the Answer

Make a Table   

Day	Seth's Page	Bob's Page
1	8	5
2	16	10
3	24	15
4	32	20
5	40	25
6	48	30
7	56	35

Bob will be reading page 35 when Seth is reading page 56.

Process Problem 3

Jerry was mowing his lawn when he noticed Christy was a so mowing her lawn next door. They stopped to talk and Jerry learned that Christy mows her lawn once every 8 days. Jerry mows his lawn once every 6 days. In how many days will they be mowing their lawns together again?

Understanding the Problem
· How often does Christy mow her lawn? (every 8 days)
· How often does Jerry mow his lawn? (every 6 days)

Planning a Solution
· In how many days will Christy mow her lawn again? (8) Then the next time?(16)
· When will Jerry mow his lawn again? (in 6 days) Then again? (12)
· Try making a table. (See solution.)

Finding the Answer
Make a Table

Christy	8	16	24	32
Jerry	6	12	18	24

Jerry and Christy will be mowing their lawns together again in 24 days

Planning for Effective Math Teaching

Important activities in planning for effective Math teaching

• Lesson planning – making a very useful guide in every topic for good class discussion.

• Writing objective – setting a specific goal for each discussion.

• Determining appropriate content – identifying topic/s and related topic/s to be discussed.

• Determining appropriate approaches and methods – setting your own way of discussing or presenting certain topics.

• Determining appropriate learning activities – planning different activities for collaborative learning.

• Determining appropriate materials and tools – using various kinds of materials in presenting/teaching. Technology is a useful tool in teaching Mathematics.

• Determining appropriate evaluation - making quizzes, mastery tests, projects, etc. to assess students’ performance.

Other important things to consider:

• make examples that are within the students’ level.

• explain briefly each lesson, especially formulas.

• relate lessons to everyday life.

• engage students actively.

• provide abundant experience in using tools (ex. Measure stick).

Reported by:

Garcia, Kalvin L.