Mathematics, Problem Solving

Grade 5- 8

Objective

Students learn different strategies for solving math problems.

Directions

Facts to Know
Some problems can't be solved just by following a plan or looking for code words. The way these unconventional problems are written requires you to try different strategies until you hit on a reasonable solution. Sometimes you may have to try two or three different strategies before you hit on the correct approach.
In these problems follow these steps:

1. Read the problem carefully, twice.
2. State the problem to be solved in your own words.
3. Try each strategy until you get one that works.

Problem-Solving Strategies
Guess and Check
Your coach bought 7 balls. The baseballs cost $3.98 and the basketballs cost $19.98. The total cost was $75.86. How many baseballs and how many basketballs did he buy?
You know:

• the cost of each type of ball
• the total cost
• the number of balls purchased

You guess:

• 1 baseball ($3.98) plus 6 basketballs ($119.88) equals $123.86--too high
• 3 baseballs ($11.94) plus 4 basketballs ($79.92) equals $91.86--too high but closer
• 4 baseballs ($15.92) plus 3 basketballs ($59.94) equals $75.86--exactly right

Working Backwards
When Peter started selling greeting cards, he spent half of his money to buy the cards. Then he spent half of what he had left on advertising. He only has $50.00 now. How much money did he start with?

You know:	Check:
how much money he now has	$200.00 divided by half is $100.00
the fractional amount he spent each time	$100.00 divided by half is $50.00

Work Backwards:

• He has $50.00 now.
• He had twice $50.00 ($100.00) before he spent half on advertising.
• He had twice $100.00 ($200.00) before he spent half on cards.

Make a Visual (chart, diagram, graph, list, or table)
There are four baseball teams in a league. How many games must be played so that each team plays every other team once and only once? There are six games altogether. Make a chart (or diagram):

• Team 1 plays Team 2
• Team 1 plays Team 3
• Team 1 plays Team 4
• Team 2 plays Team 3
• Team 2 plays Team 4
• Team 3 plays Team 4

Resources

• pencils
• Problem-Solving Strategies activity pages