Searching for SolutionsDrawing a Diagram
Searching for Solutions
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Strategy 5 - Drawing a Diagram
Some problems are difficult to solve without making a visual representation of the information. Drawing a picture or a diagram is an excellent strategy for solving problems.
For example, how many different ways can you make $1.00. Although a dollar bill would be an easy solution, there are many, many ways to use coins to make $1.00. Actually, there are almost 300 ways to do it. Can you list more than 1/2 of them?
Now try this one: Roger and his friends went on a week-long bicycle ride. The total distance for the trip was 350 miles. On the first day, they rode 1/10 of the total distance. On the second day, they rode 1/3 of the remaining distance. At the end of the second day, they divided the mileage they still needed to travel equally amongst the last five days.
 | How far did they ride on the first day? How many miles were left? |
| How many miles did they ride on the second day? How many miles were remaining in their trip? |
| How many miles had they traveled by the end of the third day? |
| On the last day, how many miles did they ride? |
For this next problem, you will need a piece of graph paper and a ruler. Draw a large rectangle which covers most of the graph paper and label as follows: Top = High Street; Bottom = Main Street; Right Side = Second Avenue; Left Side = First Avenue. Read each of the clues and decide where each location will fit on the grid.
| Uncle Abe lives halfway between Main Street and High Street and halfway between First Avenue and Second Avenue. |
| Cousin Kay lives the same distance from Main Street as Uncle Abe but 1/4 the distance from First Avenue to Second Avenue. |
| Sister Celia lives the same distance from First Avenue as Uncle Abe but 3/4 the distance from Main Street to High Street. |
| Uncle Don lives 1/3 the distance from Second Avenue to First Avenue and 1/4 the distance from High Street to Main Street. |
| Brother Bart lives 2/3 the distance from First Avenue to Second Avenue and 1/4 the distance from Main Street to High Street. |
| Auntie Em lives between Uncle Don and Brother Bart and 7/8 the distance from Uncle Don's to Brother Bart's. |
Can you find where each member of the family lives?
Now let's move on to some problems on the Internet. As you read through these problems, remember to take notes, draw pictures, or make visual representations to help you solve the problems. Keep in mind that many problems contain information that may not be needed to solve the problem, so be a careful reader!
| MathCounts Problem of the Week at http://mathcounts.org/ - Click on Problem of the Week! |
| Brain Teasers at the Education Place at http://www.eduplace.com/math/brain/index.html |
| FunBrain Puzzlers at http://funbrain.com/ |
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© Searching for Solutions - A Web-Based Problem-Solving Unit - Developed by Judy Campf, e-Learning Specialist.
