Playing Detective, Following the Clues, Solving the Question

When we have a math problem to solve, it helps if we pretend to be detectives. We have information, clues and a mystery to solve -- so if we organize our thoughts and information in a logical way, we can figure out the answer.

When he first reaches the crime scene, every TV detective pulls out a note book and pencil. Then he lists the information and details of the case. These help him organize his thoughts so that he can have a clear picture of the crime in his mind. If he's a good detective, he should be able to solve the crime.

Using a "To Find, Given, Solution" Format

When we have to solve a problem with math, we should always approach it by listing:

1) What we want to find, 2) What we know from the information and clues in the problem, 3) What methods we will use to solve the question.

Sometimes, the word problem includes extra or useless information. It's a good idea to cross it out since it often includes numbers we don't need to find our solution. Here's an example.

George drove 309 miles during a 2-day trip. His speed was 55 mph.
If he drove 135 miles the first day, how far did he drive on the 2nd day?

The extra information is "His speed was 55 mph." Since we know the whole trip was 309 miles, and he drove 135 miles the first day, we simply subtract 135 from 309 to find he drove 174 miles on the 2nd day. His speed doesn't change the distance he travelled, so we would cross out this sentence.

Example 1

The Horse, Cheetah and Ostrich are 3 African animals that run quickly. The Ostrich can grow to
8 feet tall. One of them can run 40 miles per hour, another can run at 60 miles per hour, and the third runs at 52 miles per hour. The Horse is the slowest and the Cheetah is a little faster than the Ostrich.
a) Identify the extra information in the question and b) decide how fast can each animal run?

Solution:

a) The extra information is The Ostrich can grow to 8 feet tall.

b)

Example 2

Mark, Tracy and Sylvia are talking about their pets. One has a black cat, the other has a dog and the third has a pet rabbit. Mark says his pet's favorite food is carrots. Both Sylvia and her mother are allergic to cats. Who owns which pet?

Making a Decision Table

Another approach to this question and others like it is to make a table to diplay the data or information. When we fill in our obvious conclusions, the solution becomes clear.
The table for this question looks like this:

	cat	dog	rabbit
Mark	NO	NO	YES
Tracy			NO
Sylvia	NO		NO

From the information in the question, we definitely know that Sylvia doesn't have a cat, so we write NO in the 1st cell of Sylvia's row. We also know that Mark has the rabbit because they love carrots, so we write YES in the Mark/Rabbit cell. Now that we know Mark has the rabbit, we can write NO in the other 2 cells of his row and NO in the Tracy/Rabbit and Sylvia/Rabbit cells.

Since each person has a pet, there has to be one YES in each row. Sylvia's row has one blank spot under "dog", so she must have the dog. And that leaves the cat for Tracy. We figured out who has which pet by eliminating (ruling out) the other possibilities.

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Working with a Bar Graph

Sometimes, the information we need to solve the puzzle is presented as an image -- a diagram or a graph. From it, we can read the data and answer the questions.

Example 3

This graph shows the number of sunny days in each month of 2003 in Burlington, Vermont.
Use the data to answer the questions.

QUESTION	ANSWER
1) Which month was the sunniest?	July was the sunniest month.
2) Which month had the fewest sunny days?	December had less than 10 sunny days.
3) Which months had exactly 20 sunny days?	April and September had 20 sunny days.

Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.

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Practice Exercises

Use whichever approach best suits the problem. Write full sentences for your answers.

1) Use the graph above to answer these questions.(hint: open the graph in a new window)

a) What summer month was the rainiest?

b) About how many sunny days were there in all in December, January and February?

c) Which months had exactly 10 sunny days?

d) Name 3 pairs of months with the same number of sunny days.

2) Together, Neptune and Mars have 10 moons. Neptune has 6 more moons than Mars.
How many moons does each planet have?

3) Susan, Anita and Mai-Lee are going to the park to play their favorite sports. One will swim, another will play baseball and the third will play tennis. Anita is afraid of water and Mai-Lee just bought a new tennis racket. If each girl plays only one sport, what one will each girl play?

4) A young panda bear eats about 20 pounds of bamboo every day. An adult panda eats about
35 pounds of bamboo every day. About how many pounds of bamboo does a family of
2 young and 2 adult pandas eat every day?

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Solutions

1)

a) Rainiest summer month: August

b) Sunny days in December, January and February: 31 or 32

c) Months with exactly 10 sunny days : January and November

d) 3 pairs of months with equal sunny days: January / November, Feb / March, April / Sept

2)

3) Susan will swim, Mai-Lee will play tennis, and Anita will play baseball.

	swim	baseball	tennis
Susan	YES	NO	NO
Anita	NO	YES	NO
Mai-Lee	NO	NO	YES

4)

what do we want to know?	How many pounds of bamboo the pandas eat each day.
what information is given?	a young panda eats 20 pounds of bamboo per day an adult panda eats 35 pounds of bamboo per day, family of 2 young and 2 adult pandas.
what method do we use?	addition the young pandas eat 20 + 20 or 40 pounds a day, the adult pandas eat 35 + 35 or 70 pounds a day,. 70 + 40 = 110 pounds of bamboo per day Solution: The family eats 110 pounds of bamboo a day.

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