|
Also called guessing and checking. |
 |
| Use the following steps to help you
solve a problem. |
1.
Read the problem
2. Make a plan to solve the problem. This may
involve making a chart or just thinking of some math hints to help
you make a best guess.
4. Make your "guess"
and check it.
5. Eliminate the possibilities until you get the
right answer. |
Here are two examples to help you
understand the concept of trial and error
A new movie was released and ran for 5 weeks. Word got out that the movie
was good. Each week, the number of people who watched the movie was
twice the previous week. At the end of the 5 weeks, the total number of
people who watched the movie was 6200. How many people watched the movie
the first week it ran?
For this problem, we need to first make plan. It will be
helpful to make a chart to check our answers with.
For choice A
|
Week 1 |
2 |
|
Week 2 |
4 |
|
Week 3 |
8 |
|
Week 4 |
16 |
|
Week 5 |
32 |
|
Total |
62 |
For choice B
| Week 1 |
20 |
| Week 2 |
40 |
| Week 3 |
80 |
| Week 4 |
160 |
| Week 5 |
320 |
| Total |
620 |
For choice C
| Week 1 |
200 |
| Week 2 |
400 |
| Week 3 |
800 |
| Week 4 |
1600 |
| Week 5 |
3200 |
| Total |
6200 |
By trying the answers given and then checking them, we can find the
one answer that works.
A farmer planted
351 apple trees in his orchard. He planted at least
20 rows, and each row has the same number of trees in it. How many trees
are in each row?
As part of our plan, we can see that we need to use multiplication
and division to solve this problem..
Our hints:
 |
There are at least 20 rows.
|
|
|
We also know the number
of trees in each row can't end in a 5 or a 0 since multiplying by either
of these can never result in a -9 at the end of the number. |
|
|
We can also
rule out all even numbers. If you multiply anything by an even number
the answer is even. |
|
|
The answer to the problem
will be a whole number. |
Let's make our first guess! The obvious place to start is 21.
| 351 |
÷ |
21 |
= |
16.714285714285714285714285714286 |
|
What is the next odd number we can try? |
| 351 |
÷ |
23 |
= |
15.260869565217391304347826086957 |
|
The next odd number would be 25, but we already said the answer can't
end in a 5. What's after that? |
| 351 |
÷ |
27 |
= |
13 |
|
We got a whole number! |
The farmer planted 13 trees in each row. We also know he planted 27
rows of trees!
Let's Practice!
click here
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