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Problem
Solving Strategy
~ Solve a Simpler Problem ~ |
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Content
Process Problem 1
Sometimes a problem is too complex to solve in one step. When this
happens, it is often useful to Simplify the problem by dividing it into cases and solving
each one separately.
Use the hints provided to solve each of the following problems.
1. How many palindromes are there between 0 and 1000?
(A palindrome is a number like 525 that reads the same backward or forward.) |
| Simplify the problem. Find the number of one, two, and three digit
palindromes separately.Make a list. Use the list I've started, and look for a pattern! |
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a. How many of the numbers 1 through
9 are palindromes?
All nine numbers are palindromes. |
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b. How many of the numbers 10 through 99 are palindromes?
11
22 nine
:
:
99 |
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c. Find the number of palindromes from 100 through 999.
| 1 0 1 |
2 0 2 |
......... |
9 0 9 |
| 1 1 1 |
2 1 2 |
......... |
9 1 9 |
| 1 2 1 |
2 2 2 |
......... |
9 2 9 |
| 1 3 1 |
: |
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: |
:
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:
: |
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:
: |
| 1 9 1 |
2 9 2 |
......... |
9 9 9 |
9 columns x 10 palindromes/column = 90
90 palindromes from 100- 999 |
| Use the list I've started, and look for a pattern! |
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d. What is the answer to this original question?
There are 108 palindromes between 0 and 1000 |
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Process Problem 2
A pie can be cut into seven pieces with three straight cuts. What
is the largest number of pieces that can be made with eight straight cuts?
| Cuts |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
| Pieces |
2 |
4 |
7 |
11 |
16 |
22 |
29 |
37 |
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Process Problem 3
Tony's restaurant has 30 small tables to be used for a banquet.
Each table can seat only one person on each side. If the tables are pushed together to
make one long table, how many people can sit at the table?
Strategies involved
Simplify the problem
Draw a picture
Make a table
Look for a pattern
| No. of tables |
No. of people |
| 2 |
6 |
| 3 |
8 |
| 4 |
10 |
| 5 |
12 |
| 6 |
14 |
| : |
: |
| : |
: |
| 30 |
62 |
Pattern: 2 times the number of tables plus 2
===> 2 x 30 = 60 ===> 60 + 2 = 62
62 people can sit at the table.
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Process Worksheet: Solve a
Simpler Problem
1. How many squares are in this figure?
2. How many triangles are there in this figure?
3. A total of 28 handshakes were exchanged at a party. Each person
shook hands exactly once with each of the others. How many people were present at the
party?
4. Find the thickness of one page in your mathematics text book.
5. Mike is paid for writing numbers on pages of a book. Since
different pages require different numbers of digits, Mike is paid for writing each digit.
In his last book, he wrote 642 digits. How many pages were in the book?
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