8
Example:
The length of three rods are 7 cm, 9 cm, and 12 cm. How can you use these rods to measure a length of 10 cm?
Solution:
a b c The diagram b shows how to get the measure of 10 cm length.
b. Making a Systematics List
A systematic or an organized list in the form of table or chart is very useful tool to represent and classify information in the problem. A list, a chart or a table can be made systematically by certain
characteristics to account possibilities and sort it. By using complete ordered lists students will be able to check for repeated answers or patterns and derive solutions. This strategy is very useful when the
problem involves a great dela of data or sequence of posiible answers.
Example
There are a number of students and a number pens. If 3 pens are given to each students, 1 pen will be left over. If one students receive 5 pens, three students will not receive any pen. How many students
and pens are there?
Solution:
No. of students 1
2 3
4 5
6 7
8 9
10 11
No. of pens based on
situation one 4
7 10
13 16
19 22
25 28
31 34
No. of pens based on
situation two -
- -
5 10
15 20
25 30
35 40
There are 8 students and 25 pens.
Example
There are some tables and chairs. Each table has four legs, while each chair has three legs. Someone looks there are 43 legs. How many tables and chairs are there?
No. tables 1
2 3
4 5
6 7
8 9
10 11
No. of table legs 4
8 12
16 20
24 28
32 36
40 -
No. of legs for chairs
39 35
31 27
23 19
15 11
7 3
- No. of chairs
13 -
- 9
- -
5 -
- 1
-
Notes: - means impossible
The possible answers are: one table and 13 chairs, 4 tables and 9 chairs, 7 tables and 5 chairs, and 10 tables and 1 chair.
7 cm 9 cm
12 cm
4 cm
7 cm 9 cm
12 cm
10 cm
7 cm 9 cm
12 cm
14 cm
9
2. Making a Calculated Guess
It is sometimes useful to make random guess when students facing a chalenging problem. Although it seldom happens, making random guess might led to a solution. Instead of making random guess, it is
better to make calculated guess. At first, initial guess may be made randomly, then followed by the next guess chosen by revising the initial guess that better satisfies the problem conditions. Sometimes,
students need to look for patterns among the data given or generated. In other cases they may make some suppositions about the problem situation.
c. Guessing and Checking
Guess and check is also known as trial and error. Students sometimes use this strategy to answer a question in a problem. Howver, trial and error is frequently unsuccessful in getting the solution. In using
this strategy, students should make guesses systematically, use table to record it, check it against information or conditions required in the problem, then refine it if it is an error. Analyzing the
unsuccessful guess can provide useful information about the problem and can help students decide how to improve further guesses.
Example
There are a number of students in a class. Each student has the same number of marbles. The total number of marbles of all students is 161. If every student has at least 2 marbles, how many students are
there? Assume that the number of students is larger than the number of marbles of each student.
Solution:
Since the last digit of 161 is 1, it is necessary to consider only the product of two numbers whose last digit is 1, 3, 7, or 9.
No. of marbles of each student
No. of students
Total number of marbles
Check: Equals 161?
Reasonable answer? 1
161 161
Yes No, doesnt satisfy the condition
11 11
121 No
11 21
231 No
3 37
111 No
3 47
141 No
3 57
171 No
13 17
191 No
7 13
91 No
7 23
161 Yes
Yes 9
9 81
No 9
19 171
No The resasonable answer is that there 23 students in the class each has 7 marbles.
d. Looking for Patterns
Observing patterns and relationships is one of the strategies frequently used for solving mathematical problems. Patterns can appear in a number sequence, figures, systematic lists or tables. The ability to
identify and recognize a pattern or a relationship among the elements in a given problem is sometimes very useful to simplify a problem-solving process and times. Students need to learn and improve their
