Problem 1

The houses on Main Street are numbered consecutively from 1 to 150. How many

house numbers contain at least one digit 7?

Strategy A

1. Understanding the problem (read and explore)

How many numbers from 1 to 150 that contain digit 7?

Keywords: digit 7, from 1 to 150.

2. Devising a plan (planning a solution; draw a table)

To make the work easy, we could draw a table. Each of table columns should

contains number 1 to 10 until number 150.

3. Carry out the plan

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

101 102 103 104 105 106 107 108 109 110

111 112 113 114 115 116 117 118 119 120

121 122 123 124 125 126 127 128 129 130

131 132 133 134 135 136 137 138 139 140

141 142 143 144 145 146 147 148 149 150

From the above diagram, we can see that the numbers of digit 7 are 24.

4. Looking back / check your answer

As we can see, the strategy used to solve the problem gives correct answer.

This is due to the number of digit can be easily count from the diagram used in

the strategy.

Strategy B

1. Understand the problem (read and explore)

How many numbers from 1 to 150 that contain digit 7?

Keywords: digit 7, from 1 to 150.

2. Devising a plan (planning a solution; make and orderly list)

Make and orderly list the number from 1 to 150, so that we can clearly see

the quantity of digit 7 in the sequence.

3. Carry out the plan

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

101 102 103 104 105 106 107 108 109 110

111 112 113 114 115 116 117 118 119 120

121 122 123 124 125 126 127 128 129 130

131 132 133 134 135 136 137 138 139 140

141 142 143 144 1451 146 147 148 149 150

Thus, the numbers of digit 7 are 24.

4. Looking back / check your answer

The digit 7 can be clearly seen in the list and can be count from top to

below. Thus, the strategy use can be use and proven to solve the

problem.

Problem 2

The figure below shows twelve toothpicks arranged to form three squares. How can

you form five squares by moving only three toothpicks?

Strategy 1

1. Understand the problem

How can we form five squares by moving only three toothpicks?

2. Devising a plan ( planning a solution; guess and check)

Use the guess and check strategy to find the solution as it may let us get

various way to get the solution.

3. Carry out the plan

1st guess:

2nd guess:

3rd guess:

4th guess:

Thus, the 4th guess is the most accurate guess since it gives the accurate

solution.

4. Looking back/ Check your answer

As we can see, the numbers of squares are five. The fifth square is at the

outline of the biggest square. On the other hand, move the toothpicks from a

place to another place to get the most correct shape and number of square

just only by moving three toothpicks.

Strategy 2

1. Understand the problem

How can we form five squares by moving only three toothpicks?

2. Devising a plan

Draw a picture as a strategy to find the solution. Then show the

movements of the toothpicks from the starting point.

3. Carry out the plan

3

2

1

4. Look back / check your answer

As there are five squares could be seen on the above diagram (solution).

Four on the same size squares and the last square is formed by the outer

boundary of the arrangement. There was no requirement that each of the

five squares must be congruent to each of the others.

Problem 3

Pedar Soint has a special package for a large group to attend their amusement park:

a flat fee of $20 and $6 per person. If a club has $100 to spend on admission, what is

the most number of people who can attend?

Strategy 1

1. Understand the problem

In order to make sure that students are understood of the question, we may

ask the questions below:

Asking questions:

a) What are you asked to find out?

b) How many money is given to spend?

c) How much is the flat fee and the necessity of paying the fee?

d) How much is the fee per person?

Expected answers:

a) We need to find out the numbers of people that can attend

b) $100 is given to spend.

c) $20 of flat fee and it is necessary no matter how many person will enter.

d) Each person is charged $6.

2. Devise a plan

Making a table is suitable to use because table can make them clear about

the number of people that can attend the amusement park. They are only

given $100 and not allowed to over budget. A table of number of people,

cost for that number of people, flat fee, total fee and result is prepared.

3. Carry out the plan

a. A table is made.

Number of people

Cost(number of people X $6)

+ $20(flat fee)

Total fee Result

8 48 20 68 Too low

9 54 20 74 Too low

10 60 20 80 Too low

11 66 20 86 Too low

12 72 20 92 Too low

13 78 20 98 Almost $100

14 84 20 104 Higher $100

a) The cost for 8 people is $48 plus flat fee $20 is $68 which is too low.

Hence, number of people is added to 9 people. Total fee is $74 and it is

too low.

b) After that, the cost is tried for 13 people. The result get is moderate

which is $98, almost to $100. As for 14 people, result achieved is $104.

It is again too high for the $100 provided.

c) Therefore, we know that 13 people attending the amusement park are

most suitable amount with $2 balance. The answer would be 13 people

with balance $2.

4. Looking back / check your answer

To ensure the answer is correct, we are required to look backward.

How much is the number of people attended and how much is the total if it is

times with $6? How much is the total amount if added up with flat fee?

a) 13 (number of people attended) x $6 = $78

b) $78 + $20 (flat fee) = $98.

The answer is correct because it is not more than $100 and still have

balance if $2.

Conclusion: This is a very good method to solve the problem because we

can easily see the number of people that are allowed to attend and also the

total amount of money used and also the balance. The students will not get

confused because everything is clearly shown in the table. Hence, making a

table is a good method to solve this kind of problem.

Strategy B

1. Understand the problem

Firstly, ask some question to make sure that students are understand of the

question. We can ask question below:

Asking questions:

a) What are you asked to find out?

b) How many money is given to spend?

c) How much is the flat fee and the necessity of paying the fee?

d) How much is the fee per person?

Expected answers:

a) We need to find out the numbers of people that can attend

b) $100 is given to spend.

c) $20 of flat fee and it is necessary no matter how many person will enter.

d) Each person is charged $6.

2. Devising a plan

To solve this kind of problem, we can use the method of working backward. It

is quite easy because the steps can be clearly shown and easy to understand.

We can use $100 as the basic and we start to deduct from there.

3. Carry out the plan

Step 1: The money that is provided is $100. The amount that must be paid is

flat fee which is $ 20. So $100- $20= $80. $ 80 left over is used to determine

how many workers are going to the amusement park.

Step 2: $80 that is left over need to be divided by $6 as the entrance fee for

everyone is $6. The answer of division will tell us how much people will be

able to attend. $80 ÷ $6 = 13 left over $2.

Step 3: 13 people will be attending and there are $2 left over

4. Looking back / check your answer

In order to ensure the answer is correct, looking backward is very important.

$6 x 13 = $78. $78 is the entrance fee. So if $78 is added with flat fee of $20.

It will be $98. So using $100 to deduct $98, remaining will be $2. This shows

that the answer obtained is correct.

Conclusion:

This method if easy for lower primary school students because they only can

master subtraction, addition, multiplication and division. Hence, this method

can let them understand easily and also triggers their thinking skill. This

method of solving can also enhance their mathematics counting skill.

THE MOST EFFICIENT STRATEGY

After studied all the strategies in the problem solving, we found that guess and check

is the best way to solve a problem. This is because this type of strategy would make

us to use the logical thinking to solve the problem that we have. Furthermore, using

these strategies can teach me to make a smart decision. From that, I had design a

new problem to show that using this strategies is the easiest way and more efficient

to get a more logical answer.

DESIGNED PROBLEM

There are six empty boxes arranged in the triangle as showed below. Each box must

contain a number between numbers 1- 6 only. The sum of the number on each side

is 12.

Step 1: Understand the problem

Clues / Information (asking question)

There are six empty boxes

Arranged in the triangle

Each box must contain a number

Number between numbers 1- 6 only

The sum of the number on each side is 12

Step 2: Plan a strategy

First, put a number into the boxed randomly

Find the total number of each side

If the total side is lower or more than 12, change the number in the boxes

again until the total of each of the side is 12.

Step 3: Do the plan

Put a number into the boxed randomly

Find the total number of each side

6

21

45 3

6 + 1 + 5 = 12

6 + 2 + 4 = 12

5 + 3 + 4 = 12

Step 4: Check your work

Work backwards.

Check your guess by putting different number at the box.

CONCLUSION

We can conclude that there are many types of problem solving that can be

used in solving daily problem. In Problem 1 we had chosen draw a table and make

and orderly list as strategies to solve the problem. We find that these strategies are

the easiest way to solve this kind of problems. This is because, we used the data that

we can get from the question and we can make a table and a list that formed from

the solution.

We used guess and check and draw a picture to solve Problem 2. We need to

use logical thinking and some kind of imagination while using this method. We

believe most of the problem could be solve using these strategies especially guess

and check. Thus, we made the guess and check strategy as our strategy in the

Designed Problem.

In Problem 3, we had given a problem that could be solved using draw a table

and working backward. We studied that these strategies only can be used when the

problem is regarding money and counting on logic. If not, we cannot do this type of

strategy. Because of that, we think that this strategy is not suitable to use in making a

smart guess.

In conclusion, we realize that there are many types of strategies can be used

to solve a problem. It depends on us how to choose what type of method that we are

willing to use strategies in which will bring us to the solution.