GROUP MEMBERS:

-THAEWENDRAN A/L MARNOKARAN-GUGANESWAREE A/P GOVINDAH-LAAVANYAH A/P SUPRUMANIAM

BASIC MATHEMATICS

PROBLEM SOLVING

PROBLEM 6

Sixteen toothpicks are arranged as shown. Remove four toothpicks so that only four congruent triangles remain.

Figure 6.1

Problem Solving Strategy 1: Build a model•Understand the problem: Asking questions: What am I asked to do?

How many toothpicks can be removed?Answering question: I am asked to form four -congruent triangles. I can only move four toothpicks.

•Congruent triangles are triangles that have the same size and shape. Hence, the corresponding sides and the corresponding angles are equal.

•Device a plan:To solve my problem, I choose the strategy “build a model”. As the question is mentioned on concrete matter, I can build it up. Besides that, I can take a clearer look by using this method.•Carry out the plan:I choose pens because it is easier to see. Thus, I carry on my solution.

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.1 shows the diagram from the question. Then, Figure 6.2 shows that four pencils are removed from the sixteen pencils. After the pencils in the dotted line are removed, there are left exactly four congruent triangles. The final solution is shown in Figure 6.3 successfully. •Look back:Read the questions again to confirm what it asks. Is there only four toothpicks are removed? Are there four congruent triangles formed? Thus, my method solving is correct. Build a model enables me to solve my question.

Problem Solving Strategy 2: Guess and check•Understand the problem: Asking questions: What am I asked to do?

How many toothpicks that can be removed?Answering question: I am asked to form four congruent triangles.

I can only move four toothpicks

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.•Device a plan:In order for to solve my problem, I choose the method of “guess and check”. It is one of the most powerful methods of solving different situations, which are involving an unknown function and its derivatives. Guessing often produces the wrong answer but guess and check often produces right answer.

•Carry out the plan:At first, draw it out exactly to Figure 6.1

Figure 6.1

Figure 6.4 (First guess and check)

Figure 6.4 shows the first guess and check. However, my answer is wrong because it does not form four congruent triangles.

Figure 6.5 (Second guess and check)

Figure 6.5 shows my second guess and check. I remove four toothpicks but it does not form four congruent triangle as well.

Figure 6.6 (Third guess and check)

.

•Look back:Read the questions again to confirm what it asks. Is there only four toothpicks are removed? Are there four congruent triangles formed? Thus, my method solving is correct. Guess and check enables me to solve my question.

Figure 6.6 shows my third answer. It does form four congruent triangles after removing four toothpicks

PROBLEM 7

•

Suppose that you buy a rare stamp for $15, sell it for $20, buy it back for $25 and finally sell it for $30. How much money did you make or lose in buying and selling this stamp?

•Understand the problem : Asking questions : What am I asked to do? : How much money can make or lose in buying and selling the stamp? Answer question : I am asked to find the money which can make or lose in

buying and selling the stamp. : I have to buy a rare of stamp for $15, and sell it for $20,

buy it back for $25, and finally sell it for $30.

Make is the profit we gain from the selling and buying the stamp while lose is which we cannot make the profit from the selling and buying the stamp.

•Device a plan : In order to solve my problem, I choose the method of “ act it out ”. As the question is about selling and buying the stamp which are make profit or lose. It is one of the most powerful methods to solve with easily and faster. I can solve this problem by act it out as stamp seller , stamp buyer , artificial money and stamp. Besides this, using this method can make myself to count and decide about the profit and lose with clearly and easily.

Problem Solving Strategy 1 : Act Out / Simulation

At first, I choose a person as a stamp buyer and another person as stamp seller. In addition, the artificial coins and stamp used by the buyer and seller to this process, that is selling and buying the stamp. I choose this characters and object because it is more easier and simple to solve this problem . Thus, I carry on my solution : Firstly, the buyer rare of a stamp for $15.

$ 10$ 10 $ 5 $ 5 $ 20 - $ 15 = $ 5 ( profit )

+

Secondly, buyer sell it to $20.

$ 10$ 10 $ 5 $ 5 $ 5 $ 5+ +

Then, the buyer buy the stamp back for $25. 

$ 20 - $ 25 = $ 5 ( lose )

$ 5 $ 5+

Lastly, buyer  sell it again for $30. 

$ 10$ 10 $ 5 $ 5 $ 5 $ 5

$ 5 $ 5 $ 5 $ 5 $ 5 $ 5

+ +

+ ++

$30 - $25= $ 5 ( profit)

Explanation for this process :

First the stamp bought for $15. For make profit, the buyer sold the stamp for $20. The buyer gain is $5. After that, buyer bought again the stamp for $25. Its make lose for the buyer $5. Because of this, there is no any profit or lose to the buyer , that is $0. Finally, the stamp was sold again by buyer for $30. Its make money for buyer to make profit again is $5. Thus, from selling and buying the stamp twice, a profit is can made by the buyer that is $5. The final solution is shown is successfully.

•Look back : Read the questions again to confirm what its asks. Is the rare of stamp for $15, and sell it for $20, buy it back for $25, and finally sell it for $30? Is the solution make money profit or lose to the buyer in buying and selling the stamp? Thus, my method solving is correct. Act it out / simulation strategy enables me to solve this question.

Problem Solving Strategy 2 : Analogy

•Understand the problem : Asking questions : What am I asked to do? : How much money can make or lose in buying and

selling the stamp? Answer question : I am asked to find the money which can make or

lose in buying and selling the stamp. : I have to buy a rare of stamp for $15, and sell it for $20,

buy it back for $25, and finally sell it for $30.

Make is the profit we gain from the selling and buying the stamp while lose is which we cannot make the profit from the selling and buying the stamp.

•Device a plan :

In order to solve my problem, I choose the method of “ analogy ”. As the question is about selling and buying the stamp to find the profit or gain, I use artificial coins and stamp . Besides that, using this method can make myself to count and decide about the profit and lose which clearly and easily. •Artificial coins •$10 – 3 coins•$ 5 – 4 coins•A stamp

$ 20 - $ 25

 = $ 5  ( lose )

•Carry out the plan

At first, I use artificial coins and stamp to this process of the selling and buying the stamp. I choose this object because it is easier to solve this problem with easily. Thus, I carry on my solution :

$ 10$ 10 $ 5 $ 5

Firstly, buy a rare of stamp for $15

$ 20 - $ 15= $ 5 ( profit )

Secondly, sell it to $20.

+

$ 10$ 10 $ 5 $ 5 $ 5 $ 5

Then, the stamp buy back for $25. 

$ 10$ 10 $ 5 $ 5 $ 5 $ 5 $ 5 $ 5

                              

++

++

+

$30 - $25= $ 5 ( profit )

$ 10$ 10 $ 5 $ 5 $ 5 $ 5

$ 5 $ 5 $ 5 $ 5 $ 5 $ 5

Lastly, buyer sell it again for $30.

+ +

++

Explanation for this process :

First the stamp bought for $15. For make profit, the buyer sold the stamp for $20. The buyer gain is $5. After that, buyer bought again the stamp for $25. Its make lose for the buyer $5. Because of this, there is no any profit or lose to the buyer , that is $0. Finally, the stamp was sold again by buyer for $30. Its make money for buyer to make profit again is $5. Thus, from selling and buying the stamp twice, a profit is can made by the buyer that is $5. The final solution is shown is successfully.

Look back :

Read the questions again to confirm what its asks. Is the rare of stamp for $15, and sell it for $20, buy it back for $25, and finally sell it for $30? Is the solution make money profit or lose to the buyer in buying and selling the stamp?Thus, my method solving is correct. Act it out / simulation strategy enables me to solve this question.

PROBLEM 10

Three apples and two pears cost 78cents.But two apples and three pears cost 82 cents .What is the total cost of one apple and one pear?

METHOD 1 (SIMULTANEOUS EQUATION)

3a+2p=78…………(1)2a+3p=82……………(2)

(1)× (2)    (2)× (3)

6a+4p=156………….(3)6a+9p=246 …………(4)

(4) – (3)5p=90P=18

 

Sub P=18 into (1)

3a+2(18)=78     3a+36=42            3a=42              a=14

a= 14cents          p=18cents

METHOD 2 (MATRICS)

    3 22  3

9P

= 7882

9P

=3 22  3

-1

7882

3 22  3 = 1

9-43 -2-2  3

=    15

3 -2-2  3

 3/5    -2/5-2/5     3/5=

 3/5    -2/5-2/5    3/5

= 7882

=3/5  (78)  -2/5(82)-2/5(78)  +3/5(82)

= 1418

THANK YOU