1. Ayu, Syah, and Kui F uncovered a strongbox containing some gold nuggets. They gave
half of the nuggets to the orphan at Kampung Tengah and divided the remaining
nuggets evenly among themselves. Syahirah received 2,000 gold nuggets. How many
nuggets were in the strongbox?
UNDERSTANDING THE PROBLEM
- Do you know how many gold nuggets were in the strongbox? (no)
- Do you know how many gold nuggets were left after they gave to the orphan at
Kampung Tengah? (no)
- Do you know how many gold nuggets after they divided the remaining nuggets
evenly among themselves? (yes, 2000 for each person)
PLANNING A SOLUTION
- If Syahir received 2000 nuggets, the other person Ayu and Kui also will get the
same amount.
- So that, all the nuggets they have are 6000 gold nuggets.
- It means that, they have half of the gold nuggets while the other half of gold
nuggets were gave to orphan at Kampung Tengah.
- We can use the method work backwards because the question mentioned one
value that can be used to get another value.

2. FINDING THE ANSWER
Work Backwards
Start with the number of nuggets Syahir received. There are 2000 of gold nuggets.
There are 3 people who are Ayu, Syahir and Kui
So that 2000 X 3 = 6000.
Then, multiply by 2 for the half they gave to orphan at Kampung Tengah.
6000 X 2 = 12000
Therefore, there were 12000 gold nuggets in the strongbox.
LOOKING BACKWARDS
Read the problem again to be sure the question was answered.
Yes, I found the total number of gold nuggets in the strongbox.
Check the math to be sure it is correct.
x 12000 = 6000 They gave half of the nuggets to the orphan at Kampung
Tengah
Remaining of the gold nuggets
12000 – 6000 = 6000
6000 ÷ 3 = 2000 Divide the remainder among
three peoples
Then, we will know that each person will get 2000 of gold nuggets. As the mention in
the question, Syahir was received 2000 of gold nuggets.

3. Ayu, Syahir, and Kuiuncovered a strongbox containing some gold nuggets. They gave
half of the nuggets to the orphan at Kampung Tengah and divided the remaining
nuggets evenly among themselves. Syahir received 2,000 gold nuggets. How many
nuggets were in the strongbox?
UNDERSTANDING THE PROBLEM
- Do you know how many gold nuggets were in the strongbox? (no)
- Do you know how many gold nuggets were left after they gave to the orphan at
Kampung Tengah? (no)
- Do you know how many gold nuggets after they divided the remaining nuggets
evenly among themselves? (yes, 2000 for each person)
PLANNING A SOLUTION
- If Syahir received 2000 gold nuggets, the other person Ayu and Kui also will get
the same amount. So that, we can draw three people with value 2000 of gold
nuggets that they got.
- So that, all the nuggets they have are 6000 gold nuggets.
- It means that, they have half of the gold nuggets while the other half of gold
nuggets were gave to orphan at Kampung Tengah. We draw the image of
Kampung Tengah and put the value on that diagram.
- We can use the method draw diagram to increase the understanding of students
towards this problem.

4. Making a diagram
Strongbox
? I got 2,000
gold nuggets.
I got 2,000
gold nuggets.
Kui I got 2,000
Syahir Ayu
gold nuggets.
The totals of number that they got are 6,000.
Orphan
I got half of the
gold nuggets.
The totals of number that orphan got are 6,000.
Therefore, the totals of number that Kui, Syahir and Ayu got and the totals of number
that orphan got were added.
6000 + 6000 = 12000
So that, the number of gold nuggets in the strongbox is 12000.

5. LOOKING BACKWARDS
Read the problem again to be sure the question was answered.
Yes, I found the total number of gold nuggets in the strongbox.
Check the math to be sure it is correct.
x 12000 = 6000 They gave half of the nuggets to the orphan at Kampung
Tengah
Remaining of the gold nuggets
12000 – 6000 = 6000
6000 ÷ 3 = 2000 Divide the remainder among
three peoples
Then, we will know that each person will get 2000 of gold nuggets. As the mention in
the question, Syahir was received 2000 of gold nuggets.

6. JUSTIFICATION
The method work backwards is the more efficient method. It is because we can easily
find the answer and detect any mistake that have done. Besides that, we also can get
the exactly answer because the last answer was given first before we can solve the
value after that. Everyone also can understand this method. This method is easy
because we only need to inverse the symbol from the work forward.
PROBLEM EXTENSION
The three men decided to place half of the nuggets in the bank first, bury half of the
remaining nuggets, and then divide the nuggets that were left evenly among them.
Again, each man received 2,000 nuggets. How many nuggets were in the strongbox?
UNDERSTANDING THE PROBLEM
- Do you know how many gold nuggets were in the strongbox? (no)
- Do you know how many gold nuggets were left in the bank? (no)
- Do you know how many gold nuggets that they buried? (no)
- Do you know how many gold nuggets will three people get? (yes, 2000 each
person)

7. PLANNING THE SOLUTION
- If each men will get 2000 nuggets its mean that the total of number that all of
them will get 6000.
- When we do the method of work backwards, the value of half that mention in the
question will change to 2.
- We can use the method work backwards because the question mentioned one
value that can be used to get another value.
FINDING THE ANSWER
Start with the number of nuggets that each man received. There are 2000 of gold
nuggets.
There are 3 men.
So that 2000 X 3 = 6000.
Then, multiply by 2 for the half that they placed in the bank.
6000 X 2 = 12000
Then, multiply by 2 for the half that they bury.
12000 X 2 = 24000
Therefore, there were 24000 gold nuggets in the strongbox.

8. LOOKING BACKWARDS
The three men decided to place half of the nuggets in the bank first, bury half of the
remaining nuggets, and then divide the nuggets that were left evenly among them.
Again, each man received 2,000 nuggets. How many nuggets were in the strongbox?
Read the problem again to be sure the question was answered.
Yes, I found the total number of gold nuggets in the strongbox.
Check the math to be sure it is correct.
Half of the gold nuggets were placed in the bank.
x 24000 = 12000
The remainder of the gold nuggets after the half
24000 – 12000 = 12000 was placed in the bank
Half of the gold nuggets were buried.
x 12000 = 6000
The remainder of the gold nuggets after half
12000 – 6000 = 6000 was buried
Then the remainder was divided by three
6000 ÷ 3 = 2000 men.
Then, we will know that each person will get 2000 of gold nuggets. As the mention in
the question, each man was received 2000 of gold nuggets.