Here is learning trajectory of proportion for students grade six.
Activity I
Realistic examples of proportion :
One day there are many ‘pempek’ which will be given to 12 students at class. Each student get 3 ‘pempek’. The 12 students are divided into three groups consisting of respectively 2, 3, and 4 students. How many ‘pempek’ each group will get?
Possible answer:
Since every student gets 3 pempek,
2 students in group I get 6 pempek
3 students in group II get 9 pempek
4 studetns in group III get 12 pempek
Teacher gives problems, students list possible proportion:
Rice is priced Rp 6.000,- per kilo. Find various quantitiy of rice and how much each of which will cost?
The possible answer by students is:
1 kg – Rp 6.000,-
2 kg – Rp 12.000,-
3 kg – Rp 18.000,-
500 g – Rp 3.000,-
250 g – Rp 1.500,-
100 g – Rp 600,-
The conclusion of the first activity is:
- The core insights used here are unitizing and iterating.
- The goal of this activity is to introduce unitizing and iterating method.
- We expect throug this activity is the students’ math thinking are able to use unitizing and iterating method to list possible proportion of two units.
Activity II
Introducing ratio table :
After the students listed various quantity of rice and its each price, then the teacher asks the students to mention their answers and then she writes down it in ratio table. Undirectly the teacher gives stimulation to the students and some of the students think that such table written by the teacher is good and later on, they try to use ratio table in next exercise.
The weight of rice (kg) | 1 | 2 | 3 | 0,5 | 0,25 | 0,1 |
Cost (Rp) | 6.000 | 12.000 | 18.000 | 3.000 | 1.500 | 600 |
Solving problems using ratio table :
After most students become more familiar with ratio table, the teacher gives task to the students in this following questions:
- the cost of 400 gram sugar is Rp 5000,- , how much is the cost of 300 gram sugar?
the possible answer of students
Weight (gram) | 400 | 100 | 300 |
Price (Rp) | 5.000 | 1.250 | 3.750 |
- Andi and Budi has thrown ball to basket for several time and resulted the score in the following table :
Name | The number of throwing | Ball that scored |
Andi | 12 | 7 |
Budi | 9 | 6 |
Which one of them is the better shooter in throwing the ball?
The conclusion of the second activity is:
- The core insight used in this activity is ratio table
- The goal of this activity is introducing ratio table concept
- We expect through this activity that the students’ math thinking are able to find their own ratio table and solve proportion problem by using it.
Activity III:
Introducing Unit Method :
Weight (gram) | 400 | 100 | 300 |
Price (Rp) | 5.000 | 1.250 | 3.750 |
By looking at the previous answer using ratio table, regarding to the improved understanding of the studetns, the teacher come to introduce unit method by giving students several exercises resembling the problem of sugar above. However, the quantitiy of two units is simpler such as integer between 1 and 20. The work gradually doesn’t use ratio table anymore like shown in this following method:
4 – 20
1 – 5
3 – 15
Solving problems related to proportion
The teacher gives task in the following problem
we have two kind of rectangle. The first rectangle consist of 7 cm in length and 3 cm in height. if the height of the second rectangle is 5 cm, how about the length of the second rectangle?
The conclusion of the third activity is:
- The core insight used in this activity is unit method.
- The goal of this activity is to introduce more formal method to use proportion problem namely unit method.
- We expect that this activity leads students to use their own way in solving some proportion problems by their own method and finally have good understanding about proportion.
Fajar, Septy, and Rully
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