Control on proportionality in maths fifth (5ème).

There are different types of proportionality in mathematics, but I will focus on direct proportionality, which is often taught in the fifth grade.

In general, one quantity is said to be proportional to another if when the first quantity is multiplied by a number, the second quantity is multiplied by the same number. It can be written mathematically as follows:

Si x est proportionnel à y, alors il existe une constante k telle que y = kx

For example, if we know that the time it takes to travel a distance is proportional to the speed at which we are moving, then we can write :

Si x est le temps qu'il faut pour parcourir une distance, et y est la vitesse à laquelle on se déplace, alors y = kx

The constant k is called the coefficient of proportionality and indicates how the two quantities are related. In the previous case, the proportionality coefficient indicates how long it takes to travel a unit distance at a given speed.

It is important to note that for direct proportionality to exist between two quantities, it is necessary and sufficient that the proportionality coefficient is constant. This means that if you know the proportionality coefficient for two values of x and y, you can determine the proportionality coefficient for all other values of x and y.

Here are some examples of situations where direct proportionality occurs:

The price of a good is proportional to its quantity. If you buy twice as much property, you will pay twice as much.
The area of a square is proportional to the length of its side. If you double the length of one side, the area will be multiplied by four.
The volume of a ball is proportional to the cube of its radius. If you double the radius of a ball, its volume will be multiplied by eight.

In general, direct proportionality is an important concept in mathematics and science because it allows us to understand how quantities are related and how they vary in relation to each other. This can be useful for solving concrete problems using simple mathematical formulas.

A math test on proportionality in fifth grade.

PROCTORED ASSIGNMENT

Exercise 1: (3 pts)

By specifying the steps of calculation, classify these numbers in ascending order.

$\frac{13}{12};\frac{7}{6};1;\frac{1}{2};\frac{2}{3};,\frac{7}{8};\frac{5}{4}$ .

Exercise 2: (4 pts)

1) By writing your calculations, tell if the following tables are proportionality tables:

4,5	0,75	5
7,2	1,2	8

5	9,5	8,4
4	7,6	6,3

2) After calculating the proportionality coefficient for each table, fill in the blanks (write a calculation for each box to be filled in):

25,5	17
30,6		13,8

7,4	8
	2,8	0,91

Exercise 3: (2 pts)

1) By writing the calculations, convert the following times into minutes:

a. 4 h 52 min b. 2 days 10 h 25 min

Exercise 4: (6 pts)

8 meters of cable weighs 12.8 kg.

With the help of a proportionality table, and by writing the calculations, answer the following questions:

1. What would be the weight of 21 meters of cable?

2. What length of cable would weigh 4 kg?

3. By writing the calculations, convert the following times into hours (decimal writing):

3h 48 min 39 min

4. By writing the calculations, convert the following times into hours and minutes:

1.2 hrs 3.35 hrs

Exercise 5: (5 pts)

If the results are not correct, round them to two decimal places.

15L of diesel costs 14,10€.

1. How much would it cost to fill up with 48 L ?

2. With 30€, how many liters can we buy ?

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Control on proportionality in maths (5th grade)

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