Percentage as a part of the whole

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Learning objectives

You will discover the notion of the percentage.

Learning effect

You write the percentage as a part of the whole.
You convert the percentages to the fractions and the fractions to the percentages.
You use English to describe the notion of the percentage.

Prepare for the lesson:

some labels/containers of the food products or cosmetics including the percentagepercentagepercentage share of these products,
20 squared cards of identical size,
the piece of paper presented below:

Table
The number of the students in the class
The number of girls in the class
The number of the boys in the class
The number of students wearing glasses

Task 1

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nagranie abstraktu

Analyse the labels/containers you have prepared and answer the following question:

What does the symbol of % written on the labels/containers mean?
What information can be recorded by using that symbol?

Notice, that:

the symbol of % means the percentagepercentagepercentage,
the percentagepercentagepercentage is used to specify the composition of the food products or cosmetics.

The word “percentagepercentagepercentage” comes from the Latin expression “pro centrum”, which is translated as „per hundred”.

Therefore the percent is the one hundredthone hundredthone hundredth of the wholewholewhole.

Today you are going to find out how to write the percentagepercentagepercentage in a form of the fractions. First, answer the following questions:

What do the expression „I will do it for the hundred percent”, “I understand it for the hundred percent” mean? What does the expression “fifty fifty” mean?

Compare your answers to the information below:

One hundred percent is the wholewholewhole, and fifty percent is the half of the certain amount.
If we mark this amount as a, we can write as following: $1 % a = \frac{1}{100} a$ what can be written as: $1 % a = \frac{1}{100} a$ .

Task 2

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nagranie abstraktu

Write the following percentages in a form of the common and decimal fractions:

Task 3

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nagranie abstraktu

Use the labels/containers you have prepared for the lesson.

a) Put the values of the percentage composition of the products on the label/container in the ascending order.

b) Convert the percentages on the labels/containers in the common and decimal fractions.

Discuss the method of converting the fractions in the percentage.

Notice, that:

We convert the fraction to the percentage by multiplying it by 100%.

Task 4

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nagranie abstraktu

Use the drawings below to complete the following task.

What part of the figure was shaded?
Write the answer in a form of the common fractioncommon fractioncommon fraction.

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Percentage of the figure

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Task 5

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nagranie abstraktu

Use the squared cards you have prepared for the lesson.

Make the memory gamememory gamememory game on your own. On one card write the percentage, on the other the relevant fraction. Repeat the activity to get 10 pairs of cards.
Mix the memory cards and put them upside down in the front of you. Start the game. Try to find all the pairs.

Task 6

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nagranie abstraktu

Think of the students of your class .Complete the table and answer the following question:

Table
The number of the students in the class
The number of present students
The number of girls in the class
The number of the boys in the class
The number of students wearing glasses

What fraction of the students are there present students? What is the percent of the students?
What fraction of the students are there the girls? What is the percent of the students?
What percentage of the students is represented by the boys?
What percentage of the students doesn’t wear glasses?
What percentage of the students is represented by the boys?

Task 7

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nagranie abstraktu

An extra task:

Conduct a survey among your 20 friends on any topic you like. The results of the survey present in the table using the percentages.

Remember:

One percent of the certain amount is the one hundredthone hundredthone hundredth of it, what is written as the following: $1 % a = \frac{1}{100} a$ .
Converting the percent in the fraction we divide the fraction by 100%.
Converting the fraction in the percentage we multiply the fraction by 100%.

Exercises

Exercise 1

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Determine which sentences are true.

0,2 of certain amount is more than 21% of this amount.
35% of certain weight is more than 0,34 of this weight.
40% of certain sum is less than $\frac{3}{5}$ of this sum.
$\frac{1}{4}$ of certain weight to 25% of this weight.
60% of certain volume is more than 0,6 of this volume.

zadanie

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Exercise 2

The pie chart presents the percentage share of the continents in the total area of the land.

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Rysunek przedstawia wykres procentowego udziału poszczególnych kontynentów w całkowitej powierzchni lądów na Ziemi: 21 procent Africa, znak zapytania Europe, 13 procent South America, 17 procent North America, 32 procent Asia, 9 procent Antarctica. Nad wykresem napis: The area of the continents. — The area of the continents
Source: GroMar, licencja: CC BY 3.0.

Answer the following questions depending on the chart:

Which continent has the largest area?
What percentage of the total area of the land is the area of Europe?
Which continents are smaller than North America?
Are the area of both Americas larger than the area of Asia?
Is the area of Asia more than 1/3 of total area of land?

Exercise 3

The drawing below presents the containers filled with water.

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Rysunek przedstawia pojemniki częściowo wypełnione wodą. W pojemniku A wypełniono 3 części z 5. W pojemniku B wypełniono 3 części z 4. W pojemniku C wypełniono 7 części z 10. — Source: GroMar, licencja: CC BY 3.0.

a) Use the common fraction to write what part of these containers was filled with water.

b) Use the percentages to write what part of these containers was filled with water.

c) Describe the method of converting the common fraction to the percentage in English.

Container A: $\frac{3}{5} = 60 %$

Container B: $\frac{3}{4} = 75 %$

Container C: $\frac{7}{10} = 70 %$

Exercise 4

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Indicate which pairs of expressions or words are translated correctly.

procent - percentage
ułamek zwykły - common fraction
ułamek dziesiętny - decimal fraction
jedna setna - one hundredth
całość - conversion
zamiana - division

zadanie

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Match Polish terms with their English equivalents.

decimal fraction
one hundredth
percentage
jedna setna
ułamek dziesiętny
całość
common fraction
whole
ułamek zwykły
procent

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Glossary

common fraction

ułamek właściwy

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wymowa w języku angielskim: common fraction

conversion

zamiana

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wymowa w języku angielskim: conversion

decimal fraction

ułamek dziesiętny

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wymowa w języku angielskim: decimal fraction

division

dzielenie

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wymowa w języku angielskim: division

memory game

gra memory

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wymowa w języku angielskim: memory game

multiplication

mnożenie

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wymowa w języku angielskim: multiplication

one hundredth

jedna setna

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wymowa w języku angielskim: one hundredth

percentage

procent

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wymowa w języku angielskim: percentage

what is the part of

jaką część stanowi

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wymowa w języku angielskim: what is the part of

whole

całość

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wymowa w języku angielskim: whole

Keywords

common fractioncommon fractioncommon fraction

decimal fractiondecimal fractiondecimal fraction

one hundredthone hundredthone hundredth

percentagepercentagepercentage

wholewholewhole

Scenariusz

Exercises

Glossary

Keywords