Topicma11d07afef1cbcf6_1528449000663_0Topic

Percentage calculations

Levelma11d07afef1cbcf6_1528449084556_0Level

Second

Core curriculumma11d07afef1cbcf6_1528449076687_0Core curriculum

V. Percentage calculations. The student:

1) shows the part of the volume as a percentage of this size;

2) calculates the number a equal to p percent of the given number b;

3) calculates what percentage of a given number of b is the number a;

4) calculates the number b, of which p percentage is equal to a;

5) uses percentage calculations to solve problems in a practical context, also in cases of repeated increases or decreases in a given size.

Timingma11d07afef1cbcf6_1528449068082_0Timing

45 minutes

General objectivema11d07afef1cbcf6_1528449523725_0General objective

Doing simple calculations mentally or using the long method in more difficult examples, using these abilities in practical situations.

Specific objectivesma11d07afef1cbcf6_1528449552113_0Specific objectives

1. Doing percentage calculations.

2. Applying calculating percentage calculations to d text exercises.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesma11d07afef1cbcf6_1528450430307_0Learning outcomes

The student:

- does percentage calculations,

- applies calculating percentage calculations to do text exercises.

Methodsma11d07afef1cbcf6_1528449534267_0Methods

1. Situation analysis.

2. Educational game.

Forms of workma11d07afef1cbcf6_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionma11d07afef1cbcf6_1528450127855_0Introduction

Students discuss in pairs ways of doing tasks with percents.

Procedurema11d07afef1cbcf6_1528446435040_0Procedure

The teacher divides students into groups. The task of each one of them is to prepare a poster with sentences that start with phrases.

- To calculate p% of the given numberp% of the given numberp% of the given number a, we need to…

- To calculate a number based on its percentpercentpercent, we need to…

- To calculate what percentpercentpercent of the given number b is number a, we need to…

Groups present their posters. Students write down conclusions.

Conclusions:

- To calculate p% of the given a number, we need to convert this percent into fraction and multiply it by the number a.
- To calculate number a based on its percent, we need to convert percent into fraction and divide the given number a by this fraction.
- To calculate what fraction of the given number b is number a, we need to calculate what fraction of number b is number a first. Then, we need to convert obtained fraction into percent.ma11d07afef1cbcf6_1527752263647_0- To calculate p% of the given a number, we need to convert this percent into fraction and multiply it by the number a.
- To calculate number a based on its percent, we need to convert percent into fraction and divide the given number a by this fraction.
- To calculate what fraction of the given number b is number a, we need to calculate what fraction of number b is number a first. Then, we need to convert obtained fraction into percent.

Task

Students work individually, using computers. Their task is to see the interactive illustration, that explains the idea of percent points.

In elections for the president of the fishing club there were two candidates. 100 people voted and results are presented in posters.

Analyse information presented in the illustration. Write down conclusions.

[Interactive illustration]

Conclusion:

- Percent points is a unit of difference between two values of one quantity expressed in percents.ma11d07afef1cbcf6_1527752256679_0- Percent points is a unit of difference between two values of one quantity expressed in percents.

Students work in groups and do exercises, using any of the methods they know.

Task

Write solutions of exercises and answers to them. The number obtain as a result indicates number of the next task to do.

[Table]

The teacher evaluates the students’ work and clarifies doubts.

An extra task:
There is a certain two‑digit number in which the digit of tens is $33\frac{1}{3}\%$ smaller than the digit of ones. What is this number?

Lesson summaryma11d07afef1cbcf6_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

- To calculate $p$% of the given $a$ number, we need to convert this percentpercentpercent into fractionfractionfraction and multiply it by the number $a$.
$p$% of number $a$ is $\frac{P}{100}\cdot a$.

- To calculate number $a$ based on its percentpercentpercent, we need to convert percent into fractionfractionfraction and divide the given number $a$ by this fraction.

- To calculate what fractionfractionfraction of the given number $b$ is number $a$, we need to calculate what fraction of number $b$ is number $a$ first. Then, we need to convert obtained fractionfractionfraction into percentpercentpercent.

- PercentpercentPercent points is a unit of difference between two values of one quantity expressed in percents.

Selected words and expressions used in the lesson plan

converting fraction into percentconverting fraction into percentconverting fraction into percent

final pricefinal pricefinal price

fractionfractionfraction

given percent of numbergiven percent of numbergiven percent of number

initial priceInitial priceinitial price

p% of the given numberp% of the given numberp% of the given number

percentpercentpercent

percent pointpercent pointpercent point