Topicm436a2883b511bb10_1528449000663_0Topic

Percentages

Levelm436a2883b511bb10_1528449084556_0Level

Third

Core curriculumm436a2883b511bb10_1528449076687_0Core curriculum

I. Real numbers. The student:

1) performs operations (addition, subtraction, multiplication, division, exponentiation, square roots, logarithms) in a set of real numbers.

Timingm436a2883b511bb10_1528449068082_0Timing

45 minutes

General objectivem436a2883b511bb10_1528449523725_0General objective

Performing calculations on real numbers, also using a calculator, applying the laws of mathematical operations in transforming algebraic expressions and using these skills to solve problems in real and theoretical contexts.

Specific objectivesm436a2883b511bb10_1528449552113_0Specific objectives

1. Communicating in English, developing mathematics skills, scientific, technical and IT competences; developing learning skills.

2. Developing accounting efficiency in the scope of performing percentagepercentagepercentage calculations.

3. Consolidation and systematization of knowledge of percentages.

Learning outcomesm436a2883b511bb10_1528450430307_0Learning outcomes

The student:

- performs operations with percentages,

- calculates the percentages in simple situations related to interest rates on cash deposits.

Methodsm436a2883b511bb10_1528449534267_0Methods

1. Case study.

2. Competition.

Forms of workm436a2883b511bb10_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm436a2883b511bb10_1528450127855_0Introduction

Students review their knowledge of operations on percentages. The mini‑task contest will help them to do it.

The calculations in Task 1 should be performed as soon as possible. The winner of the competition will be awarded with a very good grade.

Task
Calculate.

1. 124% of the number 45.

2. 33$\frac{1}{3}$% of the number 333.

3. Calculate the number of which 2,5% is equal to 130.

4. Calculate the number that 360% is equal to 45.

5. Calculate what percentagepercentagepercentage of the number x is the number y, if:
a) x = 1320, y = 330,
b) x = 64$\frac{3}{4}$, y = 4$\frac{5}{8}$.

6. The number x is 66$\frac{2}{3}$% of the number y. What percentage of the number x is the number y?

7. The number x is 125% of the number y. What percentage of the number x is the number y?

The teacher summarizes the results of the competition, explains the doubts.

Procedurem436a2883b511bb10_1528446435040_0Procedure

The teacher informs students that during the lesson they will solve various word problems related to the calculations of percentages.

Students work in three‑person teams. Using computers, they will get acquainted with the animation showing the interest rateinterest rateinterest rate on cash deposits with the use of compound interest.

Task
Open the Geogebra applet.

[Geogebra applet]

Definition

- Compound interestcompound interest- Compound interest - the interest rate on the cash contribution in which interests for a given interest period are added to the contribution (they are subject to capitalization).

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest:m436a2883b511bb10_1527752263647_0Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest:

where:
K - value of the final capital,
KIndeks dolny 0₀ - value of the cash contribution,
n - number of saving years,
m - number of capitalization periods during the year,
r - annual interest rateinterest rateinterest rate (written in decimal form).

Students learn the formula for compound interestcompound interestcompound interest and do the following task based on it.

Task
Michał deposited 5000 złoty into the bank for an interest‑bearing deposit of 5% on an annual basis. Calculate how much money will Michał have after 2 years.
Consider two cases: capitalization of interest on a quarterly basis and capitalization of interest once a year. Which way is better for Michał?

An extra task:
A. The interest rateinterest rateinterest rate on the bank deposit was 3,5% and increased by 2 percentagepercentagepercentage points. How much has the interest rate increased?

B. After the product price has been reduced twice, each time by the same percentage, its final price is 81% of the initial price. By what percentage was the price of the goods reduced every time?

C. The price of a certain item was increased by 15% and then decreased by 15%. What percentage of the initial price was the final price?

Lesson summarym436a2883b511bb10_1528450119332_0Lesson summary

Students do the revision exercises.

Then they summarize the lesson together and formulate conclusions to remember,

- Percentage - this is one hundredth part of the whole.
- Percentage point - unit of difference between the values of one size and the second size, given in percent.
- Compound interest - is the interest rate on a cash contribution in which interest for a given interest period is added to the contribution (subject to capitalization).m436a2883b511bb10_1527752256679_0- Percentage - this is one hundredth part of the whole.
- Percentage point - unit of difference between the values of one size and the second size, given in percent.
- Compound interest - is the interest rate on a cash contribution in which interest for a given interest period is added to the contribution (subject to capitalization).

Selected words and expressions used in the lesson plan

compound interestcompound interestcompound interest

diagramdiagramdiagram

interest rateinterest rateinterest rate

percentagepercentagepercentage

percentage concentrationpercentage concentrationpercentage concentration

percentage pointspercentage pointspercentage points