Percent and equations (Procent och ekvationer)

Ämne / Topic

Solving equations involving percent

Inlärningsmål / Learning Goals

Be able to calculate the percent of a number

Be able to solve equations involving percent

Be able to connect real-world problems to equations

Google Slides & Videos

Lektionssteg / Steps in the lesson:

1. Lektionsuppvärmning / Lesson warm up / Hook / Review from previous lesson

Warm-up problems

1. Solve for x:

a. 5x + 2 = 3x + 10 b. 27 - (12 - 2x) = 96 - x

2. A square has a 6 cm longer perimeter than an equilateral triangle. The triangles sides ar 1 cm longer than the square. Calculate the area of the square.

3. How do we solve the equation 40/2x = 40?

2. Introduktion till lektionen / Introduction to the lesson content

The main activity of the lesson will start off with the learners watching a video on where algebra can be used in real world situations - this will help the learners see the relevance of algebra. After watching the video, the learners will work with a partner and come up with a real world algebraic question, relative to their lives as teenagers.

3. Aktiviteter / Key Activities

After the introduction (watching the video and coming up with own questions) is complete, the teacher will continue the lesson, by going through different examples based on the equations.

Example 1: (Teacher led example)

In a school vote, 91 students voted that they liked football. This corresponded to 28% of all students who voted.

How many students voted altogether?

Make your unknown x

Cross Multiplication Method:

28 = 91 (number of students who voted)

100 x (total number of students in the school)

28 = 91

100 x (Multiply 28 and x = 28x)

28 = 91 (Multiply 91 and 100 = 9100)

100 x

28x = 9100 (Divide both sides by 28)

28 28

x = 325

So, 325 students took part in the school vote

Example 2: (Learners work together with Teacher)

The population in a municipality decreased by 3% this year to 46 075 people.

What was the size of the population?

Make the population last year equal x

Cross Multiplication Method:

100 - 3 = 46 075 (population in the town now)

100 x (old population)

97 = 46 075 (multiply 97 and x = 97x)

100 x

97 = 46 075

100 x (multiply 46 075 and 100)

97x = 4 607 500 (divide both sides by 97)

97 97

x = 47 500

So, the population decreased from 47 500

Example 3: (Learners do on their own)

In a survey, 9072 people replied that they think it would be good if a skyscraper is built in Stockholm.

a. Suppose there were x people who were asked. Draw an expression for 84% of x people?

0.84 . x

b. Draw an equation and calculate how many people were asked.

84 = 9072

100 x

84x = 9072 x 100

84x = 907 200

84x = 907 200

84 84

x = 10 800

So, 10 800 people were asked to do the survey.

4. Kolla vad eleverna kan / Check for understanding / Exit ticket

Learner will complete three questions on the white boards that have been provided with. After a couple of minutes to complete the question, the teacher will say 'times up' and learners will need to hold up their boards with their answers.

1. Solve the equation: x + 0,25x = 15

2. The price of a book was reduced by 35%. The reduction was equivalent to SEK 63.

a. Draw an equation and calculate the original price of the book.

b. What is the new price of the book?

5. Stängning / Closure / Summary of lesson

Learners sharing and explaining their answers with the rest of the class.

Resurser & Materiel / Resources & Materials

http://webbapp.liber.se/matematikboken-z/#

http://webbapp.liber.se/matematikboken-z/#/2-algebra

Textbook Practice:

ETT pg. 83 no. 2086 abc, 2087 ab

TVÅ pg. 84 no. 2094 ab, 2095

TRE pg. 85 no. 2097, 2098, 2099, 2100, 2101

FYRA pg. 86 no. 2103, 2104, 2105, 2106,2107