Equations (Ekvationer)

Ämne / Topic

Solving linear equations (equations only involving numbers and x terms - no x², x³, etc.)

Inlärningsmål / Learning Goals

Be able to solve linear equations with variable on one or both sides.

Google Slides & Videos

Copy of 2.3 Equations

Lektionssteg / Steps in the lesson:

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

Warm-up - Learner based activity

Material: Equation and answer cards

Players: 2 - 3 players

Instructions:

1. Place a cross on the back of all the equation cards.

2. Place all cards face down.

3. Player 1 starts by turning over an equation card and solving the equation.

4. Player 1 then selects an answer card and turns it over.

5. If the answer card matches the players answer, the player keeps both the equation and answer cards and goes again.

6. If the players answer does not match the answer card selected, both the equation and answer cards are placed back, face down.

7. Player 2 then goes.

8. The game continues until all pairs are found.

9. The player with the most pairs wins.

2. Introduktion till lektionen / Introduction to the lesson content

The main part of the lesson, will start with the learners watching a video on simplifying expressions (see attached).

While the video is playing, the teacher will stop it at various points and ask learners questions on what was said, to gauge their understanding and keep them active in the lesson.

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)

2a + 3 = 11

Method 1: (stabiliser method)

2a + 3 = 11

-3 2a + 3 = 11 -3 1. Cancel out constants

/2 2a = 8 /2 2. Cancel out coefficients

a = 4

Method 2: (moving method)

2a + 3 = 11

2a = 11 - 3 1. Move the +3 across the equal sign

2a /2 = 8/2 2. Divide both sides by the coefficient

a = 4

Example 2: (Teacher/learner interactive example)

2a + 5 = a + 9

How do you think we should solve this equation?

2a + 5 = a + 9 Move terms with the variable to one side

Move constants to the other side

Method 1: Stabiliser method

-5 2a + 5 = a + 9 -5 1. Cancel out constant on the one side

-a 2a = a + 4 -a 2. Cancel out variable on the one side

a = 4

Method 2: Moving method

2a + 5 = a + 9

2a = a + 9 - 5 1. Move the +5 across the equal sign

2a - a = 4 2. Move the variable across equal sign

a = 4

Example 3: Involving brackets

3(x - 2) = 2(x - 4)

Method 1: Stabiliser method

3(x - 2) = 2(x - 4) 1. Remove the parentheses by multiplying 3x - 6 = 2x - 8

3x - 6 = 2x - 8

+6 3x - 6 = 2x - 8 +6 2. Cancel out constant on one side

-2x 3x = 2x - 2 -2x 3. Cancel out variable on the one side

x = -2

Method 2: Moving method

3(x - 2) = 2(x - 4) 1. Remove the parentheses by multiplying 3x - 6 = 2x - 8

3x - 6 = 2x - 8

3x = 2x - 8 + 6 2. Move -6 across the equal sign

3x - 2x = -2 3. Move the variable across the equal sign

x = -2

Example 4: Word problem

Mary is 5 years older than Jack. Twice Mary's age plus 3 times Jack's age is 125.

Write an equation to represent this information and solve the equation to find Mary's age.

Jack: x

Mary: x + 5

Expression: 2(x + 5) + 3(x) = 125

Method 1: Stabiliser method

2(x + 5) + 3(x) = 125

2x + 10 + 3x = 125 1. Remove the parentheses by multiplying

5x + 10 = 125 2. Add like terms

-10 5x + 10 = 125 -10 3. Cancel out constants on one side

/5 5x = 115 /5 4. Cancel out coefficients

x = 23

So, Jack is 23 years old, so Mary is 28 years old

Method 2: Moving method

2(x + 5) + 3(x) = 125

2x + 10 + 3x = 125 1. Remove the parentheses by multiplying

5x + 10 = 125 2. Add like terms

5x = 125 - 10 3. Move +10 across equal sign

5x / 5 = 115 / 5 4. Divide both sides by the coefficient

x = 23

So, Jack is 23 years old, so Mary is 28 years old

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. 4(x - 2) = 8

2. 2(s - 1) + 3(s - 3) + s = 1

3. The current price of an apple is x cents. The price of an apple increases by 4 cents and Alan goes to the shop and buys 4 apples plus a magazine costing 2 euro. His total bill came to 4.44 euro