Algebraic substitution

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

Good morning!

Schedule: 

• Learning goals 
• Revision
• Starter + algebraic substitution
• Car rental problem
• Math Puzzle

Learning goals 

At the end of this lesson I can:

• Evaluate a mathematical expression by substituting a value for a variable
• Collaborate to solve a puzzle

1. −x​2​​+9−17xy
2. 9
3. −x​2​​+xy+9
4. none of these answers

Sort like terms together: 

3x2 - 4x2 - 8xy + 9xy + 9 = 

-1x2 + 1xy + 9 = 

-x2 + xy + 9 

If x = 5 and y = 6, find the value of

2x−​y​​12​​

Given f = 2, g = -1 and h = -4, evaluate:

h​2​​−fg

Starters

Question 1

If x = 5 and y = 6, find the value of 

2x−​y​​12​​

2x−​y​​12​​=2⋅5−​6​​12​​

Starters

Question 1

If x = 5 and y = 6, find the value of 

2x−​y​​12​​

2x−​y​​12​​=2⋅5−​6​​12​​

=10−2

Starters

Question 1

If x = 5 and y = 6, find the value of 

2x−​y​​12​​

2x−​y​​12​​=2⋅5−​6​​12​​

=10−2

=8

Starters

Question 2

Given f = 2, g = -1 and h = -4, evaluate: 

h​2​​−fg=(−4)​2​​−2⋅(−1)

h​2​​−fg

To avoid confusion with signs, write negative substitutions in brackets!

Starters

Question 2

Given f = 2, g = -1 and h = -4, evaluate: 

h​2​​−fg=(−4)​2​​−2⋅(−1)

=16−2⋅(−1)

h​2​​−fg

To avoid confusion with signs, write negative substitutions in brackets!

Starters

Question 2

Given f = 2, g = -1 and h = -4, evaluate: 

h​2​​−fg=(−4)​2​​−2⋅(−1)

=16−2⋅(−1)

=16+2

h​2​​−fg

To avoid confusion with signs, write negative substitutions in brackets!

Starters

Question 2

Given f = 2, g = -1 and h = -4, evaluate: 

h​2​​−fg=(−4)​2​​−2⋅(−1)

=16−2⋅(−1)

=16+2

h​2​​−fg

=18

To avoid confusion with signs, write negative substitutions in brackets!

Car rental

The formula c = 0.1a + 42 is used to calculate the cost in dollars (c) of renting a car for one day from Poole’s Car Hire Ltd, where a is the number of kilometres travelled on that day. 

a. How would you describe 42 in context of this problem? and 0.1? 

b. Determine the cost of renting a car for one day if the distance travelled is 220 kilometres.

Car rental

The formula c = 0.1a + 42 is used to calculate the cost in dollars (c) of renting a car for one day from Poole’s Car Hire Ltd, where a is the number of kilometres travelled on that day. 

a. 42 dollars is the set cost you have to pay to rent any car. You pay 0.1 dollars per kilometer that you drive. 

b.

a = 220

c = 0.1 (220) + 42 

c = 64

Extra practice 

https://www.transum.org/Maths/Visual/Substitution.asp

Perimeter 

The perimeter of a garden is 128 cm with L = length and W = width. 

Give an equation for the perimeter of the garden: 

128 = ............

L

W

Perimeter 

The perimeter of a garden is 128 cm with L = length and W = width. 

Give an equation for the perimeter of the garden: 

L

W

Perimeter = W + L + W + L 

Perimeter = 2W + 2L 

Perimeter = 128 cm 

128 = 2W + 2L 

Perimeter 

The perimeter of a garden is 128 cm with L = length and W = width. 

The length of this garden is 47 cm. Find the width. 

L

W

Perimeter 

The perimeter of a garden is 128 cm with L = length and W = width. 

The length of this garden is 47 cm. Find the width. 

L

W

128 = 2L + 2W

L = 47              W = ?

Perimeter 

The perimeter of a garden is 128 cm with L = length and W = width. 

The length of this garden is 47 cm. Find the width. 

L

W

128 = 2L + 2W

L = 47              W = ?

substitute L in the equation:

128 = 2(47) + 2W

128 = 94 + 2W 

34 = 2W 

17 = W

What to do

Open this LessonUp on your device. 

Work on the slides with the appropriate color: 

- Got the question right                               I really want a challenge!

- Got the question right                               I think a bit more practice will help me!

- Got the question incorrect/correct     I think more practice will help me! I                                                                                         would like some more help. 

Let's get to work! 

p. 168: 8H1             1abcde, 2, 4aeicgk

p. 169: 8H2             1abcd

p. 169: 8H1              4aeicgk, 5bfjdhl

p. 169: 8H2             1aei, 2bfjcgk

p. 169: 8H1              5bfjdhl

p. 169: 8H2              1aei, 2bfjcgk

P. 170:                         activity 2

Math Puzzle!

Use the given values for each variable to evaluate each expression. 

Once complete, show your answer to the teacher. If correct, you will earn a piece of the puzzle. 

For every correct answer you will get a puzzle piece!

If you show inappropriate classroom behavior, you will have to hand in all your pieces and start over!