Learn Alberta – video essons&lesson=m6lessonshell11.swf Solving Equations… (Unit

Learn Alberta – video

http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell11.swf

Solving Equations… (Solving Equations… (Unit Unit 1111))

Questions:1. What is the difference between an “equation” and

an “expression?”

2. What do equations use when solving problems?

(hint: What are some key words we use to represent operations?)

Solving Equations… (Solving Equations… (Unit Unit 1111))

What do the models below have in common?

How are they different?

ExpressionsExpressions & & EquationsEquations……Student Outcome: Understand the difference between an

expression and equation

x x=

• A single constant (1,2,3…any number)• A single variable (x,y,x…any letter)• A numerical coefficent (2y, 5x, 9/x…)• A combination of operations with constants,

variables or numerical coefficients. (2y + 4…)

An An ExpressionExpression can be written can be written as a…as a…

Student Outcome: Identify constants, numerical coefficients and variables.

2y - 7

numerical variable constantcoefficient

Investigate the Investigate the ExpressionExpression below…below…

Student Outcome: Identify constants, numerical coefficients and variables.

Model Expression Constant Variable Numerical Coefficient

+ 4 Z 6(multiply)

Write the expression for the models below.

1.

2.

3. +

Write the “Write the “ExpressionExpression”…”…Student Outcome: Identify constants, numerical coefficients and

variables.

x x

Model or write a phrase for the expressions below.

1. Three times a number minus five

2. A number divided by two plus four

3. +

Identify the “Identify the “ExpressionExpression”…”…Student Outcome: I will learn how to model and solve problems

with equations

x x

• Mathematical statement with two expressions that have the same value

• Both expressions have equal value and are separated by an equal sign (=)

• Write the mathematical statement (2 expressions).

• Write the equation in a phrase.

An “An “EquationEquation” is a…” is a…Student Outcome: I will learn how to model and solve problems

with equations

• What are the two expressions that make up this equation?

• What is the equation?

1.

2.

Write the Write the ExpressionExpression & the & the EquationEquation

Student Outcome: I will learn how to model and solve problems with equations

• Page 393: # 5, 7, 9, 10ab

• Page 394: # 11ab, 12ab, 14, 15

Practise & Apply Practise & Apply

Practical Quiz #1Practical Quiz #1

On the front

On the back

Example:Aaron and his mother spend $56 to take the ferry from Vancouver to

Victoria, Aaron knows that the cost for each person is $11. So, the cost for

two people is 2 x $11 = $22, but they must pay for their truck to go on

the ferry as well. He decides to model the situation with the equation..

t + 22 = 56Where t is the cost of the truck to be on the ferry. How could he determine

the cost of the truck?

One-Step Equations:1. Model it (pictures & numbers)

2. Solve it: remove the numbers from one side to leave the variable alone… do the same to the other side.

Solve One-Step Equations: Solve One-Step Equations: x + x + a = ba = b

Student Outcome: I will learn how to solve and model problems with equations.

C + 22 = 56

+ $22 (- $22) = 56 (- $22)

= $34

Solve One-Step Equations: Solve One-Step Equations: x + x + a = ba = b

Student Outcome: I will learn how to solve and model problems with equations.

You Try It:Hilda’s grandmother gives her $5 for her birthday. Hilda puts this in per

piggy bank and now has $12. How much did she have before her birthday?

One-Step Equations:

1. Write the equation (including a variable, which is what you’re looking for)

2. Model It (pictures and numbers…5 loonies, 12 loonies, and a piggy bank)

3. Solve it: remove the numbers from both sides to until the variable is left alone.

Solve One-Step Equations: Solve One-Step Equations: x + x + a = ba = b

Student Outcome: I will learn how to solve and model problems with equations.

Hilda’s grandmother gives her $5 for her birthday. Hilda puts this in per

piggy bank and now has $12. How much did she have before her birthday?

Solve One-Step Equations: Solve One-Step Equations: x + x + a = ba = b

Student Outcome: I will learn how to solve and model problems with equations.

Write it Model it Solve it (remove from both

sides)

P + 5 = 12 =

=

• An operation that “undoes” another operation

• The opposite operation of subtraction is ______________

• The opposite operation of division is ______________

• Remember…to keep the equation balanced, whatever operation is used on one side of the equation must be done on the other.

• “Isolate the variable,” means to

get the variable by itself.

• Another name for opposite

operation is called …

“inverse operations”

Apply the “Apply the “opposite operationopposite operation””Student Outcome: I will learn how to solve an equation using opposite

operations

Example:

1. x + 34 = 55

x + 34 - 34 = 55 – 34

x = 21

Complete the examples below:

1. X - 24 = 48

2. 17 + 35 = y - 31

Find & Use the “Find & Use the “inverse inverse operationoperation””

Student Outcome: I will learn how to solve an equation using inverse operations

3 Ways to 3 Ways to SOLVESOLVE……

Solve by “Inspection”

Solve by

“Modelling”

Solve by

“Isolating The Variable”

- Using mental math…- inspect what number

minus 24 is equal to 48

Draw a picture…use dots and then cross out on both sides.

Use “opposite operations” to isolate

the variable!

X - 24 = 48

• Page 399: # 6, 7, 8, 10cd, 12ab

• Page 400: # 14, 16, 17

• EXTEND #19, 21, 22

Practise & Apply Practise & Apply

Practical Quiz #2Practical Quiz #2

On the front

On the back

Don’t be afraid of multiplication or division operations

Just remember to use the inverse operation

to get the number or variable to the other side.

Remember: try to get the variable on its own!

Example: 5g = 25

Solve One-Step Equations: Solve One-Step Equations: ax ax = b= b

Student Outcome: I will learn how to solve and model problems with equations.

Operation Inverse Operation

Division (÷) Multiplication (x)

Multiplication (x) Division (÷)

3f = 21Use “mental math” to solve each

equation.

Use cups and marbles to model this

equation.

=

Solve One-Step Equations: Solve One-Step Equations: ax ax = b= b

Student Outcome: I will learn how to solve and model problems with equations.

Ask yourself: “3 times what number gives

21.”

Divide to apply theDivide to apply the “Inverse “Inverse Operation”Operation”

Student Outcome: I will learn how to solve and model problems with equations.

7 = d

5Re write the equation

d = 7

5

Use the “opposite operation” to get

the variable by itself.

Divide to apply theDivide to apply the “Inverse “Inverse Operation”Operation”

Student Outcome: I will learn how to solve and model problems with equations.

• Sylvie and Murray earn money delivering groceries. Last weekend, Murray earned $29. This was one third of the amount Sylvie earned. How much money did Sylvie earn?

Questions to answer:

1. What are we looking for (this is the variable)?

2. What is the algebraic equation?

3. Solve the equation using opposite

operations. (Show your work)

Divide to apply theDivide to apply the “Inverse “Inverse Operation”Operation”

Student Outcome: I will learn how to solve and model problems with equations.

Answers:

1. What are we looking for (this is the variable)?

Sylvie’s earnings

2. What is the algebraic equation?

S = $29

3

3. Solve the equation using opposite

operations. (Show your work)

• Page 406: # 9ab, 10, 12ab,

14ab, 15ab

• Page 407: # 17, 18

Practise & Apply Practise & Apply

Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c

Student Outcome: I will learn how to solve and model problems with 2-step equations.

A clothing store is having a sale. Jake pays $19 in total for two

T-shirts and a pair of $5 sunglasses. How much does Jake pay

for each T-shirt?

Model Two-Step Equations:

• All Boys: use simple drawings

(t-shirt, sunglasses and $19)• All Girls: use the balance scale with algebra tiles

Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c

Student Outcome: I will learn how to solve and model problems with 2-step equations.

Model Two-Step Equations:

• All Boys: use simple drawings

(t-shirt, sunglasses and $19)

+ + = $19

$5.00

Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c

Student Outcome: I will learn how to solve and model problems with 2-step equations.

Model Two-Step Equations:

• All Girls: use the balance scale

S S

Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c

Student Outcome: I will learn how to solve and model problems with 2-step equations.

A clothing store is having a sale. Jake pays $19 in total for two

T-shirts and a pair of $5 sunglasses. How much does Jake pay

for each T-shirt?

Everyone Solve It: 2S + 5 = 19

HINT: get rid of values before your divide/multiply…in other words apply the

“REVERSE” order of operations

Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c

Student Outcome: I will learn how to solve and model problems with 2-step equations.

Maurie saw this sign advertising T-shirts and socks. He pays

$30 in total for two T-shirts and four pairs of socks (2$/pair).

What is the price of one T-shirt?

• All Girls: use simple drawings

(t-shirt, socks and $30)• All Boys: use the balance scale with algebra tiles

• Everyone: Solve it and show your work!

Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c

Student Outcome: I will learn how to solve and model problems with 2-step equations.

Maurie saw this sign advertising T-shirts and socks. He pays $30 in total for

two T- shirts and four pairs of socks (2$/pair).

What is the price of one T-shirt?

• All Girls: use simple drawings

(t-shirt, socks and $30)

Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c

Student Outcome: I will learn how to solve and model problems with 2-step equations.

Maurie saw this sign advertising T-shirts and socks. He pays $30 for two T-

shirts and four pairs of socks (2$/pair). What is the price of

one T-shirt?

• All Boys: use the balance scale with algebra tiles

Solve Two-Step EquationsSolve Two-Step Equations ax + ax + b = cb = c

Student Outcome: I will learn how to solve and model problems with 2-step equations.

Maurie saw this sign advertising T-shirts and socks. He pays $30 for two T-

shirts and four pairs of socks (2$/pair). What is the price of one T-shirt?

• Everyone: Solve it and show your work!

• Page 411: # 4ab, 5a

• Page 412: # 8, 11ab, 12d, 16

Practise & Apply Practise & Apply