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Learn Alberta – video http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=l essons&lesson=m6lessonshell11.swf Solving Equations… (Unit 11)

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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… (Unit 11)

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What do the models below have in common? How are they different? Expressions & Equations… Student Outcome: Understand the difference between an expression and equation xx =

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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 Expression can be written as a… Student Outcome: Identify constants, numerical coefficients and variables. 2y - 7 numerical variable constant coefficient

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Investigate the Expression below… Student Outcome: Identify constants, numerical coefficients and variables. ModelExpressionConstantVariableNumerical Coefficient + 4Z6 (multiply)

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Write the expression for the models below. 1. 2. 3. + Write the “Expression”… Student Outcome: Identify constants, numerical coefficients and variables. xx

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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 “Expression”… Student Outcome: I will learn how to model and solve problems with equations xx

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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 “Equation” is a… Student Outcome: I will learn how to model and solve problems with equations

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What are the two expressions that make up this equation? What is the equation? 1. 2. Write the Expression & the Equation Student Outcome: I will learn how to model and solve problems with equations

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Page 393-394 12,13,14,15 9 1,5,10,11,12 1,3,4,5,7 Practise & Apply

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Show Me What You Know #1 On the front On the back

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Activity Guess My Number (see handout) Alien Invasion (see handout)

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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 = 56 Where 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: x + a = b Student Outcome: I will learn how to solve and model problems with equations.

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C + 22 = 56 + $22 (- $22) = 56 (- $22) = $34 Solve One-Step Equations: x + a = b Student Outcome: I will learn how to solve and model problems with equations.

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You Try It: Hilda’s grandmother gives her $5 for her birthday. Hilda puts this in her 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: x + a = b Student Outcome: I will learn how to solve and model problems with equations.

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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: x + a = b Student Outcome: I will learn how to solve and model problems with equations. Write itModel itSolve it (remove from both sides) P + 5 = 12 = =

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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 “opposite 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

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Complete the examples below: 1. X - 24 = 48 2. 17 + 35 = y - 31 Find & Use the “inverse operation” Student Outcome: I will learn how to solve an equation using inverse operations

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3 Ways to SOLVE… 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

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Page 399-400 3,18-22 143,4,6,8,9,15-18 1,3,4,6,8,9,12,13 Practise & Apply

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Show Me What You Know #2 On the front On the back

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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: ax = b Student Outcome: I will learn how to solve and model problems with equations. OperationInverse Operation Division (÷)Multiplication (x) Division (÷)

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3f = 21 Use “mental math” to solve each equation. Use cups and marbles to model this equation. = Solve One-Step Equations: ax = b Student Outcome: I will learn how to solve and model problems with equations. Ask yourself: “3 times what number gives 21.”

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Divide to apply the “Inverse Operation” Student Outcome: I will learn how to solve and model problems with equations. 7 = d 5 Re write the equation d = 7 5 Use the “opposite operation” to get the variable by itself.

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Divide to apply the “Inverse 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)

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Divide to apply the “Inverse 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)

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Page 405-407 3,16,17,18,19,20,21 13 3,6,8,10,15,16,17,18 3,4,8,10,11,14,15 Practise & Apply

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Solve Two-Step Equations ax + b = 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

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Solve Two-Step Equations ax + b = 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

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Solve Two-Step Equations ax + b = 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 SS

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Solve Two-Step Equations ax + b = 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

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Solve Two-Step Equations ax + b = 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!

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Solve Two-Step Equations ax + b = 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)

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Solve Two-Step Equations ax + b = 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

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Solve Two-Step Equations ax + b = 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!

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Page 411-412 3,16,17,18,20,21 15 3,7,11,14,17,18 3,4,6,7,8,11,14 Practise & Apply

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Unit Review Questions: Pages 414-416 #3,5,6,11cd,12,16,19,20,21,22 http://www.quia.com/ba/143047.html

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