MSA 3.3 – Writing Equations 1) Learning Target: I will write and solve symbolic equations with one variable. 2) Homework packet p. 5-7: 1) Complete p. 5-7 and Correct with the KEYs. 3) Warm Up: Marta’s mom gives her $5 for her birthday and then $0.50 for each day that she completes her homework. Write an equation that represents the amount of money she receives during the school year. Use the equation to find the number of days Marta needs to buy new shoes that cost $20. After 15 days of doing homework, how much money has Marta earned?

y = 0.5x + 5 or m = 0.5d + 5 20 = 0.5x + 5 x = 30 days y = 0.5(15) + 5 Marta’s mom gives her $5 for her birthday and then $0.50 for each day that she completes her homework. Write an equation that represents the amount of money she receives during the school year. Use the equation to find the number of days Marta needs to buy new shoes that cost $20. 3. After 15 days of doing homework, how much money has Marta earned? y = 0.5x + 5 or m = 0.5d + 5 20 = 0.5x + 5 x = 30 days y = 0.5(15) + 5 y = $12.50

An equation states that two quantities are equal. 85 = 70 + 15 85 and 70 + 15 are equal. What do you do to maintain equality (balance)? If you subtract 4 from one side: 85 – 4 You must also subtract 4 from the other: 70 + 15 – 4 85 – 4 = 70 + 15 – 4 81 = 81 If you divide by 5 on one side: 85 ÷ 5 You must also divide by 5 on the other: 70 + 15 ÷ 5 85 ÷ 5 = (70 + 15) ÷ 5 17 = 17 To maintain balance do the same thing to both sides.

MSA 3.3: Writing Equations packet p. 5 The picture shows a situation from Problem 3.2. We can write the following equation to represent the situation: 2x + 4 = 12 We can use Nichole’s method from Problem 3.2 to write this equation: 2(x+2) = 12 Because the number of gold coins in each pouch is unknown, you can let x represent the number of coins in one pouch. You can let 1 represent the value of one gold coin. = x = 1

2 pouches and 4 coins = 12 coins are balanced. 2x + 4 = 12 How does Nichole’s equation also fit? 2(x + 2) = 12 2x + 4 = 12 and 2(x + 2) = 12 are equivalent expressions. Two or more expressions are equivalent if they have the same value, regardless of what number is substituted for the variable. They are an example of the of Distributive Property. 2(x + 2) = 2x + 4 12 = 12

In this problem, you will revisit situations with pouches and coins, but you will use symbolic equations to represent your solution process. Visual Equation: 1. Describe the Steps for Finding the Coins in Each Pouch: Symbolic Equation: Use x to represent the number of gold coins in each pouch Use the number 1 to represent each coin Remember the Balance Check = x = 1

Visual Equation: 2. Describe the Steps for Finding the Coins in Each Pouch: Symbolic Equation: = x = 1

Visual Equation: 3. Describe the Steps for Finding the Coins in Each Pouch: Symbolic Equation: = x = 1

Visual Equation: 4. Describe the Steps for Finding the Coins in Each Pouch: Symbolic Equation: = x = 1

3x = 12 = x = 1 Now flip the process: Symbolic Equation: Describe the Steps for Finding the Coins in Each Pouch: Draw the Visual Equation: = x = 1

2x + 5 = 19 = x = 1 Symbolic Equation: Describe the Steps for Finding the Coins in Each Pouch: Draw the Visual Equation: = x = 1

4x + 5 = 2x + 19 = x = 1 Symbolic Equation: Describe the Steps for Finding the Coins in Each Pouch: Draw the Visual Equation: = x = 1

4x + 5 = 2x + 19 = x = 1 Symbolic Equation: Describe the Steps for Finding the Coins in Each Pouch: Draw the Visual Equation: = x = 1

x + 12 = 2x + 6 = x = 1 Symbolic Equation: Describe the Steps for Finding the Coins in Each Pouch: Draw the Visual Equation: = x = 1

3(x+4) = 18 = x = 1 Symbolic Equation: Describe the Steps for Finding the Coins in Each Pouch: Draw the Visual Equation: = x = 1

Challenge: Find the Mystery Number a. If you add 15 to 3 times the mystery number, you get 78. What is the mystery number?   b. If you subtract 27 from 5 times the mystery number, you get 83. What is the mystery number? c. Make up clues for a riddle whose mystery number is 9.

MSA 3.3 – Writing Equations Did I reach my Learning Target? I will write and solve symbolic equations with one variable. 2) Homework packet p. 5-7: 1) Complete p. 5-7 and Correct with the KEYs.