*Remember to teach students to read inequalities from left to right. Which ever end they come to first is how it is read.

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1 Equations

2 Teacher Equations N.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. 7.N.1.3 Use properties of the real-number system to explain reasoning and to formulate and solve real-world problems. N.2: Understand the meaning of operations and how they relate to one another. 7.N.2.3 Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips, markups, commission, profit, simple interest). A.2: Represent and analyze mathematical situations and structures using algebraic symbols. 7.A.2.1 Write verbal expressions and sentences as algebraic expressions and equations: a. evaluate algebraic expressions, b. solve simple linear equations. 7.A.2.2 Use variables and appropriate operations to write an expression, an equation, or an inequality that represents a verbal description. 7.A.2.3 Use the order of operations to evaluate algebraic expressions When teaching students to write equations it is important they understand what all parts of the equation mean. For example, A=B means that A is equal to B and vice versa. The main concept is that students are able to transfer information into a way to find the correct answer, and in order to do this they must be able to decipher the raw information given. There are many different aspects to equations that must be considered. Basics: *Students need to decide what is variable in the word problem, meaning what part of the word problem can change depending on how many it wants. The goal is to make both sides of the equation equal to each other, so adding/subtracting or multiplying/dividing the same quantity to both sides of the equation maintains equality. Adding/subtracting and multiplying/dividing are inverse operations. They are used to undo each other and keep the equation equal. *The most difficult part of writing equations is variables, and where to put them. Stress this concept! Inequalities: Students must also know that of means multiply and which signs go with each inequality. Greater than: A>B Greater than or equal to: A B Less than: B<A Less than or equal to: B A

3 *Remember to teach students to read inequalities from left to right. Which ever end they come to first is how it is read. Percents: Simple percents. Move the decimal point two spaces to the right to make the number a percent. Sales tax-convert the percent to a decimal so students can use the decimal to multiply. Teacher Sample: 1. Bob hired a painter to paint his house. The painter charges $25 to come to your house and $45 a day for painting. If Bob has $300, find the greatest number of days possible that Bob can have the painter working on his house. 45d The local party supply store sells helium balloons for $1.50 each. They will deliver the balloons anywhere in town for a $25 delivery charge. Find the cost of having 12 balloons delivered to your home. Then write and equation for c-the total cost of delivering balloons, and b-balloons. 3. The local soccer team needs new uniforms and balls. Write an equation to show how many uniforms and balls they can purchase if each uniform is $25 and each ball is $5. If the team has $600 to spend, how many uniforms and balls can the team buy if they want an even amount of each?

4 Teacher Sample: Answers 1. Bob hired a painter to paint his house. The painter charges $25 to come to your house and $45 a day for painting. If Bob has $300, find the greatest number of days possible that Bob can have the painter working on his house. 45d First subtract the 25 from both sides 45d (+ 25) (300) (-25) (-25) This removes 25 from the left side and makes the right side d 275 Next divide both sides by 45 45d (/45) 275 (/45) d 6.1 since you have a remainder and the student is looking for the greatest amount of days without going over, the painter can work 6 days 2.The local party supply store sells helium balloons for $1.50 each. They will deliver the balloons anywhere in town for a $25 delivery charge. Find the cost of having 12 balloons delivered to your home. Then write and equation for c-the total cost of delivering balloons, and b-balloons. Students know they have to multiply the cost of the balloons by 12 balloons. $1.50 x 12 = $ They have to add the delivery charge of $25, so the total cost is $43. Writing an equation is where students struggle. They need to realize the number of balloons a person can buy is the variable. No matter how many balloons a person buys, it will always cost $25 for delivery so that is the constant. $1.50b+$25 = C 3.The local soccer team needs new uniforms and balls. Write an equation to show how many uniforms and balls they can purchase if each uniform is $25 and each ball is $5. If the team has $600 to spend, how many uniforms and balls can the team buy if they want an even amount of each? The problem calls for an even amount of balls and uniforms so they will have the same variable. 25x + 5x = $600 30x= $600 30x(/30)=600/30 = 20 uniforms and balls

5 Student Practice 1. The mall is having a sale on MP3 players. Which store offers the better deal? Store A regularly sells the MP3 player for $200 and they are offering a 25% discount and no sales tax. How much will a MP3 player cost at Store A? Store B is selling the MP3 player for $150 with 8% sales tax. What will be the total cost for a MP3 player at Store B? If you have $160, will that be enough money to buy the MP3 player at Store B? 2. Your dog keeps getting out of the back yard, so your parents want to have a new fence installed. If fencing material is $24 a meter and installation is $200 find: The total cost for 60 meters of fence installed. Write an equation using variables for x the amount of meters and I for installation If you only have $1200 to spend, how many meters of fence can you have installed? 3. Ben found a book he wanted at the bookstore. The original cost of the book is $12.95, and they are offering a 15% discount. What will be the total cost of the book with 7% sales tax? If you pay with a $20 bill, what will be your change?

6 4. Janice rented a moving van for one day at a rate of $30 per day plus $0.25 per mile. Which of the following equations can she use to calculate c, the cost, in dollars, of renting the van for one day and driving it m miles? A. c = 55m B. c = 30.25m C. c = m D. c = m 5. Which situation is best represented by the equation x 4 = 16? 6. A. Miranda picked 16 apples and ate ¼ of them. What is x, the number of apples she had left? B. Felipe ran for 16 minutes and walked for 4 minutes. What is x, the difference between the time he spent running and the time he spent walking? C. Jordan spent $4 of his allowance and had $16 left. What is x, the total amount of Jordan s allowance? D. Cecilia has hit 4 of the last 16 balls pitched. What is x, the total number of balls pitched?

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8 Student Practice Answers 1. The mall is having a sale on MP3 players. Which store offers the better deal? Store A regularly sells the MP3 player for $200 and they are offering a 25% discount and no sales tax. How much will a MP3 player cost at Store A? 200 x.25 = $ =$150 is the cost at store A Store B is selling the MP3 player for $150 with 8% sales tax. What will be the total cost for a MP3 player at Store B? 150 x.08 = $ = $162 is the cost at Store B If you have $160, will that be enough money to buy the MP3 player at Store B? The MP3 player costs $162 at Store B so you do not have enough money 2. Your dog keeps getting out of the back yard, so your parents want to have a new fence installed. If fencing material is $24 a meter and installation is $200 find: a. The total cost for 50 meters of fence installed. 50 x $24 = installation = $ x = c b. Write an equation using variables for x the amount of meters and c for total cost c. If you only have $1200 to spend, how many meters of fence can you have installed? 24x = x = x/24 = 1000/24 X = So you have enough money to install 41 meters of fence

9 3. Ben found a book he wanted at the bookstore. The original cost of the book is $12.95, and they are offering a 15% discount. What will be the total cost of the book with 7% sales tax? If you pay with a $20 bill, what will be your change? x.15 = 1.94 is amount of discount = x.07 tax = = total cost after discount and tax 4. Janice rented a moving van for one day at a rate of $30 per day plus $0.25 per mile. Which of the following equations can she use to calculate c, the cost, in dollars, of renting the van for one day and driving it m miles? E. c = 55m F. c = 30.25m G. c = m H. c = m $0.25 is the variable because the amount of miles can change. $30 is the constant you have to pay for rental no matter how many miles you travel G is the correct equation 5. Which situation is best represented by the equation x 4 = 16? E. Miranda picked 16 apples and ate ¼ of them. What is x, the number of apples she had left? F. Felipe ran for 16 minutes and walked for 4 minutes. What is x, the difference between the time he spent running and the time he spent walking? G. Jordan spent $4 of his allowance and had $16 left. What is x, the total amount of Jordan s allowance? H. Cecilia has hit 4 of the last 16 balls pitched. What is x, the total number of balls pitched? G. is the correct answer. He spent so it is subtraction, what he has left is what it equals

10 6. He has one package of 5 pens, and it does not tell us how many packages of 2 pens he buys so that is the variable. The correct answer is D. 7. D. the number of parents who attended the function.