Lesson 8.2B Content Objective: I can substitute a number in for a variable and solve for the expression I can turn word problems into expressions, equations, and inequalities and solve for the variable. Language Objective: I can describe a real life situation that an expression could represent. Assignment: 8.2B Due Quiz 8.2 after Lesson 8.2C 1
Lesson 8.2B Expressions & Variables For each problem below decide whether the expression 2d + 5 can represent the answer to the question. If it can, explain what d stands for in that situation. 1.) Lucy bought two tickets to a symphony concert and five tickets to a movie. How much did she pay? 2.) Sam bought several pens for $2 each and a notebook for $5. How much did he spend altogether (total)? I can substitute a number in for a variable and solve the expression. 7.2.3.2 I can turn word problems into expressions, equations, and inequalities and solve for the variable. 7.2.2.4 3.) A herd (group) of zebras walk a certain distance to a watering hole. On the return trip (way back), a detour (had to go around something) added an extra 5 km. How many kilometers did the herd walk altogether? 4.) There are two dogs in the house and five more in the yard. How many dogs are there altogether? 5.) Because their parents were sick, Neva and Dario spent twice as many hours as usual doing housework during the week plus an extra 5 hours on the weekend. How many hours of the housework did they do? 6.) Blake gets paid $5 for every hour he babysits plus a $2 bonus on weekends. How much money does he earn if he babysits on Saturday? 2
Describe a situation that can be represented by each expression. 7.) 4m 3, if m stands for the number of pages in a book. 8.) 4m 3, if m stands for the distance in kilometers from home to school. 9.) 4m 3, if m stands for the number of eggs in a waffle recipe. 10.) 4m 3, if m stands for the number of milliliters of water in a beaker of water. A single expression can represent numerous (many) situations, depending on what the variable represents. Example Consider the expression c + 10. If c is the number of cents in Koto's piggy bank, c + 10 could represent the number of cents in the bank after she drops in another dime. If c is the number of gallons of gas left in Ms. Flores' gas tank, c + 10 could represent the number of gallons after she adds 10 gallons. If there are c members in the science club, c +10 could represent the number of members after 10 new students join. Think of some other situations c + 10 could represent. When a variable is squared, think area. L2 For example: If L is the length of a square piece of paper, 2 then could be the area of half the sheet of paper. (Remember when you see a variable squared think of...) 3
Restrictions on Variables Sometimes variables are restricted or have limits on what they can be. You need to ask yourself if it makes sense for a variable to be any number or are there numbers that do not make sense. Some common questions you can ask yourself. Does it make sense for the variable to be decimal numbers or fractions? Example: I cannot buy 3.75 books at a store, but I can read 3.75 books (I just have not read all of my fourth book yet) Does it make sense for the variable to be negative numbers? Example: I cannot buy 4 gallons of gas, but the temperature could be 4 degrees. Is there a number that the variable cannot drop below or go above? Example: I cannot sleep in (sleep late) 9 days of the week. Example: I cannot vote in a U.S. presidential election if I am under 18 years of age. Describe the numeric values that the variable is allowed to be. 13.) Michael and Joseph bought b dvds at the store. 14.) Irene bought a dozen (twelve) doughnuts, she ate d of them. 15.) Jason works w days out of the year. 16.) I bought p pounds of hamburger at the grocery store. 17.) We go to visit my grandma m months out of the year. 4
18.) My mom travels x miles to work everyday. 19.) I had a $20 bill, I used it to buy a movie for k dollars. 20.) Adam read h hours today. 21.) I went to the movies with g dollars, I bought my ticket for $8 and a box of popcorn for $7.50. 5