HW A) SWBAT identify the properties of operations Create flashcards or a some type of foldable that shows the following properties of operations including examples:
HW B) SWBAT apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 1. A regular octagon has a side length of 3 4 x 1. A regular hexagon has a side length of 12 x. 4 3 4 x 1 4 12 - x The difference between the perimeters of the two shapes is represented by the expression 8 6(12 x). Write an expression equivalent to 8 6(12 x) using the fewest possible terms. Show all work neatly and clearly. 2. Which expression(s) is/are equivalent to 8 2(5x 3). Explain or show work to justify your decision. Expression Equivalent? (yes or no) Explain 6(5x 3) 8 10x + 6 8 (10x 6) 8 10x 6 10x + 14 3. Use factoring to rewrite each expression in an equivalent form. Use the fewest number of terms possible. Show each step of your work. a. 4x + 8 + 2 b. 3x 12 + 6x + 9
HW C) SWBAT explain how rewriting equivalent expressions in different forms can help support problem solving in real- world contexts. Andrew sells treats from his ice cream cart. The items he sells along with their prices are shown in the table. Item Price Quantity Frosty Mango Pop $1.75 a Frozen Fruit Yogurt $2.25 b Sundae Swirl Cup $2.75 a Chocolate Chip Cone $2.25 c Fudge Sandwich $1.75 b Suppose Andrew sells the quantities of each item given by the variables in the table. 1. What does the expression 1.75a+2.25 b+2.75a+2.25c+1.75b represent in the context of this problem? 2. An expression equivalent to the one above is 4.5a+4b+2.25c. What does the first expression show about the quantities in this problem that the second expression does not show? HW D) SWBAT recognize that equivalent expressions representing the same real- world context have the same meaning, and in some cases one form may be more useful than the other. The width of the rectangle is x inches and the length is (3x + 2) inches. 3x + 2 x x 3x + 2 1. Brit represented the perimeter of the rectangle using the expression: x + (3x + 2) + x + (3x + 2). Explain how Brit s expression represents the perimeter of the rectangle.
2. Abbey represented the perimeter of the rectangle with the expression 8x + 4. Determine if Abbey s expression is equivalent to Brit s expression. Justify your reasoning. 3. Explain what the second expression, 8x + 4, indicates about finding the perimeter of the rectangle. HW E) SWBAT apply the properties of operations to solve multi- step real- world and mathematical problems involving positive and negative rational numbers in any form. A Florida factory produces fishing reels at a rate of 800 per day, every day. In April, they are forced to cut their production by 15 due to an aluminum shortage. 1. A chain of sporting goods stores orders 20,000 fishing reels. Will the factory be able to produce enough fishing reels in the 30 days of April to meet this order? Explain how you know. 2. How many days will it take the factory to produce the 20,000 fishing reels? HW F) SWBAT assess the reasonableness of answers using mental computation and estimation. 1. Jordan earned $200 this month delivering newspapers. His mom said he must put 20% into his savings account. He wants to buy headphones that cost $99.95 and two shirts that cost $17.99 each. He also has to pay 7% sales tax on his purchases. Jordan said, No problem. I will put 20% into savings, buy the things I want and still have about $10 left. Use estimation to determine if Jordan s calculation is reasonable. Show your work. 2. The circumference of Earth is about 40,030.02 km. The formula for circumference is C = 2πr where π is about 3.14. Jennifer determines the radius of earth is about 12,700 km. Use estimation to determine if Jennifer s measurement is reasonable. Show your work.
HW G) SWBAT compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations in each approach. Stephanie bought a 3D printer for $1249.99 and some cartridges for $79.95 each. She paid a total of $1809.64. Haley and Luis calculated the number of cartridges Stephanie bought in two different ways. Luis s Method: 1809.64-1249.99 559.65 559.65 79.95 7 Stephanie bought 7 cartridges. Haley s Method: Let x equal the number of cartridges Stephanie bought. 1249.99 + 79.95x = 1809.64-1249.99-1249.99 0 + 79.95x = 559.65 79.95x = 559.65 79.95 79.95 x = 7 Stephanie bought 7 cartridges. 1. Luis used arithmetic to solve the problem. Identify the operations (add, subtract, multiply, or divide) he used in order. 2. Haley used algebra to solve the problem. Identify the operations she used in order. 3. Compare the sequence of operations used by Luis and Haley. What is the same or different? 4. In Haley s method, what is the significance of 79.95x in terms of the story context? How is this represented in Luis s method? HW H) SWBAT give examples of linear equations in one variable with one solution, infinitely many solutions or no solution. 1. Write an equation that has one solution using the variable x. Explain your reasoning. 2. Write an equation that has no solution using the variable y. Explain your reasoning. 3. Write an equation that has infinitely many solutions using only the variable z. Explain your reasoning.
HW I) SWBAT compare the properties of two functions represented in different ways. HW J) SWBAT interpret the definition of a linear function as y = mx + b, whose graph is a straight line. Describe as many defining properties of linear functions as you can. List only properties that are unique to linear functions. HW K) SWBAT give examples of functions that are not linear. Give an example of a nonlinear function. You can describe this function in one or more of the following ways: with a table, graph, or equation. Be sure to specify what are the inputs (the independent variable) and what are the outputs (the dependent variable). Then explain how you know your example is nonlinear.
HW L) SWBAT prove or disprove each step in determining an equivalent expression using the properties of operations. 1. Nathan wrote the following steps to prove the equation: Given: 3(x + 2) = 6x + 3 Prove: x = 1 Step Mathematical Statement Justification 0 3(x + 2) = 6x 6 + 3 Given 1 3x + 6 = 6x + 3 Distributive Property 2 6 = 3x + 3 Commutative Property of Addition 3 3 = 3x Subtraction Property P of Equality 5 x =1 Division Property of Equality Which step of justification is incorrect, and what should the justification for that step be to solve the equation? 2. Error Analysis: Describe and correct the error in solving the equation. 2(7 y) + 4 = 4 14 2y + 4 = 4 10 2y = 4 2y = 6 y = 3 HW M) SWBAT write and extend compound inqualities represented in real- world and mathematical problems. Solve each compound inequality and graph its solution. 1. 2.
3. The recipe for baking the cookies states that the cookies must be baked between 16-20 minutes. The baking time must be greater or equal to 16 minutes and less than or equal to 20 minutes. a. Write this as 2 distinct inequalities. b. Write this as a compound inequality. c. Graph this inequality. 4. The doctor told the mother that the expected weight for the baby for her age was between 20 and 25 pounds. The expected weight must be greater or equal to 20 pounds an dless than or equal to 25 pounds. a. Write this as 2 distinct inequalities. b. Write this as a compound inequality. c. Graph this inequality. 5. The teacher decided to separate his students and asked that they report to separate rooms to review their math exams. All students earning above a 90 or below a 60 were asked to report to room A for additional instructions. a. Write this as 2 distinct inequalities. b. Can you write this as a compound inequality? c. Graph this inequality. 6. The laboratory chemicals were very sensitive to heat, so the supervisor installed alarms to alert the staff if the temperature rose above 72 or below 60. a. Write this as 2 distinct inequalities. b. Can you write this as a compound inequality? c. Graph this inequality.
HW N Equations & Functions Applications 1. Use the following expression below to answer parts (a) and (b). a. Write an equivalent expression in standard form and collect like terms. b. Express the answer from part (a) as an equivalent expression in factored form. 2. Use the following information to solve the problems below. a. The largest side of a triangle is six more units than the smallest side. The third side is twice the smallest side. If the perimeter of the triangle is 25 units, write and solve an equation to find the lengths of all three sides of the triangle. b. The length of a rectangle is (x+3) inches long, and the width is 325 inches. If the area is 15310 square inches, write and solve an equation to find the length of the rectangle. 3. A picture 1014 feet long is to be centered on a wall that is 1412 feet long. How much space is there from the edge of the wall to the picture? a. Solve the problem arithmetically. b. Solve the problem algebraically. c. Compare the approaches used in parts (a) and (b). Explain how they are similar. 4. In August, Cory begins school shopping for his triplet daughters. a. One day, he bought 10 pairs of socks for $2.50 each and 3 pairs of shoes for d dollars each. He spent a total of $135.97. Write and solve an equation to find the cost of one pair of shoes. b. The following day Cory returned to the store to purchase some more socks. He had $40 to spend. When he arrived at the store, the shoes were on sale for 13 off. What is the greatest amount of pairs of socks Cory can purchase if he purchased another pair of shoes in addition to the socks?
5. Ben wants to have his birthday at the bowling alley with a few of his friends, but he can spend no more than $80. The bowling alley charges a flat fee of $45 for a private party and $5.50 per person for shoe rentals and unlimited bowling. a. Write an inequality that represents the total cost of Ben s birthday for p people given his budget. b. How many people can Ben pay for (including himself) while staying within the limitations of his budget? c. Graph the solution of the inequality from part (a). 6. Jenny invited Gianna to go watch a movie with her family. The movie theater charges one rate for 3D admission and a different rate for regular admission. Jenny and Gianna decided to watch the newest movie in 3D. Jenny s mother, father, and grandfather accompanied Jenny s little brother to the regular admission movie. a. Write an expression for the total cost of the tickets. Define the variables. b. The cost of the 3D ticket was double the cost of the regular admission ticket. Write an equation to represent the relationship between the two types of tickets. c. The family purchased refreshments and spent a total of $18.50. If the total amount of money spent on tickets and refreshments were $94.50, use an equation to find the cost of one regular admission ticket.