Summer Math Practice: 7 th Pre-Algebra Entering 8 th Algebra 1 Dear Students and Parents, The summer math requirement is due to Mr. Cyrus the first day back in August. The objective is to make sure you have a solid foundation to help you make a successful transition to the pace and depth of Algebra 1 coursework. There are two distinct parts. The first part is skill practice to reinforce skills already in place. The list below gives a reference to IXL if you need reminders. If you don't remember a skill, please get help to fill in the gap. Don't just guess or fill something in. Take advantage of your digital notes and your math notebook. Calculators are not permitted. Please be thorough, legible, and show your thinking. IXL Level I and J References for Pre-Algebra Skills Fraction Applications and Computation Percents Algebraic Expressions Solving Equations with One Variable Inequalities Proportional Relationships Linear Equations in Two Variables Slope Linear Systems - Solve by Graphing IXL Level I, skills G1 - G18 IXL Level I, skills L1 - L10 IXL Level I, skills R1 - R7; R10; R13 - R16 IXL Level J, skills W1 - W15 IXL Level J, skills X1 - X9 IXL Level I, skills K1 - K8 IXL Level I, skills U7, U8 IXL Level J, skills Y1 - Y8 IXL Level J, skills AA1, AA2 The second part - sunglasses - is applied problem solving. These real-world applications are focused on reasoning with rational numbers and percent. Calculator use is permitted when necessary. All thinking and steps must be shown - 'one number' answers are not acceptable. Please make sure to fit this work sensibly into your summer schedule, and to especially spread the work throughout the summer. Read questions and directions carefully. Legibility and proper steps are expected. Make sure your answer is reasonable and answers the question asked. When you are unsure about a concept or skill, please use your resources to figure it out. This will be the first work Mr. Cyrus has from you. Impress him! I know you can! Thank you for your efforts this year. Have a wonderful summer! Mrs. Matthews If your work was done with help from a tutor, we would like to know. Please write the name of the tutor or program here
7 th Pre-Algebra: Entering 8 th Algebra 2018 Summer Practice Part 1: Skills NO Calculators, Please. Show all thinking and work. Circle answers, please. Fraction Applications 1.) Find the LCM and the GCF. Use any method. a.) 28 and 29 (is there a pattern?) b.) 120 and 84 2.) It takes 4/5 of a yard of fabric to make a play costume. How many costumes can be made from 52 yards? 3.) Heights of students at a school vary from 2!! feet to 5! feet. Find the range of the!"! heights, expressed in feet. (no decimals). 4.) Find the area of this right triangle. All measurements are in inches. 2!! 5!!" 4!! 5.) I used! of a 5! pound bag of apples to make a pie.!! a.) How many pounds did I use? b.) How many pounds are left?
6.) Ralphie has a large tropical fish collection. He gives 2/3 of his fish to a local high school. Then he gives 2/5 of the remaining fish to an elementary school. In the end he has 30 fish left. How many did he have at first? Fraction Computation 7.) 5!! 9!! 8.)!"!"!"!" 9.)!!" 32 10.) 1!! 4!!" 11.)!!!"!"!!" 12.) 3!! 1!"!" 13.) 5 2!! 2!! 14.) 6!! 3!!!!
Algebraic Expressions and Equations 15.) Evaulate the expression following order of operations. 90 12 0.3 2! 16.) The perimeter of a rectangular garden is 30 feet. The length is 3 more than half the width. a.) Label the rectangle with variable expressions for its width and length. My variable is ; it stands for b.) Write and then solve an equation to find the width AND length of the garden. Show work below; fill in answers here: width = ft length = ft Solve these equations. Show all steps. 17.) 5x + 3 x 14 = 8 18.) 5x x 5 + 7 = 15 19.)! x! +! = 6!!! 20.)!! x!! +!! = 6 21.) 3x 8 = 8x 12 22.) 7 6x = 10 2x
Inequalities 23.) Write the sentence as an inequality; solve and graph the solution. "Five more than the quotient of a number and negative 6 is at least 9." Direct Proportions 24.) Ralphie paints clay figurines to sell at a crafts fair. The graph shows the number of figurines he paints, y, is directly proportional to the number of days he paints, x. a. Write a direct variation equation in the form y = kx. b. What does the constant of proportionality represent in this situation? Be specific. 25.) In this table, p is directly proportional to q. Fill in the blanks. Linear Equations / Slope 26.) Make a table of values following our guidelines (three x values: pos, zero, neg). Then graph the equation. y = 1 x + 4 3
27.) Which is steeper, the boat ramp or a road with a 12% grade? Support your answer with solid reasoning about slope. 28.) Sketch a line with a negative slope and a positive y-intercept. Through which quadrants does the line pass?. 29.) Find the slope of the line passing through each pair of points. No graph. Use the slope formula to support your answer. A(-2, 3) B( -4, -1) 30.) Find the slope of each line from the graph. a.) b.) 31.) Solve for y to express in slope-intercept form; then use the slope-intercept form to graph the equation. No table of values. 4x + 2y = 6
7 th Pre-Algebra: Entering 8 th Algebra 2018 Summer Practice Part 2: SUNGLASSES Calculators okay IF necessary. SHOW ALL THINKING! Who doesn't like to wear sunglasses in the summer? Think about the math involved in the design, construction, and business of making and selling a simple pair of sunglasses. A company needs to think about fashion, materials, eye protection, sizing, advertising, and of course the bottom line (profits). Think about buying sunglasses and how much they cost. Complete these problems by the pool with your coolest pair of shades. 1.) Suppose that 1/3 of the population of the city of Tulsa buys new sunglasses in June and 1/8 of those people buy a pair of black Ray-Bans. Find the population of the city of Tulsa. Use the fractions to find how many people buy new sunglasses in June and how many buy the black Ray-Bans. Think how to sensibly express your answer; it represents numbers of people. Should your answer include a long decimal? Population of Tulsa: Number of sunglass buyers: Number of Ray-Ban buyers: 2.) Sunglasses come in different sizes, and there are different parts to measure. Choose a pair of sunglasses at your house. Measure several of the dimensions of the sunglasses in inches and fractions of an inch to the nearest fourth. (For example, 3 ¼ inches). Make your own sketch of the sunglasses with labeled dimensions or just label this sketch. (Which dimensions, you may ask. Up to you. Which dimensions make sense to measure?) Your 6 year-old cousin wants a pair just like yours, but they need to be three-fourths the size. What would those dimensions be? Make a sketch labeling the smaller dimensions. Again, you are answering a real question. Does how your answer is presented make sense?
3.) Even small changes in design can make big changes in the amount of material used in manufacturing. A design change saves a company 0.32 grams of plastic per pair of sunglasses. How much plastic would be saved in 5 years if 25,000 pairs are manufactured each year? 4.) a.) Please watch this short video and describe the situation it shows. http://threeacts.mrmeyer.com/doublesunglasses/act1/act1.mov b.) What question do you have? Write your question clearly and completely. c.) Answer your question; show your thinking of course. 5.) This table shows results of a survey on product preference for four different styles, with 41% of those surveyed choosing not to buy any of the four styles shown. Fill in the table. Style A Style B Style C Style D Percent of people who prefer the style 12% 8% 24% 15% Number people out of 50,000 who would buy the style Profit on style per pair sold $10 $12 $4 $8.50 Total profit on style given number sold.
6.) These Oakley sunglasses are on sale. What was the original price? 7.) A pair of sunglasses is 35% off the original price of $54.95. Sales tax is 8.5%. What do I pay? 8.) Last year, the sunglasses I liked cost $25.50. This year, they cost $29.00. What is the percent increase from last year to this year? Round to nearest tenth of a percent, please. 9.) This graphic shows % markups for some types of designer fashion products. (http://www.businessinsider.com/products-high-markups-2014-7) Eyeglass frames have a large markup - much higher than markups we used in problems we did in class. Use the graphic to answer these questions. a.) Write the markup % for eyeglass frames as a decimal. b.) Suppose it costs $7.50 to manufacture a pair of frames. Use the % markup to find the selling price. c.) Suppose the selling price for a pair of frames is $175. Use the percent markup to find the company's cost to manufacture the frames. Careful: You are finding the whole, not the part! d.) These prices do not even include lenses! Do you think designer sunglasses are worth it? Tell why or why not in one or two complete sentences.
10.) This table shows how the thickness of the lens of one kind of material affects the percent of visible light that is transmitted by the material. Independent variable: Dependent variable: As the lens thickness increases, the % of visible light Plot these numbers on this coordinate grid. You MUST have titles, axis labels, and choose an appropriate scale. Does this show a positive or negative slope? Is this a linear relationship? How do you know? What transmission percent would you expect for a thickness of 0.9 mm? 1.9 mm? Lens % visible light thickness transmitted (mm) 1.0 50% 1.1 45% 1.2 41% 1.3 36% 1.4 33% 1.5 30% 1.6 27% 1.7 24% 1.8 22% CHECK BACK OVER YOUR WORK. DID YOU SHOW YOUR THINKING? WILL MR. CYRUS BE IMPRESSED WITH YOUR EFFORT, ACCURACY, AND ATTENTION TO DETAIL?