Summer Math Practice: 7 th Math Entering 8 th Pre-Algebra

Transcription

1 Summer Math Practice: 7 th Math Entering 8 th Pre-Algebra 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 8 th grade pre-algebra 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 7 th Math Skills Integers Fraction Applications and Computation Percents Algebraic Expressions Solving Equations IXL Level I, skills C1 - C9 IXL Level I, skills G1 - G18 IXL Level I, skills L1 - L10 IXL Level I, skills R1 - R7; R10; R13 - R16 IXL Level I, skills S1 - S8 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

2 7 th Math: Entering 8 th Pre-Algebra 2018 Summer Practice Part 1: Skills NO Calculators, Please. Show all thinking and work. Circle answers, please. Integers / Decimals Find the sum or difference: 1.) ) ) ) 5 - (-25) 5.) -5 - (-25) 6.) ) (-9) 8.) 15 + (-42) 9.) ) 27 + (-27) 11.) ) (-27) 13.) Show on a number line. Clearly show the start place, what direction you moved, and the ending place. a.) b.) ) Find the product: a.) b.) 4.37 ( 52)

3 15.) Find the quotient: a.) 32.5 / 13 b.) 52.2 / 0.6 Fraction Problem Solving 16.) Find the perimeter AND the area of this right triangle. (measurements are inches; please label units) 3/4 7/8 5/6 17.) One serving of chicken noodle soup is 1!! soup. How many servings do they have? cups. The cafeteria makes 65 cups of 18.) Right now there are 5!! gallons in my car's gas tank. The tank can hold 11!! gallons of gasoline. How much more gas is needed to fill the tank? (no decimals) 19.) I ran 2 ½ times around a 4 ⅔ mile trail. How many miles did I run? 20.) Fill in >, <, = by using number sense. No computation needed! a.) ½ b.) 6 ½ 6 x 2

4 21.) 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? 22.) My garden takes up 1/3 of my yard; I plant tomatoes in 1/2 of the garden. Write and solve the equation shown by the diagram to tell what fraction of my yard is tomatoes. Fraction Computation 23.)!! + (!! ) 24.)!! +!! 25.) 5!! + 3!! 26.) 15 8!!" 27.) 3!! 1!!" 28.) 1!! 4!! Percents Write the percent as a decimal. 29.) 180% 30.) 5% 31.) 8.04% Write the decimal as a percent. 32.) ) ) 0.005

5 Write the percent as a fraction or mixed number in simplest form. 35.) 240% 36.) 3.5% 37.) 24% Write the fraction as a percent. 38.) 3!!" 39.)!!"# 40.)!! Find the percent of the number. Support your method/thinking. 41.) 75% of ) 70% of ) 120% of ) 35% of 180 Find the whole. Support your method/thinking. 45.) 25% of what number is 21? 46.) 125% of what number is 25? 47.) Of the 240 students, 45% are girls and the rest are boys. How many students are boys?. 48.) 55% of the amount in Ralphie's savings is $550. How much does he have in his savings?

6 Expressions Evaluate the expressions following order of operations. 49.) ! 3 50.) (-5 + 2) Evaluate the expressions when x = 4 and y = -8. Show substitutions. 51.) x + xy 52.) y + 3(x 6) Write an algebraic expression. 53.) The sum of twice a number and 5 54.) 9 less than a number 55.) Circle the expression that says "three times the sum of a number and 7" 3x + 7 3(7x) 3(x + 7) x Distribute to write an equivalent expression. 56.) 5(3x + 12) 57.) 7(2x + 8) Simplify the expressions. (Distribute if possible; then combine like terms) 58.) 3x 2 8x ) 5 3x 7 + 2(8x + 10) State whether each pair of expressions are equivalent. 60.) 8 3 5x and 24 40x 61.) 3 7x 4 and 12 21x 62.) Write an expression with two terms that has a negative coefficient and a positive constant.

7 Equations Write the sentence as an equation. Then solve the equation with proper steps. 63.) Three-fourths more than a number n is equal to two and three-eighths. 64.) Nine less than a number n equals negative two. Solve each equation with proper steps. Circle answer, please. 65.) 3.4x = )!!!.! = ) 2x 5.4 = ) 3x 3 = ) 2 x = ) 3x + 2 8x 5 = 15

8 7 th Math: Entering 8 th Pre-Algebra 2018 Summer Practice Part 1: SUNGLASSES Calculators okay if necessary 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 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. a.) What fraction of the population buys the black Ray-Bans? b.) 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. 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.

9 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 of sunglasses were manufactured each year? Show thinking, of course. 4.) a.) Please watch this short video and describe the situation it shows. b.) What question do you have? Write your question clearly and completely. c.) Answer your question; show your thinking. 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. 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.

10 6.) These Oakley sunglasses are on sale! What is the percent discount? 7.) I buy a cool pair of sunglasses for $ Sales tax is 8.5%. What is the amount of tax? How much do I pay in total? Show thinking. 8.) This graphic shows % markups for some types of designer fashion. ( Eyeglass frames have a very 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 amount of markup. Remember? markup amount = cost * percent of markup (write % as a decimal) c.) Find the selling price by adding the markup amount to the $7.50 cost. d.) This price does not even include lenses! Do you think designer sunglasses are worth it? Tell why or why not in one or two complete sentences.

11 9.) Company research shows sales of Style A to Style B are typically in a 2:5 ratio. The Tulsa store sells 2450 pairs this month, and the store's sales follow the typical style ratio. a.) Use the information above to fill in the table and to find how many of each style sold. Style Ratio Tulsa Store Sales A B TOTAL b.) The OKC store claims their customers like aviator glasses (style A) way more than people in the typical store. (Remember, the typical store is a 2:5 ratio for Style A to B) The OKC store sold 1200 pairs of Style A and 1600 pairs of Style B. Do these numbers support their claim? Support your answer with ratio reasoning. 10.) a.) A manufacturer sells sunglasses to department stores at a price of $10 each, and each pair costs $2.48 to manufacture. What is the amount of profit for the manufacturer per pair of sunglasses? (Note: profit is revenue minus cost) b.) The manufacturer spent $220,000 in the design process and plans to spend $750,000 in advertising. Based on the profit for each pair calculated in part a, how many pairs of sunglasses would the company have to sell in order to recover those initial costs? CHECK BACK OVER YOUR WORK. DID YOU SHOW YOUR THINKING? WILL MR. CYRUS BE IMPRESSED WITH YOUR EFFORT, ACCURACY, AND ATTENTION TO DETAIL?