SEPTEMBER 11, 2017 SUMMER MATH PACKET 7TH GRADE INTO 8TH GRADE MIDDLE SCHOOL MATH TEACHERS EASTAMPTON COMMUNITY SCHOOL

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1 SEPTEMBER 11, 2017 SUMMER MATH PACKET 7TH GRADE INTO 8TH GRADE MIDDLE SCHOOL MATH TEACHERS EASTAMPTON COMMUNITY SCHOOL

2 This Math Packet is to be completed by students entering Grade 8 in September, Mathematics is a cumulative discipline, which means that each course builds upon previously learned concepts, incorporating more rigor and higher levels of complexity, more integration and more work that is independent. To ensure that students have a sound mathematical foundation before moving onto a more challenging math class, I have developed Summer Math Packets that address key concepts that students should know from specific levels of the elementary and middle school math curriculum. These packets provide students with extra practice on needed skills to help maintain mastery, so they are fully prepared for the following year s mathematics class. The topics addressed in this packet, and that you are expected to know, include: Ratios and Rates Constant Rates of Proportionality Sums and Differences of Fractions and Decimals Proportional Relations Number Sense Products and Quotients of Fractions and Decimals Unit Conversions Simplifying Expressions Equations and Inequalities Vertical, Complementary & Supplementary Angles Perimeter, Area and Volume Unit Conversions & Scale Measurements Theoretical and Experimental Probabilities If you find that your son/daughter could use some additional practice and reinforcement, there are a number of websites available that your he/she will be familiar with from elementary school: Make sure that all students bring this packet completed to class during the first week of school. This packet will be collected and graded as a homework assignment and class assignment. Thank You Mr. Foglia, 5 th Grade Math Teacher Ms. Wood, 6 th Grade Math Teacher Mr. Galarza, 6 th /7 th Grade Math Teacher Mr. Shoukry, 7 th /8 th Grade Math Teacher Ms. Stofko, 6 th /7 th /8 th Grade Math Teacher

How many teaspoons of salt are needed for each teaspoon of pepper used?

4 Domain 1 Ratios and Proportional Relationships. 1) A recipe calls for 2¼ teaspoons of salt for every 1⅛ teaspoons of black pepper used. How many teaspoons of salt are needed for each teaspoon of pepper used? 2) Aaron designed a robot for a contest. His robot can move ¾ meter in ½ second. What is the robot s unit rate of speed in meters per hour? 3) Write the constant of proportionality for the pairs of values in each table. 4)

5 5) The wolf population of a park was 200 in the year It increased by 20% from 2000 to It then increased by 15% from 2005 to What was the wolf population in the park in 2010? 6) Identify the constant of proportionality from the diagram. Then write an equation to represent the relationship shown by the diagram. Does your equation also show the constant of proportionality? Explain.

6 7) The graph shows the distance that a trucker drives during a one-day job. a) Determine the unit rate of the distance that the truck driver has driven. b) Does this graph show a proportional relationship? If so, what do the following points represent in this situation: (1, 60) and (2, 120)? c) If the driver drives at a constant rate, what would be the distance driven after 24 hours? Explain your reasoning.

7 Domain 2 The Number System 8) Which decimal is equivalent to ⅞? 9) What is the sum of ( ) + ( 13.22)? 10) A loop around a park is 1¾ miles. If Sandy runs ⅖ of the way around the loop, how far does she run? Use the number lines to find each sum or difference. 11) 4 + ( 5) 12) ) ) 1 ( 4)

8 Rewrite each expression as the sum of two addends. Then find the sum. 15) ) ) 1⅞ ( ⅛) 18) 1⅛ + 2⅔ ( 1⅝) ¼ Convert each fraction to a decimal. If the decimal repeats, place a bar over the repeating digit(s). 19) 20) 21) 22) 23) 24) 25) On January 1, Rose s bank balance was $200. During the month, she wrote checks for $ and $ and made one deposit of $ Which best represents her checking account balance at the end of the month?

9 26) Casey s bank statement was ripped, as shown. What is the closing balance of Casey s bank statement? 27) A fish tank is shaped like a rectangular prism. Its volume can be found by multiplying the length times the width to find the area of its base, and then multiplying that area by the height. The length of the tank is 1⅔ feet, its width is ¾ foot, and its height is ⅘ foot. What is the volume of the fish tank, in cubic feet? 28) Ken buys 12 pencils at $0.15 each, 4 erasers at $0.15 each, and 6 pens at $0.20 each. He writes this expression to calculate his total cost, in dollars: (0.15) ( ). Will this expression yield the correct total cost? If not, write an accurate expression and use it to find the total cost.

10 Domain 3 Expressions and Equations 29) Factor completely 2ab + 6a + 12abc into a simplified expression. 30) Solve for x: 5.1(x + 2) = ) A rectangular garden has a length of 6.8 meters and a perimeter of 20.6 meters. What is the width of the garden? 32) Simplify the following expression 5.8y 7.2y ) Matt needs $1,800 to buy a used car. He has already saved $1,065. He earns $12.25 per hour working as a supermarket stockperson. Write and solve an equation to determine how many hours he needs to work at his job in order to buy the car?

11 Use the distributive property to expand each expression. 34) 0.1(10m + 600) 35) ¾( 2x 16) 36) 37) A store must pay a credit card company $0.35 for each transaction, plus 2% of the cost of the purchase. If a customer pays for a stereo costing $180 with a credit card, how much does the store pay to the credit card company? 38) For each babysitting job she does, Emily charges $7 for each hour, x, she works plus $2 for bus fare. Emily wants to earn at least $23 for her next babysitting job. Write, solve and graph an inequality that will shows all the possible numbers of hours she could work and earn that amount?

12 39) Veronica built a shelf that is exactly 30½ inches long. She wants to place the shelf in the center of a wall that is 60¾ inches wide. How many inches from the edge of each wall does she need to place the shelf? 40) A landscaper charges $30 for each job, plus an additional $22.50 for each hour worked. If the landscaper charges exactly $120 for a job, write and solve an equation to determine h, the number of hours he worked during that job. How would the number sentence change if the landscaper earned more than $120 for the job? Use m for the number of hours he would have needed to work in that case. Solve and graph the inequality.

13 Domain 4 Geometry Use a ruler to measure the dimensions of the drawing. Then find the actual dimensions for the object it represents. 41) Scale: 0.25 cm = 1 m 42) Scale: ½in. = 6 ft 43) One of a pair of vertical angles measures (5x 2 1), and the other measures (4x 1 10). What is the measure of each of the angles?

14 44) How many cubic inches of cheese can this plastic container hold? Determine the value of x in each diagram. 45) 46)

47) The congruent cubes below were glued together. If the edges of each cube measure 4 millimeters, what is the total volume of the solid figure? 48) Janna has three flat plates, each the same size.

15 47) The congruent cubes below were glued together. If the edges of each cube measure 4 millimeters, what is the total volume of the solid figure? 48) Janna has three flat plates, each the same size. She stores them in an L- shaped drawer, as shown, so that they fit snugly inside, with no space between the edges of the drawer and the plates. Approximately how many square centimeters of the bottom of the drawer are not covered by plates? Show and explain your work.

16 49) The scale drawing below shows a floor of a library. If wall-to-wall carpeting will be installed on this floor, how many square meters of carpeting will be needed? Show and explain your work. Modify the scale drawing to show how you decomposed the figure, and label the actual dimensions of the parts.

Domain 5 Statistics and Probability For 50 51, describe each event as

50) randomly selecting a green (G) marble from this box 51) spinning

17 Domain 5 Statistics and Probability For 50 51, describe each event as likely, unlikely, or neither likely nor unlikely. 50) randomly selecting a green (G) marble from this box 51) spinning the letter B 52) The table shows the results of an experiment in which Max drew tiles from a bag. If Max conducts this experiment again and performs 200 trials, which is the best prediction of how many times he will draw a blue tile?

18 For 53 54, determine the theoretical probability. Simplify, if possible. 53) There are 12 gumballs, each a different color, in a bag. One of them is red. What is the probability of reaching into the bag without looking and selecting a red gumball? 54) There are 19 boys and 19 girls in the school pep band. If Trey randomly selects a member of the pep band to interview for the school newspaper, what is the probability that he will select a girl?

19 55) A survey found that 3 out of every 8 voters in Tallytown support a new law that prohibits people from walking their dogs in town parks. If there are 4,800 voters in Tallytown, estimate the number of voters who support the new law. 56) Below are two bags, each filled with same-sized lettered tiles. Pablo will reach into each bag and draw a tile without looking. Create a sample space to show all the possible outcomes of his experiment. Then determine the probability that Pablo will choose two tiles with the same letter on them. Explain how you found your answer.

First Name: Last Name: Select the one best answer for each question. DO NOT use a calculator in completing this packet.

First Name: Last Name: Select the one best answer for each question. DO NOT use a calculator in completing this packet. 5 Entering 5 th Grade Summer Math Packet First Name: Last Name: 5 th Grade Teacher: I have checked the work completed: Parent Signature Select the one best answer for each question. DO NOT use a calculator