Spartanburg School District 5 Summer Math Learning Packet Students entering Grade 9

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1 Spartanburg School District 5 Summer Math Learning Packet Students entering Grade 9 The summer math activities will enable your child to review math concepts and reinforce skills learned this year. Just a few minutes each day spent thinking and talking math will help reinforce the math that has been learned and begin to bridge the foundation for extending to the concepts that will be developed next year. The goal is for your child to have fun thinking and working collaboratively to communicate mathematical ideas. While your child is working, ask him how the solution was found and why a particular strategy was chosen. The math practice in this summer packet addresses 3 critical areas in grade 8: 1. formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations, 2. grasping the concept of a function and using functions to describe quantitative relationships, 3. analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. Packet contains: Math problems for June and July with an answer key Literature, APP, and website recommendations Math journal directions Suggested Use: Complete at least 15 math days each month Spend at least 10 minutes 4-5 times a week Keep a math journal to record work Make a summer math goal with your child Student mathematicians - keep your mathematics skills sharp and have a safe and enjoyable summer.

2 Grade 9 Students Why Math Journals? Math journals are important tools to help build note-taking skills and mathematical communication. They can be used to record your thinking from the calendar math problems as well as the other summer math ideas to explore. DIRECTIONS: Do your best to complete as many of these summer math activities as you can! Record all your work in your math journal. In August, share your Math Journal with your ninth grade teacher. Each journal entry should: Have the date of the entry Have a clear and complete answer Be neat and organized Here are two examples of Great journal entries: June 1, 2014 If 3 books cost $18, then I know 1 book costs $6. 7 books would cost $42. With $54, I could purchase 9 books since 9 X 6 = 54. June 7, 2014 Thinking Blocks Ratios APP: I practiced problems to review how to find the missing quantity in a ratio. I built my model using a bar diagram. Using a bar model helps me to visualize the problem. I was able to correctly answer 5 problems. Summer Math Ideas Math Books to Read: Evil Genius by Catherine Jinks Forever Changes by Brendan Halpin All of the Above by Shelley Pearsall Hannah Divided by Adele Griffin Guinness Book of Records by Time Inc. Mathematicians are People Too by Luetta Reimer & Wilbert Reimer Websites to Explore: Worksheets to Practice Math: APPs to Try: Grades 6-9 Everyday Mathematics, Beat the Computer, Multiplication Everyday Mathematics, Divisibility Dash Everyday Mathematics, Equivalent Fractions Fill the Cup Pizza Fractions 1 Operation Math Tony s Fraction s Pizza Shop Pearl Diver Lobster Diver Factor Samurai Ninja Chicken Fraction App by tap to Learn Dare to Share Fairly Long Division Touch Math Ninja HD Quick Math Wuzzit Trouble Sushi Monster Deep Sea Duel Super 7 Chicken coop fractions All Grades KENKEN Kakooma Quick Math Arithmetic & Times Tables Pick-a-Path Sumdog Conundra Math Thinking Blocks Fast Facts Addition, Subtraction Fast Facts Multiplication, Division Learn Zillion Khan Academy Symmetry shuffle Math matrix Ratio rumble Math doodles Flash to Pass Slice It! 2048

3 June 2014 Entering Ninth Grade Mathematics Calendar Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 2 A trainer for a professional football team keeps track of the amount of water players consume throughout practice. The trainer observes that the amount of water consumed is a linear function of the temperature on a given day. The trainer finds that when it is 90 F the players consume about 220 gallons of water, and when it is 76 F the players consume about 178 gallons of water. Part A: Write a linear function to model the relationship between the gallons of water consumed and the temperature. 3 Which of the expressions is not equivalent to 1/25? A B C D X Y If a line contains the points in the table above, the equation of the line is A. y = 2x + 5 B. y = 2x 5 C. y = 5x 2 D. y = 5x 2 5 Visit the website /vlibrary.html Challenge yourself with fun activities! List them. 6 David currently has a square garden. He wants to redesign his garden and make it into a rectangle with a length that is 3 feet shorter than twice its width. He decides that the perimeter should be 60 feet. Determine the dimensions, in feet, of his new garden. Show your work. 7 8 Part B: Explain the meaning of the slope in the context of the problem. 9 k l Line k is parallel to line l. m EDC = 41 and m ABC = 32. Find the m BCD. Explain in detail how you know you are correct. Add additional lines and points as needed for your explanation. l k B D A E C 10 Go to website: oma/kakooma?gametype=ne gatives Choose a level and enjoy practicing your quick calculations. 11 a. Dilate triangle OPQ from center O with scale factor r =. Label the image OP Q. b. Find the coordinates of P and Q. c. Are OQP and OQ P equal in measure? Explain. 12 Continuation from June 11. Use the same diagram as shown on June 11. a. What is the relationship between the lines PQ and P Q? Explain in terms of similar triangles. b. If the length of segment OQ = 9.8 units, what is the length of segment OQ? Explain in terms of similar triangles. 13 The cost of five protractors is $14.95 at Store A. The graph below compares the cost of protractors at Store A with the cost at Store B. Estimate the cost of one protractor at Store B. Use evidence from the graph to justify your answer. 14

4 15 16 Students sold 275 tickets for a fundraiser at school. Some tickets are for children and cost $3, while the rest are adult tickets that cost $5. If the total value of all tickets sold was $1,025, how many of each type of ticket was sold? 17 Determine the equation of the line connecting the points (0,-1) and (2, 3). Show all work. 18 Will the line described by the equation you found on June 17 intersect the line passing through the points (2, -4) and (-3, 3)? Explain why or why not. 19 Visit the website /vlibrary.html Challenge yourself with fun activities! List them. 20 At USC in 2013, the cost of the weekly meal plan options could be described as a function of the number of meals. Is the cost of the meal plan a linear or non-linear function? Explain. 8 meals: $125/week 10 meals: $135/week 12 meals: $155/week 21 meals: $220/week Go to website: Search.aspx?view=search& gr=6-8 Choose a resource to explore. 24 You have a cylinder with a diameter of 15 inches and height of 12 inches. What is the volume of the largest sphere that will fit inside of it? 25 You want to fill the cylinder shown below with water. All you have is a container shaped like a cone with a radius of 3 inches and a height of 5 inches; you can use this cone-shaped container to take water from a faucet and fill the cylinder. How many cones will it take to fill the cylinder? 26 Randy began completing the table below to represent a particular linear function. Write an equation to represent the function he used, and complete the table for him. x ½ y Create the graph of the function from the table and equation from June Three consecutive integers have a sum of 234. What are the integers?

5 July 2014 Entering Ninth Grade Mathematics Calendar Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 Determine the volume in terms of π. 2 Solve the following equation for a number, x. Verify that your solution is correct. 7(2x + 5) = 4x 9 x 3 Choose an activity at Math Illuminations. 4 Holiday 5 Record what you did. 6 7 Play a strategy game. Examples include Monopoly, Parcheesi, Mancala, and Connect Four. What strategy did you use? 8 Gil is reading a book that has 276 pages. He has already read some of it last week. He plans to read 20 pages tomorrow. By then, he will be ⅔ of the way through the book. How many pages did Gil read last week? 9 Can Figure A be mapped onto Figure B using only translation? Explain. Use drawings, as needed, in your explanation. 10 A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is your walk if you walk diagonally across the park than along two sides of the park? 11 Visit the website: Play a game with positive & negative integers Ofelia has a certain amount of money. If she spends $12, then she has 1/5 of the original amount left. How much money did Ofelia have originally? Show your work. 15 Play Sudoku from the newspaper. How did logic help you to solve the puzzle? 16 Visit the website Figure this and solve a real life math challenge. html 17 Using an example, illustrate and explain the Pythagorean Theorem. 18 Find the distance between the points (3,1) and (5,6). 19

6 20 21 Visit the website: and play Connect Three with positive & negative integers. 22 There is still controversy about whether or not Pluto should be considered a planet. Though planets are mainly defined by their orbital path (the conditional that prevented Pluto from remaining a planet) the issue of size is something to consider. The table below lists the planets, including Pluto and their approximate diameter in meters. Planet Mercury Venus Earth Mars Jupiter Approximate Diameter (m) 4.88 * * * * * Line l 1 and line l 2 are shown on the graph below. Use the graph to answer the question. What is the y-intercept of l? What is the y-intercept of l? Write a system of linear equations representing lines l and l. 24 A group of students were asked to report their gender and how many times a day they typically wash their hands. Of the 738 males, 66 said they wash their hands at most once a day, 538 said two to seven times per day and 89 said eight or more times per day. Of the 204 females, two said they wash their hands at most once a day, 160 said two to seven times per day and 42 said eight or more times per day. Summarize these data in a twoway table with rows corresponding to the three different frequency-of-handwashing categories and columns corresponding to gender. 25 Use the problem from July 24 to answer the following: Do these data suggest an association between gender and frequency of hand washing? Support your answer with appropriate calculations. 26 Saturn 1.2 * 10 8 Uranus 5.12 * 10 7 Neptune 4.96 * 10 7 Pluto 2.3 * 10 6 Name the planets (including Pluto) in order from smallest to largest Jeremy rides his bike at a rate of 12 miles per hour. Below is a table that represents the number of hours and miles Kevin rides. Assume both bikers ride at a constant rate. Time in hours (x) Distance in miles (y) Use the information from July 28 to answer the following question: Write an equation for a third biker, Lauren, who rides twice as fast as Kevin. Use y to represent the number of miles Lauren travels in x hours. Explain your reasoning. 30 Use the problem from July 22 to answer the following: Comparing only diameters, about how many times larger is Jupiter than Pluto? 31 Use the problem from July 22 to answer the following: Assume you were a voting member of the International Astronomical Union (IAU) and the classification of Pluto was based entirely on the length of the diameter. Would you vote to keep Pluto a planet or reclassify it? Why or why not? YOU DID IT! Please bring your journal to your ninth grade teacher on the first day of school! Which biker rides at a greater speed? Explain your reasoning.

7 Grade 9 Answer Key Answers will vary for many of the activities depending on the choices students make. Here are the answers for activities with specific solutions. June 2 Part A: y = 3x 50 Part B: For every one degree increase in temperature, the number of gallons consumed increases by 3. June 3 D June 4 C June 6 11 feet wide and 19 feet long Let w = width 2w 3 = length 2(w + 2w 3) = 60 2w + 4w 6 = 60 6w = 66 w = 11 2w 3 = 19 Other processes may also result in the correct answer. June 9 The measurement of the angle is 73. Student used auxiliary lines to solve the problem, while providing substantial reasoning in written explanation including information about congruent angles being equal, straight angles having 180, triangle sum being 180, sum of remote interior angles equal to exterior angle of a triangle, etc. June 11 a. Student drew a triangle ΔOQ P according to the scale factor and labeled the points. b. the coordinates of Q are 6, 38. The coordinates of P are (6, 2). 9 c. Student states that OQP = OQ P. Student explanation includes mathematical language. Reasoning includes that D( OQP) = OQ P, and dilations are degree preserving. June 12 a. Student states that PQ P Q. Student uses mathematical language in explanation or reasoning. Reasoning includes the following facts: At least two pairs of corresponding angles are equal, e.g., O = O and/or OQP = OQ P and/or OPQ = OP Q, then by AA criterion for similarity, ΔOPQ~ΔOP Q. Then, by FTS PQ P Q. b. OQ 4. 4 units. Student uses mathematical language in explanation or reasoning. Student referenced similar triangles in reasoning. Student reasoning includes that the ratio of lengths are equal to scale factor. June 13 Student used the information provided about Store A to determine the unit rate of protractors and referenced the unit rate at Store A in the justification of their estimate. Student wrote an estimate that made sense (e.g., less than Store A, about half as much) and used evidence from the graph in their justification (e.g., comparison of slopes, size of angles). June children s tickets and 100 adult s tickets were sold June 17 y = 2x 1 June 18 The slope of the line on June 17 is 2. The points used on June 18 give a slope of -7/5. The lines will intersect because the slopes are different. June 20 The meal plan is non-linear. Explanation includes substantial mathematical reasoning. Graph may or may not be used as part of the reasoning. June 24 The largest sphere that will fit inside the cylinder would have a diameter of 12 inches since that is the limit to the height of the cylinder. The formula for the volume of a sphere is 4/3πr 3. If the diameter is 12 inches, then the radius is 6 inches. V = 4/3π(6) 3 = 288π in 3

8 June 25 It will take cones to fill the cylinder. June 26 The equation to describe the function is written correctly as y = 3x + 4. All four of the outputs are when x = 1, y = 1; when x = 1, y = 11 ; when x = 1, y = 7; and when x = 2, y = June 27 Student graphs the input/outputs correctly. The input/outputs appear to be linear. June 30 The first number is 77, the second is 78, and the third is 79. July 1 48π mm 3 July 2 The distributive property was used correctly, then simplifying/ transposing the equation leading to a correct solution (x= -4). To verify, student should put the solution into the original equation and simplify each side demonstrating that each side is equal to the other. July 8 Gil read 164 pages last week. July 9 No. Figure A cannot be translated to Figure B. Notice the piece of the object sticking out. Student may have used pictorial explanation to enhance mathematical explanation. July 10 If you walked along two sides of the park you would walk 14 miles. Use the Pythagorean Theorem to determine the length of the diagonal: c 100 c 10 c 2 14 miles 10 miles = 4 miles You would walk 4 miles less if you walked along the diagonal. July 14 x 12 = 1 x or equivalent equation 5 x = 15 Ofelia had $15 originally. July 17 Student uses different examples to explain the Pythagorean Theorem using appropriate mathematical vocabulary. One sample example is a triangle with side lengths 7cm, 24, cm and 25 cm. July July 22 Pluto, Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, Jupiter July 23 The y-intercepts of l 1 and l 2, (0, 4) and (0, 2), respectively. x y = 2 The system is or a system equivalent to this given one x + 2y = 8 July 24 A 3 2 two-way table is created, including appropriate labels.

9 July 25 Student calculates the six conditional proportions, compares them, and draws an appropriate comparison (e.g., 20% of females wash eight or more times compared to 12% of males). July 28 Jeremy rides 12mph while Kevin rides 11.5 mph, therefore, Jeremy rides at a faster speed. Student also provides a strong mathematical explanation as to which biker rides at a greater speed by referencing a graph (slopes of each line where one slope is steeper) or a numerical comparison of their rates. July 29 The correct equation is y = 23x or an equivalent equation. Student explains twice as fast in terms of distance traveled for a given time interval compared to the data for Kevin given in the table. July 30 Jupiter is approximately 62 times larger than Pluto. July 31 Students stated their position and provided a compelling explanation to defend it.