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Dear Sixth Grade Parents and Guardians, For middle school students, summer is all about getting rest, exploring new places and enjoying time with family and friends. At the same time, students need to feed their curiosity with books, games and other challenging activities. Reading is the most important part of a long summer vacation, and strength in reading comprehension is closely related to success in math. We encourage all students to read over the summer because becoming a ferocious reader often is a great way to become successful in anything, including math. The provided packet is simply a suggestion for summer practice. It is not designed as a required assignment. Each student will be given a letter from his or her teacher outlining the topics to make a priority to review over the summer. Answer keys have been provided to all worksheets. Teachers will not collect this work in September, but if your child would like feedback about the work, he or she can turn it to the teacher in September. It is also important to make math relevant to a student's daily life. Although we provide you with a packet in case you wish to follow a more structured work plan in math during summer months, we strongly recommend you try to make math a part of daily activities, instead of just going through worksheets. Either on a long road trip or a flight, exploring a new city or hiking a mountain, take the opportunity to communicate with your child through mathematics. You can be very creative with these simple “facts” of daily life, and they can add a lot of fun to cultural and natural expeditions. When students connect the concepts they are studying in their math class to real life experiences, it is incredibly valuable to their long-term development as mathematicians. In other words, trying to make use of fractions, ratios and proportions, percent, and unit conversion, all of which are constantly used when traveling, is a great way to “do” math in summer. We are sure that with your child’s curiosity and creative answers, you would enjoy math in a totally different way as well. Have a great summer! Ms. Ferrick, Ms. Simpson and Ms. Yoo Summer Math Packet Factors And Exponents Name : Score : Teacher : Date : Find the Greatest Common Factor for each number pair. 1) 8 , 30 2) 60 , 15 3) 12 , 20 4) 15 , 40 5) 24 , 30 6) 10 , 15 7) 3 , 8 8) 8 , 20 9 ) 120 , 24 10 ) 120 , 24 Math-Aids.Com Name : Score : Teacher : Date : Find the Greatest Common Factor for each number pair. 1) 8 , 30 2 2) 60 , 15 15 3) 12 , 20 4 4) 15 , 40 5 5) 24 , 30 6 6) 10 , 15 5 7) 3 , 8 1 8) 8 , 20 4 9 ) 120 , 24 24 10 ) 120 , 24 24 Math-Aids.Com Name____________________________ Date _______ Greatest Common Factor Using a Gradual Method Many students can not look at a pair of numbers and immediately find the greatest common factor. Using the following method, students can find the GCF by first finding any common factor (other than 1) to start with. 24, 42 Example: What is the GCF of 24 and 42? Common factors of 24 and 42. You must multiply all common factors you used at the end to find the GCF! 2 24, 42 2 24, 42 12, 21 1) What number can fit into the two numbers given? 2) Because both numbers are even we can start with two. 3) Because 2 goes into 24 12 times, write 12 under 24. Because 2 goes into 42 21 times, write 21 under 42. 4) Can any factor evenly fit into the two new numbers you have? YES! Three can fit into 12 and 21 so make another bracket and divide. Write the results at the bottom(4 and 7) 5) The resulting numbers, 4 and 7 share no more common factors besides one. If that is true than you must stop. Multiply all of the numbers you wrote on the left side. 2 x 3 = 6 The G.C.F. = 6 3 12, 21 4, 7 G.C.F.= 6 1) 14, 64 2) 36, 93 3) 24, 72 4) 16, 48 5) 25, 125 6) 44, 99 7) 42 , 75 8) 32, 68 9) 40, 120 10) 13) 45, 60 14) 17) 26, 46 18) ID# 0239 copyright 15, 60 40, 48 24, 140 Maisonet Math 2012 11) 13, 39 12) 27, 132 15) 55, 150 16) 24, 84 36, 54 20) 62, 100 19) www.mrmaisonet.com CCSS 6.NS.4 Name____________________________ Date _______ Greatest Common Factor Using a Gradual Method Many students can not look at a pair of numbers and immediately find the greatest common factor. Using the following method, students can find the GCF by first finding any common factor (other than 1) to start with. 24, 42 Example: What is the GCF of 24 and 42? Common factors of 24 and 42. You must multiply all common factors you used at the end to find the GCF! 14, 64 1) 2 24, 42 2 24, 42 12, 21 3 12, 21 4, 7 G.C.F.= 6 2) GCF = 2 5) 25, 125 40, 120 6) 45, 60 10) 26, 46 14) 40, 48 GCF = 8 18) GCF = 2 ID# 0239 15, 60 24, 140 GCF = 4 copyright Maisonet Math 2012 4) GCF = 24 7) 42 , 75 11) 13, 39 8) 55, 150 12) 36, 54 GCF = 18 www.mrmaisonet.com 27, 132 GCF = 3 16) GCF = 5 19) 32, 68 GCF = 4 GCF = 13 15) 16, 48 GCF = 16 GCF = 3 GCF = 15 GCF = 15 17) 44, 99 24, 72 3) GCF = 11 GCF = 40 13) 36, 93 GCF = 3 GCF = 25 9) 1) What number can fit into the two numbers given? 2) Because both numbers are even we can start with two. 3) Because 2 goes into 24 12 times, write 12 under 24. Because 2 goes into 42 21 times, write 21 under 42. 4) Can any factor evenly fit into the two new numbers you have? YES! Three can fit into 12 and 21 so make another bracket and divide. Write the results at the bottom(4 and 7) 5) The resulting numbers, 4 and 7 share no more common factors besides one. If that is true than you must stop. Multiply all of the numbers you wrote on the left side. 2 x 3 = 6 The G.C.F. = 6 24, 84 GCF =12 20) 62, 100 GCF =2 CCSS 6.NS.4 Name : Score : Teacher : Date : Find the Least Common Multiple for each number pair. 1) 3 , 2 2) 3 , 40 3) 8 , 24 4) 60 , 2 5) 12 , 8 6) 40 , 15 7) 30 , 8 8) 10 , 40 9) 20 , 2 10 ) 60 , 24 Math-Aids.Com Name : Score : Teacher : Date : Find the Least Common Multiple for each number pair. 1) 3 , 2 6 2) 3 , 40 120 3) 8 , 24 24 4) 60 , 2 60 5) 12 , 8 24 6) 40 , 15 120 7) 30 , 8 120 8) 10 , 40 40 9) 20 , 2 20 10 ) 60 , 24 120 Math-Aids.Com Name________________________________ Date ______ COMMON FACTOR STORY PROBLEMS Directions: Use common factors to answer each question. Show your work and CIRCLE your answer! 1) Harry has 16 chocolate chip cookies and 24 peanut butter cookies. Harry wants create at least 2 bags of cookies so there are some chocolate chip and some peanut butter cookies in each bag. He also wants to make sure that all the bags he creates have the same contents as every other bag. How many ways can he bag the cookies so every bag is identical in contents to each other. There should be no cookies left-over. 2) In problem number one, what is the largest amount of cookies that Harry could place in each bag? 3) In Gym class, there are 12 boys and 18 girls. The gym teacher wants to divide groups into just boys and just girls. How many people could the teacher place in each group so that all groups have the same number of people in them and still keep boy and girl only groups? 4) Marietta had 24 red licorice twists and 30 black licorice twists. How many ways could she bag them so that the two kinds are in separate bags, yet all bags would have the same number of twists in them? 5) Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the marbles up into even numbered groups. How many marbles could he place in each group so there would be the same number in the red groups as well as the blue groups? ID# 0238 copyright Maisonet Math 2012 www.mrmaisonet.com CCSS 6.NS.4 Name________________________________ Date ______ COMMON FACTOR STORY PROBLEMS Directions: Use common factors to answer each question. Show your work and CIRCLE your answer! 1) Harry has 16 chocolate chip cookies and 24 peanut butter cookies. Harry wants create at least 2 bags of cookies so there are some chocolate chip and some peanut butter cookies in each bag. He also wants to make sure that all the bags he creates have the same contents as every other bag. How many ways can he bag the cookies so every bag is identical in contents to each other. There should be no cookies left-over. 2 16 , 24 8 12 8 16 , 24 2 3 4 16 , 24 There are 3 ways to bag the cookies. Harry can bag the cookies the following ways: 2 bags 4 bags 8 bags 8 CC 12 PB in each bag. 4 CC 6 PB in each bag. 2 CC 3 PB in each bag. 4 6 2) In problem number one, what is the largest amount of cookies that Harry could place in each bag? The largest number of cookies that Harry can bag is 20. Out of the 20 , 8 of the cookies would be chocolate chip and 12 would be peanut butter. 3) In Gym class, there are 12 boys and 18 girls. The gym teacher wants to divide groups into just boys and just girls. How many people could the teacher place in each group so that all groups have the same number of people in them and still keep boy and girl only groups? 6 12 , 18 2 3 The gym teacher can create groups of 6. The boys can make 2 groups of 6. The girls can create 3 groups of 6. 4) Marietta had 24 red licorice twists and 30 black licorice twists. How many ways could she bag them so that the two kinds are in separate bags, yet all bags would have the same number of twists in them? 6 24 , 30 4 5 Marietta can bag 6 of each kind in every bag. Red licorice = four bags of 6 = 24 Black licorice = five bags of 6 = 30 5) Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the marbles up into even numbered groups. How many marbles could he place in each group so there would be the same number in the red groups as well as the blue groups? 7 28 , 35 4 5 Malik can make groups of seven marbles for both colors. Malik can make 4 bags of 7 red marbles. Malik can also make 5 bags of 7 blue marbles,. ID# 0238 copyright Maisonet Math 2012 www.mrmaisonet.com CCSS 6.NS.4 Name_________________________________ Date_______ Assessment Exponents, GCF, LCM, Prime Factorization, Order Of Operations 5 1) Write 3 in expanded form. ___________________________ 2) Write 8 x 8 x 8 x 8 in exponential form._____________________ Evaluate the following. Circle the correct choice. 3) 3 4 4) 8 a) 12 b) 24 c) 81 d) 108 2 5) 8 + 7 x 3 - 6 = 6) a) 23 b) 25 c) 30 d) 35 a) 56 b) 64 c) 81 d) 100 2 (12 - 6) + 2 x 4 = a) 12 b) 20 c) 24 d) 44 Use the order of operations to solve the following. Circle the correct choice. 2 2 2 7) 4 + 3 - 3 = 8) 5+4÷2x3= a) 19 b) 22 c) 55 d) 60 a) 29 b) 32 c) 53 d) 60 9) (9 + 6) x 5 ÷ 5 = a) 5 b) 8 c) 10 d) 15 Use a < , > or = to compare the following values. 10) ID# 0021 5 0 1 1 copyright 11) 5 2 Maisonet Math 2012 2 4 12) 5 3 www.mrmaisonet.com 12 2 13) CCSS 6.EE.1 3 3 5 6.EE.2 6.NS.4 2 14) A carpenter wants to use screws to attach two boards together for strength. He takes the first board and drills holes every 16 inches. He asks his friend to drill holes in the other board, but his friend accidentally drills every 6 inches instead of 16 to match the other board. How many inches will it be before two holes will match up? a) 20 in. b) 32 in. c) 48 in. d) 80 in. 15) A radio station was giving away free movie passes for every 6th caller and a free DVD for every 8th caller for the first 50 callers. How many people out the first 50 callers would win movie passes and a free DVD? a) 2 callers b) 6 callers c) 8 callers d) 14 callers 16) A carpenter made a flower box that was 2 feet wide by 12 feet in length to make an area of 24 square feet. Including the dimensions of 2 x 12, how many total ways can the carpenter create a flower box that would make an area of 24 square feet? a) 2 ways b) 3 ways c) 4 ways d) 5 ways ID# 0021 copyright Maisonet Math 2012 www.mrmaisonet.com CCSS 6.EE.1 6.EE.2 6.NS.4 The following are prime factorizations of different numbers. Find what numbers they are prime factorizations of. 17) 2 • 5² 19) 2²• 3 ² 18) 3 • 5 • 7 20) What is the greatest common factor of 60 and 72? 21) List all the factors of 36. 22) What is the least common multiple of 20 and 25? Solve the following. 23) k = 27 - 5 x 4 + 2 24) d = 5 x (12 + 7) - 8 25) s = (5 - 3)² x 3 +2 Place a P next to the number if it is prime and a C if it is composite. 26) 13 ____ 27) 9 ___ 28) 30 ____ 29) 31_____ 30) 17______ Do a prime factorization of the following numbers. 31) ID# 0021 copyright 32) 28 Maisonet Math 2012 www.mrmaisonet.com 81 CCSS 6.EE.1 6.EE.2 6.NS.4 Name_________________________________ Date_______ Assessment Exponents, GCF, LCM, Prime Factorization, Order Of Operations 5 3x3x3x3x3 1) Write 3 in expanded form. ___________________________ 4 8 2) Write 8 x 8 x 8 x 8 in exponential form._____________________ Evaluate the following. Circle the correct choice. 3) 3 4 4) 8 a) 12 b) 24 c) 81 d) 108 2 5) 8 + 7 x 3 - 6 = 6) a) 23 b) 25 c) 30 d) 35 a) 56 b) 64 c) 81 d) 100 2 (12 - 6) + 2 x 4 = a) 12 b) 20 c) 24 d) 44 Use the order of operations to solve the following. Circle the correct choice. 2 2 7) 4 + 3 - 3 = 8) a) 19 b) 22 c) 55 d) 60 a) 29 b) 32 c) 53 d) 60 2 5+4÷2x3= 9) (9 + 6) x 5 ÷ 5 = a) 5 b) 8 c) 10 d) 15 Use a < , > or = to compare the following values. 10) ID# 0021 5 0 = 1 1 copyright 11) 5 2 Maisonet Math 2012 > 2 4 12) 5 3 > www.mrmaisonet.com 12 2 13) CCSS 6.EE.1 3 3 > 5 6.EE.2 2 6.NS.4 14) A carpenter wants to use screws to attach two boards together for strength. He takes the first board and drills holes every 16 inches. He asks his friend to drill holes in the other board, but his friend accidentally drills every 6 inches instead of 16 to match the other board. How many inches will it be before two holes will match up? a) 20 in. b) 32 in. c) 48 in. d) 80 in. Strategy: Use least common multiple to solve. Board one - 16 , 32 , 48 . Board two - 6, 12, 18, 24, 30, 36, 42,. 48 It would be 48 inches before a hole would match up on each board. 15) A radio station was giving away free movie passes for every 6th caller and a free DVD for every 8th caller for the first 50 callers. How many people out the first 50 callers would win movie passes and a free DVD? a) 2 callers b) 6 callers c) 8 callers d) 14 callers Strategy - Use lcm to solve. Every 6th caller out of the first 50 get a Movie Pass. The 6th, 12 th, 18th, 24 th, 30th, 36 th, 42nd, and the 48 th caller would get movie passes. Every 8th caller will get a DVD. The 8th, 16 th, 16th, 24 th, 32nd, 40nd, and the 48 th caller will receive a DVD. The 24th and 48th person will be considered every 6th and every 8th caller. So two people will receive a movie pass and a DVD! 16) A carpenter made a flower box that was 2 feet wide by 12 feet in length to make an area of 24 square feet. Including the dimensions of 2 x 12, how many total ways can the carpenter create a flower box that would make an area of 24 square feet? a) 2 ways b) 3 ways c) 4 ways d) 5 ways ID# 0021 Strategy - Find all the factor pairs that will produce 24. 1 x 24 2 x 12 3 x 8 and 4 x 6 . There are 4 different ways to make 24! copyright Maisonet Math 2012 www.mrmaisonet.com CCSS 6.EE.1 6.EE.2 6.NS.4 The following are prime factorizations of different numbers. Find what numbers they are prime factorizations of. 17) 2 • 5² 2x5x5 10 x 5 50 19) 2²• 3 ² 18) 3 • 5 • 7 3x5x7 15 x 7 105 2x2x3x3 4x9 36 20) What is the greatest common factor of 60 and 72? 12 is the GCF of 60 and 72. 21) List all the factors of 36. The numbers listed are factors of 36 because 36 is evenly divisible by each one. 1, 2, 3, 4, 6, 9, 12, 18, 36 22) What is the least common multiple of 20 and 25? 20 - 40 - 60 - 80 - 100 25 - 50 - 75 - 100 100 is the LCM of 20 and 25 Solve the following. 23) k = 27 - 5 x 4 + 2 k = 27 - 20 + 2 k=7+2 k=9 25) s = (5 - 3)² x 3 +2 s = (2) x 3 + 2 s=4x3+2 s = 12 + 2 s = 14 24) d = 5 x (12 + 7) - 8 d = 5 x 19 - 8 d = 95 - 8 d = 87 Place a P next to the number if it is prime and a C if it is composite. P 26) 13 ____ C 27) 9 ___ C 28) 30 ____ P 29) 31_____ P 30) 17______ Do a prime factorization of the following numbers. 31) 4 2 32) 28 x x 2 7 x 9 7 3 ² 2•7 ID# 0021 copyright Maisonet Math 2012 81 x x 3x3x 3 3 www.mrmaisonet.com 9 4 CCSS 6.EE.1 6.EE.2 6.NS.4 Fractions and Decimals Name__________________________________ Date_________ Percentage Practice Write the following decimals as a percent. 1) 0.24 6) 0.99 11) 0.045 16) 3.24 2) 0.08 7) 0.6 12) 0.098 17) 4.02 3) 0.12 8) 0.09 13) 0.015 18) 9.23 4) 0.8 9) 0.19 14) 0.432 19) 7.343 5) 0.03 10) 0.37 15) 0.3 20) 1.5 Directions: Express as a fraction, decimal and percent what part of each object below is shaded. 21) 22) Fraction 23) Fraction Decimal Decimal Percentage Percentage 24) Fraction Fraction Decimal Decimal Percentage Percentage 25) Explain how you can tell which of the four objects above is more than 60% shaded using mental math!! ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ID# 0269 copyright Maisonet Math 2012 www.mrmaisonet.com CCSS 6.RP.3 Draw a line matching the value on the left with its equivalent value on the right. The pie chart below represents the favorite pets of 40 students in Mr. Smith’s class. Answer the following questions using the pie chart below. Favorite Pets 0.0825 26) 0.03 25% 35% Cats 75% 27) 4.23 3 8 28) 8.25% 29) 1 8 0.6 30) 60% 3% 31) 0.375 423% 32) 9 12 0.125 33) If 100 % of is and 50% of is Draw picture here. 34) Tony answered 28 out of 35 questions correctly on his test. What percent did Tony answer correctly? copyright 20% Reptiles 20% Rodents 35) What fraction of Mr. Smith’s class said their favorite pet was a rodent? Express answers in lowest terms. 36) What fraction of Mr. Smith’s class said their favorite pet is either a cat or a dog? Express answer in lowest terms. 37) There are 40 students in Mr. Smith’s class. How many must of said that they like reptiles as pets? what is 25% of ID# 0269 Dogs Maisonet Math 2012 Directions: Using the choices given in the answer bank, write the only value which would complete the list from the greatest to the smallest value. Not all choices will be used. BANK 38) 45% _____ 0.3 7% 39) 0.8 _____ 65% 40) 25% _____ 1 5 41) 0.09 ______ 5% 42) 0.2 ______ 0.1 www.mrmaisonet.com 0.22 2 5 0.7 90% 15% 0.28 0.04 CCSS 6.RP.3 Name__________________________________ Date_________ Percentage Practice Write the following decimals as a percent. 1) 0.24 24% 6) 0.99 99% 11) 0.045 4.5% 16) 3.24 324% 2) 0.08 8% 7) 0.6 60% 12) 0.098 9.8% 17) 4.02 402% 3) 0.12 12% 8) 0.09 24% 13) 0.015 24% 18) 9.23 24% 4) 0.8 24% 9) 0.19 19% 14) 0.432 43.2% 19) 7.343 734.3% 5) 0.03 3% 10) 0.37 37% 15) 0.3 30% 20) 1.5 150% Directions: Express as a fraction, decimal and percent what part of each object below is shaded. Express each fraction in lowest terms. 21) 23) Fraction 3 4 Fraction 2 5 Decimal 0.75 Decimal 0.4 Percentage 75% Percentage 40% 22) 1 2 Fraction 24) 0.5 Decimal Percentage 3 5 Fraction 0.6 Decimal 50% Percentage 60% 25) Explain how you can tell which of the four objects above is more than 60% shaded using mental math!! You can tell that the object in problem 21 is more than 60% shaded. 60% is a little more than half. It is easy to ________________________________________________________________________ ________________________________________________________________________ see that the figure in problem 21 is shaded significantly more than half. ________________________________________________________________________ ________________________________________________________________________ ID# 0269 copyright Maisonet Math 2012 www.mrmaisonet.com CCSS 6.RP.3 Draw a line matching the value on the left with its equivalent value on the right. The pie chart below represents the favorite pets of 40 students in Mr. Smith’s class. Answer the following questions using the pie chart below. Favorite Pets 0.0825 26) 0.03 25% 35% Cats 75% 27) 4.23 3 8 28) 8.25% 29) 1 8 0.6 30) 60% 3% 31) 0.375 423% 32) 9 12 0.125 20% Reptiles 20% Rodents 35) What fraction of Mr. Smith’s class said their favorite pet was a rodent? Express answers in lowest terms. 1 5 of the class chose rodents as their favorite pet. 36) What fraction of Mr. Smith’s class said their favorite pet is either a cat or a dog? Express answer in lowest terms. 3 5 33) If 100 % of Dogs of the class chose dogs or cats as their favorite pet. 37) There are 40 students in Mr. Smith’s class. How many must of said that they like reptiles as pets? is 20% of 40 students is the same as 0.2 x 40 is and 50% of 8 students said they like reptiles as their favorite pet. what is 25% of Draw picture here. 34) Tony answered 28 out of 35 questions correctly on his test. What percent did Tony answer correctly? 28 4 = 35 5 ID# 0269 = 80% copyright Maisonet Math 2012 Directions: Using the choices given in the answer bank, write the only value which would complete the list from the greatest to the smallest value. Not all choices will be used. 2 BANK 5 0.3 38) 45% _____ 39) 0.7 65% 0.8 _____ 40) 0.22 25% _____ 1 5 41) 7% 5% 0.09 ______ 42) 15% 0.1 0.2 ______ www.mrmaisonet.com 7% 0.22 2 5 0.7 90% 15% 0.28 0.04 CCSS 6.RP.3 Name____________________________________ Date_______ Problem Solving Decimals, Fractions and Percents 1) Henry had $24.12. His friend Greg had onehalf as much as Henry. Another friend Kasey had one-fourth of what Henry has. How much money do the three friends have altogether? 2) Dionte, George and Tayvion were growing plants for science class. Dionte’s plant grew to a height of 24 cm. George’s plant grew to a height 75% the height of Dionte’s. Tayvion’s plant grew twice as tall as Dionte’s plant. What is the total height of all three plants? 3) In 2009, a local restaurant posted annual earnings of $400,000. Because of a slow local economy, the same restaurant in 2010 posted earnings that were 80% of what they were in 2009. How much did the restaurant earn in 2010? 4) Kyla decided to go on a diet to lose a few pounds. Kyla lost 10% of her body weight after three months of dieting. If Kyla lost 15 pounds, how much did she weigh at the beginning of her diet? 5) The theoretical probability of rolling a number cube and landing on an even number is onehalf. However, when James rolled a number cube 24 times, he landed on an even number one-third of the time. How many times did James land on an even number? 6) Tyler has 80 jellybeans. His younger brother has 60% the amount Tyler has. How many jellybeans does Tyler and his brother have altogether? 7) In a town called Littleton, it rained 4.5 inches during the month of May. In June it rained three times the amount that it did in May. In July it rained one-third of the amount that it rained in May. What is the rainfall total of May, June and July? 8) Ashley earned $480 by babysitting children in her neighborhood during the summer. At the end of summer, Ashley spent 20% of her earnings and saved the rest. How much money did Ashley save? ID# 0135 copyright Maisonet Math 2012 www.mrmaisonet.com CCSS 5.NF.4 6.RP.3 Name____________________________________ Date_______ Problem Solving Decimals, Fractions and Percents 1) Henry had $24.12. His friend Greg had onehalf as much as Henry. Another friend Kasey had one-fourth of what Henry has. How much money do the three friends have altogether? $42.21 Dionte, George and Tayvion were growing plants for science class. Dionte’s plant grew to a height of 24 cm. George’s plant grew to a height 75% the height of Dionte’s. Tayvion’s plant grew twice as tall as Dionte’s plant. What is the total height of all three plants? Henry ---- 24.12 < – This amount was given. Greg ----- 12.06 <---because 1/2 of 24.12 is 12.06 Kasey ----- 6.03 < --because 1/4 of 24.12 is 6.03 Dionte — 24 cm George - 18 cm <--75% of 24 is 18. Tayvion - 48 cm <---2 times 24 is 48 90 cm 42. 21 <-- total of the three friends. In 2009, a local restaurant posted annual earnings of $400,000. Because of a slow local economy, the same restaurant in 2010 posted earnings that were 80% of what they were in 2009. How much did the restaurant earn in 2010? 3) 2) 90 cm <---- total height of three plants 4) $320,000 Kyla weighed 150 pounds at the beginning of her diet. 10% of 150 pounds is 15 pounds. To find 80% of $400,000, multiply 400,000 by 0.8. 0.8 is 80% written as a decimal. 5) The theoretical probability of rolling a number cube and landing on an even number is onehalf. However, when James rolled a number cube 24 times, he landed on an even number one-third of the time. How many times did James land on an even number? 6) In a town called Littleton, it rained 4.5 inches during the month of May. In June it rained three times the amount that it did in May. In July it rained one-third of the amount that it rained in May. What is the rainfall total of May, June and July? The total amount during the given three months is 19.5 inches. May - 4.5 June - 13.5 July - 1.5 <--- was given <---- 3 times May <--- 1/3 of may copyright 60% of 80 is 48. You must add 48 and 80 to find out how many jellybeans Tyler and his brother have altogether. 8) Ashley earned $480 by babysitting children in her neighborhood during the summer. At the end of summer, Ashley spent 20% of her earnings and saved the rest. How much money did Ashley save? Ashley saved $384 dollars. if Ashley spent 20%, she must have saved 80% 80% of $480 is $384. Multiply $480 by 0.8 to find 80% of $480. 19.5 inches ID# 0135 Tyler has 80 jellybeans. His younger brother has 60% the amount Tyler has. How many jellybeans does Tyler and his brother have altogether? 128 jellybeans James landed on an even number 8 times out of 24. 8 out of 24 is equal to 1/3. 7) Kyla decided to go on a diet to lose a few pounds. Kyla lost 10% of her body weight after three months of dieting. If Kyla lost 15 pounds, how much did she weigh at the beginning of her diet? Maisonet Math 2012 www.mrmaisonet.com CCSS 5.NF.4 6.RP.3 Name : Score : Teacher : Date : x 78.42 100 x 99.43 100 x 23.93 10 x 49.72 100 x 59.94 1000 x 63.37 10 x 86.43 1000 x 97.87 1000 x 59.27 100 x 12.98 100 x 26.18 1000 x 39.53 10 x 15.85 1000 x 96.33 100 x 13.12 100 x 45.63 1000 x 91.55 10 x 25.67 1000 x 97.71 1000 x 27.57 10 x 40.69 100 x 90.24 10 x 19.29 10 x 25.95 100 x 47.69 10 Math-Aids.Com Name : Score : Teacher : Date : x 78.42 100 7842.00 x 99.43 100 9943.00 x 23.93 10 239.30 x 49.72 100 4972.00 x 59.94 1000 59940.00 x 63.37 10 633.70 x 86.43 1000 86430.00 x 97.87 1000 97870.00 x 59.27 100 5927.00 x 12.98 100 1298.00 x 26.18 1000 26180.00 x 39.53 10 395.30 x 15.85 1000 15850.00 x 96.33 100 9633.00 x 13.12 100 1312.00 x 45.63 1000 45630.00 x 91.55 10 915.50 x 25.67 1000 25670.00 x 97.71 1000 97710.00 x 27.57 10 275.70 x 40.69 100 4069.00 x 90.24 10 902.40 x 19.29 10 192.90 x 25.95 100 2595.00 x 47.69 10 476.90 Math-Aids.Com Percent Name : Score : Teacher : Date : Percentage Calculations Round your answer to two decimal points if required. 1 ) 30% x 85 = ___ 6 ) 0.01 x 65 = ___ 2 ) 35% x 70 = ___ 7 ) 51 ÷ 97 = ___ % 3 ) 72 ÷ 0.45 = ___ 8 ) 50 ÷ 65 = ___ % 4 ) 68 ÷ 0.46 = ___ 9 ) 88 ÷ 76 % = ___ 5 ) 0.5 x 70 = ___ 10 ) 51 ÷ 11 % = ___ Math-Aids.Com Name : Score : Teacher : Date : Percentage Calculations Round your answer to two decimal points if required. 1 ) 30% x 85 = 25.5 6 ) 0.01 x 65 = 0.65 2 ) 35% x 70 = 24.5 7 ) 51 ÷ 97 = 52.58 % 3 ) 72 ÷ 0.45 = 160 8 ) 50 ÷ 65 = 76.92 % 4 ) 68 ÷ 0.46 = 147.83 9 ) 88 ÷ 76 % = 115.79 5 ) 0.5 x 70 = 35 10 ) 51 ÷ 11 % = 463.64 Math-Aids.Com Name : Score : Teacher : Date : Converting Between Percents, Decimals, and Fractions Convert Decimal to Percent 1.82 = 0.45 = 0.654 = 1.19 = 0.333 = 0.785 = 189 % = 59.8 % = 83 % = 14 % = 29 % = 19.6 % = 1.55 = 0.475 = 0.33 = 1.63 = 0.24 = 0.64 = 7 __ 50 3 __ 20 25 __ 20 45 __ 25 Convert Percent to Decimal Convert Decimal to Fraction Convert Fraction to Decimal 99 __ 50 1 __ 10 = = = = = = Convert Fraction to Percent 29 __ 25 13 __ 10 = = 1 __ 8 13 __ 50 = = 3 __ 25 23 __ 20 = = Convert Percent to Fraction 9%= 47.7 % = 69.9 % = 62 % = 138 % = 83.9 % = Math-Aids.Com Name : Score : Teacher : Date : Converting Between Percents, Decimals, and Fractions Convert Decimal to Percent 1.82 = 182 % 0.45 = 45 % 0.654 = 65.4 % 1.19 = 119 % 0.333 = 33.3 % 0.785 = 78.5 % 189 % = 1.89 59.8 % = 0.598 83 % = 0.83 14 % = 0.14 29 % = 0.29 19.6 % = 0.196 Convert Percent to Decimal Convert Decimal to Fraction 1.55 = 155 ___ 1.63 = 163 ___ 100 = 31 ___ 20 100 0.475 = 475 ___ 1000 0.24 = 24 ___ 100 = 19 ___ = 6 ___ 40 25 0.33 = 33 ___ 0.64 = 64 ___ 100 100 = Convert Fraction to Decimal 99 __ 50 1 __ 10 7 __ 50 3 __ 20 = 1.98 = 0.1 25 __ 20 45 __ 25 = 0.14 = 0.15 = 1.25 = 1.8 Convert Fraction to Percent 29 __ 25 13 __ 10 1 __ 8 13 __ 50 = 116 % = 130 % 3 __ 25 23 __ 20 = 12.5 % = 26 % = 12 % = 115 % Convert Percent to Fraction 9%= 9 ___ 62 % = 62 ___ 100 100 = 31 ___ 50 47.7 % = 477 ___ 1000 138 % = 138 ___ 100 = 69 ___ 50 69.9 % = 699 ___ 1000 83.9 % = 839 ___ 1000 Math-Aids.Com 16 ___ 25 Name : Score : Teacher : Date : Multiplying by Percents that are Powers of Ten 1 ) What is 10 percent of 15 ? 6 ) What is 10 percent of 12 ? 2 ) What is 10 percent of 87 ? 7 ) What is 1 percent of 13 ? 3 ) What is 1 percent of 38 ? 8 ) What is 100 percent of 60 ? 4 ) What is 100 percent of 84 ? 9 ) What is 100 percent of 48 ? 5 ) What is 100 percent of 92 ? 10 ) What is 10 percent of 15 ? Math-Aids.Com Name : Score : Teacher : Date : Multiplying by Percents that are Powers of Ten 1 ) What is 10 percent of 15 ? 10% x 15 = 0.1 x 15 = 1.5 2 ) What is 10 percent of 87 ? 10% x 87 = 0.1 x 87 = 8.7 3 ) What is 1 percent of 38 ? 1% x 38 = 0.01 x 38 = 0.38 4 ) What is 100 percent of 84 ? 100% x 84 = 1 x 84 = 84 5 ) What is 100 percent of 92 ? 100% x 92 = 1 x 92 = 92 6 ) What is 10 percent of 12 ? 10% x 12 = 0.1 x 12 = 1.2 7 ) What is 1 percent of 13 ? 1% x 13 = 0.01 x 13 = 0.13 8 ) What is 100 percent of 60 ? 100% x 60 = 1 x 60 = 60 9 ) What is 100 percent of 48 ? 100% x 48 = 1 x 48 = 48 10 ) What is 10 percent of 15 ? 10% x 15 = 0.1 x 15 = 1.5 Math-Aids.Com Rate Name ____________________________________________ Date _______ Equivalent Rates vs. Unit Rates Directions: Find the value to complete each equivalent rate and each unit rate. 1. 2. Equivalent Rate: Unit Rate: 6 months 3 books read 6 months 3 books read = = 12 months = 4 cookies $1.60 Unit Rate: 1 book read 3. $1.60 Equivalent Rate: = 4 cookies 20 cookies 1 cookie 4. Equivalent Rate: Unit Rate: 22,000 people 2 square miles 22,000 people 2 square miles = = 12 square miles Equivalent Rate: Unit Rate: 1 square mile 5. 3 miles 30 minutes 3 miles 30 minutes = = 9 miles 1 minute 6. Equivalent Rate: Unit Rate: 64 females 100 teachers 64 females 100 teachers = = 25 teachers Equivalent Rate: Unit Rate: 1 teacher 7. 24 candies 4 bags 24 candies 4 bags = = 54 candies 1 bag 8. Equivalent Rate: Unit Rate: ID# 0531 $500 40 hours $500 40 hours copyright = = 30 hours 1 hour Maisonet Math Equivalent Rate: Unit Rate: 1,520 miles 2 hours 1,520 miles 2 hours www.mrmaisonet.com = = 6 hours 1 hour CCSS 6.RP.A.2 6.RP.A.3 9. 10. Equivalent Rate: Unit Rate: 48 meters 6 seconds 48 meters 6 seconds = = 9 seconds Equivalent Rate: Unit Rate: 1 second 11. 24 problems = 48 minutes 24 problems = 48 minutes 240 minutes 1 minute 12. Equivalent Rate: Unit Rate: 79,200 people 3 square miles 79,200 people 3 square miles = = 15 square miles Equivalent Rate: Unit Rate: 1 square mile 13. 30,000,000 stars 3 cubic parsecs 30,000,000 stars 3 cubic parsecs = = 50,000,000 stars 1 cubic parsec 14. Equivalent Rate: Unit Rate: 36 millimeters 12 months 36 millimeters 12 months = = 3 months Equivalent Rate: Unit Rate: 1 month 15. 340 miles 5 hours 340 miles 5 hours = = 476 miles 1 hour 16. Equivalent Rate: Unit Rate: 112 km 8 hours 112 km 8 hours = = 56 km Equivalent Rate: Unit Rate: 1 hour 17. $168 7 hours $168 7 hours = = 35 hours 1 hour 18. Equivalent Rate: Unit Rate: ID# 0531 105 liters 3 minutes 105 liters 3 minutes copyright = = 70 liters 1 minute Maisonet Math Equivalent Rate: Unit Rate: 1,750 sq. ft. 5 lbs. of seed 1,750 sq. ft. 5 lbs. of seed www.mrmaisonet.com = = 10 lbs. of seed 1 lb. of seed CCSS 6.RP.A.2 6.RP.A.3 Name ____________________________________________ Date _______ Equivalent Rates vs. Unit Rates Directions: Find the value to complete each equivalent rate and each unit rate. 1. 2. Equivalent Rate: Unit Rate: 6 months 3 books read 6 months 3 books read = = 12 months 6 books read 2 months = 4 cookies $1.60 Unit Rate: 1 book read 3. $1.60 Equivalent Rate: = 4 cookies $8.00 20 cookies $0.40 1 cookie 4. Equivalent Rate: Unit Rate: 22,000 people 2 square miles 22,000 people 2 square miles = 132,000 people = 11,000 people 12 square miles Equivalent Rate: Unit Rate: 1 square mile 5. 3 miles 30 minutes 3 miles 30 minutes = 9 miles 90 minutes = 0.1 mile = 54 candies 1 minute 6. Equivalent Rate: Unit Rate: 64 females 100 teachers 64 females 100 teachers = = 16 females 25 teachers Equivalent Rate: 0.64 females Unit Rate: 1 teacher 7. 24 candies 4 bags 24 candies 4 bags = 9 bags 6 candies 1 bag 8. Equivalent Rate: Unit Rate: ID# 0531 $500 40 hours $500 40 hours copyright = = $375 30 hours $12.50 1 hour Maisonet Math Equivalent Rate: Unit Rate: 1,520 miles 2 hours 1,520 miles 2 hours www.mrmaisonet.com = 4,560 miles = 760 miles 6 hours 1 hour CCSS 6.RP.A.2 6.RP.A.3 9. 10. Equivalent Rate: Unit Rate: 48 meters 6 seconds 48 meters 6 seconds = 12 meters = 8 meters 9 seconds Equivalent Rate: Unit Rate: 1 second 11. 24 problems 48 minutes 24 problems 48 minutes = 120 problems = 0.5 problems 240 minutes 1 minute 12. Equivalent Rate: Unit Rate: 79,200 people 3 square miles 79,200 people 3 square miles = = 396,000 people 15 square miles Equivalent Rate: 26,400 people Unit Rate: 1 square mile 13. 30,000,000 stars 3 cubic parsecs 30,000,000 stars 3 cubic parsecs = 50,000,000 stars = 10,000,000 stars 5 cubic parsecs 1 cubic parsec 14. Equivalent Rate: Unit Rate: 36 millimeters 12 months 36 millimeters 12 months = 9 millimeters = 3 millimeters 3 months Equivalent Rate: Unit Rate: 1 month 15. 340 miles 5 hours 340 miles 5 hours = 476 miles = 68 miles 7 hours 1 hour 16. Equivalent Rate: Unit Rate: 112 km 8 hours 112 km 8 hours = = 56 km 4 hours Equivalent Rate: 14 km 1 hour 17. Unit Rate: $168 7 hours $168 7 hours = = $840 35 hours $24 1 hour 18. Equivalent Rate: Unit Rate: ID# 0531 105 liters 3 minutes 105 liters 3 minutes copyright = = 70 liters 2 minutes 35 liters 1 minute Maisonet Math Equivalent Rate: Unit Rate: 1,750 sq. ft. 5 lbs. of seed 1,750 sq. ft. 5 lbs. of seed www.mrmaisonet.com = = 3,500 sq. ft. 10 lbs. of seed 350 sq. ft. 1 lb. of seed CCSS 6.RP.A.2 6.RP.A.3 Name ________________________________________ Date _________ Unit Rates When The Amount Received Is A Fraction Directions: Solve each of the following by finding a unit rate. Express each fraction in simplest form. Write your answer in a complete sentence and as a ratio. Express the ratio as a unit rate. 1. If 5 friends equally share 4 cookies, how much 2. Twelve friends ordered 4 pizzas. If the pizzas 3. Eight prospectors looking for gold agreed that 4. Nine students needed rope for a class project. 5. Ten gardeners at a community garden equally 6. How much would each of 8 friends receive if 7. I t t o o k M e l a n i e 3 2 m i n u t e s t o r e a d 8. Twenty-seven guests shared three cakes. If both of a cookie will each friend receive? they would equally share any gold that they found. If they collectively found 2 ounces of gold, how much would each person get? shared 6 cubic feet of soil. How much of a cubic foot did each gardener receive? 64 pages. On average, how long did it take Melanie to read each page? 9. Six individuals ran a 4-mile relay. Each runner had to run an equal distance. How far did each individual run? ID# 0530 copyright Maisonet Math are equally shared, how much pizza will each friend receive? The teacher gives the students 6 feet of rope to equally share. If each student receives the same amount of rope, what length will each student receive they equally share 6 lbs. of ground beef? cakes were completely eaten, how much did each guest receive if each person ate the same amount? 10. In a hot dog eating contest, Timothy ate 12 hot dogs in 6 minutes. On average, how long did it take Timothy to eat each hot dog? www.mrmaisonet.com CCSS 6.RP.A.2 Name ________________________________________ Date _________ Unit Rates When The Amount Received Is A Fraction Directions: Solve each of the following by finding a unit rate. Express each fraction in simplest form. Write your answer in a complete sentence and as a ratio. Express the ratio as a unit rate. 1. If 5 friends equally share 4 cookies, how much of a cookie will each friend receive? Each friend will receive O of a cookie. O cookie: 1 friend are equally shared, how much pizza will each friend receive? Each friend would receive # of a pizza. # cookie: 1 friend 3. Eight prospectors looking for gold agreed that they would equally share any gold that they found. If they collectively found 2 ounces of gold, how much would each person get? Each person would receive $ of an ounce. $ ounce: 1 person 4. Nine students needed rope for a class project. The teacher gives the students 6 feet of rope to equally share. If each student receives the same amount of rope, what length will each student receive Each student would receive L of a foot. L foot: 1 student 5. Ten gardeners at a community garden equally shared 6 cubic feet of soil. How much of a cubic foot did each gardener receive? Each gardener would receive of a cubic foot. N 6. How much would each of 8 friends receive if they equally share 6 lbs. of ground beef? Each friend would receive N cubic foot: 1 gardener P of a pizza. P of a pizza: 1 friend 7. I t t o o k M e l a n i e 3 2 m i n u t e s t o r e a d 64 pages. On average, how long did it take Melanie to read each page? On average Melanie read one page in of a minute. @ @ page: 1 minute 8. Twenty-seven guests shared three cakes. If both cakes were completely eaten, how much did each guest receive if each person ate the same amount? Each guest would receive ( ) of! a cake. ( cake: 1 guest 9. Six individuals ran a 4-mile relay. Each runner had to run an equal distance. How far did each individual run? Each runner would have to run L of a mile. L mile: 1 runner ID# 0530 2. Twelve friends ordered 4 pizzas. If the pizzas 10. In a hot dog eating contest, Timothy ate 12 hot dogs in 6 minutes. On average, how long did it take Timothy to eat each hot dog? On average Timothy ate each hot dog in of a minute. @ @ minute: 1 hot dog copyright Maisonet Math www.mrmaisonet.com CCSS 6.RP.A.2 Algebraic Expressions Name ___________________________________________ Date _____________ QUIZ Identifying Parts Of An Expression Algebraic Expressions And Word Phrases 1. Identify the coefficient in the expression 9x + 4. a 4 b x a 12 b m c + d 9 c - d 10 3. Which of the following choices is an example of an algebraic expression? 4. Identify the constant in the expression 12x + 8. a 8-7 b 12y - 9 a 12 b x c 9 + 12 d 3(8 - 5) c 8 d + 5. How many terms are there in the expression 9x + 8y + 3? 6. How many terms are there in the expression 24m + 12n - 14 + 2t? a 2 terms b 3 terms a 4 terms b 5 terms c 4 terms d 5 terms c 7 terms d 10 terms 7. Which of the following algebraic expressions has the same meaning as 9 less than 12 times a a number n? 8. Select the word phrase below that has the same meaning as 3(x + 8). a 9 - 12n b 12(n - 9) a 3 times x increased by 8 b triple the difference of x and 8 c 12 - 9n d 12n - 9 c triple the sum of x and 8 d 3 times 8 increased by x 9. What algebraic expression means 7 times the difference of 15 and x? 10. Select the algebraic expression that means 8 more than x. a 7(15 - x) b 7 15 - x a 8x b 8+x c 15 - x d 15(7 - x) c 8x + 8 d x+8 7 11. In the expression 9m + 5, what two operations are being used? ID# 0438 2. Identify the variable in the expression 12m - 10. 12. Which of the following algebraic expressions means the quotient of n and 8 increased by 3? n a subtraction and division b multiplication and addition a 3 + c addition and subtraction d addition and division c n + 3 8 copyright Maisonet Math 2012 8 mrmaisonet.com b 8 +3 n d 3 + 8 n CCSS 6.EE.2 Name ___________________________________________ Date _____________ QUIZ Identifying Parts Of An Expression Algebraic Expressions And Word Phrases 1. Identify the coefficient in the expression 9x + 4. a 4 b x a 12 b m c + d 9 c - d 10 3. Which of the following choices is an example of an algebraic expression? 4. Identify the constant in the expression 12x + 8. a 8-7 b 12y - 9 a 12 b x c 9 + 12 d 3(8 - 5) c 8 d + 5. How many terms are there in the expression 9x + 8y + 3? 6. How many terms are there in the expression 24m + 12n - 14 + 2t? a 2 terms b 3 terms a 4 terms b 5 terms c 4 terms d 5 terms c 7 terms d 10 terms 7. Which of the following algebraic expressions has the same meaning as 9 less than 12 times a a number n? 8. Select the word phrase below that has the same meaning as 3(x + 8). a 9 - 12n b 12(n - 9) a 3 times x increased by 8 b triple the difference of x and 8 c 12 - 9n d 12n - 9 c triple the sum of x and 8 d 3 times 8 increased by x 9. What algebraic expression means 7 times the difference of 15 and x? 10. Select the algebraic expression that means 8 more than x. a 7(15 - x) b 7 15 - x a 8x b 8+x c 15 - x d 15(7 - x) c 8x + 8 d x+8 7 11. In the expression 9m + 5, what two operations are being used? ID# 0438 2. Identify the variable in the expression 12m - 10. 12. Which of the following algebraic expressions means the quotient of n and 8 increased by 3? n a subtraction and division b multiplication and addition a 3 + c addition and subtraction d addition and division c n + 3 8 copyright Maisonet Math 2012 8 mrmaisonet.com b 8 +3 n d 3 + 8 n CCSS 6.EE.2 Name _______________________________ Date _________ QUIZ Evaluating Expressions And Simplifying Expressions 1. Evaluate the following expression if x = 6. 2. Evaluate the following expression if y = 8. 9x 3 2x a c 40 45 6(12 y ) 8 b 55 a 32 b d 62 c 46 d 38 3. Select the expression that is equivalent to 9(x - 6). 4. Simplify the following expression: 8 g 9m 5 g 4m a 9x - 48 b 9x - 54 a 3g + 5m b 3g + 13m c 9x - 6 d 9x + 15 c 4g + 5m d 2g + 4m 5. Simplify the following expression. 6. Evaluate the following expression. Let x = 7. 8(2m 3) 4m 10 2( x 2 1) a 16m - 24 b 20m + 14 a 10 b 30 c 20m - 7 d 20m + 8 c 150 d 100 7. If m = 4, evaluate the following expression. 20m ID# 0442 26 8. Simplify the following expression. 12 m 9m 3m 9 12 a 83 b 84 a 12m + 21 b 12m - 21 c 85 d 86 c 12m + 9 d 12m + 3 copyright Maisonet Math 2012 mrmaisonet.com CCSS 6.EE.2 6.EE.3 6.EE.4 9. Simplify the following expression. 10. If y = 10, evaluate the following expression. y2 5 3 9a 9b 7 a 4b 8 a 16a + 13b - 8 b 16a + 5b - 8 a 35 b 115 c 15a + 5b - 8 d 13ab c 120 d 315 11. Mary purchased a plant that was 8 inches tall. Mary’s plant grew at a rate of 3 inches per month. If the expression below represents the height of Mary’s plant, evaluate how tall Mary’s plant will be in 9 months. Let m = months. 3m 8 12. Jarred has $45 in his savings account. Jarred decided to mow lawns for the summer to increase his savings. Jarred charges $20 per lawn. Evaluate how much Jarred will have in his savings account if he mows 30 lawns this summer and places all of his earnings in his savings account. Use the expression 20g + 45 to solve. Let g = the number of lawns cut. a 32 inches b 24 inches a $600 b $620 c 28 inches d 35 inches c $632 d $645 13. Simplify the following expression. 14. Evaluate the following expression if b = 32. 9b 12( x 5) a 12x + 60 b 12x - 5 a 288 b 41 c 12x - 60 d x - 60 c 272 d 312 15. Simplify the following expression. 16. Simplify the following expression. 4( x 2) 4k 5k 3k ID# 0442 a k b 16k a 288 b 4x + 8 c 2k d 12k c 272 d 312 copyright Maisonet Math 2012 mrmaisonet.com CCSS 6.EE.2 6.EE.3 6.EE.4 Name _______________________________ Date _________ QUIZ Evaluating Expressions And Simplifying Expressions 1. Evaluate the following expression if x = 6. 2. Evaluate the following expression if y = 8. 9x 3 2x a c 40 45 6(12 y ) 8 b 55 a 32 b d 62 c 46 d 38 3. Select the expression that is equivalent to 9(x - 6). 4. Simplify the following expression: 8 g 9m 5 g 4m a 9x - 48 b 9x - 54 a 3g + 5m b 3g + 13m c 9x - 6 d 9x + 15 c 4g + 5m d 2g + 4m 5. Simplify the following expression. 6. Evaluate the following expression. Let x = 7. 8(2m 3) 4m 10 2( x 2 1) a 16m - 24 b 20m + 14 a 10 b 30 c 20m - 7 d 20m + 8 c 150 d 100 7. If m = 4, evaluate the following expression. 20m ID# 0442 26 8. Simplify the following expression. 12 m 9m 3m 9 12 a 83 b 84 a 12m + 21 b 12m - 21 c 85 d 86 c 12m + 9 d 12m + 3 copyright Maisonet Math 2012 mrmaisonet.com CCSS 6.EE.2 6.EE.3 6.EE.4 9. Simplify the following expression. 10. If y = 10, evaluate the following expression. y2 5 3 9a 9b 7 a 4b 8 a 16a + 13b - 8 b 16a + 5b - 8 a 35 b 115 c 15a + 5b - 8 d 13ab c 120 d 315 11. Mary purchased a plant that was 8 inches tall. Mary’s plant grew at a rate of 3 inches per month. If the expression below represents the height of Mary’s plant, evaluate how tall Mary’s plant will be in 9 months. Let m = months. 3m 8 12. Jarred has $45 in his savings account. Jarred decided to mow lawns for the summer to increase his savings. Jarred charges $20 per lawn. Evaluate how much Jarred will have in his savings account if he mows 30 lawns this summer and places all of his earnings in his savings account. Use the expression 20g + 45 to solve. Let g = the number of lawns cut. a 32 inches b 24 inches a $600 b $620 c 28 inches d 35 inches c $632 d $645 13. Simplify the following expression. 14. Evaluate the following expression if b = 32. 9b 12( x 5) a 12x + 60 b 12x - 5 a 288 b 41 c 12x - 60 d x - 60 c 272 d 312 15. Simplify the following expression. 16. Simplify the following expression. 4( x 2) 4k 5k 3k ID# 0442 a k b 16k a 288 b 4x + 8 c 2k d 12k c 272 d 312 copyright Maisonet Math 2012 mrmaisonet.com CCSS 6.EE.2 6.EE.3 6.EE.4 Name _________________________________ Date __________ Evaluating Expressions Evaluate each of the following expressions. Let x = 9. 1. 3 x 4 2. x 4 3. 5( x 2) 4. 12 x 5. 3x 21 6. 2 x 3 x 7. x 3 8. 36 x 9. x(4 x) 2 11. x 9 10. 8 x 10 12. 20 x 70 Evaluate each of the following expressions. Let x = 7. 13. 8 x 23 14. x 12 15. 5( x 3) 16. 9 x 15 17. 3x 2 18. ( x 2) 3 19. x 2 x 20. x 2x 21. 8 ( x 1) 2 22. 6 x 2 x 23. x3 24. 4( x 2 1) ID# 0440 copyright Maisonet Math 2012 mrmaisonet.com CCSS 6.EE.2 Name _________________________________ Date __________ Evaluating Expressions Evaluate each of the following expressions. Let x = 9. 2. x 4 1. 3 x 4 23 3. 5( x 2) 13 4. 12 x 5. 3x 21 108 35 6. 2 x 3 x 48 8. 36 x 7. x 3 729 45 9. x(4 x) 4 2 11. x 9 10. 8 x 10 82 117 12. 20 x 70 9 110 Evaluate each of the following expressions. Let x = 7. 13. 8 x 23 14. 33 15. 5( x 3) 19 16. 9 x 15 17. 48 3x 2 50 18. ( x 2) 3 147 19. x 2 x 20. 56 x 2x 125 21. 8 ( x 1) 2 21 22. 6 x 2 x 23. 56 ID# 0440 x 12 x3 72 24. 4( x 2 1) 343 copyright Maisonet Math 2012 200 mrmaisonet.com CCSS 6.EE.2 Coordinate Geometry Name : Score : Teacher : Date : Four Quadrant Ordered Pairs YA . 9 Z 8 . . 7 X W 6 5 4 3 . < -9 -8 -7 . -6D -5 -4 -3 . 2 A E 1 -2 -1 1 2 5 . 6 7O 8 . . . P -3 . -4 Q . >X 9 . Y I B -5 . -6 M H 4 -1 -2 . 3 . T -7 C -8 -9 V Tell what point is located at each ordered pair. 1 ) (-9,+6 ) _____ 3 ) (-1,-5 ) _____ 5 ) (+6,-7 ) _____ 7 ) (+4,-3 ) _____ 2 ) (+9,-3 ) _____ 4 ) (+8,+6) _____ 6 ) (-9,-8 ) _____ 8 ) (+2,-3 ) _____ Write the ordered pair for each given point. 9) B _______ 11) O _______ 13) Z _______ 15) M _______ 10) E _______ 12) D _______ 14) T _______ 16) A _______ Plot the following points on the coordinate grid. 17) F (+8,+5) 19) J (+7,-7 ) 21) U (-9,+5 ) 23) R (-6,-5 ) 18) K (+3,+7) 20) N (+0,+9) 22) G (-8,+8 ) 24) S (-3,-6 ) Math-Aids.Com Name : Score : Teacher : Date : Four Quadrant Ordered Pairs . YA N . 9 G . 8 . . K 7 X . Z . . W 6 U F 5 4 3 . < -9 -8 -7 . -6D -5 -4 -3 . 2 A E 1 -2 -1 1 2 5 . R . S . M . 6 . 7O 8 . . . P -3 H 4 -1 -2 . 3 -4 Q >X 9 . Y I B -5 . -6 .. T -7 C J -8 -9 V Tell what point is located at each ordered pair. X Q C 1 ) (-9,+6 ) _____ 3 ) (-1,-5 ) _____ 5 ) (+6,-7 ) _____ I 2 ) (+9,-3 ) _____ W 4 ) (+8,+6) _____ Write the ordered pair for each given point. (+3,-5 ) (+7,-1 ) 9) B _______ 11) O _______ 10) E (+1,+1) _______ 12) D (-6,-1 ) _______ H 6 ) (-9,-8 ) _____ Y 7 ) (+4,-3 ) _____ P 8 ) (+2,-3 ) _____ 13) Z (+4,+8) _______ 15) M (-5,-7 ) _______ 14) T (+1,-7 ) _______ 16) A (-3,+1 ) _______ Plot the following points on the coordinate grid. 17) F (+8,+5) 19) J (+7,-7 ) 21) U (-9,+5 ) 23) R (-6,-5 ) 18) K (+3,+7) 20) N (+0,+9) 22) G (-8,+8 ) 24) S (-3,-6 ) Math-Aids.Com Name : Score : Teacher : Date : Four Quadrant Graphing Puzzle YA 9 8 7 6 5 4 3 2 1 < -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 >X -1 -2 -3 -4 -5 -6 -7 -8 -9 V Connect each sequence of points with a line. (-5,9) , (1,9) , (1,8) , (-3.5,2) , (1,2) , (1,1) , (-5,1) (-5,2) , (-.5,8) , (-5,8) , (-5,9) End of Sequence What is the shape ? Math-Aids.Com Name : Score : Teacher : Date : Four Quadrant Graphing Puzzle . . . . . YA 9 8 7 6 5 4 . . . < -9 -8 -7 -6 -5 -4 -3 . . 3 2 1 -2 -1 1 2 3 4 5 6 7 8 9 >X -1 -2 -3 -4 -5 -6 -7 -8 -9 V Connect each sequence of points with a line. (-5,9) , (1,9) , (1,8) , (-3.5,2) , (1,2) , (1,1) , (-5,1) (-5,2) , (-.5,8) , (-5,8) , (-5,9) End of Sequence What is the shape ? The Letter Z Math-Aids.Com Name : Score : Teacher : Date : Find the Slope of Each Line Y^ 5 1) 5 2) 4 . Y^ 4 . 3 2 3 2 1 < -5 -4 -3 -2 -1 1 1 2 3 4 -1 > . -2 -3 < -5 5X -4 -3 -2 -1 -4 -5 -5 5 -4 -3 -2 . 3 2 1 1 1 2 3 4 > < -5 5X . V . Y^ 5 1 4 > < -5 5X -2 -5 V Y^ 5 -2 -1 1 Y^ 5 1 -2 -3 > < -5 5X -4 -3 -2 -1 slope = ______ slope = ______ . 1 2 3 4 -1 -2 -4 -5 -5 V > 5X slope = ______ -3 -4 V . 4 2 4 > 5X V 1 3 4 -5 3 2 slope = ______ -4 8) 1 3 -3 2 -1 2 -2 3 -1 . -2 . 4 -3 -3 -1 . -4 -4 -4 slope = ______ -3 . 4 2 3 > 5X 5 1 2 4 Y^ 3 1 3 V 2 -1 2 -5 3 -1 < -5 1 -4 6) 4 7) -1 -3 . . -2 -2 -5 -2 -3 -1 -4 -3 -4 slope = ______ -3 -4 slope = ______ 4 2 -2 < -5 . 5 4) -1 5) > 5X Y^ 3 -1 4 V 4 < -5 3 -3 -4 Y^ 2 -2 slope = ______ V 3) 1 -1 . Math-Aids.Com Name : Score : Teacher : Date : Find the Slope of Each Line Y^ 5 1) 5 2) 4 . Y^ 4 . 3 2 3 2 1 < -5 -4 -3 -2 -1 1 1 2 3 4 -1 > 5X . -2 -3 < -5 - _12 slope = ______ -4 -3 -2 -1 -4 -5 -5 5 -4 -3 -2 . 3 2 1 1 1 2 3 4 > < -5 5X . V . Y^ 5 1 4 > 5X -2 -3 -5 V -3 Y^ 5 -2 -3 -2 -1 1 V Y^ 5 1 -2 -3 > < -5 5X -4 -3 -2 -1 1 2 3 4 -1 - 10 slope = ______ -2 -3 -4 -4 -5 -5 V . 4 2 4 . 1 _ 5 slope = ______ -5 1 3 > 5X -4 3 2 4 -3 8) 1 3 -2 2 -1 2 -1 3 -1 . -4 . 4 -4 < -5 - _52 slope = ______ . -4 . 1 _ 5 slope = ______ 4 2 3 > 5X 5 1 2 4 Y^ 3 1 3 V 2 -1 2 -5 3 -1 < -5 1 -4 6) 4 7) -1 -3 . . -2 -2 -5 -2 -3 -1 -4 -3 -4 10 slope = ______ -3 -4 4 2 -2 < -5 . - _12 slope = ______ 5 4) -1 5) > 5X Y^ 3 -1 4 V 4 < -5 3 -3 -4 Y^ 2 -2 V 3) 1 -1 V > 5X 10 - __ 3 slope = ______ . Math-Aids.Com Slope-Intercept Form Worksheet- Name: _____________________ Review - Unit 3 lessons 5 & 6 1) Find the slope of the line through each pair of points. Slope = y 2 − y1 x 2 − x1 a. (8, -7) and (5, -3). b. (-5, 9) and (5, 11). c. (-8, -4) and (-4, -9). 2) For each graph: Write the equation of the line in SLOPE-INTERCEPT FORM m = _______b =_______ m = ________b = ______ ________________________ _________________________ m= _______ b =________ m = ________b=________ ________________________ _______________________ m = ______b =______ _______________________ m = ______b =_______ ________________________ 3) In each linear equation, identify the slope (m) and the y-intercept (b) 2 5 19 a. y = 4x – 5 b. y = − x c. y = x − 3 2 8 m = ______b =______ d. y = 11 + 2 x 3 m= _______b =_______ e. 2x + y = 8 m = _______b = ________ m=_________b = ________ m=_____b=_______ f. y – 4x = -2 m = _____b =________ 4) Find the equation of the line in slope-intercept form (y = mx + b) a. m = 2 and b = - 7 c. m = -5 and b = 0 b. b = 4 and m = -5 d. m = 4/5 and b = -2 5) Graph the line for each equation: 5a) y= 3 x −3 4 Slope = 5b) 5 y = 4− x 3 Slope = 5c) Y-Intercept = Y-Intercept = 2x + y = −2 Slope = Y-Intercept = 6. Sara rented a car for x amount of days. The linear equation below represents y, the total cost of Sara renting a car. y = 17x + 130 a. What is the slope of the line represented by this equation? b. Explain what the slope tells you about renting a car. c. What is the y-intercept of the line represented by this equation? d. Explain what the y-intercept tells us about Sara’s rental. e. If Sara rents a car for 9 days, how much will it cost her? Show how you got your answer. 17. The slope of a line is 3 and the line contains the points (5, 9) and (3, a). What is the value of a? 2 18. The slope of a line is -2 and the line contains the points (7 ,4) and (x, 12). What is the value of x? KEY: m = -1 b=3 y = -1x + 3