6th Grade - Summer Math Packet Multiplication and Division (no calculator) (Sixth graders should know all fact families 0-12 with speed and accuracy). Write the answers to the following math facts: 1.) 7 x 9 = ____ 4.) 4 x 6 = ____ 7.) 6 x 9 = ____ 10.) 5 x 12 = ____ 2.) 6 x 6 = ____ 5.) 6 x 7 = ____ 8.) 7 x 8 = ____ 11.) 7 x 12 = ____ 3.) 8 x 4 = ____ 6.) 8 x 6 = ____ 9.) 9 x 4 = ____ 12.) 9 x 12 = ____ Solve the following problems. Show all of your work. Draw a box around your final answer. 13.) 14.) 74 423 x 13 x 30 15.) 16.) 69 307 x 58 x 46 17.) 18.) 675 ÷ 9 1440 ÷ 24 1 6th Grade - Summer Math Packet Factors and Multiples (no calculator) Use the clues to determine the secret numbers: 1. ________ Clue 1: The number has 2 digits. Clue 2: The number has 13 as a factor. Clue 3: The sum of the digits is 11. 2. _________ Clue 1: The number is prime. Clue 2: The number is less than 19. Clue 3: The sum of the digits is greater than 7. 3. _________ Clue 1: The number has three digits. Clue 2: The number is less than 140. Clue 3: The number has 7 as a factor. Clue 4: The number is even. Clue 5. The sum of the digits is less than 9. 4. __________ Ms. Goldman is thinking of a number that is less than 20 and has three factor pairs. She says that if she adds the factors in each factor pair the sums are 19, 11 and 9. What is her number? 5. List all the factors of 12_________________________________________________________ 7__________________________________________________________ 36_________________________________________________________ 80_________________________________________________________ 225________________________________________________________ 2 6th Grade - Summer Math Packet 6. Find the common factors of 12 and 20 .Circle the Greatest Common Factor (GCF)______________________________ 7. Find the common factors of 24 and 48. Circle the GCF_____________________________________ 8. Find the common factors of 30 and 72. Circle the GCF_____________________________________ 9. Graham is planning a party for his younger sister. He has 36 prizes and 24 balloons. How many children can he have at the party so that each child gets an equal number of prizes and an equal number of balloons? Explain your answer using complete sentences.__________________________ _______________________________________________________________________________________ 10. A number has 4 and 5 as factors. What other numbers must be factors? Why? What is the smallest number this number could be?_________________________________________________ 11. List 10 multiples of 12.____________________________________________________________ 12. List 10 multiples of 13_____________________________________________________________ 13. List 20 multiples each of 5 and 8. List all the multiples they have in common. What is the Least Common Multiple (LCM) of 5 & 8? ________________________________________________________ 14. Can you find the Greatest Common Multiple? Why or why not?____________________________ 15. Is the number 26 divisible by 2? 3? 5? Or 9? How do you know?___________________________ _______________________________________________________________________________________ 16. Is the number 432 divisible by 2? 3? 5? 6? 9? 10?_______________________________________ 17. Two radio stations are playing “Old Bald Men.” WXRT plays the song every 18 minutes and WNPR plays it every 24 minutes. Both stations play the song at 3:00 PM. When is the next time the stations will play the song at the same time?_______________________________________________ 18. Mike and Duane are performing live at a Parker MX. This year they want to incorporate a crazy light show. They spoke with Mr. Early and decided that red lights would flash every 5 seconds, blue lights would flash every 8 seconds, and yellow lights would flash every 10 seconds. How many seconds or minutes into the show will all three lights flash at the same time?___________________ 19. You just joined a soccer team and it’s time to choose your number. You decide you want a prime number, but it must be between 20 and 40. What do you choose and how can you prove it’s a prime number?_______________________________________________________________________________ 20. Make up a word problem about multiples or factors and show it to someone in your family.____ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ 3 6th Grade - Summer Math Packet Measurement (Customary Length) review 12 inches = 1 foot 3 feet = 1 yard 5,280 feet = 1 mile 1,760 yards = 1 mile Use the chart above to help you solve the following problems. Show all your work. 1.) 6 yards = ________ feet 2.) 6 feet = _________ inches 3.) 2 miles = ____________ feet 4.) 2 miles = _____________ inches 5.) 39 yards = _____________ inches 6.) When you are converting (changing) a larger unit of measurement to a smaller unit of measurement, do you multiply or divide? Draw a picture that proves your answer. 7.) 36 inches = ________ feet 8.) 36 inches = _________ yard(s) 9.) 63 feet = ____________ yards 10.) 108 inches = _____________ feet 11.) 45 feet = _____________ yards 12.) When you are converting (changing) a smaller unit of measurement to a larger unit of measurement, do you multiply or divide? Draw a picture that proves your answer. 4 6th Grade - Summer Math Packet Fractions (no calculator) 1.) The denominator is 5 and the numerator is 4. Write the fraction.___________________ 2.) Find 5 fractions that are equal to 1/5.__________________________________________ 3.) Which is bigger, 2/3 or 3/5.? How can you prove your answer? Show at least two ways. 4.) 3/8 + 2/8 ____________________________________________________________________ 5.) 5/8 + 7/8 ____________________________________________________________________ 6.) 3/8 +1/4_____________________________________________________________________ 7.) Write a fraction that is greater than 1/2 and less than 3/4 ? How do you know it is correct? _______________________________________________________________________________ Find the missing numerator or denominator. Show all your work. 8.) 3/7 = 9/? Denominator = 9.) 4/24 = 1/? Denominator = 10.) 6/48 = ?/8 Numerator = 11.) 28/35 = ?/5 Numerator = 12.) 48/72 = 6/? Denominator = 13.) Fiona bought a brand new Harley Davidson motorcycle. Since the weather was nice, she decided to go out for a ride with some of her friends. Before leaving town, she stopped to fill up her motorcycle with gas so that she had a full tank. If Fiona’s motorcycle has a 4 gallon gas tank, and she only had to add 2 4/7 gallons, how much gas was in the tank before she filled up? Show all your work ______________________________ ________________________________________________________________________________________ 14.) Change 13/8 to a mixed number.______________ 15.) Change 24/5 to a mixed number.______________ Write the following words as a fraction: 16.) three and nine fifteenths ________________________________ 17.) twelve and fourteen twentieths________________________________ Change the following into an improper fraction: 18.) six and two thirds ___________________________________________ 19.) ten and six sevenths ________________________________________ 5 6th Grade - Summer Math Packet Simplify the following: 20.) 14/2 ________________________________ 21.) 1 8/32 22.) 8/24 _____________________________ _______________________________ 23.) 32/64 _____________________________ 24.) 5/15 ______________________________ 25.) 20/45 _______________________________ Decimals and Percents (no calculator) 1.) Write a fraction to represent each decimal. Make sure the fraction is in simplest form. 0.3 = 0.21 = 0.4 = 0.37 = 0.5 = 2.) Match up the fractions with the decimals they are equal to. 0.5 9/12 0.75 1/5 0.2 3/10 0.10 1/10 0.3 ½ What place value do the underlined digits carry, and how many of each are there? 3) 10,367 4) 5,234.23 5) 10.2001 6) 9.16 7) 0.579 8) 210.552 6 6th Grade - Summer Math Packet Round the following numbers to the nearest tenth. Reminder: Since you are rounding to the nearest tenth, you need to refer to the digit in the hundredth’s place value. If the digit in the hundredth’s place value is 5 or greater, the digit in the tenth’s place value will round up. If the digit in the hundredth’s place value is less than 5, the digit in the tenth’s place value will remain the same. (Example: 10.067 = 10.1) 9.) 15.245 = 10.) 7.321 = 11.) 1.58 = 12. ) 235.262 = Round the following numbers to the nearest whole number. Reminder: Your answer must be just the whole number. No answer with a decimal will be correct. (Example: 50.861 = 51) 13.) 213.56 = 14.) 10.39567 = 15.) 95.459 = 16.) 12.107 = 17.) Arrange the numbers below on the place value lines so they create the greatest value possible. 6, 8, 1, 3, 2 _________ ______. ______ ______ 18.) Arrange the numbers below on the place value lines so they create the smallest value possible. 6, 8, 1, 3, 2 _________ ______. ______ ______ 19) Katherine was on an airplane to Spain. The trip would take exactly 12 hours. So far she had flown 3 hours. What percentage of the trip has Katherine completed so far? 20.) Marc had to walk to the grocery store which was exactly 50 meters from his house. So far he has walked exactly 21 meters. What percentage of a mile has he walked? 21.) Leigh bought new shoes that will last for 500 miles. She has walked 20% of the recommended usage. How many miles has she walked so far? 7 6th Grade - Summer Math Packet Geometry Use the numbers below to solve 1, 2, & 3. 50º 75º 36º 179º 150º 130º 25º 62º 160º 90º 142º 10º 1. Draw a circle around each acute angle. 2. Draw a rectangle around each obtuse angle 3. Leave each right angle as it is. Show all your work, including pictures if they help, as you find the answers to the questions! Ms. Hamilton wants to put a decorative iron fence (rather like Winnie’s in Tu ck Ever last in g) around her yard. The yard is a perfect rectangle: its length is 24.75 feet and its width is 12.75 feet. Home Depot charges $50 a yard for iron fencing. 4. How many feet of fencing does Ms. Hamilton need to buy?_____________________________ 5. What do you call the distance around a rectangle? _____________________________ 6. How much will the fencing cost?____________________________________________________ Directions: Using your knowledge of lines, line segments, rays, and intersecting lines, answer the following questions. Use your ruler for straight lines. 7.) Dr aw lin e seg m en t AB an d h ave it in t er sect w it h lin e TR at p o in t S. 8.) Dr aw t w o in t er sect in g lin es, lab el t h em , an d h ave t h em in t er sect at p o in t C. 9.) Cr eat e o n e d r aw in g t h at sh o w s t h r ee r ays sh ar in g o n e en d p o in t . 10.) Name 5 kinds of quadrilaterals 8 6th Grade - Summer Math Packet For the following remember P=Perimeter l=length w=width A=Area. P= (l + w) x 2 and A= l x w 11.) Draw a rectangle with a length of 15 cm and a width of 6 cm. Find the Perimeter and Area. Draw three examples of a rectangle that have an area of 30. Calculate the perimeter of each. 12.) 13.) 14.) 15.) Look around your room. Draw and identify 10 polygons. 9

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