Math Summer Packet For. Students Entering 6 th Grade

Transcription

1 Name: Period: Math Summer Packet For Students Entering 6 th Grade

2 Doral Academy Prep School Math Department Dear Parents and Students, We are assigning this work in an effort to prepare our students for a successful school year, and to provide them with an appropriate way to assist them retaining basic mathematical knowledge needed for the 6 th grade. This work is not intended to be completed in one sitting. It is intended to be completed at a steady pace throughout the summer. It will be the first grade to be entered in the grade book upon returning to school. All exercises have space to show calculations, and calculator answers will not be accepted. All work must be shown to receive the credit. The students may be assisted, and we encourage you use the Glossary included in the school s website, on Mrs. Linette Prats page. Additionally, each section begins with examples to be followed, and you may refer to the provided FCAT 2.0 Reference Sheet. Remember that the educational process is a team effort and we all play vital roles- teachers, parents, and students. Your partners in education, Doral Academy s Math Department Team 2

3 Grades 6 8 FCAT 2.0 Mathematics Reference Sheet Area Rectangle A bh Parallelogram A bh Triangle Trapezoid A A 2 bh Circle A π r 2 2 h (b b 2 ) b h w d r base height width diameter radius slant height KEY A B C V P S.A. 22 Use.4 or for π. 7 Circumference C πd or C 2πr area area of base circumference volume perimeter of base surface area Volume/Capacity Total Surface Area Rectangular Prism V V bwh or Bh S. A. = 2 bh + 2 bw + 2 hw or SA.. = Ph + 2 B Right Circular Cylinder V V πr 2 h or Bh S.A. 2πrh 2πr 2 or S.A. 2πrh 2B Right Square Pyramid V Bh S.A. P B 2 Right Circular Cone V V πr2 h Bh or 2 SA.. = ( 2 r ) + B Sum of the measures of the interior angles of a polygon = 80(n 2) Measure of an interior angle of a regular polygon = where: n represents the number of sides 80(n 2) n Florida Department of Education

4 Grades 6 8 FCAT 2.0 Mathematics Reference Sheet Pythagorean theorem Simple interest formula a c a 2 b 2 c 2 I prt b Slope-intercept form of a linear equation y mx b where p principal, r rate, t time Distance, rate, time formula d rt where m slope and b y-intercept where d distance, r rate, t time Conversions within a System of Measure yard feet mile,760 yards 5,280 feet acre 4,560 square feet cup 8 fluid ounces pint 2 cups quart 2 pints gallon 4 quarts pound 6 ounces ton 2,000 pounds inch 2.54 centimeters foot 0.05 meter mile.6 kilometers meter 00 centimeters 000 millimeters kilometer 000 meters liter 000 milliliters 000 cubic centimeters gram 000 milligrams kilogram 000 grams minute 60 seconds hour 60 minutes year 52 weeks 65 days Conversions between Systems of Measure When converting from Customary to Metric, use these approximations. centimeter 0.9 inch meter.28 feet kilometer 0.62 mile C ( F 2).8 F ( C.8) 2 cup 0.24 liter gallon.785 liters ounce 28.5 grams pound kilogram When converting from Metric to Customary, use these approximations. liter 4.2 cups liter gallon gram ounce kilogram pounds Temperature conversions between Celsius and Fahrenheit Florida Department of Education

5 Big Idea : BIG IDEA Develop an understanding of and fluency with multiplication and division of fractions and decimals. Objective: Identify and determine equivalent forms of proper fractions as decimals, percents, and ratios. 2 Examples: Write as a decimal. Method : 2 Change to a fraction with a denominator of 0, 00, or 000 EX: 2? 00 (Use 00, since divides into 00 evenly) 2 x4 x as a decimal 00 Method 2: Divide 2 by Therefore: ) Write as a decimal. Use method 2.) Write as a decimal. Use method ) Write as a decimal. Use method 2 4.) Write as a decimal. Use method ) Write 4 as a decimal. Use method 6.) Write 5 as a decimal. Use method

6 Objective: Compare and order fractions and decimals. Ordering fractions only: ) determine the least common denominator (LCD) of the fractions 2) rewrite each fraction as an equivalent fraction using the LCD ) Compare the numerators EX: order the fractions.) ; 2 ) LCD of 2, 8, and 2 is ) ) Comparing the numerators: Order the fractions 2 ; 5 ; 6 7 ; from least to greatest from least to greatest Ordering fractions and decimals: ) Change the fractions to decimals 2) Compare the decimals EX: order the numbers 0.; ; and 0.8 from 8 least to greatest ) ) Compare the decimals: 2.) 0. < 0.75 < 0.8 Therefore: Order the numbers 0.78; ; and 0. 8 from least to greatest 4.) Order the fractions ; ; 6 from least to greatest 4.) Order the numbers ; 0 ; and 0. from least to greatest 5 5.) Order the fractions ; 2 5 ; from least to greatest 6.) 9 24 Which number has the greatest value? 0.94; ; or 20 4

7 Objective: Find the prime factorization of a number using a factor tree. ) Determine whether the number is prime or composite 2) If composite, use any factor pair of the number other than and itself, since one is neither prime nor composite. ) Continue factoring all composite factors of the number, until only prime numbers remain. 4) Write the remaining prime numbers as a product, in ascending order. EX: EX: 24 = 2 x 2 x 2 x 0 = 2 x x 5.) 72 2.) 56.) 44 4.) 5.) 6.) 5 4 5

8 Objective: Add and subtract fractions and mixed numbers and express answers in simplest form. Adding and Subtracting Fractions: 5) determine the least common denominator (LCD) of the fractions 6) rewrite each fraction as an equivalent fraction using the LCD 7) Add or subtract the fractions 8) Simplify if necessary EX: Add 2 8 EX: Subtract 5 6 ) LCD of 2 and 8 is 8 2) ) 7 8 4) (can t be simplified) 4.) 6 ) LCD of 5 and 6 is 0 2) ) 2 0 4) (can t be simplified) 2.) ) 2 4.) ) Shelly has two pieces of yarn. One is 2 yards long and the other is 2 yards long. How much yarn does 4 she have altogether? 6.) Marty weighs 64 ¼ pounds and Nathan weighs 76 ½ pounds. How much more does Nathan weigh than Marty? 6

9 Objective: Adding and subtracting decimals. Example: Rewrite the sum or difference so that the decimal points so that they are exactly aligned Bring the decimal point down to the sum or difference..) ) ) ) ) Michael went to the store to buy groceries to make some sandwiches. He bought a loaf of bread for $.98, a pound of ham for $7.99, and a pack of cheese slices for $.49. He paid the cashier with a $20 bill. How much change did he get back? 6.) During a recent storm, 4.79 inches of rain fell in Doral, 9.56 inches of rain fell in Kendall, and 0.7 inches of rain fell in Miami Lakes. How much more rain fell in Miami Lakes than in Doral? 7

10 Objective: Estimate to determine the product of a decimal and a whole number Example: Multiply 6.45 X 7. Round to the nearest whole numbers rounds to 6 Since 7 is already a whole number, it stays the same. 2. Multiply the rounded numbers 6 X 7. Answer 42 Estimate each of the following multiplication problems. Round all decimals to the nearest whole number..) 6 X.65 2.) 0.82 X 4.) X ) 2.9 X 7 5.) Three pairs of shoes are priced at $9.95 each. Estimate the total cost for the all pairs of shoes. 6.) If you work 6 hours at $6.5 an hour, estimate how much you would make? 8

11 Objective: Estimate to determine the quotient of a decimal. Example: Divide Estimate to the nearest tens rounds to 50 0 stays the same Divide with estimated numbers.. Answer. 5 Estimate each of the following division problems. Round all numbers to the nearest ten..) 2.) ) ) ) Franchesca and twelve of her friends shared the cost of their lunch. If the lunch cost $75.90, estimate how much would each one have to pay? 6.) Lucia and 5 of her friends bought sodas after their lacrosse game. If the drinks cost $4.29, estimate how much each person would owe ifi the cost is divided equally? 9

12 Big Idea 2: BIG IDEA 2 Connect ratio and rates to multiplication and division. Objective: Identify and determine equivalent forms of proper fractions as decimals, percents, and ratios. Key Concept: Ratio: a comparison of two numbers A ratio can be written in ways: ) a : b, 2) a to b or ) a b EX: Write the ratio as a fraction simplest form: 4 wins to 6 losses 4 2 Since the ratio can be written as: we can the simplify to or 2 : or 2 to 6.) Write the ratio as a fraction simplest form: 2 boys to 5 girls 2.) Write the ratio as a fraction simplest form: 20 books to 24 magazines.) Write the ratio as a fraction simplest form: 0 circles to 5 triangles 4.) Write the ratio as a fraction simplest form: 8 cups to 2 servings 5.) Write the ratio as a fraction simplest form: 50 cars to 00 trucks 6.) Write the ratio as a fraction simplest form: 9 pencils to pens 0

13 Big Idea : BIG IDEA Write, interpret, and use mathematical expressions and equations. Objective: Write an algebraic expression to represent unknown quantities. A variable is a symbol, usually a letter, used to represent a number. Algebraic expressions are combinations of variables, numbers, and at least one operation. Examples: The sum of 5 and some number is written as: 5 + n because the operation that is associated with the word sum is addition. The difference of a number and three tenths word difference is subtraction. is written as: n - 0. because the operation thatt is associated with the.) 2.) a number plus 2 a number minus 7.) 4.) the difference of twenty-one hundredths and a number the sum of a number and forty-six 5.)Frankie has sixty-five more football cards friend, John. than his 6. Jacky is five-eighths of an inch shorter than Barbie.

14 Objective: Evaluate numeric expressions using order of operations. A numerical expression is a combination of numbers and operations. The Order of Operations tells you which operation to perform first so that everyone gets the same final answer. The Order of Operations is: Parentheses, Exponents, Multiplication or Division (left to right), and Addition or Subtraction (left to right.) Examples: 48 ( + ) 2 2 original expression simplify the expression inside the parentheses calculate divide 48 by 6 4 subtract 4 from 8.) 2.) (8 + ) x 2 x ) 4.) 88 6 x x 4 5.) 6.) x (5 2 + ) x (8 + 9) 0 2

15 Supporting Idea 4: Geometry and Measurement Geometry and Measurement Objective: Estimate and determine the area of a triangle with whole number dimensions. The area (A) of a triangle is one half the product of the base (b) and the height (h). The formula for finding the area of a triangle is: A = ½ bh and is measured in square units. Examples: 5 cm 4 cm 5 cm 4 cm A = ½ bh A = ½ x 4 x 5 A = ½ x 20 A = ½ bh A = ½ x 4 x 5 A = ½ x 20 A = 0 cm 2 A = 0 cm 2.) Determine the area of the triangle. 2.) Determine the area of the triangle. 7 cm A = cm 2 8 cm A = 5 cm.) Determine the area of an obtuse triangle with a height of cm and a base of 22 cm. A = 9 cm 4.) Determine the area of an isosceles triangle with a base of cm and a height of 26 cm. A = 5.) World famous pastry chef, Zoe, is designing a birthday cake for his son, who is a Geometry teacher. He has 4 layers, all triangles. He wants to put the largest layer (in area) on the bottom and the smallest layer on the top. Determine the area of each layer and order them from largest to smallest (4 = largest, = smallest) 6.) Jennifer s dorm room is shaped like a triangle. The college brochure says it has an area of 875 square feet. The room is 5 feet long. Determine the width of the room at its widest point. Milk Chocolate layer b = 2 h = 6 A = Yellow cake layer b = 7 h = A = Dark Chocolate layer b = 4 h = 7 A = White cake layer b = 9 h = 9 A =

16 Objective: Estimate and determine the volume of rectangular prisms with whole number dimensions. The amount of space inside a three-dimensional figure is the volume of the figure. Volume (V) is measured in cubic units. The volume of a rectangular prism is related to its dimensions. Volume (V) = length (l) x width (w) x height (h) Examples: V = lwh 5 cm 4 cm 20 cm V = 20 x 4 x 5 V = 400 cm.) Determine the volume of the rectangular prism. Please show your work. 2.) Determine the volume of the rectangular prism. Please show your work. V = V = 8 cm 6 cm 4 cm 9 cm 7 cm 2 cm.) Determine the volume of a rectangular prism with a length of cm, a width of 55 cm, and a height of 65 cm. Please show your work. 4.) Determine the volume of a rectangular prism with a height of 5 cm, a length of 89 cm, and a width of 5 cm. Please show you work. 5.) Jake has a fish tank that measures 6 in. long, 24 in. high, and 8 in. wide. He wants to fill the fish to a height of 4 inches. What will be the volume of water in the tank? Please show your work. V = Draw the tank and label the dimensions. Draw the water level. This does not need to be drawn to scale. 6.) Camila has a lamp that she wants to send to her sister in Baltimore. The lamp is in the shape of a rectangular prism. It measures 4 high, 9 wide, and long. She wants to buy a box so that there is all around the lamp for bubble wrap. What should be the dimensions of the box? What is the volume of the box? Please show your work. 4

17 Objective: Determine the missing measure of a square or rectangle given the area using whole number dimensions. The area (A) of a rectangle or square can be found by multiplying the length (l) by the width (w). The missing measure of a square or rectangle can be determined by using division. A = l x w Examples: 6 cm w A = l x w 64 = 6 x w 6 6 A = 64 cm 2 4 = w The width of the rectangle is 4 cm..) Determine the missing side of the square. Please show your work. A = 8 cm 2 2.) Determine the missing side of the rectangle. Please show your work. w w = l 5 cm 9 cm.) Determine the missing side of a rectangle with an area of 44 cm 2 and a width of 8 cm. Please show your work. A = 65 cm 2 l = 4.) Determine the missing side of a rectangle with an area of 480 cm 2 and a length of 2 cm. Please show your work. 5.) Jeremy plans to paint a bright green rectangle on the bottom of his pool. He has enough paint to cover an area of 27 square feet. He wants the width of the rectangle to be feet. Determine what the length of the rectangle should be. Please show your work. 6.) Jamie wants to put stickers, to celebrate her birthday, on top of chocolate bar wrappers. The bar is 48 mm wide and has an area of 428 mm 2. What must be the length of the sticker to cover the top of the bar? 5

18 Supporting Idea 5: Number and Operations Number and Operations Objective: Identify and determine equivalent forms of proper fractions as decimals, percents, and ratios.. Key Concept: Percent (%) is a ratio that compares a number to 00 Fraction to Percent: 9 EX: Change to a percent Since % means out of 00, 9 x4 x % ? 00 Percent to fraction: EX: Change 75% to a fraction in simplest form 75% means 75 out of 00 75% Write the percent as a fraction with a denominator of 00 Simplify 7.) Change to a percent 2.) Change 84% to a fraction in simplest form 20.) Change 4 to a percent 4.) Change 90% to a fraction in simplest form 24 5.) Juan answered questions correctly on his quiz. What percent of the questions did he get correct? 6.) 78% of the class completed their homework last night. What fraction of the class completed their homework? 6

19 Suporting Idea 6: Data Analysis Data Analysis Objective: Determine the measures of central tendency (mean, median, and mode) and the range. A number that helps describe all of the data in a data set is a measure of central tendency. The mean is the sum of the data divided by the number of pieces of data. The median is the middle number of the ordered data (least to greatest.) The mode is the number or numbers that occur most often. The range is the difference between the greatest and least values of the data set. Examples: Jacket Prices ($) Find the mean, median, mode, and range of the data. Mean = = 444 = 7 The mean price of a jacket is $7. 2 Median = (data ordered) = = 6.5 The median price of a jacket is $ Mode = $27 because it is the only piece of data that occurs more than once. Range = 6 5 = $46.) Find the mean, median, mode, and range for each set of data. 6, 9, 2, 4,, 6, 5 2.) Find the mean, median, mode, and range for each set of data., 7, 7, 9, 7, 5,, 7, 2.) Find the mean, median, mode, and range for each set of data. 28, 2, 2, 4, 2, 27, 2, 4 4.) Find the mean, median, mode, and range for each set of data. 57, 24, 57, 24, 57, 9 7

20 Credit is given to the Fairfax County Public School System for the format of this work packet. 8