School District of South Orange and Maplewood

Transcription

1 School District of South Orange and Maplewood Maplewood Middle School & South Orange Middle School 6 th Grade 2015 Honors Summer Assignment Math Packet Name School

2 Summer Assignment Students Entering 6th Grade Honors Classes in September The following packet of material contains prerequisite skills and concepts that will be drawn upon from 5th grade objectives, for success in 6th Grade Honors Classes. The mathematical topics contained in this packet fall within the range of concepts and skills developed in 5th grade. I. Number Concepts, Relations, and Operations Estimation Whole Numbers and Decimals Applications II. Fractions Concepts and Relations (Representation, Equivalence, Comparisons) Operations: Adding, Subtracting, and Multiplying Applications

3 Whole Numbers and Decimals: Concepts, Relations, and Operations Use an estimate to correctly place a decimal point in the following equations. Show your estimate beneath each equation. 1) 6.49 x = ) /2.19 = ) = ) x 30.2 = ) Order the following numbers on the number line below. A B C D E F least greatest 6) Eight elephants had to equally share 24,862 pounds of peanuts. How many pounds did each elephant receive?

4 Compare each expression using >, <, and = signs. 7) ) twenty three hundredths ) ) one hundred and six hundredths ) *what does this mean? 12) ) ) 1.64 x ) Find the perimeter of the following shapes cm 6.9 cm Shape 1 Shape cm 5.01 cm a) What is the difference between the shape s perimeters? 16) Three cowboys share 25.6 pounds of bacon. How many pounds of bacon does each cowboy receive? 17) 459 meters of ribbon is going to be cut into pieces that are 0.6 meters long. How many pieces that are 0.6 meters can be cut from 459 meters?

5 18) Dandy s Candies ordered 152 boxes of lollipops. If each box of lollipops contains 144 lollipops, how many total lollipops should Dandy s receive? 19) Solve the riddle: When rounded to the nearest tenth, this number is 7.7 the nearest hundredth, this number is 7.74 Which of the following could be the actual number? a) b) c) d) When rounded to 20) Mrs. Dugan buys a newspaper everyday. The price of a paper on Mondays through Saturdays is $0.75 per day. On Sunday, the paper is $1.25 How much does Mrs. Dugan spend on newspapers in total every week? 21) The value of the expression 24,325 6 is between: a) 3,000 and 4,000 c) 5,000 and 6,000 b) 4,000 and 5,000 d) 6,000 and 7,000 How do you know? (2 pts) 22) The value of the expression 596 x 50 is between a) 10,000 and 20,000 c) 30,000 and 40,000 b) 20,000 and 30,000 d) 40,000 and 50,000 How do you know?

6 23) Ed bought 4 cans of tennis balls. Each can contained 3 tennis balls. He paid $10.95 for all 4 cans and plans to sell each ball for $1.00. If he sells all of the tennis balls, what is the difference between what he spent, and what he earned? Show work. 24) A super value meal at Nathan s costs $5.15 and includes 1 hot dog, 1 order of fries, and 1 soda. If you don t buy the super value meal, each item costs $1.99. If you want 1 hot dog, 1 soda, and 1 order of fries, should you buy the super value meal or each item separately? Show work and explain. 25) On January 15 th, you have to take your pet squirrel to the veterinarian. The normal charge is $75.80 but it s a weekend, so you are charged 1.5 times for the visit. How much do you have to pay?

7 Fraction Concepts and Relations Show all work for all problems (using numbers, pictures, and/or words). Simplify all fractions that are part of a solution. 1) Four friends want to equally share this pizza. What fraction of the whole pizza will each person receive? Explain. 2) Name 3 fraction with different denominators between 9/10 and 1. 9/10 1 3) Order these fractions on the number line from least to greatest. a. 4/5, 4/6, 4/3 least greatest b. 3/8, 7/10, 3/6 least greatest 4) Rewrite the number 37/4 as mixed number.

8 5) Imagine you really love pizza and are really hungry, would you rather have 3/4 of a pizza or 7/8 of a pizza? Why? Explain and prove your solution 6) Compare these numbers with >, <, or = signs. a) 2/3 3/4 c) 2 1/5 11/8 b) 5/8 1/2 d) - 5/6-9/10 7) An arrow is used to indicate a reading on each ruler. Write each reading as a fraction or mixed number in lowest terms. a. inches 1 2 b. inches 8 9

9 8) Which of the following is true if a b = 2 i) a is double the value of b ii) ii) b is double the value of a a and b are the same 9) If the numerator of a fraction is greater than its denominator, which is true? i) The value of the fraction is less than 1. ii) The value of the fraction is 1. iii) The value of the fraction is greater than 1. 10) Fill in the missing number. Show all work ) Which design has the largest fraction of stars? Show all work. Design A Design B

10 12) What fraction of this rectangle is shaded? 13) Compare these fractions using >, <, or = signs. 19/20 8/9 Without computing or using common denominators, explain how you know. 14) What fraction of this square is shaded?

11 15) Use the diagram below to answer the following questions. A B C D E F G H I Answer 3 of the following 4 questions: Which point is 1/2 the distance between points A & G? Which point is 1/4 the distance between points A & I? Which point is 3/4 the distance between points D & H? Which point is 2/3 the distance between points B & H? Answer 1 of the following 2 questions: If the distance between C&D is ¼, what length equals 1? If the distance between C&D is 1/3, what lengths equal 1?

12 Fraction Operations 1) Juan bought 2/3 lb. of Swiss cheese and 3/4 lb. of American cheese. How much cheese did he buy all together? Show all work. 2) Fluffy the cat is 5½ times heavier than Ralph the hamster. If Ralph the hamster is ¾ lbs, how much does Fluffy the cat weigh? Show all work. 3) One pitcher of lemonade requires ⅜ of a cup of sugar. How many pitchers of lemonade can be made with 2¼ cups of sugar? 4) Mia has to paint the fence shown below. If she can paint 2/3 of each section in 1 hour, how long will it take her to paint the entire fence? Show all work. one section

13 5) What is the perimeter of this rectangle? Show all work. Perimeter = distance around an object 5 1/9 1 5/6 perimeter: in. 6) The Jack s pantry has 48 pieces of fruit; half are apples, one-third are plums, one-eighth are peaches, and the rest are oranges. How many are apples? Plums? Peaches? Oranges? Show all work. a) Apples: b) Plums: c) Peaches: d) Oranges: 7) In 2012, Woody the Beaver chewed 303 3/8 lbs of wood. In 2013, he chewed 289 9/10 lbs of wood. How many more pounds of wood did Woody chew in 2013? Show all work.

14 8). Calculate the area of the rectangle below. Area = length x width 6 1/6 in. 4 1/4 in. area: in. 2 9) A rectangle has an area of 10 1/2 in. 2 If its width of 2 1/3 in, what is its length? Show all work. 10) Ed uses 7/8 of a cup of flour, 1/10 of a cup of salt, 1/6 of a cup of baking powder, 3/5 of a cup of brown sugar, and 5/9 of a cup of regular sugar to make a cake. About how many cups of ingredients will he use? a) 1 cup b) 1 ½ cups c) 2 cups d) 2 ½ cups