December+Problems

December Problems [|Number Theory] | [|Measurement] | [|Geometry] | [|Patterns, Algebra, and Functions] | [|Data, Statistics, and Probability] | [|Grab Bag] __Number Theory__ //Start out simple...// **Family Fun - From Problem Solving Connections** 1. Four families each brought the same number of chairs to a block party. Three more chairs are needed to seat all 27 of the participants. How many chairs did each family bring?

**Consecutive Numbers** 2. An example of consecutive odd numbers is 23, 25, 27, and 29. Find four consecutive odd numbers with a sum of 160. Show your work.

//Now try to work this out...// **Opening Day** 3. It is the grand opening of a local supermarket. Every 5th customer will receive a coupon for a free turkey and every 7th customer will receive a coupon for a free half gallon of ice cream. If 400 customers come in on opening day, how many will get a free turkey and a free half gallon of ice cream?

**Kennel Klub** 4. Four dozen dogs live in 6 different colored kennels. The smallest kennel has 6 dogs and the orange kennel is the largest with 10 canines. The yellow kennel and the green kennel are the only ones with the same number of dogs. The 13 youngest pups are in the red and blue kennels with the least number of dogs. The purple kennel has 2 more dogs than the blue kennel. How many dogs are in each kennel? Make a chart.

//This will really challenge you...// **Car Rental** 5. Sam needs to rent a car for his upcoming trip. CheapWheels charges $20.25 per day plus $.14 a mile. Easy Rider charges $18.25 a day plus $.22 a mile. San plans to do a lot of driving on his 3-day trip. Which company should Sam go with? Explain your choice. Does the difference in cost go up or down as mileage increases? Support your answer.

__Measurement__ //Start out simple...// **Flooring** 6. Mr. and Mrs. Corkwood were going to tile their den floor. They had tiled the kitchen floor earlier in the year with ceramic tile. The kitchen was 14ft by 10 feet. The den is 20 ft. by 14 ft. The kitchen tile job cost the Corkwoods $1400 including labor. How will this help them determine the price of the den floor?

//Now try to work this out...// **Squares** 7. Look at this picture of squares. The area of square F is 16 square units. The area of square B is 25 square units. The area of square H is 25 square units. Find the area for square D and square E. Explain how you got your answer.

//This will really challenge you...// **Try It** 8. A rectangular sheet of wood has 4 small squares removed. It is then cut to make a box that is 5 centimeters by 4 centimeters with a volume of 60 cubic inches. (Four pieces of wood size A-4 are removed.) Find the area of the original sheet of wood.

__Geometry__ //Start out simple...// **The Shape of Things** 9. Look around your classroom and find as many different shapes as you can. Make a tally to help you determine which shapes are used most often. Why do you think this is so?

//Now try to work this out...// **Map It** 10. Willy Wonka went to Kandy Korners to see his friend. His friend told him how the town was set up and where to find the candy factory. Draw a map and put in the candy factory. //This will really challenge you...// 11. Look at this shape. How would you go about finding the total area of this shape? Show how you would do this and then find the total area.
 * Sweet Street, Rocky Road, and Almond Avenue are all parallel.
 * Lollipop Lane is perpendicular to Rocky Road and ends at Sweet Street.
 * Chocolate Boulevard is diagonal to Almond Avenue.
 * The candy factory is bordered by Sweet Street, Lollipop Lane, Sour Patch Place, and Chocolate Boulevard.

__Patterns, Algebra, And Functions__ //Start out simple...// **Rafting - From Problem Solving Connections** 12. You are pulling a raft up a river. You can make 15 miles a day. At night, while you are asleep, however, the current pushes the raft 3 miles back downstream. If you set out on Tuesday to get to a town 85 miles upstream, on which day will you arrive?

//Now try to work this out...// **Stepping Up** 13. Study this picture. How many blocks would you need for a 20-step staircase? Set up an algebraic equation to solve.

//This will really challenge you...// **Wacky Walter** 14. Walter and his parents are a little unusual. If he does an acceptable job of doing his chores, he gets paid $3.33 for that day. If he does an outstanding job, he gets $3 more. During one 10 day period, Walter received $42.30 for his work. How many days did Walter earn the extra money?

__Data, Statistics, And Probability__ //Start out simple...// **Happy Halloween** 15. Pete went out for Halloween. He got tons of candy. He put all of his candy in a shopping bag. He got 80 different things. 30 were chocolate, 20 were gum, 25 were plain, and 5 were cookies. Make a circle graph to display his loot.

//Now try to work this out...// **Mean or Median** 16. Sam made the following scores on unit tests for the term: 92, 98, 15, 92, 87, 92 Sam's teacher said that his grade would be based on the mean of his grades. Sam argued that his grade should be based on the median score of his grades. Find the mean and the median of Sam's grades. Which do you think best reflects Sam's work for the term? Explain your answer.

//This will really challenge you...// **Perfection** 17. From 11 positive integer scores on a 10-point quiz, the mean is 8, the median is 8, and the mode is 7. Find the maximum number of perfect scores possible on this test.

__Grab Bag__ **Be Careful** Tony's father is a driver for Brank's Armoured Truck Company. They take money from businesses to the bank. His last stop is at the largest hotel in the city where he collects a large sum of money. A map of part of the city showing the location of the hotel and the bank looks like this: If Tony's father must take a different route every day to prevent a robbery attempt, how many different paths //down// and to the //left// can he take from the hotel to the bank? December Solutions [|Number Theory] | [|Measurement] | [|Geometry] | [|Patterns, Algebra, and Functions] | [|Data, Statistics, and Probability] | [|Grab Bag] //Remember: These are open-ended problems. There could be other solutions than the ones we are giving.// __Number Theory__ 1. Each family brought 6 chairs. 2. 37, 39, 41, 43 3. 400/35 = 11 times 4. Orange = 10 dogs, yellow = 8, green =8, red = 6, blue = 7, purple = 9 5. Sam should go with CheapWheels. The difference increases with mileage.

 __Measurement__ 6. The area of the den is double that of the kitchen so the cost should double. 7. Square E - If B is 5 by 5, and F is 4 by 4, then E is 1 by 1. Square D - If B is 5 by 5 and E is 1 by 1, then C is 6 by 6 and D is C + E. D = 7 by 7 = 49 square units 8. L x W x H = V 5 x 4 x H = 60 H = 60/20 H = 3 so each square is 3 x 3. Original dimensions are l = 11 and w= 10 so original area is 110 cm squared.

 __Geometry__ 9. Answers will vary. 10. Several possible answers. 11. In order to do this problem, you need to divide the shape into smaller shapes. You will have a large rectangle 35 x 26; a rectangle 35 x 4; 2 rectangles 4 x 26 and 2 right triangles 4 x 26. The total area is 1570 cm squared.

 __Patterns, Algebra, And Functions__ 12. Tuesday of next week. 13. 210 blocks 14. 3 outstanding days

 __Data, Statistics, And Probability__ 15. Check graphs. Gum is 1/4 of the circle, Plain is about 1/3, Chocolate is a little more than 1/3 and Cookies are what is left. 16. Mean = 79.3; Median = 92. Decide if student's logic makes sense but should reflect the idea that all of Samantha's grades were terrific except 1. Therefore, that grade should not count as heavily. 17. Two

 __Grab Bag__ 18. Answers will vary. Check diagrams.