February+Problems

February Problems [|Number Theory] | [|Measurement] | [|Geometry] | [|Patterns, Algebra, and Functions] | [|Data, Statistics, and Probability] __Number Theory__ //Start out simple...// **Volunteering** 1. Jack, Art, Fran, and Megan work as volunteers at the local kennel. Jack gives the dogs baths every 4 days; Art cleans out cages every 6 days; Fran feeds the animals in Section B every 2 days; and Megan helps the receptionist every 3 days. How many times in 12 weeks will all 4 helpers be at the clinic on the same day?

**TV Watching Time** 2. For a school Project, Ron recorded how much TV he watched in one weekend and what kinds of programs he watched. This chart shows the time he watched TV: SATURDAY: 9:30-10:30AM; 1:00-3:30PM; 8:00-10:00 PM SUNDAY: 1:00-2:30PM; 8:00-10:00PM Ron watched sports programs for one half of the time. He watched movies for one third of the time. He watched cartoons with his sister Ronnette the rest of the time. How many minutes did Ron watch cartoons? Make sure you explain all of the steps and label your answers. //Now try to work this out...// **Tadpoles and Minnows** 3. In one pond in the forest, scientists found that a sample of pond water contained 45 minnows for every 27 tadpoles. How many tadpoles would they expect to find in a sample that contained 315 minnows? Make a chart to show the relationship between tadpoles and minnows.

**Fabulous Fudge** 4. The Fabulous Fudge Emporium serves fudge made from an old secret recipe. Marvin works at the shop after school. He does not know what all of the ingredients are, but he knows that in 3 days they use 15 pounds of dark chocolate, 30 pounds of sugar, and 21 pounds of butter. When Marvin orders chocolate, sugar, and butter for 3 weeks, how many pounds of each ingredient does he order?

//This will really challenge you...// **Gassing Up** 5. Derrick started his car, an automatic, and drove 8 miles. He spent 2 minutes at a stop light. Dawn drove her car, manual shift, and went 9 miles with no stops. Who used more gas? Use this chart and justify your answer.


 * __TABLE OF GAS MILEAGE__ ||
 * || Automatic || Manual ||
 * Idling || .16 Gal/Min. || .16 Gal/Min. ||
 * Starting || .05 Gal. || .05 Gal. ||
 * Moving || 1 Gal/22 Miles || 1 Gal/20 Miles ||

__Measurement__ //Start out simple...// **Plastic** 6. Each American throws away about 60 pounds of plastic packaging each year. At this rate, about how many years will it take one person to throw away a ton of plastic?

//Now try to work this out...// **Movin' On** 7. Mr. and Mrs. Quigley just moved into a new home with a lot of land. They need to plant grass seed. The problem is that they are not sure how to figure the new amount that they need. At their old house, they knew that the lawn was 10 ft. by 20 ft. and needed 5 pounds of seed. Their new lawn is 100 ft. by 50 ft. How will knowing the amount of seed needed from their old house help them with buying seed for the new lawn?

//This will really challenge you...// **Fencing** 8. The Andersons are buying a new home. They need to fence the yard because they have a dog. The yard is 72 ft. by 120 ft. Each fencing section is 8 ft. How many sections will they need? How many posts will they need? (a post is needed at the end of each section). What else will they need?

__Geometry__ //Start out simple...// **Diagonally Speaking** 9. What is the maximum number of diagonals in an octagon? Solve this without drawing the shape. (Start with smaller polygons and search for a pattern). Once you have determined the pattern, what is the maximum number of diagonals in a ten sided figure? A 12 sided figure?

//Now try to work this out...// 10. Draw a picture of a house with exactly 24 right angles, 6 acute angles, and 2 obtuse angles.

//This will really challenge you...// **Tomato Plants** 11. Guiseppe is planting a garden full of tomato plants. He can place 7 plants so that they form 5 straight lines with 3 plants on each line. How is this possible? Place 7 counters on your desk to represent the plants. Using 5 "sticks" experiment with arranging them into the 5 lines of 3 each.

__Patterns, Algebra, And Functions__ //Start out simple...// **Barking Dogs** 12. The number of times a dog barks is dependent on the number of passing cars. How many cars have passed when a dog barks 34 times? If 20 cars pass, how many times will the dog bark?
 * Barking Dogs ||
 * Cars || Barks ||
 * 6 || 4 ||
 * 7 || 7 ||
 * 8 || 10 ||
 * 9 || 13 ||
 * 10 || 16 ||

//Now try to work this out...// **Zooming Zucchini** 13. Gordon Greenthumbs likes to grow huge plants. He once grew a zucchini that started out at 6 inches, then grew 9 inches to be 15 inches on the second day. Each day the zucchini grew by the same amount as the day before plus another 3 inches. On which day would the zucchini be longer than 11 feet?

//This will really challenge you...// **Balancing Act** 14. The sides of the following scale balance. Each shape is worth 1 to 10. Each shape has its own unique value that stays the same wherever the shape appears in the diagram. The total weight of the whole diagram is 32. What weight does each shape represent?

__Data, Statistics, And Probability__ //Start out simple...// **Cards** 15. These questions are based on a standard deck of 52 playing cards.
 * Give a set that would have a probability of 1/2.
 * Give a set that would have a probability of 3/13. (12 cards)
 * Give a set with a probability of 1/26. (2 cards)
 * Give a set with a probability of 1/13. (4 cards)

//Now try to work this out...// **Popsicle Picking** 16. A box of 12 popsicles has equal numbers of cherry, orange, lime, and grape. Alex likes everything but lime. What is the probability that when Alex reaches into the box randomly, he will select a popsicle that he likes? Two days later, 2 cherry, 1 grape, and 1 lime have been eaten. Have Alex's chances of randomly choosing a lime popsicle gone up or down? Explain your answer.

//This will really challenge you...// **Friendly Firefighters - From BRAINTEASERS** 17. Truck 57-1 pumps 750 gallons of water per minute Truck 57-2 pumps 1000 gallons of water per minute Truck 57-3 pumps 1250 gallons of water per minute Truck 57-4 pumps 1500 gallons of water per minute Truck 57-5 pumps 1750 gallons of water per minute Chief Greg Henry and firefighters Chuck, Darren, Jim, and Vanessa drove the trucks from District 57 responding to a multiple alarm fire. The driver and crew of each truck worked to extinguish the fire. Who drives each truck, and how much water did each crew use to douse the fire?
 * Vanessa and her crew pumped 45,000 gallons of water on the fire in half an hour.
 * Chief Greg and his crew worked for 45 minutes pumping more water than Vanessa's crew, but less than Jim's crew did in an hour.
 * Chuck and his team pumped the same amount of water as Vanessa's crew in the same amount of time as Jim's crew.
 * Darren's crew worked for 45 minutes and pumped the most water on the flames.

February Solutions [|Number Theory] | [|Measurement] | [|Geometry] | [|Patterns, Algebra, and Functions] | [|Data, Statistics, and Probability] //Remember: These are open-ended problems. There could be other solutions than the ones we are giving.// __Number Theory__ 1. 7 times 2. Cartoons for 1 1/2 hours = 90 minutes 3. 189 tadpoles 4. Chocolate = 105 pounds; Sugar = 210 pounds; Butter = 147 pounds 5. Derrick = .05 + .36 +.32 = .73 gallon Ron = .05 + .45 = .5 gallon

 __Measurement__ 6. About 33 years. Accept 33 or34. 7. You know that 40 square feet are covered by 1 pound. You have 5000 square feet, so you need 125 pounds of seed. 8. 47 sections, 1 gate, 46 posts.

 __Geometry__ 9. 5 diagonals; 6 diagonals 10. Many possible answers. 11.

 __Patterns, Algebra, And Functions__ 12. 16 cars; 46 times 13. Day 9 14. Triangle = 4; Rectangle = 5; Circle = 3

 __Data, Statistics, And Probability__ 15. Many possibilities. 16. 75% or 9/12. Gone up. Now it is 2/8, which equals 1/4. 17. 57-1: Chuck; 45,000 gallons 57-2: Jim; 60,000 gallons 57-3: Greg; 56, 250 gallons 57-4: Vanessa; 45,000 gallons 57-5: Darren; 78, 750 gallons