March+Problems

March Problems [|Number Theory] | [|Measurement] | [|Geometry] | [|Patterns, Algebra, and Functions] | [|Data, Statistics, and Probability] __Number Theory__ //Start out simple...// **Tables And Stools** 1. Vladmir builds 3 legged stools and 4 legged tables. Last month he used 72 legs to build 3 more stools than tables. How many stools and how many tables did he build?

**Rainforests** 2. Rainforests cover only a small part of the Earth, but they are home to more than half the world's plants and animals. It is estimated that rainforests are cut down at the rate of 100 trees in a minute. At this rate, how many are cut down every 24 hours? Every week? Explain your answer.

//Now try to work this out...// **Who Are We?** 3. There are 2 prime numbers between 100 and 199 such that the tens digit is a prime number, the ones digit is a prime number, and the tens and ones digits taken together are a 2 digit prime number. Find the sum of these 2 prime numbers.

**Decisions, Decisions** 4. Seymore has just gotten a new job. On his first day, the boss gave him 2 choices for his salary. First Choice: Start at $30,000 and get a 5% raise at the end of every year. Second Choice: Start at $23,000 and get a $5000 raise at the end of each year. Calculate how much Seymore would be making at the start of the 5th year. Which is the better choice? Explain how you got your answer.

//This will really challenge you...// **Car Shopping** 5. Shawn bought a car for $5600. He sold it to Rachael for 5/6 the price he paid for it. Rachael sold it to Ray for 1/5 less than she paid for it. Ray sold it to Rick for 3/4 what he paid. What did Rick pay for the car?

__Measurement__ //Start out simple...// **Cubit** 6. The ancient Egyptians used a measurement called a cubit to build the pyramids. A cubit was the distance from the bent elbow to the end of the middle finger. Using your own self as a measurement, find out how many inches in a cubit. If a pyramid is 100 cubits long, about how many inches is that?

//Now try to work this out...// **Mayan Pyramids** 7. The Mayans of Mexico and Central America built huge pyramids of solid stone block.. The square base of one pyramid is 32 blocks. Each block is 6' x 6' x 6'. What is the surface area of the base before the next layer is put on? Use only the sides you can see.

//This will really challenge you...// **Surface Area** 8. Here is a sketch of a city park. It is 400 ' long and 300 ' wide. The sidewalks are 6 ' wide. What is the surface area of the sidewalk?

__Geometry__ //Start out simple...// **L** 9. There are 9 cubes joined together in the shape of an L. If this is dipped in red paint and then taken apart, how many faces will be red?

//Now try to work this out...// **Hexagonal Tiles (from PROBLEM SOLVING CONNECTIONS)** 10. In the center of Memorial Park is a fountain in the shape of a hexagon. Workers are ringing the fountain in hexagonal tiles. The first ring of tiles is made of black tiles. The next ring is made of white tiles. The next black, and so on. How many hexagonal tiles will the workers use in the fourth ring? In all, the workers completed 15 rings. What color were the tiles in the fifteenth ring? How many did they need for this ring?

//This will really challenge you...// **Triangular Tessellation** 11. This is an equilateral triangle with sides 3 feet long. Gary plans on filling in the entire triangle with the smallest triangles. How many would he need? How many would he need to make a design that tessellates 12 ' long and 6 ' wide?

__Patterns, Algebra, And Functions__ //Start out simple...// **Mile Swim** 12. Tiana and Shana are training for a mile swim. Each time they tried to get better times. The first week the best time for each of them was 70 minutes. Then Tiana had a best time of 66 minutes the second week, 67 the third week, 63 the fourth week and 64 the fifth week. Shana had a best time of 69 minutes the second week, 67 the third week, 66 the fourth week, and 64 the fifth week. If they continued at this rate, who would have the best time after 12 weeks of training? What would that time be?

//Now try to work this out...// **Legos** 13. Jody, Amy, and Tim are building a model out of Legos. The top level is a 1 by 2 rectangle. The level directly underneath is a 2 by 3 rectangle. The level underneath is a 3 by 4 rectangle. How many Legos will they need if their building is to be 12 levels high? Make a chart to show your work.

//This will really challenge you...// **Coin Count (from MATH FORUM)** 14. Everyday when Lisa returns from school she puts her change from buying lunch into a jar on her dresser. This weekend she decided to count her savings. She found that she had 72 coins—all nickels and dimes. The total amount was $4.95. How many coins of each kind did she have? See if you can find 2 different ways to solve this. Don't forget to explain your process.

__Data, Statistics, And Probability__ //Start out simple...// **Jellybean Jumble (from MATH FORUM)** 15. Mr. Cal Q. Later has a bag of jellybeans. As he walks around the room, he places a few jellybeans on everyone's desk—everyone's, that is, except Leo. On Leo's desk he places the bag with the remaining jellybeans. Here are the numbers: 17: Harumi 14: Melissa 13: Marcus, Evelyn 12: Kim, Toby, Lori 11: Jason 9: Efram, Inga 8: Hannah 6: Geoff 3: Luc 2: Muriel Muriel and Luc are not worried because they know that Mr. Later is fair. Mr. Later tells the students that Leo's jellybeans are all that remain in the bag. If they figure out how many are in there, they will each get to eat the average number of jellybeans which is 10. How many jellybeans are in Leo's bag? //Now try to work this out...// **The Prom** 16. The Prom Committee is setting up card tables for the prom. One table seats 4, 2 tables together would seat 6, 3 tables 8. No table seats more than 12. Show 3 different ways that 16 couples could be seated for the Prom.

//This will really challenge you...// **Graph It!** 17. Make a double bar graph for the following information: Mark's Math Test Scores SEMESTER 1: 99, 87, 90, 76, 100 SEMESTER 2: 100, 85, 100, 95, 90 Now, find the range, median, mode, and mean for each semester.

March 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. 9 tables and 12 stools 2. 144,000 in 24 hours; 1,008,000 a week 3. 137 + 173 = 310 4. The first choice would give him $36,465 at the beginning of the fifth year; the second choice would give him $43000. 5. $2700

 __Measurement__ 6. Depends on length of arm measurement. If the measurement is 17 ", then one cubit is 17 " and 100 cubits = 1700" 7. 4608 sq. ft. sides; 36,864 sq.ft top; 41,472 total 8. 12,276 sq. ft

 __Geometry__ 9. 38 faces 10. Ring 1 = 6; ring 2 = 12; ring 3 = 18; ring 4 = 24; 15 x 6 = 90 11. 16; 224

 __Patterns, Algebra, And Functions__ 12. Tiana at 51 minutes 13. 728 Legos 14. 45 nickels and 27 dimes

 __Data, Statistics, And Probability__ 15. 47 + 3 = 150 16. Check answers. 17. Check graphs for title, scale, labels, and accuracy. Semester 1: Mean = 90.4, Median = 90, Range = 24, Mode = none Semester 2: Mean = 94, Median = 95, Range = 15, Mode = 100