January+Problems

January Problems [|Number Theory] | [|Measurement] | [|Geometry] | [|Patterns, Algebra, and Functions] | [|Data, Statistics, and Probability] __Number Theory__ //Start out simple...// **French Fry Fun** 1. There are about 20 potatoes in a 5 pound bag. A restaurant uses about 2 potatoes per order of French Fries. They charge $.95 for an order of Fries. How much money does the restaurant take in on a day that they use 400 pounds of potatoes?

**Odd** 2. The object of this activity is to find the sum of the first 25 odd counting numbers. One way is to add 1 + 3 + 5...continuing until you have added the first 25 odd numbers. However, this is too much work for the problem. Look for patterns and combinations to find a much easier way to solve this. Apply what you have learned from this problem and find the sum of the first 25 even counting numbers.

//Now try to work this out...// **Pump, Pump, Pump...** 3. Your heart pumps about 5 quarts of blood through its chambers every 60 seconds. A swimming pool (20 ft. x 60 ft.) will hold about 65,000 gallons of water. This represents the amount of blood pumped by your heart in approximately how many weeks?

**Going Shopping** 4. The Carters are buying a new CD player. Three stores have the model they want on sale this week. Here are the ads: __Radio Shop__: Regular Price=$200, Discount=20% off __Discount City__: Regular Price=$180, Discount=30% off __Ralph's__: Regular Price=$210, Discount=10% off and Extra 20% off Which store will give the Carters the best buy and what will the price be? Show all of the steps and label your answer. //This will really challenge you...// **Gas It Up** 5. A car dealer claims that by buying a new car, Mike will pay 1/5 less for gas than he pays for the car he currently owns. If the car Mike currently drives costs 1/6 less to gas up than Dave's car, and Dave pays $700 per year, what will it cost Mike to put gas in a new car for 1 year? Assume all cars will be traveling the same distance.

__Measurement__ //Start out simple...// **To Scale** 6. Use 1/4 inch graph paper and make a scale drawing of your room. Use the scale 1/4" = 1 '.

//Now try to work this out...// **Farmer Felix's Field** 7. Farmer Felix needs to put up a fence around his field. The dimensions of the field are given in the diagram. But, he has a problem. He needs to be able to drive his tractor and needs 10 feet between the field and the fence. How many feet of fencing should he buy?

//This will really challenge you...// **The Great Flood Of 2000 - From MATH FORUM** 8. On one Sunday in June of 2000, there was a great storm. Mr. Lui's basement got flooded! Mr. Lui wondered just how much water had to be cleaned up with his shop vac that held 12 gallons of water. He knew that there were 7.48 gallons of water in one cubic foot of water and that he had 2 inches of water in the backwards `L' shaped section of his basement. (See diagram below.) How many gallons of water were in his basement and how many times did he have to empty his shop vac?

__Geometry__ //Start out simple...// **Spelling** 9. Write the letters M, T, and H on figures 2 and 3 so that when the figure is folded into a box, it will spell MATH around the sides of the box. Figure 1 shows the correct placement of the letters. How did you decide on the letter placement?

//Now try to work this out...// **Rotation** 10. Find 3 upper case letters that look the same when rotated 180 degrees. Then, what letter's 90, 180, and 270 degree rotations has this outline? This is also the inside lines formed by the rotation of what letter?

__Patterns, Algebra, And Functions__ //Start out simple...// **Cookies** 12. A boy ate 100 cookies in five days. Each day he ate 6 more than the day before. How many cookies did he eat on the first day?

//Now try to work this out...// **Walking To School** 13. This line represents the line on a graph that shows how long it took Khalil to walk to school. The horizontal axis shows the time and the vertical axis shows blocks covered. Explain what you think happened on Khalil's way to school?

//This will really challenge you...// **Surprise, Surprise** 14. Extravagant Ellie and Thrifty Tanya each have bank accounts. Ellie has $500 and Tanya has $200. Ellie withdraws $15 each weekend while Tanya deposits $12. At the end of 13 weeks, what is the difference in their bank accounts? Solve this algebraically. Can you find a week when there is only a $3 difference? Hint: It is before the 13th week.

__Data, Statistics, And Probability__ //Start out simple...// **What's In A Name?** **A E I O U**

15. Choose 10 students from your class. Tally the number of vowels in each person's name. Use this to predict the results for the rest of the class. //Now try to work this out...// **PE Problems** 16. Mr. Bulge has to give his class a sit-up test. There are 33 students in his class and he needs to display the data in such a way that he can easily examine the results. Think of 3 different ways that he could do this and justify your opinion.

//This will really challenge you...// **Things Change** 17. Make a double bar graph to show the changes in sales for albums (1975) and CD's (1995). What conclusions can you draw? YEAR: 1975 ALBUMS: 257,000,000 CDs: 0 YEAR: 1980 ALBUMS: 322,800,000 CDs: 0 YEAR: 1985 ALBUMS: 167,000,000 CDs: 22,600,000 YEAR: 1990 ALBUMS: 11,700,000 CDs: 286,500,000 YEAR: 1995 ALBUMS: 4,600,000 CDs: 613,000,000 January 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. $760 2. All 25 odd numbers occur between 1 and 50. 5 odd numbers occur within each decade. The sum of the ones column per decade is 25. (5x25)+(5x0)+(5x10)+(5x20)+(5x30)+(5x40) = 625 [For evens: apply the same equation, substituting '30' for '25'] (5x30)+(5x0)+(5x10)+(5x20)+(5x30)+(5x40) = 650 3. 5 weeks 4. Discount City; $126 5. Current car = $583.33 and new car = $466.66

 __Measurement__ 6. Check drawings 7. 680 feet of fencing 8. 518.4 gallons; 44 times

 __Geometry__ 9. 10. H, I, O A W

 __Patterns, Algebra, And Functions__ 12. 8 cookies 13. Khalil started out quickly, stopped for a while, walked slowly, and hurried at the end. 14. Ellie--500-15x Tanya--200 + 12 x x = number of weeks At week 11 they will be $3 apart. 15. Answers will vary.

 __Data, Statistics, And Probability__ 16. Possible answers are box and whisker, stem and leaf, histogram, line plot, cumulative frequency chart. 17. Check graphs for title, scale, labels, and accuracy. Sales of albums decreased and sale of CD's increased.