Teaching Day-by-Day: The Magic of Math

1. Celebrate the year mathematically with a month of problems and activities that engage students to think like mathematicians. Use all the digits (1, 1, 2010) from today's date (only once) to create mathematical problems. Can you create problems which equal all the numbers from 1 to 10?
2. On this date in 1929, the U.S. and Canada agreed to preserve Niagara Falls. Approximately 150,000 gallons of water flow over the falls per second during peak daytime hours. If the capacity of an average bathtub is 40 gallons, how many bathtubs could be filled in one second? In one minute?
3. Keep a record of the daily high and low temperatures in your city for this week. Use the Internet to find the daily high and low temperatures in other cities. What can you conclude from this data?
4. The cafeteria problem. Starting tomorrow, the cafeteria will serve chocolate milk with lunch every other day. Every third day, the cafeteria will serve pizza for lunch. On which days can we expect to have both chocolate milk and pizza for lunch?

5. Parallel view. Three views of the same block are shown below. Which letter is on the side parallel to the side with the letter A?
6. Fencing. Kathryn has 24 meters of fencing to use for her garden. She plans to use the back wall of the garage as one side of her garden. If the garden is rectangular in shape, what's the area of the largest garden that Kathryn can build?
7. Happy Birthday! Nicole's birthday is in October and is 15 days before Joan's. Suzanne's birthday is 23 days before Doreen' and is 24 days after Camille's. What is the date of each person's birthday? Oh yes, I almost forgot – one girl was born in January. 8 How many triangles are contained in the figure to the right?
8. How many triangles are contained in the figure to the below?
   
9. Counting cubes. Maria loves to count. One day, Ms. Fox put some cubes on Maria's desk. Maria told Ms. Fox, "When I count the cubes by three, I have one left over; when I count by four, I have one left over; when I count by seven, I have none left over." How many cubes does Maria have?

10. How many shapes can you make? Use four isosceles triangles and place all of them together along the edges with no overlapping as shown in the example. How many different
    figures can you make?
11. Weighty problem. Bobby has both five-pound and 10-pound sets of weights. The total number of weights in the five-pound set is the same as the total number of weights in the 10-pound set. Bobby has 12 weights in all, what is their total weight?
12. How much film? South Main School has 618 students. Each student will have his or her picture taken next week by a photographer. The photographer uses rolls of film that have 24 exposures each. How many rolls of film will the photographer use?
13. Rectangles galore. How many rectangles appear in the figure below?
    
14. Cute numbers. A number is called cute if it has exactly four positive integer
    divisors. What percent of the first 25 positive integers are cute?
15. How long will it take? To encourage people to attend a special concert, radio station MATH decides to give out 1024 free tickets. The DJs will give away half of the remaining tickets each day. How many days will pass until MATH has only one ticket left?
16. On the third Monday of each January, the nation honors the memory of Dr. King. This day of remembrance and tribute, is also a day of service to those in need. You don't have to find a big project to help people; you meet people every day whom you can help in small ways.
17. Imagine that each student in your class helps two other students today, then each of those students helps two more students the next day and so on. How long would it take for every student in your school to be helped in some way? Your school district? Your city?

18. Toss the dice. A pair of six-sided dice is tossed. What is the probability that the total numbers of pips (dots) showing is a prime number?
19. Look at the clothing that you and your classmates are wearing. Sort the students into groups by attributes such as solid colors, stripes, long sleeves, etc. Ask a classmate to describe each group by attribute.
20. Scavenger hunt. Your world is full of geometric figures. Go on a scavenger hunt to look for examples of cylinders, spheres, rectangular prisms, cubes and cones. Which figure do you think will be the most difficult to find? The easiest? Why?

21. Make a pan balance using a coat hanger, string and two paper plates. Use your pan balance to compare the mass of a very light object with a standard one-gram or five-gram weight. Put a small object, such as a pencil, on one side of your pan balance. Find an object that will balance your scale.
22. On January 23, 1971 the lowest temperature ever recorded in the U.S. was reported in Prospect Creek Camp, AK when the temperature fell to -80 degrees. How does this temperature compare for this day in your area?
23. Magical magic squares. Complete the magic squares to the right and below so that the sum of each group of numbers is the same when adding each row, column or diagonal.
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25. Counting squares. The steps below are made of 16 squares. If we add another row at the bottom, how many squares will we have? Continue adding rows along the bottom. Describe the pattern.
26. A lock company advertises that "thousands of combinations" are possible using the dial of its lock. For each possible combination, the user presses from one to five buttons. Once a button is pressed it cannot be reused for that combination. Is this advertisement telling the truth?
27. On this date in 1880, Thomas Alva Edison patented the electric incandescent lamp. More than a hundred years ago, a light bulb was installed in a fire station in Livermore, CA and has been burning continuously ever since. (Continued, see No. 28)
28. The bulb has been moved a few times; in 1976 it was moved to its present site at a fire station on East Avenue. Estimate how many hours of light this one bulb has provided. To see a picture of the light go to www.centennialbulb.org.
29. In Counting on Frank by Rod Clement (Houghton Mifflin, 1994), the narrator wonders how many humpback whales fit in his house. How big is a humpback whale? How many would fit in your classroom? How about peas? One cubic centimeter represents two peas.
30. Create a magic square of your own, make sure it works and then give it to a friend to solve.
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The National Council of Teachers of Mathematics is a public voice of mathematics education, supporting teachers to ensure mathematics learning of the highest quality for all students. NCTM is the world's largest organization dedicated to improving mathematics education in prekindergarten through grade 12. The Council's Principles and Standards for School Mathematics includes guidelines for excellence in mathematics education. NCTM offers a wide range of resources through journals, books and multiple websites. Find out more about these resources and membership at www.nctm.org.

Updated July 2010
January 2005, Vol.35, No.4