The “Math by the Month” activities are designed to engage students to think like mathematicians. The activities allow for students to work individually or in small groups, or they may be used as problems of the week. No solutions are suggested so that students will look to themselves for mathematical justification and authority, thereby developing confidence to validate their work.
This month’s activities are focused on investigating and exploring questions and activities related to using a calendar. Students will explore number sense and operations, logical reasoning, data analysis and probability, and algebra. These activities incorporate not only various Common Core standards but National Mathematics Content and Process Standards as well.
CALENDAR MATH: K-2
Who’s here today? Draw a picture of yourself on an index card. As you and your classmates arrive each morning, place your pictures on a large graph. Are there more girls or boys today? How many more girls or boys are there? How many people are absent? What else can you find out from your graph? As a challenge, record the number of people present each day and make a graph at the end of the week. Is there a day of the week when attendance is lower than the rest of the week? What might explain this? Do you think that this will happen next week? Find out.
Guess the day. Write a short mathematics story about a day of the week. Give hints in the story about which day you chose, but don’t tell the answer until the end. You could say, “It’s two days before the day we have music,” or “It’s the middle of the week,” or “It’s the day after the fourth day of the week.” Come together as a class, read your stories out loud, and try to guess the days.
Today’s date. Hang up a piece of chart paper with the date on it. Keep a list of how many times you encounter that number during the day. For example, on October 15 you might have music at 10:15, 15 people might order school lunches, or you might read page 15 in a book. How many times can you find the number in one day?
How many days until…? In the book Only Six More Days by Marisabina Russo, Ben is excited about his approaching birthday. “Only six more days!” he tells his sister. After listening to the story, use the calendar to pose a problem to a friend. For example, say, “Only __more days until the end of the month”Your partner can complete the sentence by looking at the calendar. Take turns posing problems. Make sure you explain out loud how you found the answer. For example, you might explain, “I knew it was eight days because it was a week plus one more day.” Try one problem that begins like this: “Eight days ago, we
CALENDAR MATH: 3-4
Did you know? With a partner, choose a day of the month and find as many mathematical facts as possible relating to that date. For example, for the number five you could list things such as: “Penta means five; therefore, a pentathlon is an athletic contest with five events. A pentagon is a figure with five sides and five angles. There are five Olympic rings!
Calendars galore! Approximately forty different calendars are used in the world today. The Gregorian calendar is the one most commonly used. Research different calendars and how they compare in terms of the number of days in the year, what they are based on (for example, planning crops, migration cycles, or annual events), whether the total number of days in the year is an odd or even number, and whether the days of the week fall on the same date each year.
The “write” date. Countries around the world have different customs when it comes to writing the date. In the United States, a month-day-year format is common: 12/25/1998 or 12-25-1998. Many other countries use a day-month-year format: 25/12/1998 or 25.12.1998. Furthermore, there is a format developed by the International Organization for Standardization in which the year is listed first, followed by the month and day. Create your own way of writing today’s date by using different representations of the numbers or by using pictures. Explain the logic of your method of writing the date and why it might be better than one of the other accepted methods.
Calendar patterns. Use this years calendar to count the number of Sundays in each month. Can you find a pattern? Do this with other days of the week. Make a list of the dates. Do you see any patterns? Which months start on the same day of the week? Why does this happen? What effect would a leap year have on this pattern?
CALENDAR MATH: 5-6
Today’s date. Using any date on the calendar, work with a partner or team to find different ways to express the number. For example, if today’s date is October 24, how many equations can you write that equal 24? Use more than one operation.
Probability. Make a set of number cards from 1-31 (one for each day of October) and place them in a paper bag. Predict the probability that you will pull out an even number, a multiple of five, and a prime number. What is the probability that you will choose a number in which the ones digit is greater than the tens digit? Set up a table to record your results. Conduct three sets of ten trials to test each prediction. What type of number is the rarest or the most common on the calendar? For example, are there more double-digit numbers, single-digit numbers, or square numbers?
Mind-reading mathematics. While looking at October’s calendar, tell a friend to choose four days that form a square in which all four numbers are touching. Ask your friend the sum of the four days and then surprise your friend with your mind-reading mathematics skills by guessing the four days. Hint: The first number is n, the second number is n + 1, the third number is n + 7, and the fourth number is n + 8. Therefore, 4n + 16 equals the sum of the four numbers. Using your friend’s number, solve for n. For example, if 20 is the given number, your equation would be 4n + 16 = 20. Once you solve for n, you can find the other three days. Ask your partner how you were able to “read” his or her mind! Give only one or two hints before explaining.
Calendar computation. Use the calendar for any month. Choose any three consecutive dates and find the sum. Compare it to 3 times the median in the series. Try comparing the sum of five consecutive numbers to 5 times the median. Try seven consecutive numbers, comparing the sum to 7 times the median. Draw a rectangle on the calendar around a 3-by-3 “square” of nine numbers. Draw several more 3-by-3 squares. Compare the sum of the numbers around the outside of each square with the number in the center. Find the mean of the nine numbers of each 3-by 3-square. What do you notice? Why do you think this happens?
Betsy Shreero, Cindy Sullivan, & Alicia Urbano. (2002). Calendar math. Teaching Children Mathematics, 9(2), 96-97. Retrieved December 15, 2009, from Research Library. (Document ID: 209591161).