Departments : Integrating Math in Your Classroom :
Happy Hundred!
By Michael Naylor
These activities for the 100th day of school can help build skills in counting, operations and number sense
Your 100th day of school will probably occur in February this year. When you plan your "100th Day" celebration, you might include these 100-themed activities and problems.
100 money (Grades K-3)
What can you buy with $100? Give each of your students a catalog and let them choose items that add up to $100. They can cut pictures from the catalog and glue them to a poster.
100 number sense (Grades K-5)
Give your students copies of the following statements, have them fill in the blanks then share their answers with the class.
I could carry 100 _____, but I couldn't carry 100 __________!
I could eat 100 _________, but I couldn't eat 100 ___________!
I wish I had 100 _________, but I don't want 100 __________!
100 lists (Grades K-5)
As the class comes up with 100 words, write them on the board. For older children, choose a category and try to list 100 things in that category.
100 time (Grades K-8)
Can your students estimate 100 seconds? Have them close their eyes and estimate 100 seconds from the time you say "begin." When they think 100 seconds have passed, they should raise their hands. Stop the clock at about 105 seconds. Who was the closest? You can repeat this whenever you need 100 seconds of quiet!
Laura Bethel-Sehn
100 exercises (Grades K-8)
Kids can do 100 jumping jacks, sit-ups or toe touches. Add a measurement component by having students take 100 baby steps, 100 giant steps or 100 hops forward and comparing the distances traveled.
100 fractions (Grades 5-8)
There are 100 fractions that have the numbers 1-10 in their numerators and denominators, such as 2/7, 3/6, 10/3, etc. Ask your students to arrange these fractions in order from least to greatest. They'll find some interesting patterns!
100 lockers (Grades 5-8)
Have one hundred students walk down a hallway of 100 lockers. The first student should open every door. The second student closes every second door (beginning at the second locker). The third student opens or closes every third door (beginning at the third locker), opening doors that are closed and closing doors that are open. This continues until all 100 students have had a turn. Which doors are open?
The following doors will be open: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. These are all square numbers. Each door will be opened or closed a number of times that depends on the number of divisors of the door's number. For example, Door 12 gets opened and closed six times, so it's shut at the end. Door 16 gets opened and closed five times, so it's open at the end.
Can your students explain why square numbers have an odd number of divisors while non-square numbers have an even number of divisors? It will help to list divisors in pairs. For example, 12 = 1 x 12 = 2 x 6 = 3 x 4. Compare with a square number like 16 = 1 x 16 = 2 x 8 = 4 x 4. The repeated 4 makes the total number of divisors odd.
100 addends (Grades 5-8)
When mathematician Carl Friedrich Gauss (1777-1855) was a boy, his teacher asked the class to find the sum of 1+2+3+4...all the way up to 100. Gauss thought for a few seconds and then gave the correct answer.
How did he do it? He paired lesser numbers with greater numbers. 1+100=101, 2+99=101, 3+97=100, etc. If you continue these pairings up to 50+51=101, there will be 50 sums of 101, or 5050 total.
Give your students examples such as "Find the sum of integers from 1 to 7, from 1 to 12, from 22 to 33, etc," and challenge them to find the sums very quickly. One way is by recognizing that there are (B-A)+1 terms in the sequence, each with an average value of AB/2, so the total is the product [(B-A)+1][AB2]. Even if your students have difficulty with the algebra for this problem, they can still find a method that accomplishes the same thing.
100s of cubes (Grades 5-8)
Ask your students to consider one million small cubes. If each cube measures two centimeters on an edge, will all of the cubes fit into the classroom?
Make two-centimeter cubes available to your students. A million small cubes could be arranged to make a big 100 x 100 x 100 cube. With two-centimeter cubes, the large cube would be about two meters on a side – it would fit in the classroom.
As a follow-up, choose another object, large or small, and have your students estimate the size of one million of that object. Thinking in terms of 100s makes it easier!
Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA.
February, 2004, Vol.34, No.5
