Halloween is a time for math fun as students explore pumpkins, spiders, and webs. And what do students do when they get home from trick-or-treating? Why, they sort and count their candy before eating it, of course!
PUMPKIN MATH
How many seeds?
Cut open a pumpkin. Have each small group estimate how many seeds are in the pumpkin.
Give each group a portion of the seeds to count.
Add up the group totals.
Whose estimate is closest to the actual number? How far off is the best estimate?
If you like, wash, lightly salt, and roast the pumpkin seeds.
How much does it weigh?
Take turns holding a pumpkin and guessing how much it weighs.
Weigh the pumpkin. Whose estimate is closest? What is the difference between the actual weight and the closest prediction?
Variation:
After making estimates and weighing one pumpkin, do the same for several other pumpkins of different sizes. Do the estimates get closer to the actual weight of each pumpkin?
What's my waistline?
Estimate the circumference of a pumpkin at its widest point.
Measure the circumference with a tape measure. Whose estimate is closest? What is the difference between the actual circumference and the closest prediction?
Variation:
After measuring the circumference of one pumpkin, make estimates and measure several other pumpkins of different sizes. Are you getting any better at estimating? Are your estimates more accurate for small pumpkins or large ones?
SPIDER MATH
Symmetrical spider
Using graph paper, draw a perfectly symmetrical spider.
Variations:
Draw one-half of a spider. Trade papers with a partner and see if you can complete each other's symmetrical spiders.
Coordinate geometry:
Near the bottom left edge of your graph paper, draw two lines that form an L. Number these lines, starting from 0 where they intersect.
Draw a simple symmetrical spider such that each line segment begins and ends at an intersection.
Make a list of the ordered pairs of coordinates so the spider can be drawn by connecting the points in sequence. (Use a symbol to show where the pencil should be lifted between certain points.)
Trade lists with a partner. See if you can draw each other's spiders by following the list of ordered pairs, without peeking at the original drawings.
Compare the original spiders with those drawn from the lists of ordered pairs of coordinates. Are they identical? If not, double-check and revise the lists as needed.
How many legs?
Get a lot of plastic spiders, or draw simple spiders on small squares of paper. Give each small group a handful.
Discuss how to figure out how many spider legs there are on 2 spiders, or 3 spiders, or all of the spiders on the table.
Make a chart showing how many legs are on one spider, two spiders, and so on. (Younger children might use a calculator to help.)
(The spider leg-counting ideas were shared by Jenny and Chris/CT/1 on the teachers.net primary elementary chatboard, October 14 and 21, 2001.)
Variation:
Using a 100 chart, circle each multiple of 8. Look for patterns on the grid. Look for patterns in the ones place digit and the tens place digit.
The math of making a spider web
Find interesting math facts about a spider's spinners and the thickness, strength, elasticity, and quantity of its silk at the spider web and thread page. You'll also see photos and step-by-step diagrams showing how an orb web is made.
Make a poster or fact sheet on the math of making a spider web. (Use your own words
Make a spider web
Research orb spider webs using the spider web and thread link above or the Garden Spider link, which includes a diagram labeling parts of the web.
Using graph paper and ruler to guide you, design an orb spider web.
Variation:
Look at pictures of different kinds of spider webs (orb, funnel, sheet, scatter, triangle). Draw a web of your choice on graph paper. Find the area and the perimeter of your web. Decide what to do with half and quarter squares.
(This idea was shared by Rheta G. on the teachers.net primary elementary chatboard, Oct. 13, 2001.)
Craft spider webs
Turn your graph-paper web into a web you can hang in a corner or a window!
a glittery web made of glue
Place a sheet of wax paper over your graph paper web. Squeeze thin lines of glue onto the wax paper, following the lines of your web.
If you like, sprinkle glitter onto the glue.
After the glue is dry, carefully peel it off of the wax paper and hang it up.
a web made of spaghetti
Cook a pot of spaghetti and drain it. (If you add a few drops of oil to the boiling water, the spaghetti won't stick together.)
In a bowl that you don't mind getting messy, mix together the spaghetti and enough glue to coat it.
Cover your graph paper web with wax paper. Lay strands of spaghetti on the wax paper, following the design of your web.
When the glue has dried, carefully peel the spaghetti web off of the wax paper and hang it up.
(Both these craft variations were adapted from ideas found at KinderKorner's Along Came a Spider Web page.)
Make a spider web with string art
Visit Math Cats' String Art for ideas and patterns to make your own string art designs. See if you can design a string art "spider web" with string, thread, or pencil.
HALLOWEEN DATA
Costume Party Categories
Collect costume data by categories during your school's Halloween parade or a class party. Possible categories might include:
scary, pretty, funny...
store-bought vs. homemade
story/movie/TV characters vs. general types (princess, ghost) or original ideas
Analyze the data the day after Halloween, comparing grade levels or boys/girls.
Candy Sort
Sort and count your Halloween candy at home after trick-or-treating.
At school the next day, organize your data from the most common to the least common type of candy.
Make a bar graph of your data.
Over the next several days, in small groups or as a class, collect and organize your data on a spreadsheet application (Excel, for example), one row per student, one column for each candy type.
Use the auto-sum feature on each column to find the most common types of candy for the group. (As an option, use the formula feature or your own calculations to find the mean number of candies of each type per student.)
Use the sort feature to reorder the data from most common to least common type of candy.
Use the graphing feature to make and print a whole-class bar graph or pie chart of your candy data. (Which type of graph is most effective for summarizing the group's candy data?)
Variation:
Younger students can bring in their candy wrappers and decide as a class how to sort the candies into several categories. Make a Venn diagram to classify the candy by different characteristics. Students even can glue their wrappers to the Venn diagram.
(This idea comes from the Halloween Candy Count activity at A to Z Teacher Stuff.)
About the Author
Wendy Petti is the creator of the award-winning Math Cats Web site, author of Exploring Math with MicroWorlds EX (LCSI, 2005), and a frequent presenter at regional and national math and technology conferences. She teaches grades 4 and 5 math at Washington International School.
Wendy Petti is the creator of the award-winning