Fractals are fun — and they team up perfectly with a study of snow. To do this activity with your students, you first need to explain what a fractal is:
A fractal is a a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation. – From Oxford Dictionaries
You can explain this definition to your students by asking them to look at a nearby body of water on a map. It probably looks pretty smooth. Ask them to imagine what the map of the body of water might look like if you only could measure with a yard stick. The edges would not be so smooth.What about a 12-inch ruler? The smaller the measuring tools, the more jagged the map would look. Since all the sides are the same length, this is a fractal.
Ask your students to draw an equilateral triangle on a piece of paper in pencil. Then ask them to divide each side of the triangle in to three equal parts and erase the middle section. Then ask them to draw two lines that are the same distance as the parts removed to create open triangles in the part that was removed. Ask them to do the same thing again. This is called a Koch snowflake.
Ask students what the shape is starting to look like. When they say it looks like a snowflake, share pictures of different snowflakes. You can use this Java applet to show students without asking them to draw the shapes themselves. Ask students to identify snowflakes as fractals or not so they understand what different fractal snowflakes might look like.
Show students different types of snowflakes and discuss whether they are fractals or not. Ask students whether the snowflakes are radially symmetrical or not and whether you can have a non-fractal be symmetrical. Are all fractals symmetrical?
Try these other fun, nerdy winter themed activities:
- Mystery of Christmas Cookies Science Experiment
- “Disaccharide J Tubes” or Candy Cane Experiment
- Chemistry of Cookies video
- Peanut Brittle Science
- Crystal Christmas Tree
- Microscopic Christmas Tree
- “Lather” printing wrapping paper and activity
- Silvered Ornaments Experiment
- Crystal Windows
With Thanksgiving around the corner, it can be hard to keep your students’ attention. Kids are excited about visiting relatives, eating turkey, and having a long weekend with their families. Thanksgiving themed activities are a great way to keep up with the holiday excitement and still keep students’ attention on learning activities. This activity is appropriate for students who are learning basic subtraction and addition and who are working on fine motor skills.
Print out the Turkey MathWorksheet and cut out the turkeys and feathers. If students are able to cut out the shapes on their own, this is a good exercise in fine motor skills. Mix up the feathers for each worksheet and then ask students to match the corresponding equation to the right turkey. For instance, the feather that says “=1-0″ corresponds to the turkey numbered “1.” After matching the feathers to the right turkey, students can glue them to the back of the turkeys to give each turkey feathers.
Planning Thanksgiving dinner on a budget is something many families do every year but children often are not part of that process. It’s a fun activity, though, and one that builds budgeting skills, math skills, and teamwork. Try it with your students by planning a Thanksgiving dinner in groups together using flyers from local grocery stores.
Thanksgiving Dinner Budget Activity
- Divide your class into groups and distribute one worksheet to each group as well as flyers from various grocery stores in the area.
- Instruct teams that their goal is to plan a Thanksgiving dinner for their group using the flyers provided. Each group must select at least one meat, one vegetable, one side dish, one dessert, and one beverage. Explain that after those basic requirements, teams can add on extra items as their budget allows. They can choose whatever they want within the category, such as corn, peas, or carrots as a side dish.
- Groups are not require to budget for condiments, plates or silverware, cooking utensils, etc.
- Part of the goal is teamwork so groups must decide together what to have for dinner within their group.
- All the purchases must be within the budget. If you want to make it more difficult, you can have students plan for applicable sales tax in your area.
- Students must fill out the worksheet to get credit for the activity.
The worksheet is available here.
More Thanksgiving dinner activities:
Math and superheroes go together like Batman and Robin. If you’re using a superhero theme for your classroom, take advantage of that. Math class? Make it your ongoing theme.
There’s a ready-made bulletin board set:
- Math Superheroes Bulletin Board Set has 8 lively posters with captions like, “Probability woman says there’s a three in four, or 75 percent chance of rain today!”
- Math problems from the Superheroes Memebase — project them when students come in for class or post them on the bulletin board, and see who can figure them out. If your students get inspired, ask them to create some more to fill up the bulletin board, or the unit!
- Numbers League game
- Batman addition game
- NEA’s Classroom Superheroes
- Which Math Superhero are You? online quiz with illustrations
Now think of all the math concepts you can cover with superheroes:
- Superman is faster than a speeding bullet. Just how fast is that? The answer is more complicated than you might think, and you can see the wide range of speeds in a hypertextbook chart on the subject. The fastest speed offered there is 5,000 feet per second. Your class will need to get a good mental image of how far 5,000 feet is (Google Earth can help here) in order for this to mean much. Challenge them to convert feet per second to miles per hour (an online calculator makes it easy) for a more familiar calculation. As it happens, someone designed a hypersonic airliner that is expected to go just that fast. Once students get a clear mental image of how fast a speeding bullet is, ask them whether Superman is fast enough to accomplish the feats he’s called upon to do in the movies or comic books. Read an essay on the question at Scienceray.
- The Flash can run at 10 times the speed of light. The speed of light is the constant (C) in the famous equation E=MC2. Nothing is faster than the speed of light — except the Flash. Divide the class into teams and have each team create word problems based on this fact: how long would it take the Flash to get from one location in the world to another, for example. (Again, Google Earth is a great resource for this activity.)
- The Superhero Database has a list of the superheroes who have super speed among their superpowers. Have students do research to find the speed of each hero (divide the list among the class) and graph their speeds.
- The Superhero Database gives the heights and weights of more superheroes than you’ve ever heard of. Use the data to create charts and graphs. Compare the sizes of superheroes with those of ordinary people. Here are the U.S. government figures for Americans age 20 and up:
- Height (inches): 69.4
- Weight (pounds): 194.7
- Height (inches): 63.8
- Weight (pounds): 164.7
The Superhero Database uses a different format for its data. For example, here are the stats of Shirnking Violet:
- Height: 5’6 // 168 cm
- Weight: 120 lb // 54 kg
As a class, determine what format to use in preparing the superhero/ordinary people chart, and convert the data so it will be consistent. This is a great time to discuss why it’s important to do this when comparing information.
- The same database lists superheroes who are able to change size as one of their superpowers. Challenge students to decide whether this would be a useful superpower in their lives. Have them calculate the size they’d like to be able to achieve, since this varies from one superhero to another, and write a paragraph explaining how they’d use this power.
- One of the most famous superhero math party tricks is the Batman Equation which shows how to plot the Batman logo. The link takes you to a very thorough explanation of how this works. Can your students create an equation that makes a superhero log, either a familiar one or one they make up?
- Angle Man was a villain, an enemy of Wonder Woman, who had a tool called the Angler which was able to bend space, warp perceptions, and move people through time and space. It’s not clear to us how the Angler works, so it looks like a great opportunity for creativity. Challenge students to figure out how angles could be used in this way, and to draw a comic book style picture of the Angle Man using his Angler. If students are using protractors, they can measure and label the angles they draw.
We can’t leave this subject without mention of a favorite book of ours, now in its second edition: The Physics of Superheroes: Spectacular Second Edition by James Kakalios. This book should give you lots of ideas for ways to explore math with superheroes for secondary level students.
Check out some posts with more superhero ideas for your math superhero classroom:
- Superhero Lesson Plans
- more about the Physics of Superheroes
- ideas for a study of heroes
- Real Life Math and Unreal Life Math
Celebrate Pi Day with pies! Josepha shows you how.
Green Eggs and Ham by Dr. Suess, a perennial favorite, was written on a bet with Bennet Cerf that Suess couldn’t write a book with only 50 words. Obviously, he could. For small children, learning the 50 words in Green Eggs and Ham is a worthwhile accomplishment.
Here are the words:
a, am, and, anywhere, are, be, boat, box, car, could, dark, do, eat, eggs, fox, goat, good, green, ham, here, house, I, if, in, let, like, may, me, mouse, not, on, or, rain, Sam, say, see, so, thank, that, the, them, there, they, train, tree, try, will, with, would, you
Put each of the words on a word card. Hold them up and read them together each morning that you’re working on the book, or on your Dr. Seuss author study, or on Read Across America lessons.
More things to do with word cards:
- alphabetize them
- sort them into rhyming pairs and those with no rhymes
- sort them from shortest to longest
- copy them so that each student has a set
- illustrate them
- combine them into as many sentences as possible
It’s traditional to serve some green eggs and ham on Read Across America Day, and here’s a collection of recipes from the simplest to the most complex, with some exotic options:
Eating green eggs and ham, whether you green it up with food coloring or pesto, gives you a chance to examine the most obvious point in the book: the willingness or unwillingness to try new things.
The narrator doesn’t want to try green eggs and ham, so Sam I Am, the green eggs and ham evangelist, offers them every more insistently in more and more situations. At last, the narrator tries them and likes them.
Have students draw and label foods they don’t like. Make a class chart of the foods showing how many students chose each food as a disliked food. Then have students raise hands for “like” or “dislike” of each food on the chart and fill in the numbers. Here’s our graph, made at Create a Graph; you can make yours on the board, in a graphing pocket chart, or on paper, too.
If you’re serving green eggs and ham, include it in the chart as well.
Having charted the class’s immediate reactions, try an experiment. Have tasters sit in a box and try again. Does it make a difference? Chart the responses to this question to get a sense of how experiments can be done. You’ll probably find that 100% of the subjects like or dislike foods equally in and out of a box.
Return to the book and discuss which factors in the book might make a difference to the taste of the green eggs and ham. You can make a graph with these as well.
More things to graph:
- How many students have eaten things in a tree?
- How many have eaten things on a boat?
- How many would give in if someone asked them as many times as Sam I Am did?
You can’t leave a lesson like this without discussing the difference between being open to new experiences and being talked into unwise decisions. Brainstorm a list of factors that might tell students it would be unwise to take a chance on a new experience:
- Is it against the rules?
- Could you or someone else get hurt?
- Would your parents allow you to do it?
- Grammarman PDF resource pack has words and pictures plus directions for games using them.
- ReadWriteThink has a lesson making a book about all the places kids can read.
- Seussville has some activities for Green Eggs and Ham.