Math Superheroes

 

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!”

 

Online resources:

• 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:

Speed

• 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.

Size

• 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:

Men:

• Height (inches):  69.4
• Weight (pounds): 194.7

Women:

• 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.

Geometry

• 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

Happy Pi Day!

Celebrate Pi Day with pies! Josepha shows you how.

Green Eggs and Ham Lesson Plans

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:

• Green Eggs and Ham on Pinterest

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?

Online resources:

• 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.

Studying Money: Classroom Activities

Money is interesting to most students, it’s an inescapable part of adult life, and it lets you study a lot of math and economics concepts, so it makes a great classroom theme — or just grab a few of these activities to knock out some framework requirements.

Need a bulletin board? U.S. Money Bulletin Board Set from Trend is clear and straightforward, showing coins and currency and their relationships, while Teacher Created Resources U.S. Money Mini Bulletin Board focuses primarily on equivalencies. Carson-Dellosa’s U.S. Money Bulletin Board Set has a chart and pieces showing both bills and coins.

Understanding U.S. money

First students need to be able to identify coins accurately, understand the place value issues of coins and currency, and recognize the value of various combinations of bills and change. Just as digital clocks have made it harder for kids to learn to tell time with analog clocks, changes in shopping have made it harder for kids to learn about money. Few elementary students today have ever seen someone count back change, fewer have run to the corner store with a $5 bill in hand to pick up a carton of milk, and many kids now get their allowance through PayPal or debit cards.

Here are some classroom activities that let kids get the money practice they might not be getting at home:

• Fair trade Have students work in pairs with classroom money. The first student offers a combination of bills and coins, and the second student must match the value. Students who need to work on recognizing coins can use the same combination exactly, while those who know the names and values of coins should have to come up with a different combination that produces the same value.
• Making change Have students use a Teaching Cash Register or a cash drawer to make change for items “bought” from catalogs. Bring mail order catalogs to class, give each student a One Hundred Dollar Bill, and let them take turns running the register and shopping.
• Draw it Have students draw items they’d like to buy and draw bills and coins totaling the price they’d pay. Have them label the drawing with “I’d pay $___ for a ____.” While you could use a cents sign, bear in mind that modern keyboards no longer have this sign, so it might be more practical for students to get used to $.01.

The value of money

Knowing that a nickel is equal to five cents is necessary, but it doesn’t really tell you the value of that nickel. Money is only worth what it can buy. Kids whose experience of shopping with parents is putting things in a cart and swiping a card may not be conscious of the relationship between goods and cash.

Try some activities that make it clear:

• Big plans Plan a class party, a trip to a fun destination, or another big event. As a class, brainstorm the things needed for the trip. Use ads from newspapers or catalogs or do internet research to find the prices for all the items needed. For older students, divide the class into teams and compete to see who can bring in the lowest total.
• Budgeting Have students create a household budget. A typical budget recommendation is 28% for housing and 15% for food, 15% for transportation and 10% for savings. That leaves a mere 32% for clothing, entertainment, insurance, medical costs, gifts, charitable giving, and everything else. Imagine a person making minimum wage at a full time job and have the class do the math. Have older students use classifieds from the local paper or online research to determine what kind of housing, transportation, etc. their sample budget would pay for.
• Global view Use Peter Menzel’s eye-opening books Material World: A Global Family Portrait and Hungry Planet: What the World Eats to get a clearer understanding of how much money people have in different parts of the world. Use Google Earth to make virtual visits to the homes of the people you learn about.

 

What Comes Next?

“What comes next?” is a deceptively simple question. Identifying a series and predicting what comes next is a critical thinking skill that lets us test comprehension of a wide range of math concepts — and one which we use as adults in reading, planning, and decision making as well.

Use craft sticks and chart stickers to create “What Comes Next?” games or centers customized for your classroom, or have students make “What Comes Next?” puzzles for each other.

It’s very easy. Use stickers on one side of a craft stick to establish a pattern. End with a question mark. Turn the stick over and add the next item in the series so the puzzle will be self-checking.

Here we have groups of pink stickers in simple patterns: one sticker, two stickers, one sticker, two stickers… Other sticks show [one, two, one, one, two] and [one, two, three,one, two, three], and so on.

You can use chart stickers to match your current classroom theme, or put all your leftover chart stickers into a box and pull it out for this project.

Use numbers of items, colors, right and left facing stickers, different items, or any concept or pattern you’re working on in class.

Stickers make this fun for younger students, but you can also create puzzles with numbers or expressions. Have students work out puzzles for one another. The steps are simple:

• Decide on an action that can be taken on any number. This could be “add 3″ or “multiply by 2 and add 1″ or “subtract the preceding number” or “multiply by the final digit of the preceding number” — anything at all.
• Choose a beginning number and write it on the left of the stick.
• Apply the action to that number to create the next number in the sequence. Repeat this step several times.
• End with a question mark.
• Flip the stick and write the next number in the sequence. You could also give the rule, such as “n-3,” and write that on the back (answer side) of the stick.

When students have completed their puzzle sticks, have them trade and work to figure out one another’s puzzles. Add an element of competition by allowing students to keep the puzzle sticks they solve and return those that stump them.

Alternatively, keep the puzzle sticks in a pencil cup, pocket chart, or shoe box for fast finishers to solve — and let them create more, too.

Teaching Fractions

A recent report of the National Mathematics Advisory Panel recommended that we as a nation get it together when it comes to teaching fractions. They didn’t phrase it quite like that, but they singled out fractions as an essential area in math that isn’t being taught successfully, and must be. It is, according to the panel, one of the big three topics that should be completely mastered in K-8. It also serves as an example for one practice the panel particularly abhors: revisiting a topic year after year “without closure” — that is to say, we teach it every year and some of the kids never get it.

Fractions can be a real source of frustration in the classroom. On the one hand, they are essential, not just for more advanced math tasks in students’ future math classes, but for daily life. We don’t really have the option of saying that some of the kids will master fractions and some won’t.

On the other hand, they are abstract enough and counterintuitive enough that, really, some of the kids will find it easy to master fractions and some won’t.

It seems unlikely that 1/2 would be larger than 1/3, when you first hear that. The process for multiplying fractions seems implausible. Fractions, one teacher told me when we were discussing her own experiences in trying to master them as a child, look spiky and weird and intimidating.

How can we overcome these obstacles? Especially when we have students in upper elementary or middle school who have been trying to grasp fractions for years, and despair as soon as they see them? Here are some things that might help:

Make them concrete.
Even students who seem otherwise too old for manipulatives should have them when they study fractions. Manipulatives add a multisensory component to your teaching, allow you to set up centers, and increase students’ comfort levels. We recently heard complaints that “manipulatives take too much time,” but we say that it’s quicker to help students learn thoroughly once than to review ten times because they didn’t grasp it. Some of our favorites are these:

• Fraction Squares I like the overhead ones for ordinary classroom use. Since the pieces are translucent, students can lay 1/4 pieces over 1/2 pieces and clearly see the relationship. In fact, these pieces can really make the whole notion of equivalent fractions click. There are also circle and triangle versions of this useful resource.
• Pizza Fractions Click the link for a really nice magnetic set to use on the board. We like the Learning Resources Pizza Fraction Fun Game, but the cardstock ones are a good start, too, and inexpensive enough that you can pass out a full set of eight to each student for practice. Teacher’s Friend Pizza Fractions! Bulletin Board is a good complement.
• Cuisenaire Rods are different-colored rods of different lengths. Ten of the shortest pieces equal one of the longest. You can lay the three-unit rod next to the ten-unit rod to see 1/3. Cuisenaire rods come in wood or plastic, hook-together or plain, and bring fractions down to their simplest form. One plus for this venerable standby is the wide range of books that use them, so you can always find new ideas.
• Base Ten Blocks are a big favorite of mine among math manipulatives, because you can literally use them for everything from counting through algebra. You can use them as you would Cuisenaire rods, but they are designed for working with larger numbers, so 49/50 or multiplying fractions will work with these, too.

Make them natural.
Fractions are not used as much in daily life (once we get past casual uses of  ”half” and “a quarter”) as decimals. But they are used. Take opportunities to use fractions in the contexts in which students see them used outside of the classroom. Recipes, building, sewing, and music all use fractions. Build a bird feeder, increase a favorite recipe to feed the whole class, or plan a quilt. Keep track of all the occasions on which fractions are used and show them in your Fractions Pocket Chart. Just taking the opportunity to say “That’s 5/8 of an inch wide — let’s show that in our pocket chart” gives you a starting point for the next fraction lesson.

Make them fun.
Games with fractions may not be what you usually do with your spare time, but they’re not hard to find. Using games in the classroom allows you to keep student attention on a single concept longer than drilling, keeps students who have caught on engaged until the others catch up, and provides motivation.

• Scholastic’sMath Games to Master Basic Skills: Fractions & Decimals has a number of quick and easy games for practicing fractions. Bingo and Tic-Tac-Toe frames are in the book ready to copy, as are multiple pages of fraction and decimal “cards” which fit the squares of those frames. You can use the cards for concentration or follow the directions to make checkers boards of construction paper using the cards.
• Frog Pond Fractions is a ready-made game suited to younger students. Students collect fractional pieces throughout the game, aiming to make a whole. This is how the popular game Trivial Pursuit is scored, too. Develop the habit, when playing games in class, of indicating scores not by counting, but by filling in parts of a pie.
• Fill in the parts of a pie with Fraction Fun, too. This is an interactive online game in which players see a pie with some parts highlighted. Type in the correct fraction and you get a point. Since 2/4, 3/6, and 1/2 are all treated alike, this can be a good review of equivalent fractions.
• BBC fraction games address a number of different fraction skills, including putting fractions in order by size identifying the largest possible fraction, and more.

 

Some students will find fractions challenging, even when we follow the suggestions of the National Math Advisory Panel and offer math instruction in an organized and systematic way. But making fractions concrete, natural, and fun can help.

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