Sure, we homeschoolers can fret about keeping learning alive during the summer months. And it’s true that there are skills to be kept up; we don’t want our children to lose all they’ve gained during the homeschool year. But I suggest a different attitude.
With so much to do during the summer — playing, gardening, crafts, hiking, sports, games — now is the time to switch from learning math to using math. By using math, kids will still keep their young minds sharp, so you won’t have to worry so much about keeping skills perfect. If you want to do that, you can get or find workbooks and worksheets. But that is not the focus of this article. The focus is how to encourage informal mathematical thinking over the summer, math without the “math.”
One approach: arts and crafts. Encourage your children to create a quipu, (“kee-poo”) an ancient Incan device with colored strings and specially placed knots. Anthropologists believe the Incans used quipus as counting devices to keep track of their stocks of animals, foodstuffs, etc. Simple Google searches will show you how to make a quipu, and how to use place knots so they represent numbers in our base-10 system (or a different base system, if you wish). You might encourage your kids to use their quipus to keep track of things they care about, like how many cards they have in their baseball card collection, or how many new ballet moves they have mastered in the course of their summer class.
There are all kinds of arts and crafts projects that involve math in one form or another. For example, making a geometric tessellations, a la M.C. Escher, involves design-making and informal math concepts on the repetition of designs in a 2-D area. Another way to stir the creative juices and learn math is planning or making a quilt; there are entire books on the geometric patterns in American quilts, and quilt-making also involves informal learning about U.S. history. For another fun activity, make geometric stained glass sun-catchers and hang them up in brightly lit windows. This involves the mathematics of symmetry and design, and who doesn’t love the look of stained glass with sunlight streaming through? For more arts and crafts projects involving math, try Google. Or check out two helpful books I’ve used: Family Math by Lawrence Hall of Science; or Math Art Projects and Activities, by Scholastic.
Don’t forget that gardening uses math. When gardening, you might ask your kids to help you plan out the garden. If you give them certain parameters (“we need to grow 10 heads of lettuce, 64 carrot plants, 10 tomato vines, and 6 eggplant vines,”) within a limited space, they’ve got a great math problem that is not at all typical “math,” yet it involves area, perimeter and space planning.
A good source for casually bringing out the math in gardening is Mel Bartholomew’s classic, All New Square Foot Gardener. Bartholomew has developed an ingenious method for planting summer crops in square-foot regions, and this can be used to teach about area, perimeter and crop yield, all informally. This book also shows how anyone can garden, no matter where you live.
While you’re outdoors in the garden, why not get the whole family involved in a unique project: making a sundial. Talk about an activity that is fun, hands-on, and teaches not just about math, but also about astronomy. You can learn how to make a sundial from many online sources, and it turns out that there are different kinds of sundials from all over the world. You will learn about latitude, longitude, sun angles, solstices, equinoxes, and how the sun’s shadow relates to our standard measurement of time. Want to get started now? Check out the North American Sundial Society online.
And once you start bringing in the delicious produce from your garden, let’s not forget that cooking with kids involves all sorts of informal math. In addition to the measurement calculations (cups, half-cups, tablespoons, teaspoons, etc.), there’s also the math involved in proportion (the recipe is for 8, but we only need enough for 6, how do we change it?). And if anyone in the family is trying to watch calories, planning a meal that fits a certain calorie count provides another excellent chance to use math informally.
Sports involve all kinds of math, and summer is a fun time to explore this, too. Going to a softball or baseball game? Why not teach your kids how to score the game using the standard symbols for scoring? You can find tips on this online at The Baseball Scorecard, and you’ll see that scoring involves all kinds of informal math, especially if you decide to gather stats for someone you’re watching, like the scorer’s brother or sister (as long as they don’t mind). I used to score my son’s baseball games, and it was great fun when my daughter started helping me out and even started scoring on her own. This is a great activity for children who like organization, and it encourages analytical mathematical thinking (how well does Theo hit when he bats leftie compared to when he bats rightie?).
If you like hiking, why not learn how to read topo maps and maybe even learn some orienteering skills. You and your kids will not only get out in the Great Outdoors, they will also learn about directions, using landmarks, elevation, compass readings, and more. Many outdoors and hiking stores have orienteering gear. Just ask around and you’ll find people who do orienteering as a fun outdoor activity. Often there’s even a club.
Another enjoyable summer pastime is playing games, and I’m a big believer that virtually any kind of board game involves some kind of mathematical thought. Even playing Candyland, young kids practice counting out their moves. Move up to Monopoly, and you’re dealing with complex decision making and strategizing, not to mention lots of skill in handling and using money.
In addition to those games, don’t forget games that require spatial reasoning skills. Chess, Checkers, Go, Chinese Checkers, and Battleship all get the spatial reasoning skills moving. And then there’s my favorite board game, Hex, which teaches kids about path analysis on a game board with hexagonally shaped spaces.
Almost any area of life involves some mathematical thinking, so sometimes the trick is just asking your kids for help with the calculations. For example, if you’re going on a road trip, why not ask your kids to help you figure out how much money you’ll need for gas. That in itself helps them use the skills of map-reading and addition to calculate total mileage. Then, using the concept of rates, your children can calculate miles per gallon, and using multiplication, they can figure out the total amount of money required for gas on the trip. Then, when you’re on the road, you might ask your children figure out how many miles per gallon your car is actually getting. Does the mileage go up or down depending on the kind of driving you’re doing? Consider awarding your young accountants with small cash rewards for doing this work, and let them spend their trip money on treats, souvenirs, t-shirts, etc.
The point is that there are many opportunities to keep the math part of the brain stimulated during the summer months. The real key is to remember that summer is a great time, not so much for “doing school-ish math,” but rather for using math, for seeing how math relates to our big complicated world and getting out there and putting it to use. After all, what else is math really for?
Josh Rappaport lives and works in Santa Fe, New Mexico, along with his wife and two children, now teens. Josh is the author of the briskly-selling Algebra Survival Guide, and companion Algebra Survival Guide Workbook. Josh is also co-author of the Card Game Roundup books, and author of PreAlgebra Blastoff!, a playful approach to positive and negative numbers. Josh is currently working on the Geometry Survival Flash Cards, a colorful approach to learning the key facts of geometry.
At his blog, Josh writes about the “nuts-and-bolts” of teaching math.
