by Josh Rappaport
For those who worry their children may forget much of what they learned in the homeschool year, here are some tips for keeping math skills sharp throughout the summer.
My suggestion is that you do PRACTICAL MATH. Here are some suggestions:
CAR TRIP MATH ...
a) Get out the map and show your kids how to find the distance from town
to town. When you're traveling, say, from Dayton to Detroit, have them find and then add up all the little legs of the trip so they can tell you the total length of the trip. Have your child convert that distance to kilometers, too, if you're interested in teaching the metric system.
b) Once your child has figured out the mileage, let her use the formula:
(rate) x (time) = (distance) to figure out how long it should take you to
reach your destination, given a particular average rate (that you give her) for the trip.
c) Miles per gallon. Fill up the car when you leave and have your child
write down your car's odometer reading at that time. Then, when you fill up again, your child needs to write down both the new odometer reading and the amount of gas it takes to fill your car at this second fill-up. Next your child needs to subtract the first odometer reading from the second reading to get the total number of miles driven. Finally your child needs to divide the total number of miles just driven by the number of gallons of gas required at the the second fill-up. This final calculation gives your child the miles per gallon that your car used on that leg of the trip. You might also have your child do this same calculation for your city/town driving. It's interesting to compare your child's figures for highway and city driving to the figures given in the owner's manual (you can usually find this online). If the mpg you're getting now is significantly higher than the owner's manual values (more than 10% higher), it may be time for a tune-up. It's also interesting to these calculations for more than one car. Doing this activity trains your child to be a savvy consumer as well as a sharp mathematical thinker.
d) If you eat at restaurants during your road trip, kids can help you calculate the "tip." If you tend to use the standard 15% tip, you can even teach your child this quick (and intuitive) way to find a 15% tip.
1st) Round off the bill to the nearest dollar. [e.g.: $43.87 rounds to $44]
2nd) Divide that amount by 10 by moving the decimal point one place to the left.
[$44.00 divided by 10 equals $4.40, about 10% of the meal's cost]
3rd) Divide by 2 to find half of the 10% amount. [$4.40 ÷ 2 = $2.20, which represents 5% of the meal's cost]
4th) Add the 5% amount to the 10% amount, giving you the 15% tip.
[$2.20 + $4.40 = $6.60, meaning that a 15% tip on this meal is $6.60]
KITCHEN / SHOPPING MATH ...
a) Find a recipe that your child will like to help out with (dare I
suggest double-chocolate chip cookies?!). If it's a good recipe, double it. But
assign your child the task of doubling all fractions correctly.
b) When shopping, take along a calculator and ask your child to figure
out which of any two comparable purchases is the better deal by calculating the price per pound, or the price per ounce for both purchases. If the store displays this, your child can check to see if the store's calculation is correct, and if the store tends to round up or down.
c) Shopping also gives your child a chance to practice the skill of
rounding off. Take a pad with you, and have your child round off each
purchase to the nearest dollar. Before you check out, have him or her tally
up the rounded-off values of all the purchases. When the cashier gives you
your exact total, ask your child how close his/her estimate was to the actual amount. I would always give my daughter a 10 cent fee for doing this calculation, and although she always refused it (for about 10 intense seconds), she always eventually took it. In addition to reinforcing the rounding off skill, you are teaching your child to be a careful shopper. (Recent studies have shown that even those electronic scanners sometimes make mistakes!)
SPORTS MATH ...
New twists on some old games —
a) Prime Basketball: Play one-on-one basketball with your child. But
instead of counting buckets the normal way — 1, 2, 3, etc. — try counting by
prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. The first player to reach the number 29 wins. And anyone who accidentally says a composite (non-prime) loses a bucket and goes down one prime. If you have studied other number sequences (the Fibonacci numbers, triangular numbers, perfect squares, composite number, etc.), you can also count by the numbers in those sequences. FYI: Knowing the first 10 primes is not just an idle exercise. As I've pointed out in earlier articles, knowing the primes helps students slash their way through the jungle of math calculations.
b) "Power" Toss. Throw a ball back and forth with your child. But each
time you toss the ball, you have to call out a power (exponential value) of
a number. For example, let's say you start with the powers of 2. The first
person to throw the ball says 2 (for 2^1). The second person who tosses
the ball says 4 (for 2^2) [By the way, ^ means that the number following
it is an exponent: that is, 3^2 means 3 to the 2nd power, or 9] . The next
person to toss calls out 8 (for 2^3). The next person says 16 (for 2^4).
See how high you can go. The person who gives the highest power wins. (A nice, fun way to encourage students to really learn their facts!) Then try this with different numbers as bases: 3, 4, 5, etc.
c) Times-Table Catch or Times-Table Soccer — Either toss or kick a ball back and forth with your child. But when you throw or kick the ball, call out some times-table fact. For example, while throwing or kicking, shout: "Seven times eight." Your child must throw or kick the ball back with the right answer. Then switch and have your child ask you the problem. It's fun to "accidentally" get the answer wrong from time to time and see if your child is alert to catch your being wrong.
d) Algebra Catch or Algebra Soccer — With this variation, you call out
algebra formula facts, and your child must complete the formula. For
example, throw the ball and call out "x to the p times x to the q." Your
child must throw it back saying, "x to the p plus q." If you're re-learning
algebra yourself, you might want to switch roles and let your child quiz
you too. They LOVE that!
HOME IMPROVEMENT MATH ...
Summer is time for home improvements, so why not let your children help
out by performing a few calculations.
a) PYTHAGOREAN THEOREM — If you are building something square or
rectangular (a garden border, a sandbox, etc.) first tell your child the
lengths of the sides, and have her/him use the Pythagorean theorem to
calculate the length of the diagonal. Then have him/her actually measure
it out with a tape measure to make sure you have a true right angle. (That's more or less how the ancient Egyptians squared up their property lines square, just as a little math-history fact.)
b) PAINTING MATH —Are you painting or repainting a room? If so, your
child can calculate how many gallons of paint you're going to need. Most paint
containers tell you how many square feet they will cover. Have your child
first calculate the square foot area of the walls and/or ceiling you need
painted. Then multiply that by the number of coats you need to apply.
Finally take that figure and divide it by the square foot area specified on the
gallon of paint. The answer will be the number of gallons you need
to buy. Remember to round up when you get the inevitable fractional answer, or you'll be short on the among of paint needed (or see if you can buy the remainder in quarts).
c) ENGLISH-METRIC EQUIVALENTS Doing any sorts of measurements
in the English system (inches, feet, yards)? Why not have your child
convert those to the metric system using metric equivalents like 2.54
centimeters equals 1 inch.
Josh Rappaport lives and works in Santa Fe, New Mexico, along with his wife and two teenage children. Josh is the author of the Algebra Survival Guide, and the companion Algebra Survival Guide Workbook, both of which will soon be available for homeschoolers as a computer-based Learning Management System, developed and run by Sleek Corp., of Austin, TX.
For those who worry their children may forget much of what they learned in the homeschool year, here are some tips for keeping math skills sharp throughout the summer.
My suggestion is that you do PRACTICAL MATH. Here are some suggestions:
CAR TRIP MATH ...
a) Get out the map and show your kids how to find the distance from town
to town. When you're traveling, say, from Dayton to Detroit, have them find and then add up all the little legs of the trip so they can tell you the total length of the trip. Have your child convert that distance to kilometers, too, if you're interested in teaching the metric system.
b) Once your child has figured out the mileage, let her use the formula:
(rate) x (time) = (distance) to figure out how long it should take you to
reach your destination, given a particular average rate (that you give her) for the trip.
c) Miles per gallon. Fill up the car when you leave and have your child
write down your car's odometer reading at that time. Then, when you fill up again, your child needs to write down both the new odometer reading and the amount of gas it takes to fill your car at this second fill-up. Next your child needs to subtract the first odometer reading from the second reading to get the total number of miles driven. Finally your child needs to divide the total number of miles just driven by the number of gallons of gas required at the the second fill-up. This final calculation gives your child the miles per gallon that your car used on that leg of the trip. You might also have your child do this same calculation for your city/town driving. It's interesting to compare your child's figures for highway and city driving to the figures given in the owner's manual (you can usually find this online). If the mpg you're getting now is significantly higher than the owner's manual values (more than 10% higher), it may be time for a tune-up. It's also interesting to these calculations for more than one car. Doing this activity trains your child to be a savvy consumer as well as a sharp mathematical thinker.
d) If you eat at restaurants during your road trip, kids can help you calculate the "tip." If you tend to use the standard 15% tip, you can even teach your child this quick (and intuitive) way to find a 15% tip.
1st) Round off the bill to the nearest dollar. [e.g.: $43.87 rounds to $44]
2nd) Divide that amount by 10 by moving the decimal point one place to the left.
[$44.00 divided by 10 equals $4.40, about 10% of the meal's cost]
3rd) Divide by 2 to find half of the 10% amount. [$4.40 ÷ 2 = $2.20, which represents 5% of the meal's cost]
4th) Add the 5% amount to the 10% amount, giving you the 15% tip.
[$2.20 + $4.40 = $6.60, meaning that a 15% tip on this meal is $6.60]
KITCHEN / SHOPPING MATH ...
a) Find a recipe that your child will like to help out with (dare I
suggest double-chocolate chip cookies?!). If it's a good recipe, double it. But
assign your child the task of doubling all fractions correctly.
b) When shopping, take along a calculator and ask your child to figure
out which of any two comparable purchases is the better deal by calculating the price per pound, or the price per ounce for both purchases. If the store displays this, your child can check to see if the store's calculation is correct, and if the store tends to round up or down.
c) Shopping also gives your child a chance to practice the skill of
rounding off. Take a pad with you, and have your child round off each
purchase to the nearest dollar. Before you check out, have him or her tally
up the rounded-off values of all the purchases. When the cashier gives you
your exact total, ask your child how close his/her estimate was to the actual amount. I would always give my daughter a 10 cent fee for doing this calculation, and although she always refused it (for about 10 intense seconds), she always eventually took it. In addition to reinforcing the rounding off skill, you are teaching your child to be a careful shopper. (Recent studies have shown that even those electronic scanners sometimes make mistakes!)
SPORTS MATH ...
New twists on some old games —
a) Prime Basketball: Play one-on-one basketball with your child. But
instead of counting buckets the normal way — 1, 2, 3, etc. — try counting by
prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. The first player to reach the number 29 wins. And anyone who accidentally says a composite (non-prime) loses a bucket and goes down one prime. If you have studied other number sequences (the Fibonacci numbers, triangular numbers, perfect squares, composite number, etc.), you can also count by the numbers in those sequences. FYI: Knowing the first 10 primes is not just an idle exercise. As I've pointed out in earlier articles, knowing the primes helps students slash their way through the jungle of math calculations.
b) "Power" Toss. Throw a ball back and forth with your child. But each
time you toss the ball, you have to call out a power (exponential value) of
a number. For example, let's say you start with the powers of 2. The first
person to throw the ball says 2 (for 2^1). The second person who tosses
the ball says 4 (for 2^2) [By the way, ^ means that the number following
it is an exponent: that is, 3^2 means 3 to the 2nd power, or 9] . The next
person to toss calls out 8 (for 2^3). The next person says 16 (for 2^4).
See how high you can go. The person who gives the highest power wins. (A nice, fun way to encourage students to really learn their facts!) Then try this with different numbers as bases: 3, 4, 5, etc.
c) Times-Table Catch or Times-Table Soccer — Either toss or kick a ball back and forth with your child. But when you throw or kick the ball, call out some times-table fact. For example, while throwing or kicking, shout: "Seven times eight." Your child must throw or kick the ball back with the right answer. Then switch and have your child ask you the problem. It's fun to "accidentally" get the answer wrong from time to time and see if your child is alert to catch your being wrong.
d) Algebra Catch or Algebra Soccer — With this variation, you call out
algebra formula facts, and your child must complete the formula. For
example, throw the ball and call out "x to the p times x to the q." Your
child must throw it back saying, "x to the p plus q." If you're re-learning
algebra yourself, you might want to switch roles and let your child quiz
you too. They LOVE that!
HOME IMPROVEMENT MATH ...
Summer is time for home improvements, so why not let your children help
out by performing a few calculations.
a) PYTHAGOREAN THEOREM — If you are building something square or
rectangular (a garden border, a sandbox, etc.) first tell your child the
lengths of the sides, and have her/him use the Pythagorean theorem to
calculate the length of the diagonal. Then have him/her actually measure
it out with a tape measure to make sure you have a true right angle. (That's more or less how the ancient Egyptians squared up their property lines square, just as a little math-history fact.)
b) PAINTING MATH —Are you painting or repainting a room? If so, your
child can calculate how many gallons of paint you're going to need. Most paint
containers tell you how many square feet they will cover. Have your child
first calculate the square foot area of the walls and/or ceiling you need
painted. Then multiply that by the number of coats you need to apply.
Finally take that figure and divide it by the square foot area specified on the
gallon of paint. The answer will be the number of gallons you need
to buy. Remember to round up when you get the inevitable fractional answer, or you'll be short on the among of paint needed (or see if you can buy the remainder in quarts).
c) ENGLISH-METRIC EQUIVALENTS Doing any sorts of measurements
in the English system (inches, feet, yards)? Why not have your child
convert those to the metric system using metric equivalents like 2.54
centimeters equals 1 inch.
Josh Rappaport lives and works in Santa Fe, New Mexico, along with his wife and two teenage children. Josh is the author of the Algebra Survival Guide, and the companion Algebra Survival Guide Workbook, both of which will soon be available for homeschoolers as a computer-based Learning Management System, developed and run by Sleek Corp., of Austin, TX.
At his blog, Josh writes about math education, offering tips and tricks. Josh also authors Turtle Talk, a free monthly newsletter with an engaging "Problem of the Month." You can see a sample issue here or subscribe at this site. Josh also is co-author of the "learn-by-playing" Card Game Roundup books, and author of PreAlgebra Blastoff!, a "Sci-Fi" cartoon math book featuring a playful, hands-on approach to positive and negative numbers.
In the summer Josh leads workshops at homeschooling conferences and tutors homeschoolers nationwide using SKYPE. Contact Josh by email @ josh@SingingTurtle.com or follow him on Facebook, where he poses two fun math Qs/day.
