October/November 2014 Newsflash: Math Matters

Now that you’re starting to settle into your fall routine, it’s time for that first report card! While this may seem like a stressful time at first, it can also be a very constructive period for you and your child. Here are a few strategies to help you make this the most productive report card season yet.

• Get a sense of the big picture on the home front and at school. Have a conversation with your child about math regardless of the grade on the report card. You may discover that your high performer is bored and ready for additional challenges … or that your struggling student desperately needs and wants help in order to make the grade! Have a good sit-down with your child’s math teacher—maybe you’ll learn something significant about your child’s attitude in class that will surprise you! Finally, a Mathnasium assessment can be especially eye-opening. Every assessment—first time or otherwise—gives a comprehensive run-down of where each individual child stands with math. Give us a call or stop by the center; we’re happy to review your child’s progress in math, whether you’re new to our center or a long-time Mathnasium Mathlete.
• Take action! Use what you've learned and, together with your child, set reasonable goals that will lead to meaningful progress in math. Then, chart out a plan to help your child get started. Revisit current study habits, organization strategies, and your at-home study space—what needs to change? Research viable options that can help your child take his or her math skills to the next level (for instance, a school study group, or math games and puzzles you can play at home). Of course, whenever you need us, Mathnasium is here as a resource for all things math!
• Breathe! Whether the report card brings good news or bad, this really is the perfect time this school year to make positive changes and turn situations around. Be positive—if you implement your action plan sooner rather than later, the report card situation may be more to your liking next time around. And remember: virtually any child can succeed in math—it’s just a matter of teaching the way that makes sense to them. Best of luck to you and your child!

August/September 2014 Newsflash: Math Matters

We hope you had a great summer! A new school year is here once again, and it’s time to get excited about possibilities that lie ahead. As you and your child navigate the back to school scramble, here are some tips to help you make the most of opportunities this time of year, whether your child’s starting the year far behind grade level in math or already ahead.

• Gear up for a running start. With things at school just getting started, now is the perfect time to come up with solutions to ensure your child stays ahead of the game. If you’re looking for an after school activity that’s fun, empowering, and guaranteed to get your child’s math muscles flexing, we can think of no better place than right here at Mathnasium. We help kids reach their potential in math by teaching in a way that makes sense to them. Register for the fall now to secure your spot, start the year strong, and soar to new heights in math!

•  Get organized! We’re talking study schedules that fit in with the daily routine, a clean and neat workspace at home free of clutter and distractions, a calendar to keep track of upcoming tests and homework deadlines, and more. Sit with your child and together, come up with structured solutions that work with his or her learning style and schedule.

•  Stay on top of what’s going on at school. Meet with your child’s math teacher to discuss goals for the school year and familiarize yourself with the curriculum. The teacher can also provide some insight on your child’s attitude and performance in class—valuable information that will help you support your child.

We hope you’ll find these pointers useful as you gear up for an exciting year ahead. Wishing you a math-tastic school year!

August/September 2014 Newsflash: Tips & Techniques

“Thinking backwards”—starting at the end of the problem and using reverse operations—can help you solve certain problems at different grade levels.

Upper Elementary and Middle School:

A certain number is doubled. That answer is tripled. Finally, that answer is quadrupled and the answer is 60. What is the original number?

Answer:

When we quadruple a number, we multiply it by 4. As division is the inverse of multiplication, 60 ÷ 4 = 15. Tripling a number means “multiply by 3,” so 15 ÷ 3 = 5. Finally, doubling a number means “multiply by 2,” thus, 5 ÷ 2 = 2.5, or 2 ½.

Algebra:

A certain number is quadrupled. 3 is added to the answer. That answer is then tripled. Finally, when that answer is cut in half, the answer is 12.

a)     Write an equation that describes this problem.

b)     What is the original number?

Answer:

a)   We’re looking for a certain (unidentified) number, x. “x, quadrupled” means “4x.” Then, we add 3 to the answer, so 4x + 3. We then triple the quantity “4x + 3”: 3(4x + 3). Finally, we split the quantity 3(4x + 3) in half in order to yield the final answer, 12, so  {3(4x + 3)} /2 = 12.          

b)     To find the original number, we solve for x, which involves “canceling out” the numbers by using inverse operations.

So, (2) {3 (4x + 3)} /2 = 12 (2) multiply both sides by 2…

{3 (4x + 3)}/3 = 24/3 divide both sides by 3…

4x + 3 – 3 = 8 – 3  subtract 3 from both sides, and…

4x /4= 5 /4  divide both sides by 4.

Thus, x = 1.25

August/September 2014 Newsflash: Math Muscle Challenge

Take the Math Muscle Challenge!

Grades 1 – 6: A racehorse can run a mile in 1 minute 40 seconds.  At that rate, how many seconds will it take the horse to run a half-furlong? (Hint – A furlong is 1/8 of a mile.)

Grades 6 and up: Brian is going on a road trip in his van. When he leaves the house, he has a half tank of gas. After driving for 4 hours, he used 80% of the gas in the tank. At that point he had 2 gallons of gas left. How many gallons of gas does the gas tank hold?

Answers to Last Math Muscle Challenge

Grades 1 – 6: 32 ducks

Grades 6 and up: 3366

Note: There are many ways to solve this problem. One way is to start by finding the second and third digit of the combination. As the problem stated, the first two digits are the same and adding them together produces the third digit. That means the third digit is actually twice as much as the second digit. We also know that the second and third digit form a perfect square whose square root is the fourth digit. Looking at the two-digit perfect roots 16, 25, 36, 49, 64, and 81, we see that there’s only one that has a third digit that’s twice as much as the second digit: 36. That means the first digit must also be a 3. Adding 3 and 3 does give 6. Now, we take the square root of 36 we get 6 so the fourth digit is also 6, which is the same as the third digit.

This means the combination is 3366.

June/July 2014 Newsflash: Math Muscle Challenge

Answers to last month's challenges:

Grades 1-6: $37.15
Grades 6 and up: 64 times larger

This month's problems:

Grades 1 - 6: 

Rick goes to the park each day and counts the number of ducks swimming on the pond. On Sunday he counts 1 duck. On Monday he counts 2 ducks. On Tuesday he counts 4 ducks.  On Wednesday he counts 8 ducks. If this pattern continues, how many ducks will Rick count on Friday?

Grades 6 and up: 

Richard put an important document into a safe with a four digit numerical combination. In order for his partner Kevin to retrieve the document he must enter the correct combination. Richard told Kevin that the first two digits are identical and the last two digits are identical (XXYY). He also said the third digit is the sum of the first two digits and the last digit is the square root of the number formed by the middle two digits. What is the combination? (*Hint – The middle two digits together form a number that is a perfect square.)

Tips and Techniques: Transposing

Transposing is an important technique for students to master as they progress from Algebra I to Algebra II and beyond. It’s the process of moving quantities across the equal sign in an equation to make the problem solving process more efficient. Here’s how it works.

 Solving an equation means isolating the variable on one side of the equation, either the right side or the left. Generally it is better to isolate the variable on the left side of the equal sign because we read from left to right.

Beginning algebra students are taught the Law of Equations:  whatever you do on one side of an equation, you must do on the other side as well. 

Using the Law of Equations, to solve 2x – 3 = 13, we can add 3 to both sides, giving us

2x – 3 + 3 = 13 + 3 ===> 2x = 16

Then, we divide both sides by 2 to find that x = 8.

To solve 2x – 3 = 13 by transposing, we do the following:

Instead of adding 3 to both sides, we can transpose the 3 that’s already there by

moving it from the left side, over the equal sign, to the right side, and changing its sign from “–” to “+.”

Now we have  2x = 13 + 3, which becomes 2x = 16, the same answer we got using the Law of Equations. Again, we find that x = 8.

The beauty of this process is that it is visually easier to see how the parts of the equation change as we solve it. Instead of writing the transposed quantity twice (once on the left and once on the right), we literally pick up the quantity and move it to the other side. The price we have to pay for doing this is changing the sign of the quantity being moved. 

Let’s solve 3y + 2x – 3 = 7 for y.

Since we want to isolate y, we can transpose 2x and – 3.

This gives us y = –2x + 7 + 3. Simplifying, we get y = –2x + 10.

If we used the Law of Equations, we would have to write out

3y + 2x – 3 = 7 ===> 3y + 2x – 2x – 3 + 3 = 7 – 2x + 3

While simplifying the above does give us y = –2x + 10, it comes with a lot more work.

Note that most classroom teachers will not allow transposing until students learn to use the Law of Equations.

Try these:

1. Solve for x: 4x + 9 = 49
2. Solve for y: 2y + 7 – 3 = 24
3. Solve for y: 3x + 9y – 7 = 49
4. Solve for a: 3b – 4a – 6 + 4 = 49
5. Solve for a: 2b + 4a + 5 – 2 = 42 – 2a

Jump Start Your Summer with Mathnasium and Math Games!

Yay, summer! As you and your kids enjoy a well-deserved break from the pressures of school, we’d like to remind you that summertime also presents many opportunities for kids to keep their math skills fresh and play around with concepts they may encounter next school year. In particular, integrating some time for math games into play dates or family nights encourages kids to flex their math muscles as they spend quality time with their favorite people! Here’s a list of our favorite math games, featuring a few classics as well as some fresh alternatives:

Monopoly

A fun, family-friendly board game in which players move around the board buying and trading properties, building up properties by buying houses and hotels, and charging the other game players rent. Play the game with “dollar” bills only—the debit card version is not as educational. 

Math War

Math War is a fun variation on the classic card game that challenges players to perform a calculation (in this case, multiplication). The player with the highest product wins the hand! 

Set

Set is a fun, portable (deck of cards) game that tests visual perception and pattern recognition by challenging players to choose three cards that all follow the same pattern or a different one.

Battleship

Battleship is an engaging game for older kids that tests memory and spatial reasoning skills. Based on a numbered and lettered grid, guess where your opponent’s game pieces are positioned. First one to “sink” all of their opponent’s battleships wins.

Are You Ready? Game Shows® (Available for K-5th Grade)

Is your child ready for the next grade? These games let kids become game-show contestants, winning pretend cash for each math or language question answered correctly. After playing, enter the game results online and get an instant online assessment that pinpoints areas where your child may need additional help. An added perk: Lakeshore Learning has a special offer just for Mathnasium: get $10 off any Are You Ready? Game Show! Enter code 9347 at checkout or click here for a store coupon. Expires 7/31/14.

PS: In search of more math-tastic summer activities? Our summer program is in full swing and everyone at Mathnasium is having a blast helping students fortify their math foundations and prepare for what lies ahead! Don’t miss out on the fun and learning—call or email us by June 30th to get a limited-time summer registration discount. For more info about Mathnasium, please call or visit our center's website. We look forward to seeing you soon!