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.