December 2014 / January 2015 Newsflash: Tips & Techniques

Upper Elementary and Middle School

Find the perimeter of the shape below. (Hint: there is enough information.)

Solution:

The length on the bottom of the rectangle is the same as the length on the top, although the top has been split into two pieces. Similarly the width on the left is 11 inches and the width on right is also 11 inches, again in two pieces. 

Now, the length of the side is given in inches and the length of the bottom is given in feet. Since we have to add to get the perimeter, the Law of SAMEness requires the units to be the same. Let’s change 2 feet into 24 inches (2 x 12). 

Note that it is not necessary to know the exact measurement of the length and width. All that matters is that we know the total length of each. 

With that, 11 in + 11 in + 24 in + 24 in = 70 inches.

Algebra 

If ax + 2a = c and x + 2 = 3, express a in terms of c. 

Solution: 

If ax + 2a = c, then a(x + 2) = c. Now, substitute “3” for “x + 2” and you get 3a = c, 

so a = c/3.

December 2014 / January 2015 Newsflash: Math Muscle Challenge

Grades 1 – 5: Jim is 6 inches taller than Bill. If Bill is 4 feet 7 inches tall, how tall is Jim?

Grades 6 and up: Three equally priced pens cost $4.50 altogether. If the cost per pen is increased by $0.50, how much will 5 pens cost at the new rate?

Answers to Last Month’s Math Muscle Challenge

Grades 1 – 5: 9 dogs and 7 owners

Grades 6 and up: 96

Mathnasium's 4th Annual TriMathlon Recap

This past weekend at Mathnasium Learning Centers around the country, elementary school students showed off their math skills and won money for their local schools by competing in our 4th annual TriMathlon.

A free, fun-filled event for 2nd, 3rd, 4th, and 5th grade students, the TriMathlon tests a mathlete’s mental fitness with three fun-filled math challenges: The Counting Game, a Magic Squares Challenge and a Mental Math Workout.

We had a wonderful event this year with more than 3,200 participants at 171 centers across the US and Canada. That's a LOT of TriMathletes showing off their math skills!  If you were able to come out to one of our events, we'd like to thank you for joining in our TriMathlon fun, and we hope you had a blast showcasing your math prowess and making new friends! 

Fun for Students!

At Mathnasium, it's always our goal to make math fun and accessible for students, and our TriMathlon offers participants a relaxing, engaging environment to challenge themselves and feel good about giving back to their local community.

From what we've heard from students, they had a great time! Wilson Fisher, a 5th grader who competed in the Johns Creek and South Forsyth TriMathlon said, "The TriMathlon was a great experience and it strained my brain. I look forward to it every year because I get to put my skills to the test...and it's in a fun way!" 

Phoebe Fisher, a 3rd grade participant, chimed in, "I get to show what I know!" 

Aubrey Lee, a 5th grade TriMathlete, was impressed with the challenges. "It is cool that it has three different sections and I like that it is not just like 6+6 or something like that." 

While the challenges certainly were brain-strainers, our TriMathletes were up to the task—three students at the Johns Creek and South Forsyth TriMathlon had perfect scores!

The Mathnasium of Brandon began their event with the Plaza Bella Goes Pink cancer walk, raising over $14,000. TriMathletes got to take a break from competing to check out the 4 Way CountDown, Corn Hole and a photo booth, complete with fun masks! 

According to Center Director Becky Daniels, there were plenty of delicious snacks in between events. "We had Popsicles for the kids after the competition, muffins while they waited and cookies after awards as a reward."

Speaking of sweet treats, Athena Ramirez, Center Director of Mathansium of Clear Lake, recalls a funny conversation prior to the TriMathlon. 

"Here's a conversation I had with one of the 4th graders:

Athena: Niki! You should join the TriMathlon. We have awesome prizes! You get to win a Medal!

Niki: Miss Athena. I'll only join if you guarantee that I get to have candy for TriMathlon!

I thought it was the funniest thing that only candy could get her to go. She did win a medal and her candy, of course."

The Clear Lake TriMathlon instructor team was ready for fun with their students when the event started. 

"We had funny gimmicks—like for the instructor name badges, instead of 'Paul, instructor', we put 'Paul, Algebra Ninja', 'Anne, Calculus Commander', 'Cassandra, Geometry Genius', etc. Our name badges were conversation starters since a bunch of the kids and parents were not Mathnasium Students." 

The Mathnasium A+ mascot got plenty of love during the Clear Lake TriMathlon as well. 

"During the 5 minute breaks in between tests, the A+ would come out. During the first break, Athena, Fraction Fairy, would do some stretches, and the A+ and the kids would follow. During the 2nd break, Paul, Algebra Ninja, had to do 3 Ninja moves. The kids loved it! It was a fun little break before we tweaked their brains again."

Rangu Mandyam, Center Director of Mathnasium Oak Park, got great response from returning participants when it was time to play the Skip Counting Game while the scores were being tabulated.

"They remembered it from previous years, even though we do this just for a few minutes before giving them some other activity, depending on how long it takes the graders to tally the scores before the awards ceremony.

We stand in a circle and I start with '1'. The next person says 'Bzz' or some other word we choose to skip the even numbers.  The third person says '3' and fourth person says 'Bzz'. This seems too easy, but it is very interesting to see how many kids have to think a bit before saying the next number. We then go to skipping multiples of three. If time permits we go to multiples of four."

"For one round the taboo word was "Bzz," for another it was "Pokemon" and for yet another it was "Ghost." I let the kids choose the word to replace the skipped number. I want to be able to go to skipping 6, 7, 8 etc., but we never have time to go that far."

Check out these fun videos of TriMathlon participants playing the Skip Counting Game:

The Mathnasium of East Round Rock also combined math fun with costume fun for their TriMathlon.

Bill Nobles, Center Director of the Mathnasium at St. Petersburg, had enthusiastic response from students, parents and teachers about their local TriMathlon. 

"I think when we started we thought if we could get 10-15 kids in the center for TriMathlon, the event would be a success, since it was our first year. Well, then the enrollments started rolling in. When they got to 30, I thought that was a good number. At 40, I was starting to think it was going to be a very busy day. At 60, I was wondering if we should shut down enrollment, and at 80, I was wondering where everybody would fit!

On the day of the event, we came in early, decorated the center with balloons, had all of our staff on, and nervously wondered how many kids were actually going to show up. As it turns out, we had just under 60 participants, spread almost evenly over the grade levels. Many of the parents, particularly parents of non-Mathnasium students, chose to stay in our waiting area, so we were able to explain the Mathnasium Method and even schedule some assessments as the day went on. We even had two teachers who came just to watch their students and to learn about Mathnasium."

Fun for Parents!

Parents were definitely impressed with the TriMathlon! Two parents at the Mathnasium of Menomonee Falls marveled at how organized their event was, with one parent and their TriMathlete driving over two hours to participate. They enjoyed the competition so much they plan to come back to Mathnasium over the summer for instruction. Another parent told Center Director Anu Deepak that she saw it as "an awesome opportunity for the kids. Her child won the 3rd place and he was so motivated by that and now he wants to do better at the next TriMathlon!"

Swheta Rohit, a parent of a 4th grader at the Mathnasium of North Manchester had this to say about the TriMathlon: "Thank you Mathnasium, kids sure had a good time!" Marney MacFadyen, another North Manchester parent of a 4th grade TriMathlon participant chimed in, "We are thrilled that Chloe was able to participate and we have been busy spreading the word via social media about the program and the TriMathlon." 

Cherie Cason, a parent of two TriMathletes, shared her thoughts on the event: "My 3rd and 5th grader participated in Mathnasium's TriMathlon at the Johns Creek location this past weekend. The instructors at the training facility were very nice, warm and welcoming. It was a great experience for my children."

Cool Prizes!

In addition to flexing their mental math muscles and winning money for their schools, each student walked away with a goody bag and a certificate of participation to show off their achievement. 

The top three scorers in each grade level received additional medals and prizes.

A few TriMathletes showed off their math fitness and their physical fitness on the same day. Martha Gagnon, Center Director of the North Manchester Mathnasium, had two 2nd grade participants who competed in the TriMathlon, then left before the award ceremony for an end-of-season soccer game. Both of them won a medal at the soccer tournament, and while they were there, their parents received an email from Martha saying they were both winners and had won another medal!

The TriMathlon was made possible thanks to generous sponsorship from You Can Do the Rubik's Cube, Lakeshore Learning, Smarties®, and PrintingForLess®.

Tie-Breaker Time!

The TriMathlon isn't over yet! Top scorers will go on to compete in a Tie-Breaker event to be held on October 26-27th. The event will consist of a top secret final challenge, which is on its way to finalist Mathnasium Centers now!

Stay tuned next week on the Number Sense blog for a recap of our TriMathlon Tie-Breaker results! For more fun pictures from our local TriMathlon competitions, check out our Facebook album.

Tell us about YOUR TriMathlon!

Were you a TriMathlon participant or parent? Let us know in the comments here or on Facebook what you thought of your TriMathlon event! 

Have your own fun TriMathlon photos? We'd love to see them! Share them with us on Facebook and/or Twitter using the hashtag #TriMathlon.

October/November 2014 Newsflash: Math Muscle Challenge

Grades 1 – 5: Annie looked into a dog park and observed the dogs and their owners. She counted 50 legs. With a total of 16 “beings” (dogs and/or owners), how many dogs and how many owners are in the dog park? (Hint: Annie is not in the dog park.)

Grades 6 and up: If 64 is 40% of a number, what is 60% of the same number?

Answers to Last Month’s Math Muscle Challenge

Grades 1 – 5:  6.25 seconds

Grades 6 and up:  20 gallons

October/November 2014 Newsflash: Tips & Techniques

From time to time, we get lucky and the computation we have to do can be solved using a specific technique or trick that allows us to do effortless mental math.

Level 1:

12 x 125 = _______

The trick to this question is to see that “12” can be broken down into “3 x 4.”

            Think of “12 x 125” as “3 x (4 x 125).”

Now 4 x 125 = 500. (4 x 100 + 4 x 25)

Then, 3 x 500 = 1,500.

Try this (mentally): 8 x 175 = ________.

Level 2:

1/5 + 1/6 = __________

When you add two fractions, and the numerators of the fractions are both 1, the numerator of the answer is the sum of the denominators, and the denominator of the answer is the product of the denominators. In this problem, the numerator is   (5 + 6), and the denominator is (5 x 6).

So, 1/5 + 1/6 = 11/30. [Note: If the denominators are not relatively prime, the answer will have to be reduced.]

Try this (mentally): 1/12 + 1/13 = _____________.

Level 3:

2,000 ÷ 16 = ____________

The trick here is to recognize that 16 is a power of 2, and that powers of 2 make division into “half-of-a-half-of-a…”

In this case, since 16 is “2 to the fourth power,” we simply cut 2,000 in half 4 times.

So,

            Half of 2,000 is 1,000,

                        Half of 1,000 is 500,

                                    Half of 500 is 250, and finally,

                                                Half of 250 is 125.

So, 2,000 ÷ 16 = 125.

Try this (mentally): 3,000 ÷ 8 = ____________.

Note that there is more than one trick for each of these questions. See if you can find others!

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