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.

Mathnasium Gives Thanks at Thanksgiving

It's that time of year when we reflect upon all that we're thankful for, and at Mathnasium we have a lot on our list! Here are just a few things we're thankful for this holiday season.


1. Our Students

We get so much joy from seeing our students' faces as they conquer a difficult math concept, and we love having fun with them as we make math make sense! It's such a satisfying feeling to take a subject that frustrates so many students, and see their attitude transform. They grow confidence and begin looking forward to school!

2. Our Parents

When parents get involved in their child's math progress, we are overjoyed. Parents know sending their child to Mathnasium is going to help them reach their math potential. So many of our parents work with their kids to practice "mathing" at home as well. Math excellence is a team effort between instructors, students, and parents, and we're glad to have such dedicated team members!


3. Our Instructors

Our instructors aren't just math whizzes, they are also cool people who love making a difference in our students' lives. They know how to make math make sense, and also how to make it FUN!

4. Mental Math Tricks

In the classroom and outside of it, you need math skills at your fingertips. We're so grateful for the mental math tricks we are able to use in our daily lives to make countless tasks simpler.


5. The STEM World Around Us

Scientists and engineers are landing on comets, designing artificial limbs to improve people's lives, building environmentally sound cars and houses, and exploring new star systems in our universe—all of this is within our fingertips because of math. What used to be sci-fi is now becoming reality!

It has never been cooler to excel at math, and we couldn't be prouder to be math nerds.


6. Report Cards

Report card time is usually considered a pretty cringe-worthy moment in any student's semester, but Mathnasium students and instructors look forward to them! Nothing makes us happier than seeing those grades jump from C's and D's to A's and B's. We love seeing your report cards, and hope you'll share them with us often!


7. Teachers 

We know so many teachers truly want their students to excel, and they do everything in their power to make that happen, including spending money out of their own pockets to create interesting lesson plans. To all the teachers who work hard each day, we are glad to have you as partners in our students' math development, and we thank you for your dedication!



What are YOU thankful for this holiday season? Let us know in the comments or on Twitter or Facebook!

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!