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

December 2014 / January 2015 Newsflash: Math Matters

This holiday season, we’re all about making math practical at home! As you and your kids enjoy quality time (and a much-needed break from school), remember that the holidays come with many opportunities for you to show your child how useful (and fun!) math can be in the real world. From cooking to gift shopping and all points in between, check out this article for our comprehensive guide to keeping your child’s math skills fresh outside the classroom.

In other news, we hope you’ll keep your child’s math progress top of mind as you begin a new year and a new semester! The new year is the perfect time for a fresh start and a new perspective. As the holiday buzz dies down, have a heart-to-heart with your child about progress in math before the second half of the school year really picks up. Here are some talking points to guide you:

•  Look toward the future and set goals. And we’re not just talking about the spring semester. Think big. What does your child want to be when he or she grows up? Having strong math skills could make all the difference as your child pursues a dream career. Help your child understand that regardless of his or her life goals, number sense and problem solving savvy are key to a well-rounded intellectual foundation. Aspiring doctors, accountants, and engineers will find themselves working with numbers day-to-day. Meanwhile, fledgling writers and artists will encounter many situations where a strong understanding of math concepts could provide extra inspiration and help them level up as they explore and utilize their creativity in professional settings. 

•  Get down to details and be realistic. Make it clear that improvement can’t and won’t happen overnight. You need an action plan, hard work, and consistent effort to progress in math. Encourage your child to commit to making math a priority in the coming year. Explore practical options that will lead to progress, including adhering to a study schedule, staying focused and attentive in class, and seeking supplemental help if needed.

•  Be positive! Success starts with the right attitude. Let your child know that you have full faith in their capabilities, and reassure them that you’ll be there every step of the way with love and support when things get tough. 

We’re really looking forward to helping your child meet their math potential in the new year! Let’s make 2015 count!

Make Math Practical this Holiday Season!

The holidays are the perfect time to make math practical at home with your family! There are recipes to be made—where those fractions come in handy, gifts to be bought—where mental math and budgeting are your best friends, and gifts to be wrapped—where geometry concepts come into play. 

The activities you can do with your child are endless, and you finally have the time off together to do them. Here are a few ways you can make math practical and fun during this holiday season!

Cooking

Whether you’re preparing a 7 course holiday feast or making a simple recipe, make sure to bring your child into the kitchen with you to play sous chef so you can make math practical together!

Here are a few tips for making math practical in the kitchen:

• Read the recipe first together to make sure you both understand what ingredients you’ll need, and what steps will be taken.

• Ask your child to collect the ingredients for the recipe on their own, and have them count out loud as they add each ingredient.

• Pretend you only have one type of measuring cup and ask them to convert the amounts using only that measuring cup. 

• Change up ingredient amounts using proportional thinking – for example, if you’re making holiday cookies, and the recipe calls for 2 ½ cups of flour, ask your child to make a half batch, and convert all the ingredients accordingly.

• Work with cooking times, changing up the variables so your child has to use proportional thinking to get the right cooking time. For example, if you have a 10 pound turkey, and you need to thaw it for 1 hour for every pound, ask your child how long you must thaw it.

• Ask your child to tell you how much the recipe costs by calculating the amount used of each ingredient vs. the total amount bought, using the store prices.

• For older students, ask them to inventory the ingredients and see how many servings would be possible using what you have on hand.

• Older students can also convert the cooking time from Fahrenheit to Celsius, or vice versa.

Remember to keep it fun and positive – boost your child’s confidence and they’ll be eager to help in the kitchen putting their math skills to use all year long!

Gift Buying

The holiday season is full of gift giving and shopping – make sure to involve your child in the budgeting and buying of gifts so they can work on their math skills! 

Here are a few ideas for math practice that can be done while gift giving:

• The holiday season is full of fantastic sales – whether you take advantage of these deals or not, make sure you and your child go through the sales, and calculate the cost of items using percentages and proportional thinking (ex. 50% off, or 2 for 1).

• Make a holiday budget, and assign your child the task of finding a combination of gifts online or in the store that maximizes the budget and yields the most gifts, or the most appropriate gifts.

• Give your child the task of finding the best deal on certain gift items, searching online and in stores for sales, and calculating the total cost, including tax and shipping.

• Have your child work on gift giving to others less fortunate by organizing a canned food drive together, or a donation box to buy gifts for needy families. Ask them to count and sort food items, and plan how they should be delivered. Have them keep track of donations, and budget where donation money goes and how it is spent.

Gift Wrapping

Gift wrapping is a great way to work with your child on measurements, geometry and proportional thinking. Here are a few fun ways to make sure math stays front and center as you make your gifts gorgeous!

• Ask your child to measure each gift, and calculate how much wrapping paper they will need to completely cover the surface of the gift.

• Using the wrapping supplies you have on hand (bows, ribbon, paper, bags), ask your child to calculate how many unique wrapping combinations you can make as you wrap gifts.

• For older students, ask them to calculate the maximum amount of material a gift box can hold, and the minimum amount of wrapping paper that would be needed to cover it, expressing it as a percentage of the total surface area of the box.

• For older students involved in calculus, pre-cal and algebra, check out this fun holiday video about gift-wrapping:

Decorating

Here are some fun decorations younger students can make themselves while also practicing their math skills!

Head over here to download this Santa addition coloring activity!

Check out these holiday graphing activities!

Here's a fun snowman activity with a moveable nose that can help your child practice skip counting!

Head over here to download a fun gingerbread house graphing activity!

Make a gingerbread house with your child, and fill out this worksheet together to make sure your math is on the right track!

Learn how to make paper snowflakes with your child here. 

Make sure to hang these decorations with pride when your child completes them, and have them explain how they made them to any guests you have over the holidays! 

Tangrams

Tangrams are always a fun exercise for students of any age, so why not work with holiday themed tangrams?

Head over here to download free printable holiday tangram templates!

Board Games

What better way to spend time with your family than by playing board games together? These games will not only give you quality time with your children, it will activate their math skills!

Loose Change

Objective: Take turns playing cards to add up to one dollar.

This is a great game to play in conjunction with holiday budgeting.

Speed!

Objective: Use multiplication facts to get rid of cards quickly

This is a fun sudden death style game that will have the whole family jumping in and working quickly, and is great for practicing skip counting and multiplication.

Goblet Gobblers

Objective: Place and move pieces on a 3x3 grid to place 3 in a row

This game is great for critical thinking, strategy, and spatial reasoning.

Remember, math is not only relevant in a classroom setting – make it practical and fun at home as you enjoy this holiday season with your family!

Do YOU have any fun holiday math-related activities you do with your family? Let us know in the comments, or share them with us on Facebook and Twitter using the hashtag #holidaymath!

Mental Math Tricks in Action: Multiplying Numbers Between 90-99

At Mathnasium we constantly stress the importance of mental math and numerical fluency to our students and parents. Not only is it incredibly useful to be able to do mental math on the spot, it's cool too! 

Need proof? Just check out this video of Houston Texans quarterback Ryan Fitzpatrick's 6 year old son Brady stealing the show from his father at a press conference with an impressive display of mental multiplication!

So how can YOU impress your friends and family by quickly multiplying numbers from 90-99? We'll show you the trick!

Let's walk through Brady's problem: 

 93 x 97 = ???? 

Step One: Find the first two digits of the answer. 

????

To do this, subtract each number from 100. 

100 - 93 = 7 

100 - 97 = 3 

Now take the largest of the two answers, and subtract it from the largest of the two numbers you are multiplying. 

100 - 93 = 7

100 - 97 = 3 

In this case, 97 is greater than 93, and 7 is greater than 3, so we'll use those.

97 - 7 = 90

Voila! We have our first two digits = 90.

(Side note: You can also subtract the smallest of the two [100-n] answers from the smallest number you are multiplying and get the same answer. In this case, we would use 93 - 3 = 90).

Step Two: Find the last two digits of the answer.

90??

Now we use the two answers we found before by subtracting from 100, and we multiply them together.

100 - 93 = 7 

100 - 97 = 3 

7 x 3 = 21

Now we have our last two digits = 21.

So our final answer is 93 x 97 = 9021. 

In the words of Ryan Fitzpatrick, "BOOM!"

Try this method for yourself!  See if you can solve this problem:

96 x 93 = ????

(Scroll down for the answer).
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Answer: 8928

First we find our first two digits: 

????
100 - 96 = 4

100 - 93 = 7 

96 - 7 = 89

Next we find our second two digits:

89??

100 - 96 = 4

100 - 93 = 7 

4 x 7 = 28

Voila! 8928 is our answer.

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!

Thanksgiving Problem Set

Want to test your math skills and get into the Thanksgiving spirit? Try our Thanksgiving word problems!

Lower Elementary:

Question: At a Thanksgiving dinner, 6 relatives are visiting from Nevada, 7 relatives are visiting from California, and 4 relatives are visiting from Arizona. How many total relatives are visiting?

Answer: 17 relatives

Solution: To find the number of relatives visiting, we need to add the members visiting from the different states. So, we need to add 6 + 7 + 4. Notice that if we add 6 + 4 first, we would get 10. So, 6 + 7 + 4 = 10 + 7 = 17. There are 17 relatives visiting.

Upper Elementary:

Question: The Morgans had pumpkin pie for their Thanksgiving dessert. The mom ate 1/4 of the pie. The dad ate 2/3 of what was remaining after the mom ate her portion. The daughter ate 1/2 of what was remaining after the dad ate his portion. How much of the pie is left after the daughter ate her portion?

Answer: 1/8 of the pie

Solution: From the whole pie, the mom ate 1/4 of it. 1 – 1/4 = 3/4. There is 3/4 of the pie left after the mom ate her portion. The dad ate 2/3 of what was remaining. Breaking 3/4 into 3 equal parts, each part is equal to 1/4. If 1/3 of 3/4 is 1/4, then 2/3 of 3/4 is 2/4 = 1/2. So the dad ate 1/2 of the pie. This means that there is 3/4 – 1/2 = 1/4 of the pie left for the daughter. The daughter ate half of what was remaining. Half of 1/4 is 1/8. There is 1/8 of the pie left after the daughter ate her portion.

Middle School:

Question: Right before Thanksgiving, a turkey went on sale from $20 to $17. What was the amount of the discount?

Answer: 15%

Solution: To find the percent discount, find the difference between the original and sale price and divide by the original price. $20 – $17 = $3. Now, we have 3/20. Since percent means for each hundred, one way to find the percent is to make the denominator equal to 100. 3/20 = 15/100. So, the turkey is on sale at a 15% discount.

Algebra and Up:

Question: The Goldmans are playing a game of football after their Thanksgiving meal. Bob threw the football and its path can be traced by the function h(t) = –t² + 3t + 10 where t is the time from when Bob threw the football in seconds. At what time will the football hit the ground?

Answer: 5 seconds

Solution: To find when the football hits the ground, we need to set h(t) = 0.
0 = –t² + 3t + 10
Multiply both sides by –1.
0 = t² – 3t – 10
Factor the polynomial.
0 = (t – 5)(t + 2).
Set each factor equal to 0 and solve for t.
t – 5 = 0
t = 5
t + 2 = 0
t = –2
t = 5 and –2. It does not make sense that the ball hit the ground –2 seconds after Bob threw the ball, so that means the ball hits the ground 5 seconds after it was thrown.