Tuesday, April 22, 2014

April/May 2014 Math Muscle Challenge!


Can you solve this month's Math Muscle Challenge?


Grades 1 – 5: A recycling center pays $1.90 for every pound of aluminum recycled and 90 cents for every pound of plastic recycled. Anthony collected 10 1/2 pounds of plastic bottles and 13 pounds of aluminum cans. If he turns the bottles and cans in to the recycling center, how much money will Anthony get?

Grades 6 and up: The volume of a cube is 8 in3. Amy created a new cube by quadrupling the length of each side of the original cube. How many times larger is the volume of the new cube than the volume of the original cube?

Answers to Last Month’s Math Muscle Challenge:

Grades 1 – 5: 3 ½ miles.
Grades 6 and up: 60 regular subs

Tips and Techniques: Finding 100% of a Number

Given a percentage of a number, how do you find 100%? We’ll show you different ways to find 100%.  

First, remember that 100% means “all of it… the whole thing.”


Example 1: 25% of what number is 5?

This question asks, “If 25% of a number is 5, then what is 100% of the number (the whole thing)?”

The strategy here is to see how many times the “percent number” (in this case, 25) goes into 100, and then count by that number until we reach 100—the whole thing.
Here, we’re told that 25% of a number is 5. So, to find 100% of the number, we count by 25s up to 100: 25, 50, 75, 100.

25% is 5, so
            50% is 10,
                        75% is 15, and
                                    100% is 20.

Example 2: A man spent $10.00, which was 20% of his money. How much money did he have to start?

If 20% of his money is $10.00, then 40% is $20.00. (20% + 20% = 40%)

Similarly, 60% is $30.00 (40% + 20% = 60%), 80% is $40.00, so 100% is $50.00—the amount of money the man had to start.

Here’s an even faster way to approach this problem. There are 5 20%s in 100%, so this problem calls for five sets of $10.00, which equals $50.00.

Example 3: 10 kids—5% of the kids enrolled at a particular school—are out sick. How many kids are enrolled at the school?

Here, 5% is 10 kids. Since there are 20 5s in 100, we multiply 20 by 10 and get 200, the total number of students at the school.

Try these:
  1. 10% of what number is 8?
  2. 20% of what number is 4?
  3. 20% of what number is 6?
  4. 50% of what number is 28?
  5. 5% of what number is 11?
  6. 1% of what number is 2?


Seize the Summer: Perfect Time to Get Ahead!

As we close the book on the 2013 – 2014 school year, at Mathnasium, we’re excited about the possibilities for our students once summer rolls around! Here are a few reasons to seize every opportunity this summer – the perfect time to get ahead.



•  Everything kids do during the summer helps them get ahead. According to a recent study, at summer’s end, students perform one month behind their progress in the spring. Because new school material is at a standstill, everything kids do during the summer to build their math skills helps them get ahead!

•  Summer is also the perfect time to revisit and fortify math foundations. Math concepts build over time, and often, we find that students fall behind because they didn’t fully understand topics taught in earlier grades. While filling in these gaps is a primary objective of the Mathnasium program 365 days a year, without school stress or homework pressure to worry about, kids have even more time to step back and master these skills over the summer.

•  We love helping our students prepare for next year’s challenges. Another summertime perk: more time to get a head start on material they’ll encounter next school year. And the more prepared students feel, the more excited they’ll be about challenges that lie ahead. Third party studies show significant increase in grade level skills after three months at Mathnasium!

Mathnasium’s summer program offers a customized program for your child, flexible scheduling, and many opportunities to make this your child’s most productive summer yet! Call or email us by May 31st to get an early summer registration discount. For more information, check out our website.

P.S. May is Teacher Appreciation Month! From all of us at Mathnasium, we’d like to say a big thank you to all teachers for giving young learners the gift of knowledge and for allowing us to support their math curriculum.

If you are planning for a year, sow rice; if you are planning for a decade, plant trees; if you are planning for a lifetime, educate people.” – Chinese proverb

Education is the most powerful weapon which you can use to change the world.” – Nelson Mandela

Friday, March 7, 2014

Math Test-Taking Strategies to Boost Confidence

Math anxiety can easily undermine the hard work students have invested throughout the year, lowering their scores on standardized tests and jeopardizing their chances to take advanced classes or enroll in the schools of their choice.


But reducing math anxiety, a well-documented phenomenon, can prevent this. Students can reduce anxiety by reviewing the mistakes they make on homework assignments and practice exams. After grouping these errors into three categories, they can easily be remembered as the “three C’s:”
  • Concept, understanding the methods needed to resolve specific problem types
  • Comprehension, determining exactly what individual problems are asking students to do
  • Calculation, solving the problem correctly without making errors or overlooking any critical details
When faced with challenging test questions, students can become gripped with math anxiety.  However, they can address the root cause by reviewing past assignments and practice tests.  Often, the cause lies in difficulties with one or more of the three C’s.  After identifying where exactly a student’s weaknesses lie, adults can help address them.  This allows students to move on from anxiety and perform at the level of their true potential.

As a first step, parents, teachers or private instructors can sit down with students and look at the types of errors made in homework assignments, regular tests and practice exams.  It’s a process that can be helpful anytime during the academic year, especially when students become anxious about math, and is particularly important when it’s time to start preparing for standardized tests.

To address concept challenges, students can be asked to break questions down into a series of meaningful parts, resolve these parts individually, and then put them back together. Children struggling with both Concept and Comprehension can be asked to read troublesome questions aloud.  This helps to strengthen the mechanics of understanding by invoking different parts of the brain. Another helpful approach is to ask students to reframe questions in their own words.

To help students overcome Calculation difficulties beyond rote practice, which is more appropriate in this situation than the others, it’s crucial to make sure a child’s written work is neat and clear.  Neat penmanship makes a huge difference in kids’ ability to think clearly and follow their own good reasoning.

As the day of the test approaches, children should also take some common-sense steps that can be applied to all types of tests, Larry Martinek, chief instructional officer at Mathnasium notes.  First, avoid last-minute cramming by learning to pace yourself and structuring a daily study plan.  Make sure to eat a healthy, high-protein breakfast the morning of the exam.  Then, in the testing room, STOP and close your eyes.  Take a moment to inhale deeply.  When you exhale, open your eyes and envision the test with an “I can do” mindset.

Studies have shown math anxiety to impact up to half of all students in various ways.  However, with the proper approach, it can be effectively addressed and need not be a permanent hindrance to performance. 

Thursday, October 3, 2013

Master Fractions and Set the Stage for Success, As Featured in The Wall Street Journal

Algebra Readiness begins in elementary school. Three essential topics in elementary school mathematics are 1) numerical fluency, which includes the effortless recall of addition facts and the times tables stemming from mental math strategies for computation, 2) foundational understanding of the nature fractions, and 3) the basics of problem solving. Mathnasium was recently featured in The Wall Street Journal and highlights our unique and effective approach to teaching fractions. Read the full article here.



As students move into middle school, work with fractions expands to embrace rational numbers (common fractions, decimal fractions, percents, ratio and proportion, and negative numbers). At the same time, student’s problem solving horizons broaden to include multi–step word problems, both routine and non–routine.

Successful mastery of these elements sets the stage for success in Algebra, the rest of high school math, and college. If any of these areas are under developed, the road ahead is fraught with danger.

Visit a Mathnasium Learning Center and see where your child stands.

- Larry Martinek

Monday, September 23, 2013

Breaking Down the Question Barrier

Children need to be exposed to the forms of mathematical thought as well as to the details. What is missing in most instruction is the timely unfolding of these basic forms of mathematical thought. The use of consistent, familiar forms clearly depicts the underlying structure and helps eliminate confusion and uncertainty.
 
Without the structure provided by the Question Forms, classroom instruction often disintegrates into the usual collection of details—facts, operations, and procedures—that have characterized unsuccessful mathematics education for decades. All students (“at–risk,” “at–level,” and “talented” alike) benefit from having new material in mathematics presented as reoccurring manifestations of the same set of basic ideas with which they have already become familiar.

Let’s start with questions in the “single-form” format. Each is a breakdown of the format of questions based on one single concept; this allows your student to lay down a base to build a foundation on.

Counting, Grouping, Intervals: 
Count from _____ to _____ by _____s 
     Count from 2 to 16 by 2s...from 1 to 15 backward by 2s.

Denomination and SAMEness:
 What is another name for _________? 
     Name 2 numbers that add–up to 15...to 25...to 75...to 100.

Subtraction and Addition:
 How far is it from _____ to _____?
     How far is it from 5 to 11?...from 13 to 20?

Order: 
_____ is greater than/less than/equal to _____ .
     Name 3 numbers that are between 7 and 10.

Multiplication:
 How much are _____ groups of _____ ? 
     If you see 8 eyes, how many people are there?...16 eyes?...100 eyes?

Division:
 How many _____ are there in _____?
     How much is 1 + 1?...2 + 2?...4 + 4?...8 + 8?...16 + 16?...(continue as far as you students can go mentally.)

Fractions and Fractional Parts:
 How much is _____ (fractional part) of _____? 
     Half of what number is 7?...is 1?...is 12?
How much is half of 8?...of 12?... of 18?... of 200?...of 1,000?

“The Whole is equal to the sum of its Parts”: _____ (whole) = _____ (part) + _____ (part) 
     A cook bought two bags of apples. One bag of apples weights 15 pounds and another weighs 10 pounds. How much is left after the cook uses 17 pounds of the apples for pies?

Percent: 
_____% of _____ is _____. 
     How much is 50% of 6?...of 20?

Ratio:
 _____ is what part of _____? 
     Is 7 half of 14, or is 7 twice as much as 14?

Change and Variation:
 As _____ gets bigger/smaller, _____ gets bigger/smaller. 
     Does it cost more to buy 5 apples or 10 apples? Why?

Proportion: 
_____ is to _____ as _____ is to _____ . 
     Does it cost more to buy 5 apples or 10 apples? Why?

- Larry Martinek

Thursday, August 15, 2013

Back to School Refresher

Did you know your student could lose anywhere from two to two and a half months worth of math knowledge over the summer months? By enrolling your student at Mathnasium now, they can move ahead in their class and continue to learn new things.

Refresh their (and your) knowledge with key terms from the Mathnasium Glossary below.

addition counting “how many altogether.” The process of forming a whole.

complement “the rest of it.” the remaining part with respect to the whole.

counting the process of determining quantity (how many, how much).
denomination the collective name of a group of similar things (apples, dogs, inches).

division counting “how many of these are there inside of that.” The process of separating a whole into equal parts.

fraction the result of breaking a whole into equal parts; one or more of those equal

group one or more of the same thing (1 apple, 9 dogs, 5 inches, 8 things).

half the first fraction. A whole divided into two equal parts; one of those parts. “Two parts the same.”

interval the distance from one number (or unit) to another. The space between two numbers.

Law of SAMEness It is only possible to add and subtract things of the same kind, things with the same name, the same denomination (an apple plus a banana is not a “banapples”).

mathematics the study of wholes and parts, and the relationship between them.

matrix literally, “mother.” That which gives form, origin, or foundation to something enclosed or embedded in it. A place of origin and growth. Related words include environment, framework, womb, structure, model; enclosed, enveloping, surrounding.

measurement the determining of quantity.

multiplication counting “in equal groups.” The process of forming a whole from equal groups.

part a component of the whole. A fragment, fraction, section, portion, region; a piece broken off.

percent literally, “for each 100,” “parts per hundred,” “how many for each hundred.”

proportion literally, “according to amount.” The relation of one part to another or to the whole; relative size. Comparison, analogy, balance, symmetry.

ratio a comparsion of two numbers by division.

subtraction counting “how far apart two numbers are” and “how much is left.” The process of removing a part(s) from a whole.

whole undivided. The one composed of the many. That which can be broken–down into parts. All of the quantity under consideration.

zero the number that counts none. That which has no parts.   

- Larry Martinek