Category Archives: #MathLovinMonday

#MathLovinMonday: Everyone is a Math Person


#MathLovinMonday

Everyone is a Math Person


There are lots of words that I don’t like to hear used in my classroom. Most of them are swear words. A few others fall into the category of, what I call, confidence killers. The worst of the Confidence Killers is one simple, five-word phrase heard in nearly every math classroom in the country, if not the world.

“I’m not a math person.”

As soon as the student utters those words you know you’re in for a battle. 

Mathematical skill is not genetic!

If your parents were good at math it doesn’t mean you automatically get a free pass into the set of students who excel at math. Likewise, if one or both of your parents were bad at math it says absolutely nothing about what your own experience in math will be like.

You wouldn’t go around telling people that your parents didn’t read well so it’s okay if you don’t read well either. If you did people would think that you were lazy and just didn’t want to put in the work to learn how to read. Why is math any different? Why is socially acceptable to be “bad at math”? When did this repetitive falsehood become the most heard response from my students when they don’t understand something right away?

Your brain grows when you make mistakes...

Math is just like any other skill that must be learned. If you don’t practice you won’t improve. Basketball players didn’t learn how to do a lay-up perfectly on the first day the skill was introduced. They spent hours practicing on their own and running drills with their teammates. If their coach asked them to do half an hour of practice on their own over the weekend most of them wouldn’t even give it a second though.

Mathematics is no different.

If you believe that you can succeed and are willing to do the work, then you will succeed.

If you don’t believe that you can learn the skills or you’re not willing to do the work, then you won’t succeed.

Just the same as everything else!

Everyone can do math!

So, what can you do to get better at math?

8 Tips to Improve Your Mathematical Skills

    1. Know and understand the basics before you go on! Mathematics is cumulative, everything you do builds on prior skills and knowledge so if you don’t understand the basic skills you won’t be successful with the intermediate or advanced skills. This might might mean going back to a skill you should have learned last year, the year before, or even before that in order to really understand the current topic. (Yep, this probably means some extra work.

    2. Take notes! Seriously, write down the examples your teacher does on the board, read through the examples in the textbook, and, for the love of all things mathematical, make yourself a formula sheet! As a teacher I can assure you that I don’t write things on the board because I need it there to teach the skill, I write it there so that my students can see what is going on as I’m talking about it. They can see it as it happens!

    3. Do your homework and do extra practice as needed.  No, really. I know it sucks to have to spend time at home doing things for school, but you have to do the practice to improve the skill. There simply is not enough time in the classroom for you to get enough time working on each skill. If you’re really having trouble with something you might even have to do some problems that aren’t assigned for extra practice. Extra practice problems can be acquired from your teacher or from numerous online resources, just google the name of the skill you’re working on!

    4. Show your work and do it as neatly as possible. Don’t try to work out the problem in your head, it might work for simple problems but when you get to the more advanced stuff it probably won’t. Also, if you’re really having a hard time with a skill don’t just write down the mathematical work, write down what you’re thinking. Maybe not word for word, but write yourself enough to know what you were thinking when you have another similar problem later on so you have someplace to start from.
    5. If at all possible, draw a picture to go with the problem. The more senses you can incorporate into your problem solving the more engaged your brain will be. Usually word or application problems lend themselves well to picture drawing. Use the picture to help you pull out the important elements of the problem and sort out the stuff that isn’t important.

    6. Learn and practice all the methods for solving a given type of problem. In math, there is almost always more than one way to solve a certain type of problem, and being able to use the various solving methods can only be a good thing. Usually people gravitate toward a favorite method, but knowing other methods can be helpful, especially since many types of problems have cases where one method is the most efficient or where one method may not work at all.

    7. Ask for help. Understand. Don’t memorize! You don’t have to do it by yourself. Even if you’re teaching yourself or don’t like your classroom teacher there are, literally, thousands of people online who have made videos and written tutorials. There are thousands of people who browse question forums everyday looking for questions that they are able to answer. People who are “good at math” ask for help when they don’t understand something. Recognizing when you don’t understand something is vitally important for the growth of mathematical skills.

    8. Don’t be afraid to make mistakes. If you never make a mistake, you will never learn anything. So write it down with confidence and if you mess up… so what. Everyone makes mistakes. Every math student has made a mistake, the good ones learn from those mistakes. The ones who think they are “bad at math” let those mistakes define them and don’t push through to find out what they did wrong. The what and the why are important. What did you do wrong and why did you do it that way?

8 Tips to Improve Math Skills

Thanks for reading! Come back next Monday for another installment of #MathLovinMonday!

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#MathLovinMonday Episode 2: Equivalent Fractions

Well, life got a little crazy and #MathLovinMonday got postponed a week, I’m sure none of you know how that goes…

Anyway, to start off our math lessons I want to focus on a topic that, in my experience, students of all skill level dislike to some degree or another.

Fractions.

As soon as I say that word in my classroom it is followed by a chorus of “No!”, “Can’t we just use our calculators?”,  and the inevitable “I hate fractions.”

Fractions aren’t scary, they only seem that way because many don’t understand how to use them correctly. Generally fractions are introduced in grade school, I don’t know exactly what age but I do know it’s before Jr. High.

If a student doesn’t understand what they are taught in grade school and is never retaught the skills associated with using fractions they are always going to be in the “I Hate Fractions” camp.

This week we are going to focus on how to determine if two fractions are equivalent.

The Basics

Alright, before we can get into the math we need to start with the vocabulary.

By definition, a fraction is a numerical quantity that is not a whole number. Fractions are written in the form:

numerator/denominator

To be a fraction both the numerator and the denominator need to be whole numbers, no decimals allowed.

Equivalent Fractions

Equivalent fractions are fractions that look different but are actually equal to each other.

For example, 5/10 and 1/2 are equivalent fractions. We would write this as

5/10 = 1/2

Alright, that’s all fine and good, but 1/2 is a pretty common fraction to use for such a lesson, right?

So, what if it’s not such a common fraction?

Take the following problem:

~Are  5/15  and  15/45  equivalent fractions?

How do we determine if the two fractions are the same?  We simplify.

To simplify a fraction, we first find the greatest common divisor (GCD) for the numerator and denominator of each fraction.  The greatest common divisor is the largest number that evenly divides, meaning leaves no remainder, both the numerator and the denominator.

So, let’s simplify the fractions from the problem above. First, we will start with the fraction 5/15[pmath] and find the greatest common divisor of 5 and of 15. To do this, I like to make a factor tree for each number.

We’ll start with 5. To make the factor tree you simply write your starting number, 5, with two branches off for the first two factors. I always start with 1 and the number I’m dividing, just in case we have a prime number.

divisors of 5As you can see above, there is only one set of factors for the number 5.

Next we will make the factor tree for 15. We start the same way, with the factors of 1 and 15, but, in this case, 15 has other factors so we add another level to our tree.

Now that we have a factor tree for both 5 and 15 we need to find the GCD. This means that we want to find the factor level that has one number in common.

GCD 5 + 15As you can see above, the second level of the factor tree for 15 and the first level of the factor tree from 5 both contain a 5 as one of the factors. Since there are no other common factors this means we have found the GCD of our numerator and denominator.

So, to simplify [pmath size=12]5/15 we divide both the numerator and denominator by 5, giving us 1/3.

We are halfway to solving our original problem, do you remember what it was?

~Are  5/15  and  15/45  equivalent fractions?

So next we need to simplify 14/45. That means we need to make our factor trees for 15 and 45. We can reuse the one for 15 from above, so we just have to make one for 45.

Remember to start with 1 and 45 because we know that a set of factors with 1 is going to be a part of every factor tree.

divisors of 45

Now we can look at each level of the factor trees. In level one of the tree for 15 and in level two of the tree for 45 we see a common factor of 15. There are other common factors between 15 and 45, we see a 3 and a 5 in both trees, however, 15 is the largest of these factors and so it is our GCD.

GCD 15 + 45

So now we will divide the numerator and the denominator by our GCD, (15÷15)/(45÷15) to get 1/3.

Therefore, since 5/15 and 15/45 both simplify to 1/3 we know they are equivalent.

Do I Have Equivalent Fractions?

Please post any questions or comments below, and remember if you have a topic you’d like to see on #MathLovinMonday let me know!

 

#MathLovinMonday Episode 1: Can’t See the Forrest Through the Trees?

Can't See the Forrest Through the Trees

I love Math.

I think that is probably fairly obvious from the title of my blog, but one should never assume, am I right?

I love the numbers, I love the logic, and I love how there is only one right answer. But, I especially love how there is almost always more than one way to get to that right answer.

I know that I am definitely in the minority on the loving math thing. However, I do think that Mathematics is a topic in which every person should have some basic knowledge. That being said, the newest addition to my weekly blog schedule is going to be #MathLovinMonday!

On Math Lovin’ Mondays I will try to provide a little Math humor, some Math history, and a brief Math lesson. I also plan to throw in some tips for parents helping out middle school and high school students with Math homework. If you have an elementary student, sorry you are SOL because I don’t know what crazy stuff they’re teaching them anymore either! (Kidding, but only kind of. Seriously what is that stuff?)

I’m not planning a 3 hour lecture or anything outlandish, but I know there are many parents out there who have kids bringing home Math homework and they simply don’t know how to help. You’re not alone and the good news is: you don’t have to be an expert on what your kids are doing to give them the support they need.

My hope is that this becomes a helpful and fun Math resource for you and your family.

If you have suggestions on topics you’d like me to cover, post a comment or use the contact form to leave me a message. Please remember middle school and high school level topics are my preference and be as specific as possible with the skill(s) you want me to address.

Without further ado, I give you #MathLovinMonday!

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I think it’s important to start a Math lesson with a good attitude, and a little humor can go a long way toward improving anyone’s outlook, so lets start with a little Math joke.

A Priest, Rabbi, and a Mathematician were waiting patiently on a platform to be decapitated.

The priest put his head in the slot and the executioner pulled the lever; the guillotine blade came speeding down the track and stopped just a few inches above the priest’s neck. The priest proclaimed that God had intervened and saved him from execution; the executioner agreed and let him go.

The Mathematician had a disbelieving, puzzled, look on his face.

Next the Rabbi put his head in the slot. The executioner pulled the lever and the blade came speeding down the track, stopping a few inches above the Rabbi’s neck. Like the Priest, the Rabbi proclaimed that God had intervened to save him. The executioner, again, agreed and let the Rabbi go.

The Mathematician, more troubled than ever, put his head in the slot and turned to look upward where he noticed something that made him smile.

Before the executioner could pull the lever, the Mathematician said “Hold on there one minute, I see what the problem is! There is a small pebble blocking the path of the blade”. He removed the pebble and announced, “There, it should work just fine now!”

The moral of the story:
Don’t get so caught up in finding a solution that you forget the original problem.

In my years of Mathematical study and teaching I think that is the single hardest thing to remember. It’s so easy to want to just find a solution and completely overlook the context in which the problem is occurring.

As a teacher, I try to remind my students to look at the big picture. There is a solution to every problem but how you get to the solution may be different than how your friends gets to the solution. It’s important to know how to do something, but it much more important to understand why something happens.

Given enough time anyone can memorize a formula or a step by step process to solve a specific type of problem.  It might take some longer than others, but anyone can learn the ‘how’.

It takes a lot more time and effort to learn the ‘why’.

If your son or daughter is struggling with a specific skill it is almost always because they don’t understand why what they were taught in class works. A teacher can only do so much in the limited time they are given in class, not every problem assigned is going to be exactly like the ones used as classroom examples. If there isn’t an underlying understanding of why each step of an example worked your student is going to struggle.

If you, as a parent, don’t know why something works either look it up! (I can hear the grumbles from the older generation Math teachers now…)

Use the internet.

Seriously.

We have it, why not use this wonderful tool that we have available. There are fantastic websites devoted entirely to Mathematics skills tutorials and problem walk-throughs. Obviously there are sites that will just give your kid the answer also, but we can’t have the good without the bad.

If you can help  your child  want to know the ‘why’ you will be giving them a wonderful gift they will cherish their whole life.

When I have a struggling student the first two sites I suggest are Khan Academy and YouTube.  (I help them in class too but sometimes there just isn’t enough hours in the day!) Both sites are free and easy to use and it is almost a guarantee that your child can find a tutorial using the method his or her teacher used in class. Plus, if the classroom method doesn’t make sense there are probably numerous other possible ways to solve the same problem outlined on these sites.

I think this is enough for one night, I’m going to leave my first Math lesson until next week.

Come back next week for more #MathLovinMonday!

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