Tag Archives: math

#TeacherThoughtsTuesday: Student Engagement

 #TeacherThoughtsTuesday

Student Engagement


Student engagement. Those words are the dream and the nightmare for every school teacher no matter what subject or age group. Everywhere.

Engagement is easily one of the hardest parts about being a teacher. Getting students to buy into what you’re teaching, without questioning the purpose or disagreeing with the usefulness, is the ultimate goal. Teachers dream of having students engage themselves in the content. Our goal is to have students who want to know more about the skills and ideas being taught.

Student engagement is the dream and the nightmare for teachers of every subject & age group. Everywhere.

I know, some of you are thinking, “When I was a in school we just had to sit, listen, and take notes. No one cared if we were into the lesson or wanted to know more about a given topic.” While that may be true (to a point), there is tremendous value in having a lesson where students can clearly see the point, the ‘why’, and have the desire to learn the about the topic or master the skill.

Without engagement in what is being taught the subject, whatever it may be, becomes stale and boring because there is no personal involvement. You can’t make students love math but you can make them want to find the answer to an engaging question. For instance, most of my students could really not care less about how to solve a system of linear equations, but if I ask them which cell phone plan is the better deal for a certain contract time they want to find the answer because they can see immediate pay-off in knowing how to find the answer.

Algebra is all around us, hidden in plain sight as normal, day-to-day consumer decisions.

In an age where many students can’t see the value in learning something that isn’t immediately applicable to their lives finding something they can relate to is vital. I’m not saying there aren’t going to be lessons (or even whole units) that won’t be immediately useful to them, but the more you can bring in the day to day usefulness of math the more likely they are to believe you when you tell them that they will, indeed, use math after high school. (Even if they don’t solve the problems the same way…)

Algebra is all around us; hidden in plain sight as normal day-to-day consumer decisions.

As a fourth year teacher, I’m really just starting out on my journey to becoming an effective teacher. I think if I can add a few great, engaging ideas to my lessons every term I’ll get there… 

Eventually.

Though, I’ve heard the really great teachers never believe they’ve mastered it all!


Do you have ideas about day-to-day consumer topics you think fit well into the math classroom? Have some of your own teacher thoughts to share?

 

I want to hear them!
♥♥♥ Leave me some comment love below. ♥♥♥

 

If you like what you just read please click to send a quick vote for me on Top Mommy Blogs- The best mommy blog directory featuring top mom bloggers
If

Learning to Multiply with Multibandz™

I received this item free or at a reduced price in return for my honest review.
May contain affiliate links.

Learning to Multiply with Multibandz

Do you have kids that are trying to learn the basic multiplication tables? 

Are you looking for a way to motivate your children to learn those important facts?

Look no more! Multibandz™ is for you.

Seriously, these are great! It combines the trend of the colorful silicone bracelets with the, perhaps less trendy, need to learn basic multiplication facts.

The Idea:

Give your child one band at a time, starting with the ones times table. As your child masters each new table, reward them with the bracelet matching the next table.

Multibandz™ are designed as a milestone reward system to keep children interested in the learning process. As an added bonus, once your child masters the one through five tables, the bands matching the x6, x7, x8, x9, and x10 tables glow in the dark. 

That’s right. They GLOW! 

Who doesn’t love glow-in-the-dark. I know some adults who might be persuaded to reacquaint themselves with their times tables for glow-in-the-dark jewelry. 

When your child gets to the x11 table they are awarded with a silver band and the x12 band is gold. What a great way to encourage your kids to go for the gold!

My Thoughts:

As a Math teacher I think this is a fantastic idea. Anything that might help get kids excited about learning Math is a great idea in my book. 

Something that will encourage kids to learn and retain basic math facts? 
That’s an even better idea.

As a high school teacher, it’s scary to see the number of kids that come into my classroom who don’t know the basic skills. They don’t remember their times tables, they can’t do simple division without a calculator. 

I think we need more ideas like Multibandz™ to get kids excited about mathematics.

Maybe some unit circle bands and trigonometric identity bands for high school trigonometry and calculus students? Or bands that help kids memorize equations for area? The possibilities are really endless. I can’t wait to see what’s next!

 Where Can You Get Multibandz™

Multibandz™ are available at Multibandz.com. The company is based in Austrailia but ships worldwide. Bulk buying options are available for schools and teachers who might be interested in using them in their curriculum.

For more information you can contact Multibandz™ at info@multibandz.com.

Check out my YouTube review! My very first. Eeek! Hopefully it’s not too terrible.

 

If you like what you just read please click to send a quick vote for me on Top Mommy Blogs- The best mommy blog directory featuring top mom bloggers

And the Job Hunt Begins…

Interview Road Trip

Some of you probably noticed my absence last week.  Sorry about that, life got crazy and there are only 24 hours in a day.

Seems like something of this caliber happens every time I decide it’s time to make some changes and announce my goals to the world.

I knew it was coming, I’d been sending in applications left and right for the last couple weeks hoping for a phone call or two. Well last week I got them.

Two calls. Two interviews. One week. No babysitter on call. (I’m a stay-at-home-mom ya know!)

The first interview was for an online teaching position, thus online interview.  My responses to the interview questions had to be recorded using my iPad and then sent off to the interwebs to be viewed by the schools hiring committee. I think the idea of online high school is intriguing and I was very excited I was chosen for an interview but the virtual interview process was just as nerve-wracking as in person.

No news yet, but hopefully soon!

The second interview required a road trip across Iowa because the job was on the other side of the state.

Usually I love road-trips; sight-seeing, picnics, a little light hiking, and lots of adventure.

Not this road-trip.

Four and half hours one way, if you don’t stop, with a 9 month old.

Wednesday afternoon Dragonling, Grandma, and I set off for Eastern Iowa. We only stopped 3 times on the way over and arrived at our hotel a little after 11:00 p.m. My interview was Thursday morning at 10:00 a.m. so in a perfect world I still had plenty of time to sleep.

Dragonling had other plans.

After two hours of baby partying I was finally able to get her to sleep next to me on the bed. She slept for about three hours; I probably slept for those three hours too but not very deeply, I was too paranoid about her being next to me. After her early morning snack we both slept again for three hours, same set up as before. (Why did I even bring the pack ‘n play?)

I was up at 7:30 to get ready for the interview. I planned for time to get ready, eat breakfast, nurse Dragonling, and go over my lesson plan. All was going well until I sat down to review my lesson and realized I had made a huge error and there was no way to fix it before I was supposed to be at the high school.

Nothing like improvising a math lesson for 25 kids you’ve never met while being observed by two instructional coaches, a classroom teacher, the assistant principal, and the head of the math department….

Stress.

The entire interview process lasted about 3 hours, after which I returned to the hotel to pack up and get ready to head back across the state.

We left for home at about 2:30 p.m. and by the time we reached Great-Grandmas to drop off Grandma it was 10:30 p.m. After driving in rain and snow all day I decided to stay the night.

Yep, you read that right.

Snow.

In April.

Gotta love Iowa.

Friday morning after breakfast, Dragonling and I finished our journey back home where I promptly collapsed. (More or less.)

At least the last leg of our trip was short and uneventful.

I spent the rest of the day Friday, all day Saturday, and most of the day Sunday and Monday in bed. I cannot remember the last time I felt so terrible.

Headache, chills, cold sweats, fever, stuffy nose, cough.

No fun.

Tuesday was the first day I started to feel almost human again.

Which brings us to now, faithful readers. Now I’m ready to get back in the game. I’m ready to write, I’m ready to work on my April goals, and I’m ready to get back to normal!

Ready?
Set.
Go!

 

#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!

**************************************************************************************

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!

*************************************************************************************

If you don’t want to miss my next installment of #MathLovinMonday don’t forget to subscribe via email. You can find the subscription panel on the right side of the page near the top.

#BigTopBlogParty

 

 

 

Let Them Eat Pi: 03.14.15

Let Them Eat Pi: 03.14.15 9:26:53

If you’ve been anywhere on social media the last month or so you’ve probably seen a variety of posts about the “Pi Day of the Century” or maybe even “The Most Irrational Day of the Century”.

Today is that day.

This special Pi day will only happen once every century so it won’t come around again until 2115.

So, What is Pi?

Pi is the sixteenth letter in the Greek alphabet, written π.

In mathematics, pi represents the ratio of the circumference of a circle to its diameter. Pi is an irrational number, which means it cannot be written as a common fraction. Since it cannot be simplified to a fraction we know that the numbers behind the decimal do not repeat or terminate.

History of Pi Day

The first big Pi Day celebration was organized by Larry Shaw, a physicist at the San Francisco Exploratorium, in 1988. During this celebration guests walked around one of their circular spaces and ate lots of pie.

In 2009, the U.S. House of Representatives passed a resolution to make March 14th National Pi Day.

In 2014 the entire month of March was celebrated as Pi Month.

Which brings us to 2015.

Written in the mm/dd/yy format, Pi Day, which is March 14, 2015, will be written as, 3/14/15. These are the first 5 digits of Pi (3.1415).
Then this morning at 9 AM and again tonight at 9PM, it will be the first 6 digits of Pi. Making those the Pi Hours. Twenty six minutes later, it will be the Pi Minute, reading  3/14/15 9:26, the first 8 digits of Pi. (3.1415926) Five seconds later we have the Pi Second, giving us the first 9 digits of Pi (3.14159265).

Now comes the neatest part, the Pi Moment. Found by expressing the fractional parts of the Pi Second in the form of decimals, so 5.35 seconds we get up to 11 digits of Pi (3.1415926535). If we were to extend decimals infinitely, as per the digits of Pi, we will pass through the Perfect Pi Moment!

Happy Pi Day everyone!

 

P.S. It’s Albert Einstein’s Birthday!

Happy Birthday Albert!

 

 

 

How America Cerealized Itself

How America Cerealized Itself Promo

March 7th is National Cereal Day.

The first cereal, Granula, appeared Dansville, New York in 1863. Cereal has been improved upon many times since then and risen in popularity to become America’s favorite breakfast food.

And what’s not to love? It’s quick and easy to prepare and it comes in so many different varieties one could go for weeks without doubling up.

Quick and easy? Check.

Lots of variety? Check.

Yep, that sounds like America to me.

Now, I know some of you are saying, ‘Not all Americans prefer the quick and easy route.’

Well that may be true, but I overwhelmingly believe that is how Americans are perceived internationally.

We have become a nation of convenience, expecting instant gratification for everything we do. (Once again not everyone, but international perception is what it is.)

Americans expect things to happen on our schedules. We want information, TV shows, movies, and social interactions on demand. We have Netflix, Amazon Prime, smart phones, and a host of other products and services for just that purpose.

Yes, there are many people who do not rely heavily on these products and services but the overarching trend is racing toward these things becoming the status quo.

As a high school teacher, I can tell you that instant gratification is something that our kids have come to expect as well. They don’t question why things happen a certain way, they just want to know the fastest route to get to the answer.

Don’t know how to do the math problem? No problem, I’ll just Google the answer. Google not fast enough? There’s an app for that. Just take a picture of the problem and it solves it for you!

Not sure how to site the source correctly in your research paper? No big deal, there’s an app for that.

Instant gratification. We’ve begun to model ourselves after our breakfast.

Don’t get me wrong: I like cereal, it’s what I eat for breakfast most days. I just think that with our food, and our society, a little more effort and a little less instant gratification would benefit us immensely.

»»»»

What is your favorite breakfast food? Bonus points if you include the recipe in the comments. =)

 

 

#BigTopBlogParty