New Guest Post!

I’m excited to present a Guest Post from Tom Jager, a professional blogger from the UK!!

Enjoy 🙂  Lisa

 

Teaching Children Math with Computer. The best tips

Technology becomes more prominent in the contemporary classroom because it provides opportunities for innovative teaching. It stimulates student engagement and assists to develop critical thinking and analytical skills, so it is perfect for use.

If you are wondering whether or how you can teach your class math using computers, you have come to the right place. In this article, I will outline the ways to use technology in math class as well as provide you with some examples of great apps.

How can math classes benefit from technology?

Math can be an intimidating subject for many students, so teachers need to assume the right strategy that will engage them in the subject matter and help to understand even the most complicated concepts. Computers are perfect for that: kids use technology every day – smartphones, tablets, computers – and enjoy it.

The Association of Mathematics Teacher Educators has recently released a statement where technology has been identified as a critical tool for teaching math in 21st-century classroom. “Appropriate mathematical software, the Internet and other digital resources, handheld computing tools and their extensions, and emerging forms of similar devices and applications” were described as necessary forms of technology for teaching math.

The statement tried to show that the ability of technology to show the students different ways to approach mathematical ideas and processes is superior if compared with traditional methods of teaching that are difficult even for high-achieving students.

“Will I even use it in everyday life?”

This is a popular question in the math class that teachers often ask them to answer in essay papers. Indeed, the knowledge of all those formulas and problems may not be required in many professions, so many children see them as useless. As the result, the engagement and motivation are low.

Technology is a great tool for teaching math in the way children see it as useful and perceive it as something they can apply in everyday life. That’s because computers allow to provide examples from real life, so the students will see that, yes, in fact, they will use the knowledge of math in similar situations.

Ways to use technology in math class

There are many ways in which you can incorporate computers in math class to make the lessons more innovative and interesting. Here are some of them.

  • Video tutorials. How about making your own math tutorials? This time, the students play the role of the educators! Instead of listening to long tutorials made by someone else, let them be the ones who explain all that formulas! This will increase engagement and motivation.
  • Take pictures or create videos of real life phenomena related to math. The pics or videos can be shown to the students in the classroom and analyzed using computers.
  • Use virtual tools for geometric constructions.
  • Play video games with embedded math problems and concepts.
  • Create dynamic graphs.

As we can see from the list above, the ways of using computers in math class are different. If you are wondering what virtual tools you should utilize, read below.

Virtual Tools for Math Class

Geogebra

This is a graphing calculator for geometry, algebra, 3D math, statistics, and calculus that allows to “see, experience, and touch” math. It demonstrates math concepts using graphical representations that can be manipulated on touch screen. The database of lessons has more than 400k options for the teachers to select from!

Kahoot

This is a great tool because it allows to design own learning game and play it with the class! The teachers can also create a series of math-related questions and problems that are projected on a computer screen while the students answer them on their own computers. Indeed, very addicting and effective tool, the effectiveness of which has been supported by research.

TEDEd Math Videos

Videos are a powerful tool in education. TEDed is a vast database of educational videos that has a lot of math-related ones. They can be used in the class to make the lesson more entertaining and improve the understanding of the concepts.

Geometry Pad

This iOS app is designed for geometry lessons and allows the users to create fundamental geometric shapes, change and explore their properties, and calculate metrics. Very useful and simple drawing app with many functions to try out.

Mathsframe

Finally, games! This is a platform with tons of math games that can be played during the class! There are more than 200 options for you to choose and they help children to develop mathematical thinking and visualize numerical relationships, patterns, and numbers.

Get the Math

This online resource has various videos and interactive experiences that show the children the role math can play outside the class! For example, there you can find videos of musicians and other people talking about how they use math in their professional activities. So the question of how math is used in everyday life will finally be answered!

Yummy Math

If you are struggling to engage the students in math, this tool will definitely be of great help. It proposes a wide range of engaging real-world math experiences for all grades. For example, you can engage your children in a challenge by asking them how many pumpkin pies are needed to feed 23 guests at a Thanksgiving dinner. All resources needed for the lessons are included.

Conclusion

Teachers should incorporate computers into math class because it engages students and encourages them to cultivate 21st-century math skills. As the result, this effort will go a long way towards preparing children to succeed in their careers!

Tom Jager is professional blogger. He works at Awriter.  He has degree in Law and English literature. Tom has written numerous articles/online journals. You can reach him at G+  or  Facebook.

Let’s Start Some Trig!

Happy New Year!

Usually at the beginning of the year, the PreCalc classes will start you on Trigonometry, which a lot of students loathe….It’s usually not too bad, but you may find that you have to memorize a little more for your trig sections. That’s OK!  Don’t be afraid to do some memorization in your math classes.

Did you know that the word “Trigonometry” means “Triangle Measure”?  That’s what trig is all about – measuring triangles (specifically, angles and sides of triangles).

I find that if the kids I tutor really liked Geometry, they usually prefer Trig to Algebra, since a lot of trig is visual.  But that doesn’t mean there isn’t a lot of algebra in trig…

Here are the sections I’ve completed on SheLovesMath.com on Trig; hope they help (and let me know if I’m missing anything).  Enjoy!   And check out my new Calculus sections – almost done!

Happy Math’ing,  Lisa 🙂

Trigonometry

Right Triangle Trigonometry

Angles and the Unit Circle 

Linear and Angular Speeds, Area of Sectors, and Length of Arcs

Graphs of Trig Functions

Transformations of Trig Functions

The Inverses of Trigonometric Functions

Solving Trigonometric Equations

Trigonometric Identities

Law of Sines and Cosines and Areas of Triangles

Polar Coordinates, Equations and Graphs

Trigonometry and the Complex Plane

Welcome Back to School – 2016!

School again!  How can that be?

Remember one thing: the teacher (and boss!) is always right (well, not always, but you know what I mean 😉 )  So hope you get a good math teacher, but it’s probably more important that you respect your teacher and always try to make a good impression (and work hard!).

I’ve posted these hints before, but they are worth mentioning again:

  • Keep up with the homework; this is probably the most important.  Sometimes we think we understand the math, but actually we can’t do the problems.  Even if you have to do 2 or 3 from each section, make sure you can do each type of problem that is assigned to you.
  • Try to go to as many school tutoring sessions that you can, if you don’t feel good about the math (or, even if you do!).  If you have the luxury of a private tutor, try to go ahead a little bit if you can, so you can hear the lecture twice.
  • See if you can get your hands on old tests, like from an older sibling, friends, etc.  I know this may seem like “cheating”, but they do (or should) change the questions every year.  This way you can have a good idea what’s expected of you.
  • Use She Loves Math or another site to read through material before you have the lecture; this way you’ll have a better chance of keeping up with the new material.   And feel free to send specific questions to me to see if I can help 🙂.

Hope this helps and let me know if you have any math questions; I’ll try to answer them!

I’m still not done with SheLovesMath, but getting there.  I’m still tackling Calculus sections, and I’ve done most of Differential Calculus and started Integral Calculus.  The Calc pages completed are Definition of the Derivative, Basic Differentiation Rules, Equation of the Tangent Line, The Chain Rule, Implicit Differentiation and Related RatesCurve Sketching, Optimization, Differentials, Linear Approximation and Error Propagation, Antiderivatives and Indefinite Integration, U-Substitution Integration, and Differential Equations and Slope Fields.

Please spread the word about She Loves Math, and let me know how it can be better!  I have almost 2 million pages views total now, and I hear from students all over the world 😉 .

Lisa

How to Prepare for Finals

Hey Math Geeks!

It’s been awhile since I’ve posted; sorry about that!  I have been plugging away and have completed more Pre-Calc sections (Sequences and Series, Binomial Expansion and Introduction to Limits), more Trig sections (Linear and Angular Speeds, Area of Sectors, and Length of Arcs), and have started Calculus!

The Calc pages completed are Definition of the Derivative, Basic Differentiation Rules, Equation of the Tangent Line, The Chain Rule, Implicit Differentiation and Related Rates, and starting Curve Sketching.

Here’s some tips I have for finals that I wrote about last year:

Trust me, I’ve haven’t aced every math test I’ve taken.  Both as a student (ions ago!) and a math tutor, I’ve found that these things really help when “studying” for taking a math test or final.  The main thing is that you don’t “study”, you “work problems” to prepare:

  1. If you are lucky enough to have your old tests for the semester (or year, if the final covers the whole year), retake them again!!  Cover up the answers and go for it!  I know it seems like a lot of work, but it’s the surefire way of knowing if you really get the stuff.  If you don’t have time to go through all the tests, go through the ones that were at the beginning of the learning period and also the ones where you didn’t do the greatest.
  2. If you can’t get your old tests back, try to work any packets, homework, or chapter reviews covering the material.  Just pick out one or two problems covering each concept.
  3. If you’re having trouble with any of the concepts when working problems, create a “cheat sheet” (not for the test!  lol) of notes that you need to study.  Remember that some things (actually a lot of things) in math you have to memorize – that’s OK.
  4. Glance over your notes one more time to see if you missed anything after doing steps 1 and 2 above.  This is not good enough though; you may think you know how to work a problem by looking at your notes, but you don’t really know unless you actually try it!  If you’re unsure about a concept, you might even check out She Loves Math!
  5. One more thing – Reviews can be deceiving!!  Don’t rely on them; many times, they don’t cover everything on the test!

Good luck, and let me know if you have any questions about anything.  And of course, when you’re taking the test, skip over any problems that stump you, put a big circle on it, and come back to it.  Time can be your enemy with math tests and we’ve all had those brain lapses.  Try not to let those times affect the rest of the test.

Happy Mathing and have a wonderful summer!  I hope to do a lot of She Loves Math writing this summer!

Lisa 🙂

Welcome Back to School!!

Well it’s here already – school again!   I always love the beginning of a new school year, in spite of summer being over….   I hope everyone ends up with a good math teacher 🙂

I’ve been busy writing more of She Loves Math; I never get as much done as I’d like, but here are some new sections I’ve added:   Trig sections, including Right Triangle Trig, Angles and the Unit Circle, Graphs of Trig Functions, Transformations of Trig Functions,  Inverses of Trig Functions, Solving Trig Equations, Trig Identities, Polar Coordinates, and Trig and the Complex Plane.   I’ve also completed  Conics, Systems of Non-Linear Equations, Introduction to Vectors, and Parametric Equations, and working on Sequences and Series.

I thought I’d give you a few hints and tips to have a productive and successful year in math:

  • Keep up with the homework; this is probably the most important.  Sometimes we think we understand the math, but actually we can’t do the problems.  Even if you have to do 2 or 3 from each section, make sure you can do each type of problem that is assigned to you.
  • Try to go to as many school tutoring sessions that you can, if you don’t feel good about the math (or, even if you do!).  If you have the luxury of a private tutor, try to go ahead a little bit if you can, so you can hear the lecture twice.
  • See if you can get your hands on old tests, like from an older sibling, friends, etc.  I know this may seem like “cheating”, but they do (or should) change the questions every year.  This way you can have a good idea what’s expected of you.
  • Use She Loves Math or another site to read through material before you have the lecture; this way you’ll have a better chance of keeping up with the new material.   And feel free to send specific questions to me to see if I can help 🙂

Hope this helps!

Please spread the word about She Loves Math, and let me know how it can be better!   And I’ll try to post blogs more often 🙂

Lisa

Happy π Day!

Today, 3/14/15, at 9:26:53, we experience a once-in-a-lifetime event:  the date and time will be the first 10 digits of the number π!  

I just saw on the news that there are some kids who can repeat the digits of π to over 2000 digits!   Much better than I can do (I’m lucky if I can get up to 10 digits 😉

She Loves Math is progressing, and now gets 3000-5000 hits a day.   I’ve completed The Inverse Trig Functions, Solving Trig Equations, Trig IdentitiesLaw of Sines and Cosines, and almost done with Polar Graphs.    Earlier trig sections includes Right Triangle Trig, Angles and the Unit Circle, Graphs of Trig Functions, and Transformations of Trig Functions.

Have some pie today!

Lisa

Converting Quadratic Functions, and Preparing for Math Finals

Hello She Loves Math readers,

First of all, I’ve been fortunate enough to be able to share a valuable article from Nghi H. Nguyen, who is a reader of my site.  The article covers “the new Transforming Method for solving quadratic equations” and is quite interesting:

Convert quadratic functions from one form to another, by Nghi H. Nguyen

Here is one more article supplied by Nghi:

Solving Quadratic Equations by the New Transforming Method, by Nghi H. Nguyen

Also, looks like another semester is about to come to a close and I’d like to repeat my math test-taking hints that talked about in an earlier blog:

Trust me, I’ve haven’t aced every math test I’ve taken.  Both as a student (ions ago!) and a math tutor, I’ve found that these things really help when “studying” for taking a math test or final.  The main thing is that you don’t “study”, you “work problems” to prepare:

  1. If you are lucky enough to have your old tests for the semester (or year, if the final covers the whole year), retake them again!!  Cover up the answers and go for it!  I know it seems like a lot of work, but it’s the surefire way of knowing if you really get the stuff.  If you don’t have time to go through all the tests, go through the ones that were at the beginning of the learning period and also the ones where you didn’t do the greatest.
  2. If you can’t get your old tests back, try to work any packets, homework, or chapter reviews covering the material.  Just pick out one or two problems covering each concept.
  3. If you’re having trouble with any of the concepts when working problems, create a “cheat sheet” (not for the test!  lol) of notes that you need to study.  Remember that some things (actually a lot of things) in math you have to memorize – that’s OK.
  4. Glance over your notes one more time to see if you missed anything after doing steps 1 and 2 above.  This is not good enough though; you may think you know how to work a problem by looking at your notes, but you don’t really know unless you actually try it!  If you’re unsure about a concept, you might even check out She Loves Math!
  5. One more thing – Reviews can be deceiving!!  Don’t rely on them; many times, they don’t cover everything on the test!

Good luck, and let me know if you have any questions about anything.  And of course, when you’re taking the test, skip over any problems that stump you, put a big circle on it, and come back to it.  Time can be your enemy with math tests and we’ve all had those brain lapses.  Try not to let those times affect the rest of the test.

Happy Mathing,

Lisa

Welcome to Trig!

Welcome from She Loves Math!   I know it’s been awhile, but I wanted to welcome everyone back to school and talk a little about Trigonometry, which is usually part of a Pre-Calc class these days.

I’ve completed the Right Triangle Trigonometry, Graphs of Trig Functions, Transformations of Trig Functions sections, and the beginning of the Inverses of the Trigonometric Functions section.

Here is an excerpt from my Right Triangle Trigonometry section to get you started with Trig:

You may have been introduced to Trigonometry in Geometry, when you had to find either a side length or angle measurement of a triangle.  Trigonometry is basically the study of triangles, and was first used to help in the computations of astronomy.  Today it is used in engineering, architecture, medicine, physics, among other disciplines.

The 6 basic trigonometric functions that you’ll be working with are sine, cosine, tangent, cosecant, secant, andcotangent.  (Don’t let the fancy names scare you; they really aren’t that bad).

With Right Triangle Trigonometry, we use the trig functions on angles, and get a number back that we can use to get a side measurement, as an example.    Sometimes we have to work backwards to get the angle measurement back so we have to use what a call an inverse trig function But basically remember that we need the trig functions so we can figure out triangles’ sides and angles that we don’t  otherwise know.  

Later, we’ll see how to use trig to find areas of triangles, too, among other things.

You may  have been taught SOH – CAH – TOA  (SOHCAHTOA)  to remember these.  Back in the old days when I was in high school, we didn’t have SOHCAHTOA, nor did we have fancy calculators to get the values; we  had to look up trigonometric values in tables.

Remember that the definitions below assume that the triangles are right triangles, meaning that they all have one right angle.  Also note that in the following examples, our angle measurements are in degrees; later we’ll learn about another angle measurement unit, radians, which we’ll discuss here in the Angles and Unit Circle section.

Basic Trigonometric Functions (SOH – CAH – TOA)

Here are the 6 trigonometric functions, shown with both the SOHCAHTOA and Coordinate System Methods.   Note that the second set of three trig functions are just the reciprocals of the first three; this makes it a little easier!

Note that the cosecant (csc), secant (sec), and cotangent (cot) functions are called reciprocal functions, or reciprocal trig functions, since they are the reciprocals of sin, cos, and tan, respectively.

For the coordinate system method, assume that the vertex of the angle in the triangle is at the origin (0, 0):

Trigonometric Functions

Keep checking back, as I’m trying to write every day, and please let me know if you have any questions or comments.    Keep working hard!   Lisa 🙂

Conics Section Done – Starting Trigonometry Sections

Sorry that it’s been awhile, guys 😉 .

Anyway, just finished the Conics: Circle, Parabolas, Ellipses, and Hyperbolas section; it was a long one.

Also, been working on some Trig sections: finished Right Triangle Trigonometry, and starting Angles and the Unit Circle – this will be an important one!!  Hope to finish that one by the start of the new school year!

You may notice that I’ve been playing around with Adsense on the site.  Hmm….thought I wouldn’t do this, but it’s nice to have a little money coming on, at least to pay for my expenses to keep the site up and running…..

As always, I love to hear from you about what you like and don’t like about the site, so keep those comments coming…..

Happy Math’ing,

Lisa

Math Tips: Exponents and Logs

Sorry it’s been awhile since I’ve posted my math tips – it’s always a little crazy getting through the holidays.  I can’t believe in a couple of months we’ll be finished with yet another school year 😉

She Loves Math continues to attract new viewers; I’m getting 1500-2000 hits a day now.  I’ve loved hearing from you and trying to help you solve math problems.

I just completed the Exponential and Logarithmic Functions section; it took me a little longer than expected – sorry about that.  Here is a short article I wrote on exponents and logs for someone; hope it’s useful:

What Is an Exponent?

First, we first need to understand what an exponent is.  An exponent just means that a number is multiplied that many times by itself.

Let’s use the following example.   If your savings account gives you interest at 5% every year (a rarity, these days!), every year your savings would be multiplied by 1.05.  This is because you get to keep what you originally put in your account, your principle (let’s say $100), and add 5% (or .05) times your amount every year.  After the first year, your account would have 100(1.05) or $105.  After the second year, your account would have 100(1.05)(1.05) or Blog 100 105 squared which is $110.25.  Do you see how, in the nth year, your account would have Blog 100 105 raise to the n dollars?  (“n” is the exponent in this case.)  It’s a confusing concept, but if you do the math year-by-year, it makes sense.  By the way, this concept of multiplying your principle by an interest amount every year is called compounding.   (Start saving and investing your money early in life; it pays!)

How Do Exponents Relate to Logs?

Now, let’s get back to logs.  Logs are related to exponents; in fact, the log of a number is an exponent.  Look at the following graphic to see how exponents and logs are related.  Remember that every exponent and log has a base, as designated by “b” in this diagram.  Our base in the example above is 1.05.

Blog Log Loop

Note: If there is no “b” next to the log, then the base is assumed to be 10.

Why Do We Need Logs?:  One Example

We are going to show an example of using logs in algebra (the branch of mathematics where letters represent values).  But why would we ever want to change an exponential algebraic expression or equation to a logarithmic one?   One important purpose of logs is for solving mathematical equations with unknowns or variables in an exponent.

Let’s say we had a beginning amount in our back account ($100) and had an ending account (say, $250), and we wanted to know how many years it took to reach that amount?  We could use the “guess and check” method to try different numbers in the exponent to get the $250 amount.  But the easiest way to get the number of years, or the exponent in the equation Blog A = is to use logs.  So a useful application of using logs is to solve for variables, or unknowns, that are in exponents. 

There are certain properties of logs that very helpful in solving equations.  One of the most useful properties is that the log of a number raised to an exponent is equal to that exponent times the log of the number without the exponent:  BLog Power Rule.  This is called the Power Property or Power Rule of logs.  This is an important property since it helps “get the exponent down” so we can solve for it using algebra.

Solving a Logarithmic Equation Using Algebra

Let’s go ahead and use logs, including the Power Property, to solve the algebraic equation Blog A = to get the number of years that it would take to go from $100 to $250 with a yearly interest rate of 5%.  We want A (the ending amount) equal to $250:

Blog Solving Log Equation

So the number of years it would take to have $250 in your account is 18.78 years.  This method is much easier than the “guess and check” method that involves just trying different numbers in the exponents and seeing if you get the $250.  And we can check our answer by using our calculator:  Blog Checking.

And this is just one of many applications of using logs; they are also used in biology (population growth), anthropology (carbon dating), geology (the Richter scale for earthquakes), chemistry (pH scales) and many other fields.

So That’s Why We Need Logs!

Logs are here to stay and are extremely powerful in mathematics. They are used in everyday applications of science and finance; in fact, logs are used at your local bank to help with the interest in your bank.  And again you can refer to the Exponential and Logarithmic Functions section of She Loves Math to learn more!