With the school year winding down, arranging for summer break Math time starts!
1) Not practicing newly acquired math skills will allow for knowledge to erode
2) Not practicing previously acquired math skills will expedite knowledge erosion
3) Not having other non-math course work will allow for
- focusing on math remedial work, or
- getting a jump on next year’s math academic growth.
Math needs are the same per subject, whether the learning setting is for advanced placement, over-age/under-educated, middle school, high school, or Veterans. BUT, the instructional approach should be different. Differentiating the approach to each student’s situation addresses learning styles (do we not all have different learning styles, which, if catered to, maximize results?).
Also, a subtle,...
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Here are 48 of my favorite math words in 12 groups of 4. Each group has words in it that can be thought of at the same time or are a tool for doing math.
What are your favorite math words? If you aren't sure, search for "mathematical words" and pick a few.
I do believe that any subject can be learned if one decides that they want to learn that subject. Its been my way of thinking throughout my career. If you want to learn and have an open mind, then it can happen!
Positive thinking is what it takes to succeed in this life. Believe in yourself and it will happen!
A question that I have heard many times from my own students and others is this: "When am I ever going to use this?" In this post and future posts, I'm going to address possible answers to this question, and I'm going to also take a look at what mathematics educators could learn from the question itself.
Let's look at the answer first. When I was in school myself, the most common response given by teachers was a list of careers that might apply the principles being studied. This is the same response that I tend to hear today.
There is some value in this response for a few of the students, but the overwhelming majority of students just won't be solving for x, taking the arcsine of a number, or integrating a function as part of their jobs. Even as a total math geek, I seldom use these skills in practical ways outside my tutoring relationships.
Can we come up with something better, that will apply to every student? I say that...
This is my all time favorite website for Math worksheets.
Reading Formulas can make or break how a student comprehends their formula when alone - outside the presence of the teacher, instructor, tutor, or parent.
Formula for Area of Circle: A = π * r^2
Ineffective ways to read the area of a circle formula are as follows:
Area is π times the radius squared.
Area is π times the radius of the circle squared.
Area of a circle is π times the radius squared.
A equals π times r squared.
>>>> Why are these ways NOT effective ways to read this formula? <<<<<
1. Students will recall and repeat what they hear their educators say.
2. If students recall letters (A) versus words (Area of a Circle) they will not realize the connection with word problems.
3. Half way reading the formula (radius versus radius of a circle) creates empty pockets or disconnects in...
Hi all algebra students. I found a great website, algebra-class.com that has an algebra calculator that you can use to check your homework. It has been very useful in our algebra classes as a tool for homework help.
I am taking from The Official Hunter College High School Test: problem 76 on page 20. We read the following.
In the expression below, each letter represents a one digit number. Where the same letter appears, it represents the same number in each case. Each distinct letter represents a
different number. In order to make the equation true, what number must replace C?
A great start is to decode each AAA, AAB, and ABC. It helps to look at this problem wholly; particularly we look at the leading sum on the left wall (of the same types). We glean that either: (1) A + A + A = 20, (2) A + A + A + 1 = 20 or (3) A + A + A + 2 = 20: its very important to remember that given three numbers each less than ten, the sum of them which is great, is at most 2 in the tens place. This means that each row can only donate a 1 or 2 to the next. We can conclude that our line is...
There are several points in grade school that involve a critical shift in the thinking that is required in the school work. Parent's should be aware of these points as they navigate through the abyss of raising a school-aged child and supporting the child as he/she moves forward through the grades.
3rd Grade - The third grader is transitioning from whole number thinking into understanding the concepts of parts. They are exposed to fractions, decimals and percentages. This is a major paradigm shift. Students are also exposed to long division at this point. Supporting children in this phase requires an emphasis on helping the child conceptualize whole things being split into parts. In addition to homework support, tutoring, and supplementary work, parents should introduce cooking chores to children at this time, and make them follow a recipe that has precise measurements. Reading comprehension and writing is also an issue here...
Four years ago, I came up with this math trick. Take a look at it, and at the end I'll show you why it works!
Let's play a game. I’m going to let you make up a math problem, and I will be able to tell you the answer from here. I can’t see what you’re doing, I’m not even in the same room as you, but I will still be able to tell you the correct answer.
Trust me. I’m a professional. Ready?
Okay. First, pick a number. It can be any number you wish, large or small. Now add 5 to that number. Got it? Okay, now double your new number (multiply by 2). Alright, now subtract 4 from the double.
Next, divide your new number by 2. Now, finally, subtract your original number from this new quotient. Got it? Okay. Here comes the cool part. Ready?
The answer is 3. Nifty, huh? What’s that? How’d I do it? Oh, magic.
Okay, okay, it’s not magic. The answer will always be 3, no matter what number you pick. Let’s illustrate this by...
Today, the future depends on you as much as it does on me. The future also depends on educating the masses in Science, Technology, Engineering, and Math, otherwise known as STEM. As a new tutor to WyzAnt, I hope to instill the importance of these subjects in student's lives, as well as, the lives around them.
Besides the fact that, "the average U.S. salary is $43,460, compared with the average STEM salary of $77,880," (Careerbuilder) these subjects are interesting and applicable to topics well beyond the classroom. Success first starts with you; I am only there to help you succeed along the way. STEM are difficult subjects. Yet when you seek out help from a tutor, like myself, you have what it takes to master them.
Please enlighten me on students looking to achieve and succeed rather than live in the past and think I can't as opposed to I can. We can take the trip to the future together, one question at a time
This week's Math Journey builds on the material in
The Function Machine. If you have not yet read that journey, I suggest you do so now.
In The Function Machine we discussed why graphing a function is possible at all on a conceptual level – essentially, since every x value of a function has a corresponding y value, we can plot those corresponding values as an ordered pair on a coordinate plane. Plot enough pairs and a pattern begins to emerge; we join the points into a continuous line as an indication that there are actually an infinite number of pairs when you account for all real numbers as possible x values.
But plotting point after point is a tedious and time-consuming process. Wouldn't it be great if there was a quick way to tell what the graph was going to look like, and to be able to sketch it after plotting just a few carefully-chosen points?
Well, there is! Mathematicians look for an assortment of clues that help to determine the shape of a function's...
Vi Hart, website: vihart.com
Sal Khan, https://www.khanacademy.org/math/algebra
Mamikon Mnatsakanian, www.its.caltech.edu/.../calculus.html
Come with me on a journey of division.
I have here a bag of M&Ms, which you and I and two of your friends want to share equally. I'm going to pour the bag out on the table and split it into four equal piles. For this example, “one bag” is our whole, and the best number to represent that whole would be the number of M&Ms in the bag. Let's say there were 32. If I split those 32 M&Ms into four equal piles and asked you how many were in one pile, you could certainly just count them. But a quicker way would be to take that 32 and divide it by the number of piles I'd made, which in this case is 4. You'd probably write that as:
32 ÷ 4 = 8
So there are 8 candies in each pile.
Seems easy enough with a large number of M&Ms, right? But what if there were less candies – what if our “whole” was less than the entire bag? Well, for a while we'd be okay – if there were 16, for example, we'd do the same thing and come up with piles of 4 instead of...
Factoring can be quite difficult for those who are new to the concept. There are many ways to go about it. The guess and check way seems to be the most common, and in my mind, it is the best, especially if one wants to go further into mathematics, than Calculus 1. But for those just getting through a required algebra course, here is another way to consider, that I picked up while tutoring some time ago:
If you have heard of factor by grouping, then this concept will make some sense to you. Let's use an example to demenstrate how to do this operation:
Ex| x2 + x - 2
With this guess and check method, we would use (x + 1)(x - 2) or (x + 2)(x - 1). When we "foil" this out, we see that the second choice is the correct factorization. But, instead of just using these guesses, why not have a concrete way to do this.
Let's redo the example, with another method.
Ex| x2 + x - 2
I am happy to announce that all my students have passed the NY State Regents examinations, except one student. The subjects varied from Algebra 1, Algebra 11/Trigonometry, English, US and Global History and Living Environment. I am so proud of them. Most of these students are students who struggled quite a bit. It was a long journey but one I would do again.
I am very proud of them as most of them will be graduating this year. The NY State Common Core examinations are next.
Several of my current Geometry students have commented on this very distinction. This has prompted me to offer a few possible reasons.
First, Geometry requires a heavy reliance on explanations and justifications (particularly of the formal two-column proof variety) that involve stepwise, deductive reasoning. For many, this is their first exposure to this type of thought process, basically absent in Algebra 1.
Second, a large part of Geometry involves 2-d and 3-d visualization abilities and the differences in appearance between shapes even when they are not positioned upright. Still further, for a number of students, distinguishing the characteristic properties amongst the different shapes becomes a new challenge.
Third, in many cases Geometry entails the ability to form conjectures about observed properties of shapes, lines, line segments and angles even before the facts have been clearly established and stated...
As a student, I found that I remembered information a lot easier when the information was in a song. I learned the 'quadratic formula song' in one of my math classes and have not forgotten the formula since. Several of my students have also found this song helpful (and catchy!), so I though I'd share:
The 'Quadratic Formula Song' (sung to the lyrics of 'Pop Goes the Weasel')
The quadratic formula is negative b
plus or minus the square root
of b squared minus four a c
all over 2a!
(Warning, this will get stuck in your head!)
Here are some of my favorite Math resources. Check back again soon, this list is always growing! I also recommend school textbooks, your local library, and used bookstores.
As a note, college-level math textbooks are often helpful for high school math students. Why is that? Isn't that a little counter-intuitive? Yes, it would appear that way! However, many college-level math textbooks are written with the idea that many college students may not have taken a math class in a year or more, so they are written with more detailed explanations. This can be particularly helpful for high school students taking Algebra, Geometry, and Trig. I have a collection of college-level math books that I purchased at a local used bookstore. The most expensive used math book I own cost $26 used. Books that focus on standardized test prep (such as the SAT, AP, or GED prep) can be helpful for all core subjects, as they summarize key ideas more succinctly than 'normal' textbooks. These are GREAT...