The above photo shows my solutions to this week's MATHCOUNTS problem. After the official solutions are published next week, this post will be updated to verify if my answers are correct.
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The above photo shows my solutions to this week's MATHCOUNTS problem. After the official solutions are published next week, this post will be updated to verify if my answers are correct. UpdateHere is the link to the published solutions for the 8/21/2017 MATHCOUNTS Problem of the Week. My answers to the first and third problems were correct, while my answer to the second problem was incorrect. Here's why. I multiplied the rate of each person by 1/2. However, I should have instead divided each rate by 1/2. Equivalently, the denominator of each ratewhich is the time that it takes each person to wire a classroomshould have been divided by two, as shown in the following image, showing my corrected solution:
This school year, my hourly rate for math tutoring is $40, paid as you go. Most students meet with me for 90 minutes ($60) per session, once or twice per week. Purchase 10 sessions in advance and receive a 10% discount. As a special offer for returning studentsgood for this month onlyan additional 10% discount will be applied to 10 prepaid sessions (for a total discount of 20%!). Better for students to start the school year off right, than to wait until getting beat up by their math classes before scheduling math tutoring.
To kick of this school year, the following image shows my worked out answers to the MATHCOUNTS Problem of the Week published on 8/14/2017. When the official answers and solutions are posted, this post will be updated to see how I did. By the way, this is an example of an enrichment activity that I do with middle school students when time allows during a tutoring session. UpdateHere is the link to the published solutions for the 8/14/2017 MATHCOUNTS Problem of the Week. My answers to the first and third problems were correct, while my answer to the second problem was incorrect. Here's why. There is only one way to pick at least one of each of the four colors, and not 24 ways (4! = 4 x 3 x 2 x 1) as I originally thought. The problem then becomes the number of ways to choose from four colors for each of the two remaining notebooks. Next, there are only four ways to choose two of the same color. What remains is the number of two color combinations. In other words, the number of ways to choose two from four items:
4C2 = 4! / (2! x 2!) = 4x3x2x1 / 2x1x2x1 = 24/4 = 6 Finally, add 4 and 6 to get the final answer of 10 for the second question.
LimitedTime Offer for Returning Students: Purchase 10 Sessions in the Month of August and Save 20%8/16/2017 As of the 20172018 school year, my rate for tutoring is $75 per 90minute session (at the hourly rate of $50). There is also the option to purchase 10 sessions in advance for a 10% discount, equivalent to 10 sessions for the price of 9. In other words, $67.50 per 90minute session (at the hourly rate of $45).
Additionally, as a limitedtime offer for returning students, purchase 10 sessions in the month of August and receive a 20% discount, equivalent to 10 sessions for the price of 8. In other word, $6o per 90minute session (at the hourly rate of $40). Don't wait until it is too late to take advantage of this offer. Also, now that the school year has started, my schedule is already filling up. So, call or message me today to get started! (702) 8826284, pro@kenmarciel.com Internet search results for tutors are saturated with third party services, through ads and search engine optimization. These third parties profit as middlemen, taking a significant percentage of the price paid for the services of the tutor. The middleman sells the labor of the tutor at full price, then compensates the tutor at less than full price. Many of these services operate nationwide and are therefore not local. This means that not all of the dollars you spend through them are not going back into your local economy.
A private tutor who is a professional educator, or an expert in his or her field of study, is a consultant who should not have to surrender a chunk of his or her fee to a middleman. It is customary and proper for consultants to work directly with clients, not through a third party. Therefore, I strongly advocate the patronage of independent local tutors instead of third party tutoring services. When you work with an independent local tutor, all of your money goes directly to the tutor and none to a middleman. This means that all of your money goes toward supporting the independent tutor, instead of being spent on advertising by the middleman. The result is a happier, fully compensated consultant who will in turn give you better service. The less you spend on middlemen services, the less demand for them and the less money they have to continue spending on advertising. So, vote with your dollars for independent local tutors. Every summer, students meet with me weekly for a math tutoring session (90 minutes) to give them a head start on the math tutoring course that they will be taking next school year. Additionally, time is allocated in each session for mental math, math for standardized tests, contest math, scientific calculator, or graphing utility, tailored to the level of the student.
My schedule is the same yearround. Monday through Thursday, I provide tutoring from 2:00 pm to 7:30 pm; and Friday through Sunday, from 2:00 pm to 5:00 pm. All of my tutoring is provided at Sahara West Library. The fee is $60 per 90minute session (at the rate of $40 hourly). Pay as you go or purchase 10 sessions in advance for a 10% discount. Call (702) 8826284 if you have any questions or would like to schedule a session. I teach using dry erase markers on mini white boards, which my students are welcome to use also. The image below provides a sample of my teaching style during a tutoring session. I also have a library of math books that I work from on my tablet computer. The image below demonstrates the factoring a fourth degree polynomial with four terms. The first step is to find the greatest common factor (GCF). Factor trees are used here to accomplish this. This technique comes in handy if you cannot come up with the GCF mentally. In the second step, a new binomial appears with its own GCF. We again use factor trees. In the third step, a difference of squares emerges. In the fourth step, the polynomial is completely factored. The next two images demonstrate the simplification of rational expressions. This time, factor trees are used slightly differently, to find the least common multiple (LCM) rather than the GCD (as used for factoring a polynomial expression). Each factor is circled in the tree where it is most numerous. All of the circled numbers are multiplied to yield the LCM, which is the lowest common denominator in the rational expression.
In the last step, we check to see if the trinomial in the numerator is factorable, which turns out it is not. If we start with the mixed number three and fiveeighths, it can be read as shorthand notation for the sum of three and five/eighths. This represents long division as follows. The whole number 3 is the quotient, the numerator 5 is the remainder, and the denominator 8 is the divisor. The mixed number can be converted to an improper fraction by multiplying quotient and divisor, adding the remainder, then dividing the quantity by the divisor. This can be represented vertically as a fraction, or horizontally as a standard order of operations. The result is 29/8, or 29 divided by 8. If long division is carried out next, the answer can be expressed in three different ways. If expressed as a decimal, the decimal point can be moved two places to the right, implicitly multiplying by 100, to get the equivalent percentage. Hence, the quantity can be expressed equivalently as a mixed number, improper fraction, decimal, or percentage. The next image shows various ways for the number to be expressed using pie and bar diagrams. Three and fiveeighths can be viewed as three whole pies or rectangles, with a fourth pie or rectangle divided into eight pieces with three pieces that are empty. As the above photo shows, the four rectangles can be stacked end to end. The pies or rectangles can be equivalently divided into 16 congruent pieces, with the fourth unit having six empty pieces. Hence, three and tensixteenths is equivalent to three and fiveeighths. The final image shows two of the whole units being stuck together, then converted to a sum of three numbers: two plus one plus fiveeighths. Using the associative property of addition, or the order of operations, the next step shows three plus fiveeights. In the final step, we return to the mixed number that we started with in this demonstration.

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