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## Set Up: By What Methods Can You Solve A Quadratic Equation

As I describe in;this video narrative, the set up for today’s lesson is about as simple as they come. ;I define a task for students, and they set to work. ;When they need me, I’ll teach a mini-lesson or two, either to small groups of students or to the entire class. ;

As students arrive, I post;Student Learning Target 6.5;on the front board, and instruct everyone to log in to their Delta Math accounts. ;Together, we read the learning target. ;I ask, “What are the three methods you need to know for solving quadratic equations?” ;They’re written in the learning target, which says, “by any method, including factoring, completing the square, and using the quadratic formula.” ;When students see the assignment on their computer screens I point out that the first two modules require them to use factoring, the next two completing the square, and the last three, to use the quadratic formula. ;”You’ll do as much as you can today,” I encourage everyone. ;”If you’re already good at all of this, that’s great. ;If you know how to factor, but not how to complete the square, then you know what you’ll need to practice today.”

## Presentation On Theme: The Impact Of Deltamath: A Study Examines The Effectiveness Of Online Homework Versus Paper

1 THE IMPACT OF DELTAMATH: A STUDY EXAMINES THE EFFECTIVENESS OF ONLINE HOMEWORK VERSUS PAPER- BASED HOMEWORK ON ALGEBRA 2 STUDENTS TEST GRADES BY: AMY LEE

4 Table 2 Degree of Congruence of State Standards as Compared to the Common Core State Standards for Mathematics

5 Table 3 Contrasting Common Core and State Standards on Cognitive Demand

6 Background: Student is very cheery and sociable. Student works hard to try to understand the concept. It takes a long time for the student take understand the concept. Student did not do so well on the past regent exams. Student is improving from 65% to 80% this marking period.

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## How Can I Learn Algebra Easily

How to Study Math: Algebra

## The Ixl Mathematics Platform

**What Is IXL?**

**IXL** is billed as immersive adaptive learning. According to their website, they offer 3,700 distinct math topics. The skills range from Pre-K all the way to Calculus, sorted by grade level. Questions are algorithmically generated, meaning students will never see the same question twice no matter how long they practice. Students start out at 0% and each correct question ups their score. Conversely, every wrong answer drops their score.

**Is It Free?**

There are a free version and a paid version. I used the free version of IXL until our school bought a subscription for the service a few years ago. The free version will only allow students to complete five problems in each topic, and the teacher cannot view students progress. I thought the free version was useful, although obviously it doesnt have the features the paid version has. According to the IXL website, the standard classroom license is $299 for up to 25 students for one subject. If a license is needed for more than one classroom, you have to contact an IXL representative for a quote.

**Pros**

**Cons**

Of course, nothing is perfect. I have found that students can pick up patterns and will be able to answer questions correctly without really understanding the concept. Also, students will try to answer questions without writing anything down which can hinder their understanding. Not writing down any work is a bad habit to get into in math class!

**What Do the Students Think**

**Final Thoughts on IXL**

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## Rational Expressions Equations Inequalities And Functions

Solution to Problem 5-2We start by stating that x = 1 and x = -2 cannot be solutions because these values make the denominator zero.Multiply all terms of the equation by \ \) in order to eliminate the denominator.\ = \dfrac – 4 \).Simplify\ = – 4 \).Write the equation with zero on the right side\ – + 4 = 0 \)Expand and group the left side\Factor the left sideSolution set:\

Solution to Problem 5-3We start by stating that x = 1 and x = – 1 cannot be included in the solution set because these values make the denominator zero.Rewrite the inequality with right hand side equal to zero.\Set all terms to the same denominator\Group the terms on the left side\The zeros of the numerator and denominator of the left side are\and they split the number line into 4 intervals\ , , \)Use test values or table of signs to determine the solutions set of the inequality which is the interval\ \cup [3/2 , +\infty) \)

Solution to Problem 5-4Group the terms in the right side to rewrite the given function as the ratio of two polynomials.\The degree of the numerator and that of the denominator are equatl, therefore the horizontal asymptote is the ratio of the leading coefficients of the numerator and the denominator and is given by\The vertical asymptotes are given by the zeros of denominator\Solve the above equation to obtain the vertical asymptotes\ and \

## Arithmetic Sequences And Series

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

**Example**

2,4,6,8,10.is an arithmetic sequence with the common difference 2.

If the first term of an arithmetic sequence is *a*1 and the common difference is *d*, then the *n*th term of the sequence is given by:

$$a_=a_+d$$

An arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, a1 and last term, an, divide by 2 in order to get the mean of the two values and then multiply by the number of values, n:

$$S_=\frac$$

**Example**

Find the sum of the following arithmetic series 1,2,3..99,100

We have a total of 100 values, hence n=100. Our first value is 1 and our last is 100. We plug these values into our formula and get:

$$S_=\frac=5050$$

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## Trigonometry And Trigonometric Functions

To each rotation correspond an angle of 2 radians. For 1000 rotations corresponds\ radians rotated in one minuteThere are 60 seconds in one minute. Hence in 1 second, the wheel rotates\ radians per second.

Solution to Problem 6-2The absolute value of the angle is larger than 2; hence we first rewrite the angle as a sum of a special angle and a multiple of 2\ = sec = sec \)we then simplify\ = 1 / cos = 1 / = 2\)

Solution to Problem 6-3180 degrees correspond to ; hence\

Solution to Problem 6-4180 degrees correspond to ; hence\ degrees

Solution to Problem 6-5We first start with the rangle of \) \) which is a sine function with amplitude 2.\) \le 2 \)We next add – 6 to all terms of the double inequality above to obtain a new double inequality \) – 6 \le 2 – 6 \)Simplify to obtain the range of the given fuction\) – 6 \le – 4 \)The range of the given function is given by the interval\For a function of the form \ + d\) the period P is given by\

Solution to Problem 6-6One way to graph the given function is by successive transformationsWe start by graphing \ \) , graph shown below We next graph \ \) by shifting the graph of \ \) to the right by \; graph shown below.We next graph \ \) , by reflecting the graph of \ \) on the x axis; graph shown below.We next graph \ + 2 \) , by shifting the graph of \ \) 2 units up; graph shown below.The last graph is close to the graph b) given above in the question; hence the answer is b)