...Algebra 1 Pacing Plan 2012-2013 1st Quarter Tools of Algebra 1.1 Using Variables 1.2 Exponents and Order of Operations 1.3 Exploring Real Numbers 1.4 Adding Real Numbers 1.5 Subtracting Real Numbers 1.6 Multiplying and Dividing Real Numbers (1.3 – 1.6 mini lessons based on need) 1.7 The Distributive Property 1.8 Properties of Numbers Solving Equations and Inequalities 2.1 Solving One-Step and Two-Step Equations 3.1 Inequalities and Their Graphs 3.2 Solving Inequalities using Addition and Subtraction 3.3 Solving Inequalities using Multiplication and Division 2.2 Solving Multi-Step Equations 3.4 Solving Multi-Step Inequalities 2.4 Ratios & Proportions (mini lessons) 3.5 Compound Inequalities 3.6 Absolute Value Equations and Inequalities 2.5 Equations and Problem Solving 2.6 Mixture Problems and Work Problems California Content Standards 1.0, 1.1, 2.0, 4.0, 10.0, 24.1, 24.3, 25.0, 25.1, 25.2 2.0, 3.0, 4.0, 5.0, 24.2, 24.3, 25.0, 25.2, 25.3 2nd Quarter Linear Equations and Their Graphs 4.1 Graphing on the Coordinate Plane 5.1 Rate of Change and Slope 5.1.1 Graphing Using Input-Output Table (Supplemented) 5.1.2 Graphing Using Slope-Intercept Form (Supplemented) 5.1.3 Graphing Using...
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...Algebra 1: Simplifying Algebraic Expressions Lesson Plan for week 2 Age/Grade level: 9th grade Algebra 1 # of students: 26 Subject: Algebra Major content: Algebraic Expressions Lesson Length: 2 periods of 45 min. each Unit Title: Simplifying Algebraic Expressions using addition, subtraction, multiplication, and division of terms. Lesson #: Algebra1, Week 2 Context This lesson is an introduction to Algebra and its basic concepts. It introduces the familiar arithmetic operators of addition, subtraction, multiplication, and division in the formal context of Algebra. This lesson includes the simplification of monomial and polynomial expressions using the arithmetic operators. Because the computational methods of variable quantities follows from the computational methods of numeric quantities, then it should follow from an understanding of basic mathematical terminology including the arithmetic operators, fractions, radicals, exponents, absolute value, etc., which will be practiced extensively prior to this lesson. Objectives • Students will be able to identify basic algebraic concepts including: terms, expressions, monomial, polynomial, variable, evaluate, factor, product, quotient, etc. • Students will be able to simplify algebraic expressions using the four arithmetic operators. • Students will be able to construct and simplify algebraic expressions from given parameters. • Students will be able to evaluate algebraic expressions. • Students...
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...polynomials. 1. Consider the parabola y=(x-3)2 +2=x2-6x+11 and the lines y=x and y=2x. The original graph is shown below (graph 1.1) Find the intersections of the parabola with y=x and y=2x, Graph 1.2. Also, label the x-values of the intersections with the line y=x as they appear from left to right on the x-axis as a1 and a2; label the x-values of the intersections with the line y=2x as b1 and b2. Now, I will using the graph and graph calculator, find the values of a1-b1 and b2-a2 and name them respectively SL and SR. SL=a1-b1=2.381966-1.763932=0.618034 SR=b2-a2=6.236068-4.618034=1.618034 Now, calculate the quantity D= │SL-SR│ D= │SL-SR│=│0.618034-1.618034│=1 By algebra calculation, D=│SL-SR│ =│ a1-b1-(b2-a2) │ =│ a1-b1-b2+a2 │ =│ (a1+ a2 )-(b1+b2) │ Now, I will try other parabolas of the form y=ax2+bx+c, a＞0, with vertices in quadrant 1, intersected by the lines y=x and y=2x. y=x2+2x+1 [pic] From the graph we can see there is no intersection of the parabola and y=x, y=2x. Using the algebra way: Solve: (a) x2+2x+1=x (b) x2+2x+1=2x (a) x2+2x+1=x x2+x+1=0 [pic] X=[pic] a1+a2= 1 (b) x2+2x+1=2x x2+1=0 x2=-1 x=±i b1+b2=0 so D =│ (a1+ a2 )-(b1+b2) │ =│ 1-0 │ =1 y=2x2+3x-1 D=│(a1+a2)-(b1+b2)│ =│(-1.366025+0.366025)+(-1+0.5)│ =│-1+0.5│ ...
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...rates are still low (Stetser, 2014). Many studies have been conducted to identify the factors that contribute to the high school dropout rate. One of the factors that has been identified is the success or lack of success in Algebra 1. Some educational professionals have proposed that an earlier exposure to Algebra 1 in middle school could assist students with being more successful in high school. Thus those students would have a greater chance of graduating with their cohort and possibly even being accepted into a post-secondary school. This action research project studied the correlation between the use of graphic organizers and concept...
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...Detailed Lesson Plan in Algebra Feb. 11, 2015 I. Objectives a. Define polynomials b. Classify polynomials according to number c. Perform operation involving polynomials, addition and subtraction. II. Subject Matter Topic: Polynomials Materials: visuals, chalk and board Reference/s: College Algebra, pages 1-4 III. Presentation A. Preliminaries 1. Opening prayer 2. Checking of Attendance 3. Checking of Assignments 4. Motivation (Video clip) B. Lesson Proper Teacher’s Activity In the video that you’ve watched, what will be our lesson for today? Yes, George? Yes it has. Anyone can tell what it is? Yes, Fred. Very good. Can someone tell what is a polynomial is? Yes Claire. Yes, very well said, any additional information? Ok, so let’s proceed. So terms that different only in their constant coefficients are called “like terms”. Polynomials and algebraic expressions can be classified(according to the number of term) as; Monomial – having one term Binomial – having two terms Trinomials – having three termsMultinomials – having more than three terms. The degree of a polyomial is determined by the hiegst exponent of its variable. Someone give me an examples of polynomials. (called several students). Thank you for your answers. Is there any question? Oko next is adding and subtracting polynomials: Rule:Add/subtract the constant coefficients...
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...(Intermediate Algebra) 4th Year High School : Quarterly Remedial Class Instructor in Mathematics 4 (Advanced Algebra and Trigonometry) Summer, 2009 :Personal Tutorial Sessions for Math-UPCAT. 2nd Semester, 2010 :Literacy Training Service 2: Kalayaan Elementary School Grade 6 Mathematics Teacher 1st Semester, 2011 :Tutor in Princeton Academy, BelAir, Sta. Rosa, Laguna 2nd Semester, 2011 : Student-instructor in UPLB Math Division’s Think Tank Toe Achievements Elementary School : 3rd Place: Metrobank-MTAP-DepEd NCR Math Challenge Sectoral Level 10th Place: Metrobank-MTAP-DepEd NCR Math Challenge Regional Level Best in Math, Valedictorian High School : Best in Math (3rd Year and 4th Year), Best in Physics (4th year), 1st place, 2008 Math Masters, Meycauayan College. College 1st Semester, AY 08-09 : 4th Placer, UPLB Math Wizard College Scholar 2nd Semester, AY 08-09 : Participant, 36th Annual Nationwide Search For Math Wizard, UP Diliman 3rd Place, Statistics 1 Quiz Contest 2nd Semester, AY 09-10 : 2nd Place, Brain Damage: ENSC 11 Quiz Contest Participant, 37th Annual Nationwide Search for Math Wizard 1st Semester, AY 10-11 : 3rd Place, UPLB Math Wizard 1st Place, Squeeze Your Mind: EE 1...
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...LONDON'S GLOBAL UNIVERSITY Mathematics with Management Studies BSc UCAS code: G1N2 www.ucl.ac.uk/prospectus/maths MATHEMATICS WITH MANAGEMENT STUDIES BSc This BSc combines a broad-based training in mathematics with highly practical courses from UCL’s Department of Management Science and Innovation, which will be of direct use to those seeking a career in management. No previous knowledge of management studies is required. Degree summary • • • • Gain transferable skills such as numeracy, problem-solving and logical thinking, which can lead to a large variety of interesting, diverse and well-paid careers. All of the courses given by UCL's Department of Management Science are validated by external experts from the private, public and charitable sectors. Many of our graduates choose to build their management knowledge and experience by following a further management qualification, such as the MBA (Masters in Business Administration). UCL's internationally renowned Mathematics Department is home to world-leading researchers in a wide range of fields, especially geometry, spectral theory, number theory, fluid dynamics and mathematical modelling. Peer Assisted Learning has been pioneered in the department, with second-year students offering support and advice to first years. Your career We aim to develop your skills in mathematical reasoning, problem-solving and accurate mathematical manipulation. You will also learn to handle abstract concepts and to think critically...
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...Many people are intimidated and afraid of mathematics and algebra largely due to the fact that upon first glance, certain problems or expressions may seem overwhelmingly large, difficult, or complicated. Along with remembering formulas, this can often times lead to anger, confusion, and frustration. There are several very important key elements and aspects involved within mathematics that helps combat this confusion and frustration and can even help the most intimidated person feel at ease and comfortable with solving these problems. This particular report will demonstrate the importance of understanding certain key mathematical principles and components and show how understanding and utilizing certain mathematical definitions can help limit the amount of confusion and intimidation one may have. These definitions include but are not limited to simplifying, adding like terms, coefficient, distributive property, and removing parenthesis. This report will also demonstrate how much easier and more simplistic mathematics and algebra can be by remembering and utilizing just a few important concepts. Example 1: 2^a(a-5) +4(a-5) This is the first example that will be used. The variable a is used. This particular example has a coefficient of two. Step 1: The distributive property can be utilized to multiply 2a by everything inside of the parenthesis (a-5 in this case) resulting in: 2a^2-10a Step 2: The distributive property is used once again to multiply 4 by everything in the...
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...06 Section 6 pp058-067.qxd 6.1 26/8/03 10:04 am Page 58 Key words Collecting like terms like terms unknown Understand which terms you can add together and which you cannot 3 ϩ 3 is two lots of 3 so 3 ϩ 3 ϭ 2 ϫ 3 a ϩ a is two lots of a so a ϩ a ϭ 2 ϫ a We write 2 ϫ a as 2a. Just as 2 ϫ 3 and 4 ϫ 3 can be added together to give 6 ϫ 3, 2a and 4a can be added together to give 6a. These terms are called like terms because they contain the same letter. Like terms can be added together – this is called collecting like terms. Instead of writing 2m ϩ 3m ϩ b ϩ 2b, we can write 5m ϩ 3b or 3b ϩ 5m. We cannot combine 5m and 3b in any simpler way than this because m and b are not like terms – they stand in for different unknown numbers. We can multiply two or more unknowns together. a ϫ b is written as ab. b ϫ a is the same as a ϫ b and is also written as ab. Instead of writing 2a ϩ 3b ϩ 3ab ϩ ba, we can write 2a ϩ 3b ϩ 4ab. We can add 3ab to ba to make 4ab because ab and ba are like terms. Example Simplify the following by collecting like terms: a) 3m ϩ 4m ϩ m ϩ n ϩ 2n b) 4mv ϩ 2z Ϫ 3mv ϩ z ϩ 3m There are eight lots of m and three lots of n. a) 3m ϩ 4m ϩ m ϩ n ϩ 2n ϭ 8m ؉ 3n b) 4mv ϩ 2z Ϫ 3mv ϩ z ϩ 3m ϭ mv ϩ 3z ϩ 3m First look at the mv terms: 4mv Ϫ 3mv ϭ 1mv (which we usually write as mv) Now look at the z terms: 2z ϩ z ϭ 3z Now look at the m terms: you have 3m Exercise 6.1 ......................................................
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...Distributive Property Kimberly Smith MAT 221 Introductions to Algebra Instructor: Andrew Halverson February 15,2014 I will be using distributive property to solve how properties of real numbers are used while I simplified the three given expression. To solve these three math problem I will use the distributive property to remove the parentheses in the problem. I will also combine like terms by adding coefficients and add or subtract when needed. Finally I would have my answer and then decide if the answer is simplified, if not I will simplify. The solving of properties of real number the properties of real numbers are important to know in all subjects, even complex numbers, because many of the properties are shared. Additionally the argument to any equation in algebra is real; therefore, algebraic expressions only manipulate reals (that is, if you have integer coefficients and no radicals). 1. 2a(a-5)+4(a-5) = The given expression 2a^2-10a+4a-20 = I will use the distributive property to remove parentheses so I can combine like terms by adding coefficient. 2a^2-6a-20 = Is simplified no combine like terms by adding coefficients 2a^2-6a-20 = Answer 2. 2w – 3 + 3(w – 4) – 5(w – 6)= The given expression 2w - 3 + 3(w - 4) - 5(w - 6) = Distributive property removes parentheses 2w - 3 + 3w - 12 - 5w + 30 = Combine like terms 2w + 3w - 5w - 3 -12 + 30 = Combine like terms by adding coefficients and add and subtract to get sum. Use the commutative...
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...student, Key Award Student (most respectable and distinguished students), and a member of the National Honors Society in Simon Gratz Mastery Charter. I rank one of the highest currently and have remained one of the highest since 9th grade. I am very self driven, active, and a goal achiever. My patients, positivity, and ability to connect with others makes me more eligible to participate in my community and help provide a safe environment. EDUCATION Simon Gratz Mastery Charter HighSchool, Philadelphia, PA - 08/2011 to Present GPA Weighted: 4.07 GPA Unweighted: 3.95 * Competed Coursework In : Literature 9, Algebra 1, Physical Science, Sophomore Seminar, Composition, and African American History (9th grade). Biology, Geometry, Internship, Literature 10, World History, and Mastery Class (10 grade), AP Literature, AP U.S history, Algebra 2, Chemistry, and Spanish 1(11th Grade) * Currently Enrolled In: AP Literature, AP Government, AP Biology, Senior Seminar, Physical Ed., Spanish 11, and Pre-Calculus STRENGTHS / WEAKNESSES: * Strengths: Easily establishes friends, gets along well with peers, accepts responsibility well, study and work skills are strong, initiates interactions with peers, appropriately assertive, grade appropriate grammar, likes to get involved, strong decision making skills, strong ability to manage behavior, strong organization skills * Weaknesses: Difficulty to speaking amongst big crowds * How Am I Approving This Weakness: I am starting...
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...DQ 1 Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. Did you reach 1 for an answer? You should have. How does this number game work? Hint. Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression. How did the number game use the skill of simplifying rational expressions? Create your own number game using the rules of algebra and post it for your classmates to solve. Think about values that may not work. State whether your number game uses the skill of simplifying rational expressions. Consider responding to your classmates by solving their number games or expanding on their games to create an even more challenging one. You may want to review responses to your number game in case you need to make changes or help another student. ANSWERS: My Answer: Here in this number game we are using the concept of a^2 - b^2 = (a-b)(a+b). First take number as a. Then square of that = a^2 , Here b is 1. So, subtract 1: a^2 -1 One less than original number : a-1. Now we need to divide a^2 - 1 by (a-1). So, (a^2 -1)/(a-1) = (a^2 -1^2)/(a-1) = (a-1)(a+1)/(a-1) = (a+1) Now, subtract the original number a: a+1 - a= 1 is the answer. So, in every case we will get 1 as the answer and a cannot be 1 because we are dividing by a-1 then it will be 1-1 =0 which is not possible, because we cannot divide by 0...
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...April Smith GCU: SED-444 August 25, 2013 Higher Order Thinking and Diverse Learners Grand Canyon University: Secondary Methods and Data-Driven Pedagogy April Smith GCU: SED-444 August 25, 2013 Higher Order Thinking and Diverse Learners This unit is designed for students in beginning Algebra classes. It is an introduction to the basic functions of algebra including the definition of an equation, using basic mathematical skills to solve equations, and applying equations to problem solving. South Carolina Standard 8-3: Through the process standards students will demonstrate an understanding of equations, inequalities, and linear functions (South Carolina Department of Education, 2007). Specific Indicators as outlined by the South Carolina Department of Education 8-3.1 Translate among verbal, graphical, tabular and algebraic representations of linear functions. 8-3.2 Represent algebraic relationships with equations and inequalities. 8-3.3 Use properties to examine equivalence of a variety of algebraic expressions. 8-3.4 Apply procedures to solve multi-step equations. 8-3.5 Classify relationships between two variables as linear or non-linear. Objectives Day 1 Objective: Students will learn the definition of an algebraic equation and the parts of an equation. Day 2 Objective: Students will apply their knowledge of addition and subtraction to solve algebraic equations. Day 3 Objective: Students will demonstrate proficiency in applying multiplication...
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...Score ACT Score None None 570 49 Total Core Course Credits 16 16 0 Grade Points Key: A=4, B=3, C=2, D=1 / # = Weighted Points (d) = Course for students with a diagnosed disability / (t) = Transfer course from another school English Courses Course Grade Points Quality Pts Credits Credits Required Credits Needed ENGLISH 3 ENGLISH 4/H ENGLISH 1 ENGLISH 2 Totals A A C C 4 4 2 2 4 4 2 2 12 1 1 1 1 4 4 0 Math Courses Course Grade Points Quality Pts Credits Credits Required Credits Needed ALGEBRA 2 PRE-CALCULUS GEOMETRY Totals A A B 4 4 3 4 4 3 11 1 1 1 3 3 0 Natural/Physical Science Courses Course Grade Points Quality Pts Credits Credits Required Credits Needed BIOLOGY 1 CHEMISTRY 1 Totals B B 3 3 3 3 6 1 1 2 2 0 Extra English/Math/Science Courses Course Grade Points Quality Pts Credits Credits Required 1 Credits Needed 0 ALGEBRA 1 Totals C 2 2 2 1 1 Social Science Course Grade Points Quality Pts Credits Credits Required Credits Needed AFRICAN AMERICAN HISTORY WORLD HISTORY Totals A C 4 2 4 2 6 1 1 2 2 0 Additional Core Courses Course Grade Points Quality Pts Credits Credits Required Credits Needed FRENCH 1 FRENCH LANGUAGE/AP FRENCH 3/H EARTH/SPACE SCIENCE Totals Grand Totals A A B C 4 4 3 2 4 4 3 2 13 50 1 1 1 1 4 16 4 16 0 0 Unused Courses Course Grade Points Quality Pts Credits AMERICAN GOVERNMENT ECONOMICS A A 4 4 ...
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...| | | Domains of Rational Expressions The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. It is the set of all real numbers for which a function is mathematically defined. The denominator can not be zero because, nothing can be divided by zero and remain a real number. The first letter of my names starts with a "T" so these are the rational expressions that I'll be solving: 1 - x^2 and 2b - 2 x 2b^2- 8 1 - x^2 This is the first given expression. Since we know that denominator is the valuable, x can not equal zero be because it will make the expression undefined, but any x other real number will solve the expression. x = 0 The zero is the excluded value. We can see that the domain for this expression is a set of all real numbers where zero is excluded from the value. The expression is written like this:D = {x| x € R b ≠ 0}. For the second...
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