...recur e.g. 0.14141414 ... Scientiﬁc notation: Sometimes called standard notation. A standard form to write very large or very small numbers as a product of a number between 1 and 10 and a power of 10 e.g. 765 000 000 is 7.65 # 10 8 in scientific notation Chapter 1 Basic Arithmetic 3 INTRODUCTION THIS CHAPTER GIVES A review of basic arithmetic skills, including knowing the correct order of operations, rounding off, and working with fractions, decimals and percentages. Work on significant figures, scientific notation and indices is also included, as are the concepts of absolute values. Basic calculator skills are also covered in this chapter. Real Numbers Types of numbers Unreal or imaginary numbers Real numbers Rational numbers Irrational numbers Integers Integers are whole numbers that may be positive, negative or zero. e.g. - 4, 7, 0, -11 a Rational numbers can be written in the form of a fraction b • 3 where a and b are integers, b ! 0. e.g. 1 , 3.7, 0. 5, - 5 4 a Irrational numbers cannot be written in the form of a fraction (that b is, they are not rational) e.g. 2 , r EXAMPLE Which of these numbers are rational and which are irrational? • 3 r 3 , 1. 3, , 9 , , - 2.65 4 5 Solution r are irrational as they cannot be written as fractions (r is irrational). 4 • 3 13 1 1. 3 = 1 , 9 = and - 2.65 = - 2 so they are all rational. 3 1 20 3 and 4 Maths In Focus Mathematics Preliminary Course Order of operations 1. Brackets: do......
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...terminology is a necessary condition for overall mathematics achievement. If the learning of mathematics is highly dependent on its language and the teaching of math vocabulary is crucial, it is doubly so for ELLs. English language learners in secondary schools should have many opportunities to communicate their mathematical ideas and questions. Talking and writing about their mathematical thinking helps ELLs build word knowledge and oral expression and clarify their thinking. Discussions with the teacher or peers are also useful monitoring tools for teachers. Through listening and recording student conversations and peer problem solving, teachers can monitor individual student progress. Mathematics is no longer viewed as isolated, individualistic, or competitive. Mathematics problems are ideally suited to cooperative group discussions because they have solutions that can be objectively demonstrated. Students can persuade one another by the logic of their arguments. Mathematics problems can often be solved by several different approaches, and students in groups can discuss the merits of different proposed solutions (Robertson, Davidson, & Dees, 1994). For this and several other reasons mentioned throughout this chapter, cooperative learning takes a central place in mathematics instruction. Teaching and Learning Meaningful Math The lesson template for ExC-ELL is the same as that described in previous chapters. It begins with stating the learning objectives, back ground......
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... |Apply properties of real numbers to algebraic expressions. | | | | |Translate English phrases to algebraic expressions. | | | |Reading |Read Ch. 1 of Beginning and Intermediate Algebra. | | | |Reading |Read the University of Phoenix Material: MyMathLab® Study Plan. | | | |Participation |Participate in class discussion, be active in classroom problem solving, | |2 | |Discussion Questions |assist in determining answers to classroom problem sets. | | | |Nongraded Activities and Preparation |Resource: University of Phoenix Material: Using MyMathLab® | | | |MyMathLab® Orientation |Complete the MyMathLab® orientation by clicking the MyMathLab® link on the | | | | |student website and selecting MyMathLab® Orientation under the Homework and| | | | |Tests tab. | | | |Nongraded......
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...in the math factory.(Time assessment for each level may differ) | JulyTime to be placed | Consultation with parent(s) and child(ren) | 30 – 60 mins. A consultation will be held, in order for the parents and child come in. We discuss their current progress, where they need to improve and how the parents can help in their development. We also discuss their strengths and how they can harness or fine tune it.This is also where we wish to gather parent and student information in these sessions also | JulyTime to be placed | Arranging of the Classes | 60 – 90 mins. Students will be sorted in their respective grade levels and competencies: * Basics * Primary * High (split between 7,8 and 9,10,11) | JulyTime to be placed | Teaching begins | Introduction of students, register is taken and lesson begins.Class Days: * Tuesday (Basic) * Wednesday (Primary) * Thursday (High)Each group will be taught on different days and each day is two hrs. each | - Time between - | - Teaching - | - Any other activities will be done on a by weekly basis and be presented as a lesson plan – | AugustTime to be placed | Math Decathlon | At the end of the Mathematic Factory each grade level will participate in a decathlon where, they will be given challenges and activities reflective on the lessons taught. * Basic:description of decathlon (will be decided near completion of math factory) * Primary School:description of decathlon(will be decided near completion of math......
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...October 10th 2013 QUESTION 1 Explain the following variables with their categories. For example: categorical, continuous, discrete or qualitative or quantitative. 1. Nominal 2. Ordinal 3. Dichotomous 4. Interval 5. Ratio Answer: We need to grasp the different types of variables we may discover while doing our dissertation. Categorical variables and Continuous variables are the main types of variables. Categorical variables are also known as qualitative or discrete variables while continuous variables are known as quantitative variables. Categorical variables can be differentiated as: * Nominal * Dichotomous * Ordinal Categorical variables have categories or rates/level that is used to describe how the variables should be controlled, measured or presented. Continuous variables can be differentiated as: * Interval * Ratio Continuous variables are always within the form of numerical value which is used to describe how variables should be controlled, measured or presented. 1. Nominal Nominal variables cannot be ordered which is meant they cannot be measured by levels (e.g. a scale from 1 to 5) but by two or more categories (e.g. blue, black, brown or blonde hair). Nominal variables can answer questions such as: a. Gender : Male or Female b. Type of property : a house, apartment or bungalow c. Hair colors : blond, brown, red hair, black, etc d. Blood type: A, B, AB or O For example: Question : What......
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...CSULB Shahriar Abachi sabachi@csulb.edu Physics & Astronomy ASTR 100L ASTRONOMY LAB Sec 02: M 11:00–1:45 & Sec 06: Tu 2–4:45 OFFICE HOURS: W 2:50–3:20, 4:50–5:30 HSCI-272a COURSE DESCRIPTION: This course comprises an introduction to techniques of Astronomical measurement and analysis of Astronomical data. Emphasis will be on understanding how scientific knowledge is constructed, i.e. answering the question: how do we know about the universe? Students will perform hands-on measurements, observations, and exercises in data analysis relating to the solar system, stars, galaxies, large-scale structure of the universe, and cosmology. REQUIRED TEXT: Astronomy Lab Manual, Kim Gordon, 4th edition REQUIRED MATERIALS: Notebook, Scantron forms (882E, ES), scientific calculator GRADES: The following provides the areas that grades will be assigned for the class: Each Lab Reports Final exam Quizzes 20 points – for a total of 240 points 80 points – consisting of 15–30 multiple choice questions 50 points Grand Total 370 points LETTER GRADES: A(330–370), B(300–329), C(270–299), D(240–269) QUIZZES: A Quiz is given at the beginning of each session asking you about the Lab of that day. GENERAL RULES: Eleven Lab sessions are planned. Preparation, on-time arrival, presence, participation, and lab reports are required. Late arrival or lack of participation may result in a 10%–50% reduction in grade or a zero for that lab or even more serious......
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...teaching GCSE maths re-sits has changed during the course. My thinking about teaching GCSE maths re-sits has changed in that I’m more focused on improving the learning of my students. Simplistically, before it may have been a case of “What do they need to know?” and then relaying what the student needs to know for that particular subject, in a clear and concise manner, which may have been “got” by most students, but then they would have forgot the method shortly afterwards when it came to a formative or a summative assessment. Now I’m more determined to help students learn in a way that is going to be enjoyable to them and help them remember what they need to for the exam. This will involve doing more kinaesthetic and visual activities as a lot of learners learn by doing. Realistic Mathematics Education (RME) The course has introduced me to Hodder Education’s range of books called ‘Making Sense of Maths’ for KS3 and KS4 (http://www.hoddereducation.co.uk/makingsenseofmaths). Mr Gough, a maths teacher and one of the authors of the aforementioned book(s) states the following: “My experience of teaching GCSE Foundation Tier is that by the time they get to KS4 they’ve already covered most of the content and they’re having the same content repeated in the same way that they found difficult in the first place so my experience of using this approach is that it seemed very different to them and it reinvigorated their interest in maths and they were very positive about......
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...national level in the United States economy. It is recommended that students take ECON 201 before ECON 202. MATH 105 is highly| |recommended but not required. (F,W,S). | |ECON 201 - Prin: Macroeconomics | |Together with ECON 202, this course serves to introduce the student to the basic ideas and concepts of modern economic analysis, and applies| |them to current economic problems, policies and issues. The focus of this course is on macroeconomics: income and wealth, employment, and | |prices at the national level in the United States economy. It is recommended that students take ECON 201 before ECON 202. MATH 105 is highly| |recommended but not required. (F,W,S). | Together with ECON 202, this course serves to introduce the student to the basic ideas and concepts of modern economic analysis, and applies them to current economic problems, policies and issues. The focus of this course is on macroeconomics: income and wealth, employment, and prices at the national level in the United States economy. It is recommended that students take ECON 201 before ECON 202. MATH 105 is highly recommended but not required. (F,W,S). 3.000 Credit hours It is the sole......
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...Goal: Students will use the trigonometric ratios (Sine, Cosine, and Tangent) to measure the real life height of various objects. How: Students will work with one partner, however they both will have to turn in individual projects. Step One Create a clinometer, by following these steps. ▪ Cut out the photocopied protractor. ▪ Glue it to your piece of cardboard. ▪ Cut out the cardboard so that it is the shape of your protractor ▪ Cut a 4-inch piece of string, tape it to the middle of the protractor by your mark. It is important that you tape your string before you tape your straw. ▪ Tape your straw to the top flat end of your protractor. ▪ At the end of the string, tape a couple pennies to it. Your clinometer should look like this: [pic] Step Two Measure the height of the wall using sine, cosine, tangent, and your clinometer. ▪ In order to measure the height of the wall, complete the Clinometer worksheet that is attached to this project sheet. ▪ After you measure the height of the wall, you will measure one more object at school, and one more at home for homework. Step Three Draw a story/cartoon that shows how you used trigonometry to solve the problem......
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...nature. Tessellations: Mathematical Art What is a term used for the tiling a surface without gaps or overlaps? The term is Tessellation. The Math Forum states that “ a tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps” (“What is a Tessellation?”, n.d) Early cultures used tessellations to cover the floors and ceilings of buildings, many of its artistic elements can be found in many early cultures (Hoopes-Myers, 2010). Tessellations are also found in the nature. A perfect example of nature’s tessellation is the honeycomb of the honeybee; there are no gaps or overlaps in its hexagonal shapes. In Ireland, a volcanic episode created tessellations in the landscape of The Giant’s Causeway (“Giant’s Causeway” n.d.). Artists like M. C Escher use tessellations to create fascinating works of art. In his works Escher concentrated on tessellations and repeated forms. Mathematicians and scientists embraced Escher’s works because they involved the concepts of “geometry, logic, space and infinity” (M.C. Escher Biography, n.d.). One doesn’t have to be a mathematician to tessellate but knowing how shapes will fit together helps in creating beautiful tiled images. Tessellations had functionality in ancient cultures, in mathematics, and in today’s real world it is considered a form of art. Tessellation History Historically the art of tessellation can be traced back as far as 4000 BC. The Sumerians decorated their homes......
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...Manual for the GMAT*Exam version 8.0 All rights reserved. No part of this manual may be reproduced for distribution to a third party in any form or by any means, electronic or mechanical, including photocopying, recording, or any information retrieval system, without the prior consent of the publisher, The Princeton Review. This Manual is for the exclusive use of Princeton Review course students and is not legal for resale. GMAT is a registered trademark of the Graduate Management Admission Council. The Princeton Review is not affiliated with Princeton University or the Graduate Management Admission Council. Permission to reprint this material does not constitute review or endorsement by the Educational Testing Service or the Graduate Management Admission Council of this publication as a whole or of any other sample questions or testing information it may contain. Copyright © 2003 by Princeton Review Management, L.L.C. All Rights Reserved. 800.2Review/ www.princetonreview.com ACKNOWLEDGMENTS Thanks to the following for their many contributions to this course manual: Tariq Ahmed, Kristen Azzara, Shon Bayer, John Bergdahl, Marie Dente, Russ Dombrow, Tricia Dublin, Dan Edmonds, Julian Fleisher, Paul Foglino, Alex Freer, John Fulmer, Joel Haber, Effie Hadjiioannou, Sarah Kruchko, Mary Juliano, Jeff Leistner, Sue Lim, Michael Lopez, Stephanie Martin, Chas Mastin, Elizabeth Miller, Colin Mysliwiec, Magda Pecsenye, Dave Ragsdale, “GMAT” Jack Schieffer...
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...methods 1. What is Educational Research? (uploaded 7.17.09) 2. Writing Research Questions (uploaded 7.20.09) 3. Experimental Design (uploaded 7.20.09) ------------------------------------------------- Experimental Design The basic idea of experimental design involves formulating a question and hypothesis, testing the question, and analyzing data. Though the research designs available to educational researchers vary considerably, the experimental design provides a basic model for comparison as we learn new designs and techniques for conducting research. Note: This review is similar to the overview of significance testing, so you will see some of the introductory material on the scientific method repeated in both places. Part I: The Scientific Method We start with familiar territory, the scientific method. To illustrate, we’ll look at a basic research question: How does one thing (variable A) affect another (variable B)? You may have seen variable A referred to as the treatment, or independent, variable, and variable B as the outcome, or dependant, variable. Let’s call variable A parental involvement and lets call variable B a test score. The traditional way to test this question involves: Step 1. Develop a research question. Step 2. Find previous research to support, refute, or suggest ways of testing the question. Step 3. Construct a hypothesis by revising your research question: Hypothesis | Summary | Type | H1: A = B | There is no relationship......
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...Gretchel M. Quinones HUMA 101 WORK SHOP 4 Essay Ricardo Serano Greek science and math the influence: Development of Science Long time ago, people lacked knowledge on why certain things happened. Without scientific answers, like we have today, the Ancient Greeks created their own answers about the world and an individual’s place in it. By doing the research for this essay I had learn a lot of the Greeks contribution in science and math methods. Science in Ancient Greece was based on logical thinking and mathematics. It was also based on technology and everyday life. The arts in Ancient Greece were sculptors and painters. The Greeks wanted to know more about the world, the heavens and themselves. People studied about the sky, sun, moon, and the planets. The Greeks found that the earth was round. Many important people contributed to Greek scientific thought and discoveries. Biology, a very vast and interesting topic, was studied by Hippocrates, Aristotle, Theophrastus, Dioscorides, Pliny, and Galen. These men were among the main researchers of Greek biology who contributed many ideas, theories, and discoveries to science. Some of their discoveries were observations, descriptions, and classifications of the various forms of plants and animal life. Other discussions in biology were natural selection and zoology. All living things were the basic concern of biology. Greek biologists were interested in how living things began, how they developed, how they functioned, and...
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...assemble a cake or build a house is important. The same holds true for evaluating any expression in math. We call this the Order of Operations. In your own words, explain the Order of Operations. • Give an example of an expression to fit this situation in math and an example in real life. • Please share any trick or mnemonic device to help you recall this order or how to use it. A mnemonic device is a memory trick such as using “The quick brown fox jumped over the lazy dog” to learn all the keys on the keyboard. Professor and Class-Good Morning! The Order of Operations- A set of rules for the order in which to solve mathematical problems. The order goes: * and /, + and -. If there are parentheses then work inside them first. Example: Correct: 1+2*3=7. Not Correct: 1+2*3=9 Rule 1: First perform any calculations inside parentheses. Rule 2: Next perform all multiplications and divisions, working from left to right. Rule 3: Lastly, perform all additions and subtractions, working from left to right. (http://www.mathgoodies.com/lessons/vol7/order_operations.html) The Order of Operations is very much like baking a cake, or driving a car, you cant change much in order to have the same outcome. The Mnemonic Device that i use it this : Please Excuse My Dear Aunt Sally-- Meaning.... Parentheses, Exponents, Multiplication, Division, Addition, Subtraction Unit 4 Linear relationships between two quantities can be described by an equation or a graph.......
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...Mathematical Programming The Mathematical Programming Add-in constructs models that can be solved using the Solver Add-in or one of the solution add-ins provided in the collection. When the Math Programming add-in is installed, several new command lines are added to the OR_MM menu. The menu items under the title Math Programming create models of the different types. Selecting an item from this list causes a dialog box to be presented which constructs a mathematical programming model. The models created by the add-in are solved with the Excel Solver, the Jensen Network Solver or the Jensen LP/IP Solver. All are Excel add-ins. Documentation for these programs can be reached by clicking the links on the lower left. The Solver add-in comes with Excel, and it can solve linear programming, integer programming and nonlinear programming models. The Math Programming add-in automatically builds Solver models and calls the computational procedures that solve the problems. All four model types can be can be solved in this way. The Jensen LP/IP Solver solves linear or integer programming problems. It is available for the Linear/Integer Programming and Network Flow Programming model types. The Jensen Network Solver can solve pure or generalized network flow models. Both linear and integer problems can be solved. It is available for the Network Flow Programming or Transportation model types. Parametric analysis can be applied to any of the math programming models. Here one parameter is......
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