KCP e-learning. test user - ability basic maths revision. During your training, we will need to cover some ground using statistics.

Size: px
Start display at page:

Download "KCP e-learning. test user - ability basic maths revision. During your training, we will need to cover some ground using statistics."

Transcription

1 During your training, we will need to cover some ground using statistics. The very mention of this word can sometimes alarm delegates who may not have done any maths or statistics since leaving school. Fear not! It is relatively painless. This Factsheet is designed to provide a refresher for those who feel they would like to get back up to speed. Arithmetic and Functional Operations You are almost certainly familiar with the four main arithmetical operations: Addition sign is + Subtraction sign is - Multiplication sign is x or * Division sign is._. or / e.g. 3._. 4 is the same as 3/4 is the same as 3 = You may be less familiar with some of the functional operations: Squaring sign is 2 This is simply multiplying a number by itself, e.g. 5 2 is the same as 5 x 5 = 25 Square Root sign is Ö This is the opposite of squaring, so, Ö 25 = 5 Throughout your RQTU training you will be able to use a calculator. To calculate a square, say, 5 2 : press 5, then the multiplication key X twice then the equals key = To calculate a square root, say, Ö25: key in the number 25, then press the Ö key

2 Symbols During the training we will use some mathematical shorthand or symbols. The main ones you will need to be familiar with are: X : this will be used for a Raw Score. A Raw Score on a test is simply the number of questions that the candidate got right. X : this is called X bar and stands for the average or mean. N : this is the number of people in a sample, so if we tested 20 graduates we could write N = 20. å : this is the capital Greek letter sigma and tells us to add something up, so, å (X - X) would be telling us to subtract the mean score from a series of raw scores then add up the results. Note here that where something is enclosed in brackets, we do whatever is inside first, then we do what the term outside the brackets tells us to do next. s : this is the lower case Greek letter sigma and is called the Standard Deviation. This is also commonly written as SD. Don t worry about what the Standard Deviation is yet - we ll cover that later. Mathematical Precedence We mentioned above that we always work out the terms within brackets first. In exactly the same way, we use an order of priority when we have an expression with multiple terms: Division and Multiplication take precedence over Addition and Subtraction So, Y = 4 + 8/(3 x 4) Here we multiply the term in the brackets first: 3 x 4 = 12 Then we divide 8 by 12 = but we round this to two decimal places: 0.67 Then we add 4 to 0.67 Therefore: Y = 4.6

3 Now, let s change our expression just a little to: Y = (4 + 8)/(3 x 4) In this case we have 4 plus 8 inside brackets So: = 12 Next we multiply the term in the second brackets: 3 x 4 = 12 Then we divide 12 by 12 = 1 Therefore: Y = 1 Measures of Central Tendency Most of us are familiar with the concept of an average. The average age of postgraduates on an English degree course at a particular university may be years. This average, or mean, is calculated by adding the ages of everybody on the course and then dividing by the number of people on the course. The formula for calculating a mean for a group of people may therefore be expressed as: = This shows that the mean (X) is equal to the sum ( å) of the raw scores (X) divided by the number of people in the group (N). The ages (in years) of 15 students on an English course are given below: 17.9, 18.0, 18.1, 18.4, 18.7, 18.8, 19.2, 19.8, 20.1, 20.5, 21.6, 28.9, 32.4, 39.1, 50.6 The mean age for the group of 15 is therefore given by: X åx N x = = The mean is the most important measure of central tendency, but there are two others which are also used. The median (or middle ) score is the point in a set of scores above which there are exactly half the scores, and below which there are the other half of the scores. In the distribution 1, 3, 5, 7, 9, 11, 13, the middle score of seven indicates the median point at which there are three scores above and three scores below. We obtain the median by arranging the scores in ascending order from the smallest to the greatest score and selecting that point above and below which there are an equal number of scores.

4 The ages (in years) of 15 students on an English Course: 17.9, 18.0, 18.1, 18.4, 18.7, 18.8, 19.2, 19.8, 20.1, 20.5, 21.6, 28.9, 32.4, 39.1, 50.6 The median age of the 15 students on the English course is 19.8 years, because there are exactly seven cases aged less than 19.8 years and seven cases aged more than 19.8 years. If the distribution (ie the set of scores) is made up of an even number of cases, the median is the mid-point between the two middle scores. The median is sometimes a useful measure of central tendency when extreme scores distort the mean. In the example above, the oldest student aged 50.6 years is much older than the others and therefore shifts the mean significantly. For some purposes, therefore, the median (19.8 years) may be a more representative measure of central tendency than the mean (24.14 years). A third measure of central tendency is the mode. The mode is the most frequently occurring score in a distribution. In the distribution 1, 1, 2, 3, 4, 4, 5, 6, 6, 7, 7, 7, 7, 8, 10, 11, 11, the mode is 7, because the score 7 occurs more times than any other. We might be interested in this because it could tell us what the most frequently occurring score was on an ability test.

5 The normal distribution Suppose we measured the height of every 30 year old female in England. If we plotted their heights as a frequency polygon, in other words as a chart showing how many women were found to be a particular height, the resulting chart would look something like the one on the left shown below. If we smoothed the left hand chart out, the curve would look like the picture on the right. This curve is known as the normal distribution. So, we would find that there were very few short people, most of the women would be arounf the average height, currently 1.637m (5 ft 4 1/2 in), and very few would be very tall. We can make similar assumptions in testing. On a particular test, most people will be around the average, with far fewer people at the extremes (very low scores or very high scores).

The Celsius temperature scale is based on the freezing point and the boiling point of water. 12 degrees Celsius below zero would be written as

The Celsius temperature scale is based on the freezing point and the boiling point of water. 12 degrees Celsius below zero would be written as Prealgebra, Chapter 2 - Integers, Introductory Algebra 2.1 Integers In the real world, numbers are used to represent real things, such as the height of a building, the cost of a car, the temperature of

More information

Section 4. Quantitative Aptitude

Section 4. Quantitative Aptitude Section 4 Quantitative Aptitude You will get 35 questions from Quantitative Aptitude in the SBI Clerical 2016 Prelims examination and 50 questions in the Mains examination. One new feature of the 2016

More information

Some of the more common mathematical operations we use in statistics include: Operation Meaning Example

Some of the more common mathematical operations we use in statistics include: Operation Meaning Example Introduction to Statistics for the Social Sciences c Colwell and Carter 206 APPENDIX H: BASIC MATH REVIEW If you are not using mathematics frequently it is quite normal to forget some of the basic principles.

More information

Math Lecture 3 Notes

Math Lecture 3 Notes Math 1010 - Lecture 3 Notes Dylan Zwick Fall 2009 1 Operations with Real Numbers In our last lecture we covered some basic operations with real numbers like addition, subtraction and multiplication. This

More information

Algebra. Mathematics Help Sheet. The University of Sydney Business School

Algebra. Mathematics Help Sheet. The University of Sydney Business School Algebra Mathematics Help Sheet The University of Sydney Business School Introduction Terminology and Definitions Integer Constant Variable Co-efficient A whole number, as opposed to a fraction or a decimal,

More information

Q 1 Find the square root of 729. 6. Squares and Square Roots Q 2 Fill in the blank using the given pattern. 7 2 = 49 67 2 = 4489 667 2 = 444889 6667 2 = Q 3 Without adding find the sum of 1 + 3 + 5 + 7

More information

F78SC2 Notes 2 RJRC. If the interest rate is 5%, we substitute x = 0.05 in the formula. This gives

F78SC2 Notes 2 RJRC. If the interest rate is 5%, we substitute x = 0.05 in the formula. This gives F78SC2 Notes 2 RJRC Algebra It is useful to use letters to represent numbers. We can use the rules of arithmetic to manipulate the formula and just substitute in the numbers at the end. Example: 100 invested

More information

Statistics and parameters

Statistics and parameters Statistics and parameters Tables, histograms and other charts are used to summarize large amounts of data. Often, an even more extreme summary is desirable. Statistics and parameters are numbers that characterize

More information

Algebra 1 Summer Assignment 2018

Algebra 1 Summer Assignment 2018 Algebra 1 Summer Assignment 2018 The following packet contains topics and definitions that you will be required to know in order to succeed in Algebra 1 this coming school year. You are advised to be familiar

More information

Central Tendency - Computing and understanding averages. different in conception and calculation. They represent different notions of the center of a

Central Tendency - Computing and understanding averages. different in conception and calculation. They represent different notions of the center of a Central Tendency The objectives of this lesson are: Understanding measures of central tendency Computing the mean of a set of scores by hand Computing the median for a set of scores by hand Determining/calculating

More information

A constant is a value that is always the same. (This means that the value is constant / unchanging). o

A constant is a value that is always the same. (This means that the value is constant / unchanging). o Math 8 Unit 7 Algebra and Graphing Relations Solving Equations Using Models We will be using algebra tiles to help us solve equations. We will practice showing work appropriately symbolically and pictorially

More information

Chapter. Algebra techniques. Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations.

Chapter. Algebra techniques. Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations. Chapter 2 Algebra techniques Syllabus Content A Basic Mathematics 10% Basic algebraic techniques and the solution of equations. Page 1 2.1 What is algebra? In order to extend the usefulness of mathematical

More information

Math 1 Summer Assignment 2017

Math 1 Summer Assignment 2017 Math 1 Summer Assignment 2017 Assignment Due: Monday, August 28, 2017 Name: The following packet contains topics and definitions that you will be required to know in order to succeed in Math 1 this year.

More information

{ }. The dots mean they continue in that pattern to both

{ }. The dots mean they continue in that pattern to both INTEGERS Integers are positive and negative whole numbers, that is they are;... 3, 2, 1,0,1,2,3... { }. The dots mean they continue in that pattern to both positive and negative infinity. Before starting

More information

Chapter. Numerically Summarizing Data. Copyright 2013, 2010 and 2007 Pearson Education, Inc.

Chapter. Numerically Summarizing Data. Copyright 2013, 2010 and 2007 Pearson Education, Inc. Chapter 3 Numerically Summarizing Data Section 3.1 Measures of Central Tendency Objectives 1. Determine the arithmetic mean of a variable from raw data 2. Determine the median of a variable from raw data

More information

A group of figures, representing a number, is called a numeral. Numbers are divided into the following types.

A group of figures, representing a number, is called a numeral. Numbers are divided into the following types. 1. Number System Quantitative Aptitude deals mainly with the different topics in Arithmetic, which is the science which deals with the relations of numbers to one another. It includes all the methods that

More information

Univariate Statistics. Z-Score

Univariate Statistics. Z-Score Univariate Statistics Z-Score The Sorted Score or Z-Score The standard score or z score of a data value gives the number of standard deviations that it differs from the mean. raw score mean z score = =

More information

Author : Dr. Pushpinder Kaur. Educational Statistics: Mean Median and Mode

Author : Dr. Pushpinder Kaur. Educational Statistics: Mean Median and Mode B.ED. PART- II ACADEMIC SESSION : 2017-2018 PAPER XVIII Assessment for Learning Lesson No. 8 Author : Dr. Pushpinder Kaur Educational Statistics: Mean Median and Mode MEAN : The mean is the average value

More information

Chapter 2. Mean and Standard Deviation

Chapter 2. Mean and Standard Deviation Chapter 2. Mean and Standard Deviation The median is known as a measure of location; that is, it tells us where the data are. As stated in, we do not need to know all the exact values to calculate the

More information

IOP2601. Some notes on basic mathematical calculations

IOP2601. Some notes on basic mathematical calculations IOP601 Some notes on basic mathematical calculations The order of calculations In order to perform the calculations required in this module, there are a few steps that you need to complete. Step 1: Choose

More information

SESSION 5 Descriptive Statistics

SESSION 5 Descriptive Statistics SESSION 5 Descriptive Statistics Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple

More information

Patterns and Relations

Patterns and Relations Where a, b and care integers. a(x.b)2c b:c,a.io ax bc :b,a:o ax=b the farm: P.2: Model and solve problems, concretely, pictorially and symbolically, using linear equations of P.1: Graph and analyze two-variable

More information

MEASURES OF LOCATION AND SPREAD

MEASURES OF LOCATION AND SPREAD MEASURES OF LOCATION AND SPREAD Frequency distributions and other methods of data summarization and presentation explained in the previous lectures provide a fairly detailed description of the data and

More information

ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t

ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t F o r S t u d e n t s E n t e r i n g A l g e b r a Allen Park High School Summer Assignment Algebra Show all work for all problems on a separate sheet

More information

Warm-up: Are accuracy and precision the same thing? (If so do you want to bet the house on it?)

Warm-up: Are accuracy and precision the same thing? (If so do you want to bet the house on it?) Obj: Students will: 1. Distinguish between accuracy and precision. 2. Examine various pieces of lab equipment for their accuracy. 3. Define and identify significant figures. Warm-up: Are accuracy and precision

More information

N= {1,2,3,4,5,6,7,8,9,10,11,...}

N= {1,2,3,4,5,6,7,8,9,10,11,...} 1.1: Integers and Order of Operations 1. Define the integers 2. Graph integers on a number line. 3. Using inequality symbols < and > 4. Find the absolute value of an integer 5. Perform operations with

More information

Section 1.1: Patterns in Division

Section 1.1: Patterns in Division Section 1.1: Patterns in Division Dividing by 2 All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8. Dividing by 4 1. Are the last two digits in your number divisible by 4? 2.

More information

Algebra 2. Outliers. Measures of Central Tendency (Mean, Median, Mode) Standard Deviation Normal Distribution (Bell Curves)

Algebra 2. Outliers. Measures of Central Tendency (Mean, Median, Mode) Standard Deviation Normal Distribution (Bell Curves) Algebra 2 Outliers Measures of Central Tendency (Mean, Median, Mode) Standard Deviation Normal Distribution (Bell Curves) Algebra 2 Notes #1 Chp 12 Outliers In a set of numbers, sometimes there will be

More information

Intermediate Mathematics League of Eastern Massachusetts

Intermediate Mathematics League of Eastern Massachusetts Meet #5 March/April 2005 Intermediate Mathematics League of Eastern Massachusetts Average team score: 86.6 Average meet for the seasion: 95.9 Meet #5 March/April 2005 Category 1 Mystery Meet #5, March/April

More information

ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t

ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t ALLEN PARK HIGH SCHOOL S u m m er A s s e s s m e n t F o r S t u d e n t s E n t e r i n g A l g e b r a This summer packet is intended to be completed by the FIRST DAY of school. This packet will be

More information

UNIT 4 NOTES: PROPERTIES & EXPRESSIONS

UNIT 4 NOTES: PROPERTIES & EXPRESSIONS UNIT 4 NOTES: PROPERTIES & EXPRESSIONS Vocabulary Mathematics: (from Greek mathema, knowledge, study, learning ) Is the study of quantity, structure, space, and change. Algebra: Is the branch of mathematics

More information

The chart below shows the fraction and decimal forms of some rational numbers. Write,, or in each blank to make a true sentence.

The chart below shows the fraction and decimal forms of some rational numbers. Write,, or in each blank to make a true sentence. Study Guide Pages 9 99 Rational Numbers The chart below shows the fraction and decimal forms of some rational numbers. Rational Number 0.7 0.8 Fraction Form Decimal Form.0 0.66. 0.7 0.8 You can compare

More information

GCSE Mathematics Non Calculator Foundation Tier Free Practice Set 1 1 hour 30 minutes ANSWERS. Marks shown in brackets for each question (2)

GCSE Mathematics Non Calculator Foundation Tier Free Practice Set 1 1 hour 30 minutes ANSWERS. Marks shown in brackets for each question (2) MathsMadeEasy 3 GCSE Mathematics Non Calculator Foundation Tier Free Practice Set 1 1 hour 30 minutes ANSWERS Marks shown in brackets for each question Grade Boundaries C D E F G 76 60 47 33 20 Legend

More information

Park Forest Math Team. Meet #3. Algebra. Self-study Packet

Park Forest Math Team. Meet #3. Algebra. Self-study Packet Park Forest Math Team Meet #3 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements 3. Number

More information

Describing Distributions With Numbers

Describing Distributions With Numbers Describing Distributions With Numbers October 24, 2012 What Do We Usually Summarize? Measures of Center. Percentiles. Measures of Spread. A Summary Statement. Choosing Numerical Summaries. 1.0 What Do

More information

5.7 Translating English Sentences into Mathematical Equations and Solving

5.7 Translating English Sentences into Mathematical Equations and Solving 5.7 Translating English Sentences into Mathematical Equations and Solving Mathematical equations can be used to describe many situations in the real world. To do this, we must learn how to translate given

More information

Chapter Three. Deciphering the Code. Understanding Notation

Chapter Three. Deciphering the Code. Understanding Notation Chapter Three Deciphering the Code Mathematics has its own vocabulary. In addition to words, mathematics uses its own notation, symbols that stand for more complicated ideas. Some of these elements are

More information

UNIT 2 MEAN, MEDIAN AND MODE

UNIT 2 MEAN, MEDIAN AND MODE Central Tendencies and Dispersion UNIT 2 MEAN, MEDIAN AND MODE Me Structure 2.0 Introduction 2.1 Objectives 2.2 Symbols Used in Calculation of Measures of Central Tendency 2.3 The Arithmetic Mean 2.3.1

More information

Mathematics Scope and Sequence Sixth Grade

Mathematics Scope and Sequence Sixth Grade Unit Common Core State Standards Approximate Time Frame One: Fractions and Decimals Two: Ratios, Rates, and Proportions 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving

More information

Foundations 5 Curriculum Guide

Foundations 5 Curriculum Guide 1. Review: Natural Numbers...3 2. Reading and Writing Natural Numbers...6 3. Lines, Rays, and Line Segments...8 4. Comparing Natural Numbers... 12 5. Rounding Numbers... 15 6. Adding Natural Numbers...

More information

Measures of Central Tendency

Measures of Central Tendency Measures of Central Tendency Summary Measures Summary Measures Central Tendency Mean Median Mode Quartile Range Variance Variation Coefficient of Variation Standard Deviation Measures of Central Tendency

More information

New Paltz Central School District Mathematics Third Grade

New Paltz Central School District Mathematics Third Grade September - Unit 1: Place Value and Numeration/Addition and Use hundred charts and number lines. Place Value October Subtraction Read and write numbers to 1,000. Pre- What is place value? Order numbers

More information

6th grade Math (5th Grade CAP)

6th grade Math (5th Grade CAP) Davison Community Schools ADVISORY CURRICULUM COUNCIL Phase II, April 20, 2015 6th grade Math (5th Grade CAP) Course Essential Questions: How do we multiply and divide ratios and rates? How does the location

More information

Chapter. Numerically Summarizing Data Pearson Prentice Hall. All rights reserved

Chapter. Numerically Summarizing Data Pearson Prentice Hall. All rights reserved Chapter 3 Numerically Summarizing Data Section 3.1 Measures of Central Tendency Objectives 1. Determine the arithmetic mean of a variable from raw data 2. Determine the median of a variable from raw data

More information

Take the Anxiety Out of Word Problems

Take the Anxiety Out of Word Problems Take the Anxiety Out of Word Problems I find that students fear any problem that has words in it. This does not have to be the case. In this chapter, we will practice a strategy for approaching word problems

More information

Introduction to Statistics for Traffic Crash Reconstruction

Introduction to Statistics for Traffic Crash Reconstruction Introduction to Statistics for Traffic Crash Reconstruction Jeremy Daily Jackson Hole Scientific Investigations, Inc. c 2003 www.jhscientific.com Why Use and Learn Statistics? 1. We already do when ranging

More information

Content Area: MATHEMATICS Grade Level:

Content Area: MATHEMATICS Grade Level: Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship

More information

Data set B is 2, 3, 3, 3, 5, 8, 9, 9, 9, 15. a) Determine the mean of the data sets. b) Determine the median of the data sets.

Data set B is 2, 3, 3, 3, 5, 8, 9, 9, 9, 15. a) Determine the mean of the data sets. b) Determine the median of the data sets. FOUNDATIONS OF MATH 11 Ch. 5 Day 1: EXPLORING DATA VOCABULARY A measure of central tendency is a value that is representative of a set of numerical data. These values tend to lie near the middle of a set

More information

GMAT Arithmetic: Challenge (Excerpt)

GMAT Arithmetic: Challenge (Excerpt) GMAT Arithmetic: Challenge (Excerpt) Jeff Sackmann / GMAT HACKS January 2013 Contents 1 Introduction 2 2 Difficulty Levels 3 3 Problem Solving 4 4 Data Sufficiency 5 5 Answer Key 7 6 Explanations 8 1 1

More information

Radiological Control Technician Training Fundamental Academic Training Study Guide Phase I

Radiological Control Technician Training Fundamental Academic Training Study Guide Phase I Module 1.01 Basic Mathematics and Algebra Part 4 of 9 Radiological Control Technician Training Fundamental Academic Training Phase I Coordinated and Conducted for the Office of Health, Safety and Security

More information

7 = 8 (Type a simplified fraction.)

7 = 8 (Type a simplified fraction.) Student: Date: Assignment: Exponential and Radical Equations 1. Perform the indicated computation. Write the answer in scientific notation. 3. 10 6 10. 3. 4. 3. 10 6 10 = (Use the multiplication symbol

More information

Elementary Statistics

Elementary Statistics Elementary Statistics Q: What is data? Q: What does the data look like? Q: What conclusions can we draw from the data? Q: Where is the middle of the data? Q: Why is the spread of the data important? Q:

More information

additionalmathematicsstatisticsadditi onalmathematicsstatisticsadditionalm athematicsstatisticsadditionalmathem aticsstatisticsadditionalmathematicsst

additionalmathematicsstatisticsadditi onalmathematicsstatisticsadditionalm athematicsstatisticsadditionalmathem aticsstatisticsadditionalmathematicsst additionalmathematicsstatisticsadditi onalmathematicsstatisticsadditionalm athematicsstatisticsadditionalmathem aticsstatisticsadditionalmathematicsst STATISTICS atisticsadditionalmathematicsstatistic

More information

GMAT-Arithmetic-3. Descriptive Statistics and Set theory

GMAT-Arithmetic-3. Descriptive Statistics and Set theory GMAT-Arithmetic-3 Descriptive Statistics and Set theory Descriptive Statistics 1). If S is a set of consecutive integers, what is the standard deviation of S? (1) Set S contains 23 terms (2) The median

More information

8.1 Frequency Distribution, Frequency Polygon, Histogram page 326

8.1 Frequency Distribution, Frequency Polygon, Histogram page 326 page 35 8 Statistics are around us both seen and in ways that affect our lives without us knowing it. We have seen data organized into charts in magazines, books and newspapers. That s descriptive statistics!

More information

Pre-Lab 0.2 Reading: Measurement

Pre-Lab 0.2 Reading: Measurement Name Block Pre-Lab 0.2 Reading: Measurement section 1 Description and Measurement Before You Read Weight, height, and length are common measurements. List at least five things you can measure. What You

More information

Northwest High School s Algebra 1

Northwest High School s Algebra 1 Northwest High School s Algebra 1 Summer Review Packet 2011 DUE WEDNESDAY, SEPTEMBER 2, 2011 Student Name This packet has been designed to help you review various mathematical topics that will be necessary

More information

32. SOLVING LINEAR EQUATIONS IN ONE VARIABLE

32. SOLVING LINEAR EQUATIONS IN ONE VARIABLE get the complete book: /getfulltextfullbook.htm 32. SOLVING LINEAR EQUATIONS IN ONE VARIABLE classifying families of sentences In mathematics, it is common to group together sentences of the same type

More information

Ratios and Proportional Relationships

Ratios and Proportional Relationships Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio

More information

+ 37,500. Discuss with your group how do you THINK you would represent 40 degrees below 0 as an integer?

+ 37,500. Discuss with your group how do you THINK you would represent 40 degrees below 0 as an integer? 6.1 Integers *I can use positive and negative numbers to show amounts in real-world situations and explain what the number 0 means in those situations. *I can recognize opposite signs of numbers as indicating

More information

6 th Grade Remediation Guide

6 th Grade Remediation Guide 6 th Grade Remediation Guide Focused remediation helps target the skills students need to more quickly access and practice on-grade level content. This chart is a reference guide for teachers to help them

More information

Alex s Guide to Word Problems and Linear Equations Following Glencoe Algebra 1

Alex s Guide to Word Problems and Linear Equations Following Glencoe Algebra 1 Alex s Guide to Word Problems and Linear Equations Following Glencoe Algebra 1 What is a linear equation? It sounds fancy, but linear equation means the same thing as a line. In other words, it s an equation

More information

Numbers and Operations Review

Numbers and Operations Review C H A P T E R 5 Numbers and Operations Review This chapter reviews key concepts of numbers and operations that you need to know for the SAT. Throughout the chapter are sample questions in the style of

More information

Chapter 1. Making algebra orderly with the order of operations and other properties Enlisting rules of exponents Focusing on factoring

Chapter 1. Making algebra orderly with the order of operations and other properties Enlisting rules of exponents Focusing on factoring In This Chapter Chapter 1 Making Advances in Algebra Making algebra orderly with the order of operations and other properties Enlisting rules of exponents Focusing on factoring Algebra is a branch of mathematics

More information

9. TRANSFORMING TOOL #2 (the Multiplication Property of Equality)

9. TRANSFORMING TOOL #2 (the Multiplication Property of Equality) 9 TRANSFORMING TOOL # (the Multiplication Property of Equality) a second transforming tool THEOREM Multiplication Property of Equality In the previous section, we learned that adding/subtracting the same

More information

MALLOY PSYCH 3000 MEAN & VARIANCE PAGE 1 STATISTICS MEASURES OF CENTRAL TENDENCY. In an experiment, these are applied to the dependent variable (DV)

MALLOY PSYCH 3000 MEAN & VARIANCE PAGE 1 STATISTICS MEASURES OF CENTRAL TENDENCY. In an experiment, these are applied to the dependent variable (DV) MALLOY PSYCH 3000 MEAN & VARIANCE PAGE 1 STATISTICS Descriptive statistics Inferential statistics MEASURES OF CENTRAL TENDENCY In an experiment, these are applied to the dependent variable (DV) E.g., MEASURES

More information

Grade 6_ Math. Alignment of Writing Strategies with Selected Common Core Standards. Essential Questions Dianne McCune, Ph.D. Grade 6.

Grade 6_ Math. Alignment of Writing Strategies with Selected Common Core Standards. Essential Questions Dianne McCune, Ph.D. Grade 6. Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between

More information

Describing Distributions

Describing Distributions Describing Distributions With Numbers April 18, 2012 Summary Statistics. Measures of Center. Percentiles. Measures of Spread. A Summary Statement. Choosing Numerical Summaries. 1.0 What Are Summary Statistics?

More information

6th Grade Math Standards and I Can Statements

6th Grade Math Standards and I Can Statements 6th Grade Math Standards and I Can Statements Standard 6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of

More information

School of Distance Education MATHEMATICAL TOOLS FOR ECONOMICS - I I SEMESTER COMPLEMENTARYCOURSE BA ECONOMICS. (CUCBCSS Admission)

School of Distance Education MATHEMATICAL TOOLS FOR ECONOMICS - I I SEMESTER COMPLEMENTARYCOURSE BA ECONOMICS. (CUCBCSS Admission) MATHEMATICAL TOOLS FOR ECONOMICS - I I SEMESTER COMPLEMENTARYCOURSE BA ECONOMICS (CUCBCSS - 014 Admission) UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION Calicut university P.O, Malappuram Kerala,

More information

Descriptive Statistics-I. Dr Mahmoud Alhussami

Descriptive Statistics-I. Dr Mahmoud Alhussami Descriptive Statistics-I Dr Mahmoud Alhussami Biostatistics What is the biostatistics? A branch of applied math. that deals with collecting, organizing and interpreting data using well-defined procedures.

More information

CH 6 THE ORDER OF OPERATIONS

CH 6 THE ORDER OF OPERATIONS 43 CH 6 THE ORDER OF OPERATIONS Introduction T here are a variety of operations we perform in math, including addition, multiplication, and squaring. When we re confronted with an expression that has a

More information

LESSON 4-5 THE LAW OF COMMUTATIVITY

LESSON 4-5 THE LAW OF COMMUTATIVITY LESSON 4-5 THE LAW OF COMMUTATIVITY Axioms [AXE ee ums] are things we assume to be true because they seem obvious but we cannot prove them. Say with me: axiom. A. For example, if three plus four is seven,

More information

Student Name: OSIS#: DOB: / / School: Grade:

Student Name: OSIS#: DOB: / / School: Grade: : Ratios and Proportional Relationships Column : In preparation for the IEP meeting, check the standards the student has already met. Column : In preparation for the IEP meeting, check the standards the

More information

Third Grade Report Card Rubric 1 Exceeding 2 Meeting 3 Developing 4 Area of Concern

Third Grade Report Card Rubric 1 Exceeding 2 Meeting 3 Developing 4 Area of Concern Concepts Assessed by Unit and Trimester Units 5, 6, 7, 8 Units 5, 6, 7 Units 5, 6, 7, 8 1 Exceeding 2 Meeting 3 Developing 4 Area of Concern Student exceeds expectations of this unit Student is meeting

More information

Finite Mathematics : A Business Approach

Finite Mathematics : A Business Approach Finite Mathematics : A Business Approach Dr. Brian Travers and Prof. James Lampes Second Edition Cover Art by Stephanie Oxenford Additional Editing by John Gambino Contents What You Should Already Know

More information

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression 1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression

More information

THE SUMMATION NOTATION Ʃ

THE SUMMATION NOTATION Ʃ THE SUMMATION NOTATION Ʃ Single Subscript Notation Most of the calculations we perform in statistics are repetitive operations on lists of numbers. For example, we compute the sum of a set of numbers,

More information

7.12 The student will represent relationships with tables, graphs, rules, and words.

7.12 The student will represent relationships with tables, graphs, rules, and words. 7.12 The student will represent relationships with tables, graphs, rules, and words. HINTS & NOTES Relation- is a set of ordered pairs. Remember to always start from the origin. Origin is (0,0) Move horizontally

More information

Agile Mind Mathematics 6 Scope and Sequence, Common Core State Standards for Mathematics

Agile Mind Mathematics 6 Scope and Sequence, Common Core State Standards for Mathematics In the three years preceding Grade 6, students have acquired a strong foundation in numbers and operations, geometry, measurement, and data. They are fluent in multiplication of multi-digit whole numbers

More information

Descriptive Statistics C H A P T E R 5 P P

Descriptive Statistics C H A P T E R 5 P P Descriptive Statistics C H A P T E R 5 P P 1 1 0-130 Graphing data Frequency distributions Bar graphs Qualitative variable (categories) Bars don t touch Histograms Frequency polygons Quantitative variable

More information

Unit Two Descriptive Biostatistics. Dr Mahmoud Alhussami

Unit Two Descriptive Biostatistics. Dr Mahmoud Alhussami Unit Two Descriptive Biostatistics Dr Mahmoud Alhussami Descriptive Biostatistics The best way to work with data is to summarize and organize them. Numbers that have not been summarized and organized are

More information

Solving Equations. Lesson Fifteen. Aims. Context. The aim of this lesson is to enable you to: solve linear equations

Solving Equations. Lesson Fifteen. Aims. Context. The aim of this lesson is to enable you to: solve linear equations Mathematics GCSE Module Four: Basic Algebra Lesson Fifteen Aims The aim of this lesson is to enable you to: solve linear equations solve linear equations from their graph solve simultaneous equations from

More information

are the objects described by a set of data. They may be people, animals or things.

are the objects described by a set of data. They may be people, animals or things. ( c ) E p s t e i n, C a r t e r a n d B o l l i n g e r 2016 C h a p t e r 5 : E x p l o r i n g D a t a : D i s t r i b u t i o n s P a g e 1 CHAPTER 5: EXPLORING DATA DISTRIBUTIONS 5.1 Creating Histograms

More information

Algebra One Dictionary

Algebra One Dictionary Algebra One Dictionary Page 1 of 17 A Absolute Value - the distance between the number and 0 on a number line Algebraic Expression - An expression that contains numbers, operations and at least one variable.

More information

Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities)

Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities) Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities) By Scott Fallstrom and Brent Pickett The How and Whys Guys This work is licensed under a Creative Commons

More information

To: Amanda From: Daddy Date: 2004 February 19 About: How to solve math problems

To: Amanda From: Daddy Date: 2004 February 19 About: How to solve math problems to Amanda p.1 To: Amanda From: Daddy Date: 2004 February 19 About: How to solve math problems There are 4 steps in solving the kind of math problem you showed me. I'll list the steps first, then explain

More information

Lesson 1.3: Algebra and Scientific Notation with Small Numbers

Lesson 1.3: Algebra and Scientific Notation with Small Numbers Specific Objectives Students will understand that in algebra, numbers and variables can be combined to produce expressions, equations and inequalities. numbers between 0 and 1 can be written using scientific

More information

Correlation of Common Core Standards (06/02/10) Grade 6 to UCSMP Pre-Transition Mathematics, 2008

Correlation of Common Core Standards (06/02/10) Grade 6 to UCSMP Pre-Transition Mathematics, 2008 Correlation of Common Core Standards (06/02/10) Grade 6 to UCSMP Pre-Transition Mathematics, 2008 Final Common Core Standards (06/02/10) Lessons Page References Ratios and Proportional Relationships Understand

More information

Vocabulary. Compute fluently with multi-digit numbers and find common factors and multiples.

Vocabulary. Compute fluently with multi-digit numbers and find common factors and multiples. 6 th Grade Math Pacing Guide Week Domain Cluster Standard Essential Questions 1 Pre- Test/Beginning of the Year Activities 2 Review Review 5 th Grade Standards 3 Review Review 5 th Grade Standards 4 The

More information

No Solution Equations Let s look at the following equation: 2 +3=2 +7

No Solution Equations Let s look at the following equation: 2 +3=2 +7 5.4 Solving Equations with Infinite or No Solutions So far we have looked at equations where there is exactly one solution. It is possible to have more than solution in other types of equations that are

More information

Agile Mind Mathematics 6 Scope and Sequence, Common Core State Standards for Mathematics

Agile Mind Mathematics 6 Scope and Sequence, Common Core State Standards for Mathematics In the three years preceding Grade 6, students have acquired a strong foundation in numbers and operations, geometry, measurement, and data. They are fluent in multiplication of multi- digit whole numbers

More information

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Variable expression. Evaluate a variable expression

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Variable expression. Evaluate a variable expression 1 Words to Review Give an example of the vocabulary word. Numerical expression 5 1 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression

More information

CHAPTER 5: EXPLORING DATA DISTRIBUTIONS. Individuals are the objects described by a set of data. These individuals may be people, animals or things.

CHAPTER 5: EXPLORING DATA DISTRIBUTIONS. Individuals are the objects described by a set of data. These individuals may be people, animals or things. (c) Epstein 2013 Chapter 5: Exploring Data Distributions Page 1 CHAPTER 5: EXPLORING DATA DISTRIBUTIONS 5.1 Creating Histograms Individuals are the objects described by a set of data. These individuals

More information

Lesson/Unit Plan Name: Algebraic Expressions Identifying Parts and Seeing Entities. as both a single entity and a sum of two terms.

Lesson/Unit Plan Name: Algebraic Expressions Identifying Parts and Seeing Entities. as both a single entity and a sum of two terms. Grade Level/Course: Grade 6 Lesson/Unit Plan Name: Algebraic Expressions Identifying Parts and Seeing Entities Rationale/Lesson Abstract: This lesson focuses on providing students with a solid understanding

More information

WSMA Algebra - Expressions Lesson 14

WSMA Algebra - Expressions Lesson 14 Algebra Expressions Why study algebra? Because this topic provides the mathematical tools for any problem more complicated than just combining some given numbers together. Algebra lets you solve word problems

More information

INTERMEDIATE 1 The Maths Pathway

INTERMEDIATE 1 The Maths Pathway Objective Code Objective Exemplification Links to Prior Objectives Resources, Enrichment, Notes etc. I1.1 Order positive and negative integers, decimals and ; use the number line as a model for ordering

More information

Common Core Math Curriculum Map

Common Core Math Curriculum Map Module 1 - Math Address Standards by: 9/3/2013 Test: 9/16-27/2013 Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.5 * 6.NS.6 * 6.NS.7 * Understand that positive

More information

MATH 117 Statistical Methods for Management I Chapter Three

MATH 117 Statistical Methods for Management I Chapter Three Jubail University College MATH 117 Statistical Methods for Management I Chapter Three This chapter covers the following topics: I. Measures of Center Tendency. 1. Mean for Ungrouped Data (Raw Data) 2.

More information

Quadratic Equations Part I

Quadratic Equations Part I Quadratic Equations Part I Before proceeding with this section we should note that the topic of solving quadratic equations will be covered in two sections. This is done for the benefit of those viewing

More information