6 th Grade Math. Full Curriculum Book. Sample file. A+ Interactive Math (by A+ TutorSoft, Inc.)

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1 6 th Grade Math Full Curriculum Book Release 7 A+ Interactive Math (by A+ TutorSoft, Inc.) info@aplustutorsoft.com Page 3 of 518

2 Copyright 2014 A+ TutorSoft Inc., All Rights Reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical method, without the prior written permission of A+ TutorSoft Inc. Printed in the United States of America 2011, 2012, 2013, 2014 Page 4 of 518

3 ABOUT THE CURRICULUM BOOK, This book is a comprehensive math curriculum book for the 6 th grade math. It contains easy to understand and fun math lessons that teach various math concepts with appropriate visuals and text. We recommend that you use the Workbook (Worksheets, Exams and Answer Keys) available from A+ Interactive Math to supplement this curriculum book. The Workbook contains worksheets for each lesson in the curriculum book and exam for each chapter along with the answer keys. It allows your student to practice problem solving and prepare for exams. This book offers the following key features: Formula reference sheets. Concise and "to-the-point" lessons that explain math concepts. Demonstration of concepts with sample problems to ensure your student fully understands how to apply concepts to real world math problems. The main subject areas covered in this book are: 1. Fractions, Decimal Numbers and Percentages Converting Fractions, Decimal Numbers & Percents Operations with Fractions and Decimal Numbers Operations with Mixed Numbers Percents, Fractions, and Decimals in Everyday Life 2. Positive and Negative Numbers 3. The Number Line and Absolute Value 4. Ratios and Proportions 5. Exponents, Roots and Scientific Notation 6. Algebra - Variables 7. Algebra - Real Numbers 8. Algebra - The Coordinate Plane 9. Algebra - Linear Equations and Formulas 10. Geometry - Angles and Polygons 11. Geometry - Circles and Solid Shapes 12. Measurements and Conversions 13. Graphs - Collecting and Displaying Data 14. Basic Statistics 15. Probability Page 5 of 518

4 Acknowledgement: A+ TutorSoft would like to thank all the individuals who helped research, write, develop, edit, and launch our Math Curriculum products. Countless weeks, years, and months have been devoted to the production of A+ TutorSoft Interactive Math Curriculum and our printed texts; for this we thank everyone who contributed in making these products a reality. Page 6 of 518

5 Fractions: Quick Reference Guide Decimal Numbers: Does not change the value = 0.35 Percentages: Percent out of 100 Percent sign % Page 7 of 518

Division Terms: Number Conversions: Converting Fractions into Decimal Numbers 1. Multiply denominator by a # to get 10, 100, 1,000 2. Multiply numerator by that # 3. Write down numerator only 4.

6 Division Terms: Number Conversions: Converting Fractions into Decimal Numbers 1. Multiply denominator by a # to get 10, 100, 1, Multiply numerator by that # 3. Write down numerator only 4. Put decimal point one place from right for every 0 in denominator Converting Decimal Numbers into Fractions 1. Write decimal number over 1 2. Move decimal point to far right of numerator 3. Add a 0 in denominator for every number after decimal point 4. Simplify if needed To Convert a Percent into a Decimal Number 1. Remove the percent sign 2. Move decimal point 2 places to left To Convert a Decimal Number into a Percent 1. Move decimal point 2 places to right 2. Add the percent sign To Convert a Percent into a Fraction 1. Remove the percent sign 2. Put number over Simplify, if necessary To Convert a Fraction into a Percent 1. Multiply denominator by some number to equal Multiply numerator by that same number 3. Write just the numerator 4. Add the percent sign Page 8 of 518

$Multiply denominators 3. Simplify, if necessary Dividing Fractions 1. Invert second fraction 2. Multiply numerators 3.$

7 Convert Mixed Fractions to Improper Fractions 1. Multiply whole number by denominator 2. Add numerator 3. Put sum over denominator GCF largest # that divides evenly into 2 or more #s LCM smallest # that is a multiple of 2 or more #s LCD the least common multiple of the denominators Fraction Operations: Multiplying Fractions 1. Multiply numerators 2. Multiply denominators 3. Simplify, if necessary Dividing Fractions 1. Invert second fraction 2. Multiply numerators 3. Multiply denominators 4. Simplify, if necessary Page 9 of 518

8 Adding Mixed Fractions 1. Add the whole numbers 2. If like denominators, add numerators and put over like denominator. 3. If unlike denominators, make equivalent fractions using LCD, then add numerators and put over like denominator. Subtracting Mixed Fractions 1. Subtract the whole numbers 2. If like denominators, subtract numerators and put over denominator. 3. If unlike denominators, make equivalent fractions using LCD, then subtract numerators and put over like denominator. Equivalent Fractions: Positive and Negative Integers: Integer number without a fractional part Positive Integers whole numbers greater than 0 {1, 2, 3, 4, 5, } Negative Integers numbers less than 0 {-1, -2, -3, -4, -5, } Adding and Subtracting: #1. Positive + Positive = Positive #2. Negative + Negative = Negative #3. Positive + Negative = Sign of larger number Multiplying: Rule 1: Like signs become positive. Page 10 of 518

Positive Positive = Positive Negative Negative = Positive Rule 2: Unlike signs become negative.

9 Positive x Positive = Positive Negative x Negative = Positive Rule 2: Unlike signs become negative. Positive x Negative = Negative Negative x Positive = Negative Dividing: Rule 1: Like signs become positive. Positive Positive = Positive Negative Negative = Positive Rule 2: Unlike signs become negative. Positive Negative = Negative Negative Positive = Negative Absolute Value: Absolute Value Absolute Value 5 5 Absolute Value -5 5 the number itself without regard to its sign distance from the origin will always be positive Ratio and Proportions: Ratio a way to compare 2 things Page 11 of 518

Equivalent Ratios 2 or more ratios with the same value Proportions say 2 ratios are equivalent To find out if these ratios are proportional, cross multiply!

10 Equivalent Ratios 2 or more ratios with the same value Proportions say 2 ratios are equivalent To find out if these ratios are proportional, cross multiply! x 1 = 8 Cross products equal x 2 = 8 4:8 = 1:2 Exponents: Exponent shorthand for repeated multiplication, or how many times a number is multiplied by itself Order of Operations: Please Excuse My Dear Aunt Sally (PEMDAS) Parentheses, Exponents, Multiplication, Division, Addition and Subtraction Rules of Exponents: Page 12 of 518

11 Powers of 3: Page 13 of 518

and Cube Roots: Cubing a Number Cube Root Multiply that number by itself 3 times

12 Square and Square Roots: Squaring a Number Square Root Multiply that number by itself The number that can be multiplied by itself to get the original number Cube and Cube Roots: Cubing a Number Cube Root Multiply that number by itself 3 times The number that can be multiplied by itself 3 times to get the original number Page 14 of 518

Powers of 10: Variables, Expressions and Equations:

Equation a letter that represents an unknown value

have different variables or are raised to different

statement that says 2 things are equal Converting

13 Powers of 10: Variables, Expressions and Equations: Variable Like Terms Unlike Terms Expression Equation a letter that represents an unknown value have the same variables raised to the same power have different variables or are raised to different powers a group of terms separated by operators a statement that says 2 things are equal Converting Common Verbal Statements into Mathematical Statements: Page 15 of 518

1415926 The Coordinate Plane: The Coordinate Plane formed by 2 intersecting and

14 Real Numbers: Real Numbers Whole Numbers 1, 2, 3, 4, Positive Integers 1, 2, 3, 4, Negative Integers -1, -2, -3, -4, Rational Numbers 1.75 and.3333 Irrational Numbers = The Coordinate Plane: The Coordinate Plane formed by 2 intersecting and perpendicular number lines Ordered Pair a set of coordinates on a coordinate plane (x, y) Page 16 of 518

Linear Equations: Linear Relation a relationship between the x and y values, which results in a straight line Linear Equation an equation for a straight line Linear Equation y = 2x +1 Linear Pattern

15 Linear Equations: Linear Relation a relationship between the x and y values, which results in a straight line Linear Equation an equation for a straight line Linear Equation y = 2x +1 Linear Pattern a change in one value results in a change in the other value, resulting in a line that repeats indefinitely in both directions How to identify linear equations: 1. Has only 1 or 2 variables 2. Variables cannot have an exponent greater than 1 3. Variables cannot be in denominator of a fraction 4. When plotting a few ordered pairs that make linear equation true, all points for this same linear equation will be on the line. Special Linear Equations have only 1 variable x = 3 and y = 7 Formula an equation that expresses a relationship among 2 or more quantities Numerical Equations have only numbers (2 + 3 = 5) Algebraic Equations have numbers and at least 1 variable 2 + y = 5 y = 3 How to Solve Linear Equations with One Variable 1. Keep the equation balanced 2. Get variable alone on one side 3. Use the inverse operation Linear Inequality: Page 17 of 518

16 Linear Inequality a statement that has infinite solutions x + 2 > 7 x > 5 How to Solve Linear Inequalities with One Variable 1. Keep both sides balanced 2. Get variable alone on one side 3. Use the inverse operation Angles: Geometry Angles Protractor studies size, shape & position of figures and the properties of space. amount of rotation that separates two rays a tool that measures angles Complementary Angles sum of measures = 90º Page 18 of 518

17 Supplementary Angles sum of measures = 180º Vertical Angles opposite angles of 2 intersecting lines Types of Angles: Polygons: Page 19 of 518

571 o 900 o Octagon 8 8 135 o 1080 o Names

18 Triangles: Names Properties of Polygons Chart Total Sides Total Angles Interior Angle of Regular Polygons Sum of Angles Triangle o 180 o Quadrilateral o 360 o Pentagon o 540 o Hexagon o 720 o Heptagon o 900 o Octagon o 1080 o Names of Triangles based on Equal Edges/Angles Page 20 of 518

19 Names of Triangles based on Type of Angle Quadrilaterals: Quadrilateral quad means four, lateral means sides any 2D shape that has 4 straight edges angles add up to 360º Circles: Page 21 of 518

20 Spheres: Sphere 3D solid shape, where all the points are the same distance from the center. Area Surface Area Volume total area of the surface of a 2D shape total area of the surface of a 3D shape the amount of space inside a 3D shape Volume = (4/3) r³ Cylinders: Cylinder 3D solid shape with 2 parallel bases, circular or elliptical, connected by a curved surface. Volume of a Sphere Page 22 of 518

21 Rectangular Prisms: Rectangular Prism 3D solid shape formed by 6 rectangular faces joined along their edges. Page 23 of 518

22 Measurements: Time: Mass and Weight: Mass Weight how much matter something has how much gravity is pulling on something U.S. Conversion Chart for Weight (Mass) 1 pound = 16 ounces 1 Ton = 2,000 pounds = 32,000 ounces Page 24 of 518

Metric Conversion Chart for Weight (Mass) 1 kilogram = 1,000 grams 1 Metric ton = 1,000 kilograms = 1,000,000 grams

Conversion Chart for Length 1 foot = 12 inches 1 yard = 3 feet = 36 inches 1 mile = 1,760 yards = 5,280 feet = 63,360

kilometer = 1,000 meters = 100,000 centimeters = 1,000,000 millimeters Converting Celsius into Fahrenheit: Converting

23 Metric Conversion Chart for Weight (Mass) 1 kilogram = 1,000 grams 1 Metric ton = 1,000 kilograms = 1,000,000 grams Length: Temperature: U.S. Conversion Chart for Length 1 foot = 12 inches 1 yard = 3 feet = 36 inches 1 mile = 1,760 yards = 5,280 feet = 63,360 inches Metric Conversion Chart for Length 1 centimeter = 10 millimeters 1 meter = 100 centimeters = 1,000 millimeters 1 kilometer = 1,000 meters = 100,000 centimeters = 1,000,000 millimeters Converting Celsius into Fahrenheit: Converting Fahrenheit into Celsius: Volume: U.S. Conversion Chart for Volume 1 cup = 8 fluid ounces 1 pint = 2 cups = 16 fluid ounces 1 quart = 2 pints = 4 cups = 32 fluid ounces 1 gallon = 4 quart = 8 pints = 16 cups = 128 fluid ounces Page 25 of 518

24 Metric Conversion Chart for Volume 1 liter = 1,000 milliliters Common Conversion Factors: Rate and Distance: Rate a ratio between 2 measurements with different units Speed how fast an object is going a ratio of distance over time Distance Formula distance = rate x time d = rt Graphs: Graphs visual tools that help us read data quickly Page 26 of 518

Stem and Leaf Plot compares frequency Why Learn about Graphs?

Many important decisions are made using data that is presented using graphs.

25 Stem and Leaf Plot compares frequency Why Learn about Graphs? Graphs become an increasing important part of one s life. Many important decisions are made using data that is presented using graphs. Graphs help you read data easier and quicker while highlighting key points and trends that are important. Surveys and Experiments: Surveys a methodology that gathers data from a sample population about a specific topic Experiment a controlled test that studies cause and effect Basic Statistics: Statistics the science of collecting, analyzing, presenting and interpreting data. Page 27 of 518

Median Middle sounds like Medium Mode Most Common Model Mean Average Sum of numbers How many numbers Statistical Range the difference between the lowest and highest valued

Combinations the chance that something is going to happen the ability to accurately predict an event the product of a series of descending numbers, excluding the number 0.

26 Median Middle sounds like Medium Mode Most Common Model Mean Average Sum of numbers How many numbers Statistical Range the difference between the lowest and highest valued numbers The Basic Counting Principal used to find the number of possible outcomes Probability: Probability Probability Factorials Permutations Permutations Combinations Combinations the chance that something is going to happen the ability to accurately predict an event the product of a series of descending numbers, excluding the number 0. the rearrangement of things in all possible orders the order is important AB BA the collection of things, in which the order doesn t matter the order is not important AB = BA Page 28 of 518

27 TABLE OF CONTENTS Chapter 1 Fractions, Decimal Numbers and Percentages.. 33 Chapter 1 1 Converting Fractions, Decimal Numbers & Percentages 34 Chapter Fractions Review 35 Chapter Decimal Numbers Review 38 Chapter Percentages Review. 42 Chapter Converting Fractions into Decimal Numbers. 45 Chapter Converting Decimal Numbers into Fractions. 49 Chapter Converting Decimal Numbers into Percents. 52 Chapter Converting Percents into Decimal Numbers. 54 Chapter Converting Percents into Fractions 57 Chapter Converting Fractions to Percents 60 Chapter 1 2 Operations with Fractions and Decimal Numbers. 65 Chapter The Greatest Common Factor Chapter The Least Common Multiple Chapter The Least Common Denominator. 71 Chapter Adding Fractions Chapter Adding Decimal Numbers Chapter Subtracting Fractions Chapter Subtracting Decimal Numbers 88 Chapter Multiplying Fractions 91 Chapter Multiplying Decimal Numbers. 93 Chapter Dividing Fractions.. 97 Chapter Dividing Decimal Numbers Chapter 1 3 Operations with Mixed Numbers 104 Chapter Mixed Numbers Review Chapter Converting Mixed Numbers into Fractions 108 Chapter Converting Fractions into Mixed Numbers 110 Chapter Adding Mixed Numbers Chapter Subtracting Mixed Numbers Chapter 1 4 Percents, Fractions, and Decimals in Everyday Life 123 Chapter Working with Percents in Everyday Life Chapter Working with Fractions in Everyday Life Chapter Working with Decimal Numbers in Everyday Life 135 Chapter 2 Positive and Negative Numbers 138 Chapter 2 1 Positive and Negative Numbers Review Chapter 2 2 Adding Positive and Negative Numbers 142 Chapter 2 3 Subtracting Positive and Negative Numbers 146 Chapter 2 4 Multiplying Positive and Negative Numbers. 151 Chapter 2 5 Dividing Positive and Negative Numbers. 154 Chapter 3 The Number Line and Absolute Value 156 Chapter 3 1 Number Line Review Page 29 of 518

28 Chapter 3 2 Comparing and Ordering Numbers on a Number Line. 160 Chapter 3 3 Comparing and Ordering Fractions on a Number Line. 162 Chapter 3 4 Comparing and Ordering Decimals on a Number Line. 165 Chapter 3 5 Absolute Value Review Chapter 3 6 Finding the Absolute Value Chapter 3 7 Finding the Distance using the Absolute Value 172 Chapter 4 Ratios and Proportions Chapter 4 1 Introduction to Ratios. 176 Chapter 4 2 Equivalent Ratios Chapter 4 3 Ratios in Simplest Form 182 Chapter 4 4 Finding Ratios in Simplified Form 185 Chapter 4 5 Introduction to Proportions 188 Chapter 4 6 Finding the Missing Number in a Proportion Chapter 5 Exponents, Roots and Scientific Notation 195 Chapter 5 1 Introduction to Exponents. 196 Chapter 5 2 Basic Rules of Exponents. 199 Chapter 5 3 Laws of Exponents. 204 Chapter 5 4 Negative Exponents Chapter 5 5 Squares and Square Roots Chapter 5 6 Cubes and Cube Roots. 220 Chapter 5 7 Simplifying Square Roots Chapter 5 8 Fractional Exponents. 227 Chapter 5 9 Simplifying Exponential Expressions Chapter 5 10 Evaluating Exponential Expressions. 235 Chapter 5 11 Powers of Chapter 5 12 Understanding Scientific Notation. 242 Chapter 6 Algebra - Variables 244 Chapter 6 1 Variables Review 245 Chapter 6 2 Like and Unlike Terms Chapter 6 3 Canceling Variables Chapter 6 4 Addition with Variables Chapter 6 5 Subtraction with Variables Chapter 6 6 Multiplication with Variables. 256 Chapter 6 7 Division with Variables Chapter 6 8 Expressions and Equations. 262 Chapter 6 9 Writing Expressions and Equations 264 Chapter 6 10 Word Problems with Variables Chapter 6 11 Evaluating Expressions with Variables 271 Chapter 7 - Algebra - Real Numbers 274 Chapter 7 1 Real Numbers Review. 275 Chapter 7 2 Properties of Real Numbers 277 Chapter 7 3 Order of Operations. 281 Chapter 8 - Algebra - The Coordinate Plane 283 Chapter 8 1 The Coordinate Plane 284 Chapter 8 2 Graphing Points on a Coordinate Plane. 290 Page 30 of 518

29 Chapter 8 3 Graphing Linear Relations 297 Chapter 8 4 Graphing Linear Relations using a t-table 302 Chapter 8 5 Making Predictions from Linear Patterns Chapter 9 - Algebra - Linear Equations and Formulas Chapter 9 1 Introduction to Linear Equations Chapter 9 2 Writing Equations and Formulas Chapter 9 3 Problem Solving using Formulas. 328 Chapter 9 4 Linear Equations with One Variable 331 Chapter 9 5 Writing Linear Equations with One Variable Chapter 9 6 Solving Linear Equations with One Variable. 337 Chapter 9 7 Linear Inequalities with One Variable. 339 Chapter 9 8 Solving Linear Inequalities with One Variable 341 Chapter 10 Geometry - Angles and Polygons Chapter 10 1 Angles Review Chapter 10 2 Polygons Review Chapter 10 3 Complementary Angles Chapter 10 4 Supplementary Angles Chapter 10 5 Vertical Angles Chapter 10 6 Triangles 367 Chapter 10 7 Quadrilaterals Chapter 10 8 Finding Missing Angles - Part A 374 Chapter 10 9 Finding Missing Angles - Part B Chapter 11 Geometry - Circles and Solid Shapes Chapter 11 1 The Circle Chapter 11 2 Circumference of a Circle 390 Chapter 11 3 Area of a Circle Chapter 11 4 Spheres Chapter 11 5 Surface Area of a Sphere Chapter 11 6 Volume of a Sphere Chapter 11 7 Cylinders 403 Chapter 11 8 Surface Area of a Cylinder Chapter 11 9 Volume of a Cylinder Chapter Rectangular and Triangular Prisms Chapter Surface Area of Rectangular and Triangular Prisms. 413 Chapter Volume of Rectangular and Triangular Prisms Chapter 12 Measurements and Conversions 420 Chapter 12 1 Systems of Measurement Chapter 12 2 Metric Numbers 425 Chapter 12 3 Time Chapter 12 4 Mass and Weight. 433 Chapter 12 5 Length Chapter 12 6 Temperature. 443 Chapter 12 7 Volume Chapter 12 8 Rate of Speed Chapter 12 9 The Rate, Time and Distance Traveled Chapter Most Common Conversion Factors 459 Page 31 of 518

30 Chapter 13 Graphs - Collecting and Displaying Data 463 Chapter 13 1 Circle (Pie) Graphs Chapter 13 2 Bar Graphs Chapter 13 3 Line Graphs Chapter 13 4 Stem and Leaf Plots 478 Chapter 13 5 Choosing the Right Graph to Use. 481 Chapter 13 6 Collecting Data through Surveys and Experiments 487 Chapter 14 Basic Statistics Chapter 14 1 Mean, Median and Mode 493 Chapter 14 2 Statistical Range Chapter 14 3 The Basic Counting Principle Chapter 15 Probability. 503 Chapter 15 1 Probability Review Chapter 15 2 Making Predictions with Probability Chapter 15 3 Factorials Chapter 15 4 Permutations and Combinations Page 32 of 518

31 Chapter 1 Fractions, Decimal Numbers and Percentages In this chapter, we will review and discuss various operations involving fractions, decimal numbers and percentages. We will cover the following topics: Fractions Review Decimal Numbers Review Percentages Review Converting Fractions into Decimal Numbers Converting Decimal Numbers into Fractions Converting Decimal Numbers into Percents Converting Percents into Decimal Numbers Converting Percents into Fractions Converting Fractions into Percents The Greatest Common Factor The Least Common Multiple The Least Common Denominator Adding Fractions Adding Decimal Numbers Subtracting Fractions Subtracting Decimal Numbers Multiplying Fractions Multiplying Decimal Numbers Dividing Fractions Dividing Decimal Numbers Mixed Numbers Review Converting Mixed Numbers into Fractions Converting Fractions into Mixed Numbers Adding Mixed Numbers Subtracting Mixed Numbers Working with Percents in Everyday Life Working with Fractions in Everyday Life Working with Decimals in Everyday Life Page 33 of 518

32 Chapter 1 1 Converting Fractions, Decimal Numbers & Percentages In this section, we will review fractions, decimal numbers and percentages. We will show you how to convert between fractions, decimal numbers and percentages. Specifically, we will lean about the following main topics. Fractions Review Decimal Numbers Review Percentages Review Converting Fractions into Decimal Numbers Converting Decimal Numbers into Fractions Converting Decimal Numbers into Percents Converting Percents into Decimal Numbers Converting Percents into Fractions Converting Fractions into Percents Page 34 of 518

$Chapter 1 1.1 Fractions Review A fraction is a part of a whole object or a whole number.$ $We can also say the fraction one-half as 1 out of 2, 1 over 2 or 1 divided by 2. There are special names for each number in a fraction.$ $There are 3 types of fractions: proper fractions, improper fractions and mixed fractions. Proper fractions have a numerator that is smaller than the denominator.$

33 Chapter Fractions Review A fraction is a part of a whole object or a whole number. Fraction part of a whole object or number For example, let s take a whole pizza and split it into two halves. Each half is a fraction of the whole pizza. We can also say the fraction one-half as 1 out of 2, 1 over 2 or 1 divided by 2. There are special names for each number in a fraction. The numerator is the top number and is the number of parts you have. The denominator is the bottom number and is the number of parts the whole is divided into. If you have a difficult time remembering which one is the denominator, just think down ominator. The division line is the line that separates the numerator and the denominator. There are 3 types of fractions: proper fractions, improper fractions and mixed fractions. Proper fractions have a numerator that is smaller than the denominator. Like 1 over 2, 3 over 4, 7 over 8 and so on. Improper fractions have a numerator that is greater than or equal to the denominator. Like 2 over 1, 3 over 2, 32 over 14 and so on. Page 35 of 518

California 5 th Grade Standards / Excel Math Correlation by Lesson Number

California 5 th Grade Standards / Excel Math Correlation by Lesson Number (Activity) L1 L2 L3 Excel Math Objective Recognizing numbers less than a million given in words or place value; recognizing addition and subtraction fact families; subtracting 2 threedigit numbers with