Math Grade 6 Flip Chart

Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Grade Grade Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-6001 666 \|xiBAHBDy01219rzu Sturdy, Free-Standing Design, Perfect for Learning Centers! Reverse Side Features Questions, Math Problems, Vocabulary Review & more!

Phone: 800-507-0966 • Fax: 800-507-0967 www.newpathlearning.com NewPath Learning® products are developed by teachers using research-based principles and are classroom tested. The company’s product line consists of an array of proprietary curriculum review games, workbooks, posters and other print materials. All products are supplemented with web-based activities, assessments and content to provide an engaging means of educating students on key, curriculum-based topics correlated to applicable state and national education standards. Copyright © 2009 NewPath Learning. All Rights Reserved. Printed in the United States of America. Curriculum Mastery® and NewPath Learning® are registered trademarks of NewPath Learning LLC. Math Curriculum Mastery® Flip Charts provide comprehensive coverage of key standards-based curriculum in an illustrated format that is visually appealing, engaging and easy to use. Curriculum Mastery® Flip Charts can be used with the entire classroom, with small groups or by students working independently. Each Math Curriculum Mastery® Flip Chart Set features • 10 double-sided laminated charts covering grade-level specific curriculum content on one side plus write-on/wipe-off charts on reverse side for student use or for small-group instruction. • Built-in sturdy free-standing easel for easy display • Spiral bound for ease of use • Activity Guide with black-line masters of the charts for students to fill-in, key vocabulary terms, corresponding quiz questions for each chart, along with answers Ideal for • Learning centers • In class instruction for interactive presentations and demonstrations • Hands-on student use • Stand alone reference for review of key science concepts • Teaching resource to supplement any program HOW TO USE Classroom Use Each Curriculum Mastery® Flip Chart can be used to graphically introduce or review a topic of interest. Side 1 of each Flip Chart provides graphical representation of key concepts in a concise, grade appropriate reading level for instructing students. The reverse Side 2 of each Flip Chart allows teachers or students to fill in the answers and summarize key concepts. Note: Be sure to use an appropriate dry-erase marker and to test it on a small section of the chart prior to using it. The Activity Guide included provides a black-line master of each Flip Chart which students can use to fill in before, during, or after instruction. On the reverse side of each black-line master are questions corresponding to each Flip Chart topic which can be used as further review or as a means of assessment. While the activities in the guide can be used in conjunction with the Flip Charts, they can also be used individually for review or as a form of assessment or in conjunction with any other related assignment. Learning Centers Each Flip Chart provides students with a quick illustrated view of grade-appropriate curriculum concepts. Students may use these Flip Charts in small group settings along with the corresponding activity pages contained in the guide to learn or review concepts already covered in class. Students may also use these charts as reference while playing the NewPath’s Curriculum Mastery® Games. Independent student use Students can use the hands-on Flip Charts to practice and learn independently by first studying Side 1 of the chart and then using Side 2 of the chart or the corresponding graphical activities contained in the guide to fill in the answers and assess their understanding. Reference/Teaching resource Curriculum Mastery® Charts are a great visual supplement to any curriculum or they can be used in conjunction with NewPath’s Curriculum Mastery® Games. Chart # 1: Chart # 2: Chart # 3: Chart # 4: Chart # 5: Chart # 6: Chart # 7: Chart # 8: Chart # 9: Chart #10: Properties of Addition & Multiplication The Coordinate Plane Introduction to Functions Introduction to Integers Adding & Subtracting Integers Multiplying & Dividing Integers Numbers & Operations Solving Equations Surface Areas of Solid Figures Area & Circ umference of Circles

Addition Properties Property of Multiplication & Addition Multiplication Properties • Addition and multiplication properties help us solve basic algebraic equations. Property Description Formula Example Property Description Formula Example 6 + 4 = 4 + 6 8 + 0 = 8 You can add numbers in any order without changing their sum. The sum of any number and zero is equal to that number. You can group any of the numbers together without changing their sum. Associative (grouping) Identity Property of Zero Property Description Formula Example Property Description Formula Example You can add the numbers inside the parentheses first and then multiply, or multiply each number in the sum and then add. Property Description Formula Example Property Description Formula Example You can multiply numbers in any order without changing their sum. You can group any of the numbers together without changing their product. The product of any number and one is equal to that number. The product of any number and zero is zero. Associative (grouping) Identity Property of One Property of Zero Distributive a x b = b x a 9 x 6 = 6 x 9 a x 1 = a 4 x 1 = 4 a x 0 = 0 3 x 0 = 0 a + b = b + a a + 0 = a © Copyright NewPath Learning. All Rights Reserved. 93-4601 www.newpathlearning.com Properties of Addition & Multiplication

Addition Properties Property of Multiplication & Addition Multiplication Properties • Addition and multiplication properties help us solve basic . Property Description Formula Example Property Description Formula Example Associative (grouping) Identity Property of Zero Property Description Formula Example Property Description Formula Example Property Description Formula Example Property Description Formula Example Associative (grouping) Identity Property of One Property of Zero Distributive Key Vocabulary Terms • algebraic equation • distributive • associative property • identity property • commutative property of zero © Copyright NewPath Learning. All Rights Reserved. 93-4601 www.newpathlearning.com Properties of Addition & Multiplication \|xiBAHBDy01682tz]

x y Quadrant II Quadrant III Quadrant IV Quadrant I y – axis origin x – axis -5 -4 -3 -2 -1 1 1 2 3 4 5 2 3 4 5 -1 -2 -3 -4 -5 0 x y 4 units right 3 units up (4, 3) -5 -4 -3 -2 -1 1 1 2 3 4 5 2 3 4 5 -1 -2 -3 -4 -5 0 • A coordinate plane is a two-dimensional surface formed by two number lines that intersect at right-angles. • Any point on a coordinate plane can be located using an ordered pair of numbers. • To plot a point, start at the origin and count along the x-axis the number of units of the x-coordinate. Count to the right for positive numbers and to the left for negative numbers. • Count along the y-axis the number of units of the y-coordinate. Count up for positive and down for negative numbers. x – coordinate (number of units to the right or left of origin) y – coordinate (number of units above or below the origin) • The two number lines form the axes. • The horizontal axis is called the x-axis. • The vertical axis is called the y-axis. • The two axes intersect at the center of the coordinate plane and divide the coordinate plane into four quadrants. • The intersection of these two axes is called the origin. The Quadrants Locating Points on a Coordinate Plane © Copyright NewPath Learning. All Rights Reserved. 93-4602 www.newpathlearning.com ordered pair Plot (4, 3) (4, 3) The Coordinate Plane

\|xiBAHBDy01688lz[ x y -5 -4 -3 -2 -1 1 1 2 3 4 5 2 3 4 5 -1 -2 -3 -4 -5 0 x y -5 -4 -3 -2 -1 1 1 2 3 4 5 2 3 4 5 -1 -2 -3 -4 -5 0 • A coordinate plane is a ___________ __________________________________ __________________________________ _________________________________ . ______________ ______________ ______________ • Any point on a coordinate plane can be located using an of numbers. • To plot a point, start at the and count along the the number of units of the x-coordinate. Count to the for positive numbers and to the for negative numbers. • Count along the y-axis the number of units of the y-coordinate. Count for positive and for negative numbers. • The two number lines form the . • The horizontal axis is called the . • The vertical axis is called the . • The two axes intersect at the center of the coordinate plane and divide the coordinate plane into four . • The intersection of these two axes is called the . Locating Points on a Coordinate Plane ______________ ______________ ______________ The Quadrants © Copyright NewPath Learning. All Rights Reserved. 93-4602 www.newpathlearning.com ordered pair Plot (4, 3) (4, 3) Key Vocabulary Terms • coordinate plane • negative number • ordered pair • origin • point • positive number • quadrant • two-dimensional surface • x-axis • y-axis The Coordinate Plane

x y -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 1 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 0 (-2 , -6) (-1 , -2) (0 , 2) (1 , 6) (2 , 10) Graphing Linear Functions • A function is a rule that is performed on a number, called an input, to produce a result called an output. • x is the input • y is the output • By substituting a number for X, an output can be determined. • Graph the functions described by the equation: • Make a function table • Graph the ordered pairs on a coordinate plane. • Draw a line through the points which represent the values of the ordered pairs. • A graph of a linear function can be used to find the value of y for a given value of x. • A table can be used to show input and output values. y = 2x + 3 is an example of a function y = 4x + 2 y = 2x + 3 7 output 2 input Input 1 2 3 4 5 6 7 8 9 10 5 7 9 11 13 15 17 19 21 23 Output Output Input Function (4x + 2) Ordered Pairs (x, y) -2 -1 0 1 2 -6 -2 2 6 10 4 (-2) + 2 4 (-1) + 2 4 (0) + 2 4 (1) + 2 4 (2) + 2 (-2, -6) (-1, -2) (0, 2) (1, 6) (2, 10) © Copyright NewPath Learning. All Rights Reserved. 93-4603 www.newpathlearning.com Introduction to Functions

x y -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 1 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 0 Graphing Linear Functions • A function is ________________________________ _____________________________________________ ____________________________________________ . • x is the input • y is the output • By substituting a number for , an can be determined. • Graph the functions described by the equation: • Make a function table • Graph the ordered pairs on a coordinate plane. • Draw a line through the points which represent the values of the ordered pairs. • A graph of a linear function can be used to find the value of for a given value of . • A table can be used to show input and output values. y = 2x + 3 is an example of a function y = 4x + 2 y = 2x + 3 output 2 input Input 1 2 3 4 5 6 7 8 9 10 Output Output Input Function (4x + 2) Ordered Pairs (x, y) -2 -1 0 1 2 Key Vocabulary Terms • coordinate plane • equation • function • input • linear function • ordered pair • output © Copyright NewPath Learning. All Rights Reserved. 93-4603 www.newpathlearning.com Introduction to Functions \|xiBAHBDy01671nzW

• Integers are a set of whole numbers and their opposites. • Positive integers are whole numbers greater than zero. • Negative integers are whole numbers less than zero. • The integer 0 is neither positive nor negative. • Integers have either a (+) positive or (–) negative sign, except zero, which has no sign. • The absolute value of an integer is the number of units from zero on a number line. • The absolute value of a number is always a positive number or zero. The symbol for absolute value is . • A number line can be used to order and compare integers. order from least to greatest • Read the numbers from left to right: • Opposite integers have the same absolute value. • A number line can be used to represent a set of integers. • The value of integers increases as you move to the right along a number line. And decreases in value as you move to the left. – 5 – 4 – 3 – 2 – 1 + 5 + 4 + 3 + 2 + 1 0 – 3 and 3 are opposites – 5 – 4 – 3 – 2 – 1 + 5 + 4 + 3 + 2 + 1 0 – 5 – 4 – 3 – 2 – 1 + 5 + 4 + 3 + 2 + 1 0 – 4 = 4 4 – 3, 0, 1, – 4, 2, 5 – 4, – 3, 0, 1, 2, 5 4 = 4 units 4 units Using Integers Integer Example – 350 + 100 – 35 – 10 350 feet below sea level 35 degrees below zero Loss of 10 yards in a football play Stock Market gain of 100 points Number Line negative integers positive integers Absolute Value Ordering Integers © C opyright NewPath Learning. All Rights Reserved. 93-4604 www.newpathlearning.com Introduction to Integers 40 50 60 70 80 90 100 110 ºF -50 -40 -30 -20 -10 0 10 20 30

• Integers are ________________ ____________________________ . • Positive integers are ________ ____________________________ . • Negative integers ___________ ____________________________ . • The integer is neither positive nor negative. • Integers have either a (+) positive or (–) negative sign, except zero, which has . • The absolute value of an integer is ______________________________________ _____________________________________ . • The absolute value of a number is always a or . The symbol for absolute value is . • A number line can be used to order and . order from least to greatest • Read the numbers from to : • integers have the same absolute value. • A can be used to represent a set of integers. • The value of integers as you move to the right along a number line. And in value as you move to the left. – 5 – 4 – 3 – 2 – 1 + 5 + 4 + 3 + 2 + 1 0 – 3 and 3 are opposites – 5 – 4 – 3 – 2 – 1 + 5 + 4 + 3 + 2 + 1 0 – 5 – 4 – 3 – 2 – 1 + 5 + 4 + 3 + 2 + 1 0 – 4 = 4 3 – 3, 0, 1, – 4, 5, 2 – 4, – 3, 0, 1, 2, 5 4 = Using Integers Integer Example – 350 + 100 – 35 – 10 350 feet below sea level 35 degrees below zero Loss of 10 yards in a football play Stock Market gain of 100 points Number Line Absolute Value Ordering Integers Key Vocabulary Terms • absolute value • integer • negative integer • number line • positive integer • whole number © Copyright NewPath Learning. All Rights Reserved. 93-4604 www.newpathlearning.com Introduction to Integers 40 50 60 70 80 90 100 110 ºF -50 -40 -30 -20 -10 0 10 20 30 \|xiBAHBDy01672kzU

– 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 • To add a positive integer, start at zero and move right on the number line, and move left to add a negative integer. move right 5 spaces from zero and then 2 more = 1 = 0 + = – 1 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 • To subtract a positive integer, move left on the number line, and right to subtract a negative number. 7 days 1 week (wk) 5 + 2 5 + 2 = 7 blue move right 4 spaces from zero and then left 6 move left 3 spaces from zero and then 7 more -3 + (-7) 4 + (-6) -3 + -7 = -10 4 + (-6) = -2 red red red red red red red red red red red red red red red red blue red red move right 5 spaces from zero and then left 3 5 – 3 5 – 3 = 2 blue blue blue blue blue blue blue move left 7 spaces from zero and then left 2 move left 6 spaces from zero and then right 4 -7 – 2 blue red red +2 5 4 -3 -6 5 – (-4) -3 -2 -7 -6 + (-7) blue blue blue -7 – 2 = - 9 7 -6 – (-4) = -2 -6 – (-4) red red red red red red red red red red red red red blue blue blue blue blue blue blue Adding Integers on a Number Line Subtracting Integers on a Number Line © Copyright NewPath Learning. All Rights Reserved. 93-4605 www.newpathlearning.com Adding & Subtracting Integers

• To add a positive integer, start at and move on the number line, and move to add a integer. move spaces from zero and then more = 1 = 0 + = – 1 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 – 5 – 4 – 3 – 2 – 1 – 10 – 9 – 8 – 7 – 6 5 4 3 2 1 10 9 8 6 0 7 • To subtract a positive integer, move on the number line, and to subtract a number. 5 + 2 5 + 2 = 7 blue -3 + (-7) 4 + (-6) -3 + -7 = -10 4 + (-6) = -2 red red red red red red red red red red red red red red red red blue red red 5 – 3 5 – 3 = 2 blue blue blue blue blue blue blue -7 – 2 blue red red blue blue blue -7 – 2 = - 9 7 -6 – (-4) = -2 -6 – (-4) red red red red red red red red red red red red red blue blue blue blue blue blue blue Adding Integers on a Number Line Subtracting Integers on a Number Line move spaces from zero and then more move spaces from zero and then move spaces from zero and then move spaces from zero and then move spaces from zero and then Key Vocabulary Terms • negative integer • number line • positive integer © Copyright NewPath Learning. All Rights Reserved. 93-4605 www.newpathlearning.com Adding & Subtracting Integers \|xiBAHBDy01663sz\

• Multiplication is repeated addition. • Multiplication with integers is commutative • Division is the inverse of multiplication • The same sign rules apply to multiplication and division of integers. – 5 – 4 – 3 – 2 – 1 – 10 – 12 – 11 – 9 – 8 – 7 – 6 5 4 3 2 1 10 11 12 9 8 6 0 7 4 x 3 means to add 3 four times: • Similarly, the product of 4 and – 3 means to add – 3 four times: Multiplying Integers Dividing Integers (-3) (-3) (-3) (-3) 4 groups of -3 = -12 3 + 3 + 3 + 3 –3 + (–3) + (–3) + (–3) –3 x (–2) = 6 5 x (–3) = –15 –15 ÷ (–3) = 5 –5 x (–3) = 15 15 ÷ (–3) = –5 6 ÷ (–3) = –2 –3 x 4 = –4 x (3) Example Rule You multiply integers just as you do whole numbers, except that you determine the sign of the product using these rules. If the factors have different signs, the product is negative. If the factors have the same signs, the product is positive. If one factor is zero, the product is zero. – 7 x 4 = – 28 – 4 x 0 = 0 – 8 x – 9 = 72 6 x 2 = 12 5 x – 3 = – 15 Example Rule • You cannot divide an integer by 0. If the dividend and divisor have different signs, the quotient is negative. If the dividend and divisor have the same signs, the quotient is positive. Zero divided by any integer equals 0. – 12 ÷ 4 = – 3 32 ÷ 4 = 8 15 ÷ (– 3) = – 5 – 21 ÷ (– 3) = 7 0 9 = 0 0 = 0 – 8 same signs product is positive different signs quotient is negative © C opyright NewPath Learning. All Rights Reserved. 93-4606 www.newpathlearning.com Multiplying & Dividing Integers

• Multiplication is • Multiplication with integers is commutative • Division is the inverse of multiplication • The same sign rules apply to multiplication and division of integers. – 5 – 4 – 3 – 2 – 1 – 10 – 12 – 11 – 9 – 8 – 7 – 6 5 4 3 2 1 10 11 12 9 8 6 0 7 4 x 3 means to times: • Similarly, the product of 4 and -3 means to times: Multiplying Integers Dividing Integers 4 groups of -3 = -12 3 + 3 + 3 + 3 –3 + (–3) + (–3) + (–3) –3 x (–2) = 6 5 x (–3) = –15 –15 ÷ (–3) = 5 –5 x (–3) = 15 15 ÷ (–3) = –5 6 ÷ (–3) = –2 –3 x 4 = –4 x ( –3 ) Example Rule You multiply integers just as you do whole numbers, except that you determine the sign of the product using these rules. If the factors have different signs, the product is negative. If the factors have the same signs, the product is positive. If one factor is zero, the product is zero. Example Rule • You cannot divide an integer by 0. If the dividend and divisor have different signs, the quotient is negative. If the dividend and divisor have the same signs, the quotient is positive. Zero divided by any integer equals 0. Key Vocabulary Terms • commutative • dividend • divisor • factor • integer • product • quotient • repeated addition © Copyright NewPath Learning. All Rights Reserved. 93-4606 www.newpathlearning.com Multiplying & Dividing Integers \|xiBAHBDy01674ozX

Expanded Form Word Form twenty one billion, fifty eight million, three hundred and forty thousand, three hundred eighty two 21,058,340,382 21,000,000,000 + 058,000,000 + 340,000 + 300 + 80 + 2 • Our number system is based on a place value system. Although there are only 10 different digits in this system, it is possible to order them in so many variations, that the numbers represented are infinite. Whole Numbers • An exponent tells how many times to multiply a number, called the base, by itself. • A number written with a base and an exponent is in exponential form. Exponents Reading Large Numbers ones tens hundr eds ones tens hundr eds ones tens hundr eds ones tens hundr eds thousands thousands millions millions billions billions ones ones • Place value is used to read and understand large numbers. • Each digit in a number has a place value. • A digit in a place value chart has a different value depending on its position in the number. • Commas are used to separate groups of 3 digits. Place Value Order of Operations 2 1 , 0 5 8 , 3 4 0 , 3 8 2 2 1 , 0 5 8 , 3 4 0 , 3 8 2 5 = 5 x 5 x 5 = 125 3 • A numerical expression is a mathematical phrase consisting of only numbers and operational symbols. Order of Operations 1. Complete the operations inside the parentheses. • If there are no parentheses or exponents, perform multiplication first. 2. Simplify all exponents. 3. Multiply or divide from left to right. 4. Add or subtract from left to right. Value Operation Word Form Exponential Form 15 + 39 ÷ 3 x 6 105 104 103 102 101 10 to the 1st power 10 x 10 10 x 10 x 10 10 x 10 x 10 x 10 10 x 10 x 10 x 10 x 10 100,000 10,000 1,000 100 10 10 10 to the 4th power 10 to the 5th power 10 to the 2nd power or 10 squared 10 to the 3rd power or 10 cubed base exponent © Copyright NewPath Learning. All Rights Reserved. 93-4607 www.newpathlearning.com Numbers & Operations

Expanded Form Word Form 21,058,340,382 21,000,000,000 + 058,000,000 + 340,000 + 300 + 80 + 2 _____________________________ _____________________________ _____________________________ _____________________________ _____________________________ • Our number system is based on a place value system. Although there are only 10 different digits in this system, it is possible to order them in so many variations, that the numbers represented are infinite. Whole Numbers • An tells how many times to multiply a number called the base, by itself. • A number written with a base and an exponent is in . Exponents Reading Large Numbers ones tens hund reds ones tens hund reds ones tens hund reds ones tens hund reds thousands thousands millions millions billions billions ones ones • Place value is used to read and understand large numbers. • Each digit in a number has a place value. • A digit in a place value chart has a different value depending on its position in the number. • Commas are used to separate groups of 3 digits. Place Value Order of Operations 2 1 , 0 5 8 , 3 4 0 , 3 8 2 2 1 , 0 5 8 , 3 4 0 , 3 8 2 5 = 5 x 5 x 5 = 125 3 • A is a mathematical phrase consisting of only numbers and . Order of Operations 1. 2. 3. 4. Value Operation Word Form Exponential Form 15 + 39 ÷ 3 x 6 105 104 103 102 101 ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ Key Vocabulary Terms • base • exponent • exponential form • numerical expression • operation • place value • whole numbers © Copyright NewPath Learning. All Rights Reserved. 93-4607 www.newpathlearning.com Numbers & Operations \|xiBAHBDy01677pzY

check check Division Equations Subtraction Equations Addition Equations check • An equation is a mathematical statement which shows that two quantities or values are equal. • Algebraic equations include at least one variable. • To solve an algebraic equation, you seek for the value of the variable that makes the equation a true statement. • The value of the variable is called the solution. • Since the equation shows subtraction, use the inverse operation, addition. • To get m by itself, add the same number (14) from both sides. • Solve the equation. • Substitute 43 for m in the equation. m = 43 • Think of an equation as a balance scale – both sides should be perfectly balanced. • When solving an equation, use inverse operations and keep the equation balanced by performing the exact thing to both sides of the equation. m + 16 = 28 • Since the equation shows addition, use the inverse operation, subtraction. • To get m by itself, subtract the same number (16) from both sides. • Solve the equation. • Substitute 12 for m in the equation. m + 16 = 28 28 = 28 m + 16 = 28 m + 16 = 28 12 + 16 = 28 -16 -16 m = 12 solve solve check solve solve • Since the equation shows multiplication, use the inverse operation, division. • Divide both sides by the same number (15). • Substitute 7 for m in the equation. 15m = 105 15m = 105 15(7) = 105 15m = 105 15 15 105 = 105 • Since the equation shows division, use the inverse operation, multiplication. • Multiply both sides by the same number (5). 5 m = 30 5 x x 5 5 m = 30 5 m = 30 5 150 = 30 m – 14 = 29 29 = 29 m – 14 = 29 m – 14 = 29 43 – 14 = 29 + 14 + 14 30 = 30 • Substitute 150 for m in the equation. ? ? ? ? m = 7 m = 150 Multiplication Equations © Copyright NewPath Learning. All Rights Reserved. 93-4608 www.newpathlearning.com Solving Equations 28 = m + 16 equal sign expression expression

\|xiBAHBDy01685kzU check check Division Equations Subtraction Equations Addition Equations check • An is a mathematical statement which shows that two quantities or values are . • Algebraic equations include at least one . • To solve an algebraic equation, you seek for the value of the that makes the equation a . • The value of the variable is called the . • Since the equation shows subtraction, use the inverse operation, addition. • To get m by itself, add the same number from both sides. • Solve the equation. • Substitute for m in the equation. m = 43 • Think of an equation as a balance scale – both sides should be perfectly . • When solving an equation, use and keep the by performing the exact thing to both sides of the equation. m + 16 = 28 • Since the equation shows addition, use the inverse operation, subtraction. • To get m by itself, subtract the same number from both sides. • Solve the equation. • Substitute for m in the equation. m + 16 = 28 28 = 28 m + 16 = 28 m + 16 = 28 12 + 16 = 28 -16 -16 m = 12 solve solve check solve solve • Since the equation shows multiplication, use the inverse operation, division. • Divide both sides by the same number . • Substitute for m in the equation. 15m = 105 15m = 105 15( ) = 105 15m = 105 15 15 105 = 105 • Since the equation shows division, use the inverse operation, multiplication. • Multiply both sides by the same number . 5 m = 30 5 x x 5 5 m = 30 5 m = 30 5 150 = 30 m – 14 = 29 29 = 29 m – 14 = 29 m – 14 = 29 43 – 14 = 29 + 14 + 14 30 = 30 • Substitute for m in the equation. ? ? ? ? m = 7 m = 150 Multiplication Equations © Copyright NewPath Learning. All Rights Reserved. 93-4608 www.newpathlearning.com Solving Equations 28 = m + 16 equal sign expression expression Key Vocabulary Terms • algebraic equation • solution • expression • value • inverse operation • variable

S 9 x 6(3.14) + 2 x 9(3.14) • Solid figures are 3-dimensional figures that have length, width, and height. • The surface area of a solid figure is the sum of the areas of all its surfaces or faces. • A net is a pattern made to show each face of a solid figure flat. Surface Area of a Prism Surface Area of a Cylinder Surface Area of a Pyramid flattened cube rectangular prism 6 in. 3 ft 9 ft 8 in. 5 ft 6 ft h 5 ft 8 in. pyramid cylinder flattened cylinder r h flattened pyramid triangular face flattened prism cube front top side • Use the formula A = • w to find the area of each face. Face A : A = 6 x 4 = 24 Face B : A = 8 x 6 = 48 Face C : A = 8 x 4 = 32 Face D : A = 8 x 6 = 48 Face E : A = 8 x 4 = 32 Face F : A = 6 x 4 = 24 S = 85 ft2 S = S2 + 4 x ( b • h ) S = 25 + 4 x 15 S = 25 + 60 S 226.08 ft2 S = h x (2 r) + 2 x ( r2) S 9 x 18.84 + 2 x 28.26 S 169.56 + 56.52 4 in. 4 in. 6 in. F A E B C D A C E B D Surface Area (S) = area of square (A) + 4 x (area of triangular face) Surface Area (S) = area of lateral surface + 2 x (area of each base) 1 2 S = 52 + 4 ( x 5 x 6 ) 1 2 lateral surface base circumference of base r base r S = 9 x 6 + 2 x 9 S = 9 x (2 x x 3) + 2 x ( x 32) S © Copyright NewPath Learning. All Rights Reserved. 93-4609 www.newpathlearning.com Surface Areas of Solid Figures top face side face side face front face opposite to front face bottom face

• Solid figures are that have length, width, and height. • The surface area of a solid figure is the of the of all its surfaces or . • A is a pattern made to show each face of a solid figure flat. Surface Area of a Prism Surface Area of a Cylinder Surface Area of a Pyramid flattened cube rectangular prism 6 in. 3 ft 9 ft 8 in. 5 ft 6 ft h 5 ft 8 in. pyramid cylinder flattened cylinder r h flattened pyramid triangular face flattened prism cube front top side • Use the formula A = • w to find the area of each face. Face A : A = 6 x 4 = 2 4 Face B : A = 6 x 4 = Face C : A = 6 x 4 = Face D : A = 6 x 4 = Face E : A = 6 x 4 = Face F : A = 6 x 4 = S = 85 ft2 S = S2 + 4 x ( b • h) S = 5 + 4 x 15 S = 25 + 60 S 226.08 ft2 4 in. 4 in. 6 in. F A E B C D A C E B D Surface Area (S) = area of square (A) + 4 x (area of triangular face) Surface Area (S) = area of lateral surface + 2 x (area of each base) 1 2 S = 52 + 4 ( x 5 x 6 ) 1 2 lateral surface base circumference of base r base r Key Vocabulary Terms • base • circumference • cylinder • face • lateral area • prism • pyramid • solid figure • surface area S 9 x 6 ( 3.14 ) + 2 x 9 ( 3.14 ) S = h x (2 r) + 2 x ( r2) S 9 x 18.84 + 2 x 28.26 S 169.56 + 56.52 S = 9 x 6 + 2 x 9 S = 9 x ( 2 x x 3 ) + 2 x ( x 32) © Copyright NewPath Learning. All Rights Reserved. 93-4609 www.newpathlearning.com Surface Areas of Solid Figures top face side face side face front face opposite to front face bottom face \|xiBAHBDy01686rzu

C = d or 2 r C = r 2 Area of a Circle Circumference of a Circle A E AB is a diameter AD, DB, and DC are radii EF is a cord B D C F center diameter circle D circumference radius chord • A circle is a plane figure formed by a set of points that are equal distance from a fixed point within it, called the center. • The diameter of a circle is the distance across the inside of a circle through the center. It is twice the measure of a radius. • The radius is half the measure of a diameter. It is a line segment with one end point at the center of the circle and the other endpoint on the edge of the circle. • The circumference of a circle is the distance around it. • A chord is a line segment that connects any two points on a circle. • The area of a circle is the space contained within the circumference. • The ratio of the circumference of a circle to the diameter of a circle is approximately equal to 3.14 or . This ratio is called Pi ( ) and is the same for all circles. 22 7 d = 12 in. ; A = ? d = 12 A = r 2 A 3.14 • (6) 2 A 3.14 • 36 A 113.04 in.2 C = 2 r C 2 • 3.14 • 5 C 31.4 ft r = 6 r = r = 5 ft ; C = ? d 2 r = 12 2 12 in. 5 ft C = d C 3.14 • 10 C 31.4 ft d = 10 ft ; C = ? • • • © Copyright NewPath Learning. All Rights Reserved. 93-4610 www.newpathlearning.com Area & Circumference of Circles

\|xiBAHBDy01665mzV C = d or 2 r C = r 2 Area of a Circle Circumference of a Circle A E AB is a diameter AD, DB, and DC are radii EF is a cord B D C F circle D • A circle is a formed by a set of points that are equal distance from a fixed point within it, called the . • The of a circle is the distance across the inside of a circle through the . It is twice the measure of a . • The is half the measure of a . It is a line segment with one end point at the center of the circle and the other endpoint on the edge of the circle. • The of a circle is the distance around it. • A is a line segment that connects any two points on a circle. • The of a circle is the space contained within the circumference. • The ratio of the circumference of a circle to the diameter of a circle is approximately equal to or . This ratio is called and is the same for all circles. d = 12 in. ; A = ? d = 12 A = r 2 A 3.14 • ( 6 ) 2 A 3.14 • 36 A 113.04 in2 C = 2 r C 2 • 3.14 • 5 C 31.4 ft. r = 6 r = r = 5 ft ; C = ? r = 12 in. 5 ft C = d C 3.14 • 10 C 31.4 ft. d = 10 ft ; C = ? • • • Key Vocabulary Terms • area • center • chord • circle • circumference • diameter • pi ( ) • plane figure • radius © Copyright NewPath Learning. All Rights Reserved. 93-4610 www.newpathlearning.com Area & Circumference of Circles

Math Grade 6

Mathematics, Grade 6

Need Help?

NewPath Learning

Solutions

Shop By Product

Shop By Grade

Shop By Subject