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Flip Charts

Math: Algebra Skills

Mathematics, Grade 6

 
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Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Algebra Skills Algebra Skills Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-6002 \|xiBAHBDy01266lz[ 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: Introduction to Algebra Properties of Addition & Multiplication Introduction to Integers Adding & Subtracting Integers Multiplying & Dividing Integers Solving Equations Multistep Equations Inequalities Introduction to Functions Systems of Equations
Algebraic Expressions Translating word phrases into algebraic expressions Evaluating algebraic expressions An algebraic expression is a mathematical phrase consisting of variables, numbers, and operations. Solving Equations An equation is a mathematical sentence which shows that two expressions or values are equal. Think of an equation as a balance scale. To evaluate an algebraic expression, replace the variable with a number Replace m with 4 in the expression The letter m is a variable which represents an unknown number. 3 x 2m is an algebraic expression evaluate m + 5 for m = 4 m + 5 4 + 5 = 9 Operation Word Phase Algebraic Expression Addition m + 9 Subtraction m 9 Multiplication 2m + 9 2 x m 2 m 2m Division A number plus 9 The sum of m and 9 9 more than a number A number increased by 9 The difference between a number and 9 A number minus 9 9 less than a number A number decreased by 9 9 more than twice a number 2 x a number A number multiplied by 2 The product of 2 and a number A number divided by 9 9 divided by a number The quotient of a number and 9 m 9 9 m m 9 28 = m + 16 equal sign What number plus 16 equals 28? Solve 16 + m = 28 Solution m = 12 12 + 16 = 28 28 = 28 Solve the equation to find the value of the variable that makes the equation true. The value of the variable is called the solution. Examples of Algebraic Expressions Addition Subtraction Multiplication Division 6 + d, or d + 6 c - 6 6 x b, or 6b a ÷ 6, or a 6 expression expression 28 16 m © Copyright NewPath Learning. All Rights Reserved. 93-4507 www.newpathlearning.com Introduction to Algebra
Algebraic Expressions Translating word phrases into algebraic expressions Evaluating algebraic expressions An algebraic expression is a mathematical phrase consisting of variables, numbers, and operations. Solving Equations An equation is a mathematical sentence which shows that two expressions or values are equal. Think of an equation as a balance scale. To evaluate an algebraic expression, replace the variable with a number Replace m with in the expression The letter m is a which represents an unknown number. 3 x 2m is an evaluate m + 5 for m = 4 m + 5 4 + 5 = 10 Operation Word Phase Algebraic Expression Addition Subtraction Multiplication Division A number plus 9 The sum of m and 9 9 more than a number A number increased by 9 The difference between a number and 9 A number minus 9 9 less than a number A number decreased by 9 9 more than twice a number 2 x a number A number multiplied by 2 The product of 2 and a number A number divided by 9 9 divided by a number The quotient of a number and 9 What number plus 16 equals 28? Solve 16 + m = 28 Solution m = 12 + 16 = 28 = 28 Solve the equation to find the value of the variable that makes the equation true. The value of the variable is called the solution. Examples of Algebraic Expressions Addition Subtraction Multiplication Division 28 = m + 16 equal sign expression expression 28 16 m Key Vocabulary Terms algebra algebraic expression difference equation increase more plus product quotient solution sum variable © Copyright NewPath Learning. All Rights Reserved. 93-4507 www.newpathlearning.com Introduction to Algebra \|xiBAHBDy01648pzY
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 -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