Cycle 2: Why Does It Matter?
|
|
- Irene Roberts
- 5 years ago
- Views:
Transcription
1 Lesson. It s All Relative 9 Part Cycle : Why Does It Matter? Lesson. It s All Relative a. Negative; $0,000 Negative; a. Loss of 0 yards Loss of 0.6 points for the day a c d The student s analogy with money is actually correct. However, that does not mean that -5 is bigger than - 4. The bigger the debt, the more the person is in the hole and the less money he or she has. Therefore, -5 is less than a. 7 7 c. 7, 7 d. a Lesson. Sign and Size, Part. a. 5. (.) ( ) ( ) 44
2 0 Cycle, Part. Answers will vary depending on the year. Possible answer: 0 ( 500) years. $0 $5 ($0 $5) $5 She will owe him $5 in total. 4. $,500 $0,000 $0,000 $,500 $8,500 She will have $8,500 after the debt is paid The team has already gained yards on the first three downs. They will need 0 7 more yards on the fourth down to have a 0-yard gain (and get a first down). Lesson.4 Sign and Size, Part. a. (0)( 5) ( )( )( 7) ()( 7) 4. a. Multiplying two negative numbers results in a positive number. For example, ( 4)( 4) 6. Adding two negative numbers results in a negative number. For example, ( 4) ( 4) 8 No. Two negative numbers can result in a positive, negative, or zero result depending on the operation. 4. Answers will vary. Possible answer: Two wrongs don t make a right. 5. Problem with parentheses Answer Problem without Parentheses New Result a. ( 4) 8 4 ( ) ( 4) c. (4) 4 d. ( )( 4) Do parentheses matter? Yes No No Yes 6. a. 6? ? 0 0? is undefined no such number
3 Lesson.4 Sign and Size, Part c. Zero divided by a number (other than zero) is zero. A number cannot be divided by zero. 7. a. Positive It depends. Possible examples: ( 7) 4, 7 4 c. Negative d. Positive e. Positive f. Negative g. Negative 8. Answers will vary. Possible calculation with a negative number: ( ) Yes. The result is always. Possible calculation with a fraction: Lesson.5 An Ounce of Prevention. 784 ( ) ( 0) Current average: To average an 80, point total 80. So her point total must be 0 points. She needs on 4 the last test to have a B average.. Answers will vary. Any scores, between 0 and 0, which add to will work. Possible answers: 7, 7, 7; 6, 7, 8; 0, 0, ; 9, 9, ; 5, 6, 0 4. Answers will vary. It s often easy to gain weight, but hard to lose it. It is easy to get in debt, but hard to get out of it. Addition is usually easier than subtraction. Multiplication is easier than division. 5. To split the check evenly, the total bill must be divided by five. You would each pay $55 $. This amount also represents the average of the individual bills. 5
4 Cycle, Part 6. a The mean income for Group is $4,000/year The mean income for Group is $5,000/year The mean is affected by one extreme value in a data set. When the last income was changed from $50,000 to $50,000, the mean increased by $0,000. c. No. For Group, a mean of $5,000/year is not very representative of the typical income since only one of the ten incomes is higher than that. 7. a. Answers will vary. Possible answer: 40, 45,50,55,60 50,55, 60, 65, 70 c. New mean: 60 d. When 0 was added to each score, the mean also increased by 0. e. To increase the mean by 8 points, the teacher should add 8 points to each student s test score. 8. a c. The mean does not tell us whether the two test scores are close to the mean of 75 or more spread out. The mean only tells us about the center, not the spread of the data. 9. a The mean is the balancing point for the data. If we think of the number line as a teeter-totter, the mean of 0 is where the data values will balance. 0. a. The average height should be in inches, not square inches. Height is a linear measurement, not an area. The average square footage should be in square feet, not feet. Square footage is a measurement of area, not length. Lesson.6 Measure Up. a. c. (4 ab) ( ab) 4 a b ( ab),744a 4 4,744ab ( x ) x 7x m 4m m 8mn 8n n b
5 Lesson.6 Measure Up. a. C r (4 in.) 5 in. Ar ( ft) ft. m V d g g / c g g c c g g c The volume will be in cubic centimeters. 4. v D 0.87 g (m/sec) m/sec m /sec m/sec m m sec sec m sec sec m m The distance will be in meters.
6 4 Cycle, Part 5. T L g ft ft/sec ft ft sec sec ft ft sec sec The time will be in seconds. Lesson.7 Count Up. No, they are not like terms. They do not have the same exponents on the x factors and they do not have the same exponents on the y factors... x xyxyx () xy( ) x xy x ( x )( xy)( xy)( x )() 6,888x y 6 6,888x y 4. The polynomial is a trinomial since it has three terms. 5. a. The student appears to have added 5x 6y to get xy, but they are not like terms and should not be combined. Instead, the xy terms should be combined and the x term and y term should be left separate. xy5x6y8 xy ( xy8 xy) 5x6y xy 5x 6y The expression still has like terms ( 5 x and 8x ) that should be combined. 5x 0xx8 x (5 8) x (0 ) x x x 6. Answers will vary. Possible answer: Expression that contains like terms: 5x 6yx
7 Lesson.7 Count Up 5 Expression that does not contain like terms: 5x 6y xy 7. S r rl ( in.) ( in.)(4 in.) = (4 in. ) (8 in. ) (4 8) in. in. 7.7in. Cycle Part Recap. a (5 x ) 5 ( x ) 5x 50x x x 0x c. d. e. f x 5x 0x x 5x 5x 5x ( 5) Concepts and Applications. a. Yes; The sum of negative numbers will always be negative. The average will then be a negative sum divided by a positive number, which will always be negative. Answers will vary. Possible answer: 0,0,0,0,0,,,,,. $50(4) $5() $00 $75() $00 $75 $00 $50 $75 $50 $5 Your net debt is $5.
8 6 Cycle, Part Part Cycle : Why Does It Matter? Lesson.9 Order Up. a. 5 5 (4 ) ( 8) a. 5x 5( ) y ( 4) x 5(0) y ( 4) 0 ( 4) 0 5x 5( 4) y (0) 0 0 undefined (weight in pounds)(70) BMI= (height in inches) (50 lb)(70) (7 in.) 05,450 lb 5,84 in. 0.4 lb/in.. Answers will vary based on the calculator used. 4. a. Knee height = 6 in..54 cm/in cm Height in centimeters (0.480) ( ) cm Height in inches cm.54 cm/in in.
9 Lesson.9 Order Up 7 Answers will vary. 5. Expression d best illustrates the process to make cupcakes. The dry ingredients are combined and the wet ingredients are combined. And then the total is divided into 4 cupcakes. 6. a. The multiplier is ($45) $49.9 The multiplier is ($75) $60 Lesson.0 Does Order Matter?. a. ( yx) z or z( x y) x ( y z). a. ( yx) z or zxy ( ) x( yz ). a. Answers will vary. Possible answer: 6 but 6 Divide 5 by 5 implies 5 5 when the intended problem is 5 5. You could say, Divide 5 by 5 or Divide 5 into 5. How you verbalize the problem matters since it indicates the order of the numbers in the division problem. 4. a. 6 Switch the 8 and the c. 8 is easier to do with repeated addition because there are fewer numbers to add and keep track of in your head. 5. a. Your friend s grade would be represented by x 5 since it is 5 points lower than yours. Your grade would be represented by x 5 or 5 x since it is 5 points higher than his. 6. Group all the positive numbers together and all the negative numbers together and then combine those results. 7. a. Commutative Property Associative Property
10 8 Cycle, Part 8. a c. The two operations commute. You can multiply first then simplify or simplify first then multiply. You will get the same answer either way. Lesson. Fair Share. a. 4( x 6 x ) 4x46x 4x 64x (x)( x) x( x) ( x) x xx x x. 77(0) a
11 Lesson. Fair Share Yes c. No 4. a. Distributive Property Commutative Property c d. Method (student s nontraditional way): Method (traditional approach):
12 40 Cycle, Part 5. a. c. ( ab)( ab) (ab)a (ab)b a ba ab b a b 495 (50 )(50 ) 50,500, (70 )(70 ) (70 )(70 ) 70 4, ,896 Commutative Property for Multiplication 6. Each output is one less than three times the input value. Input Output n n Lesson. Seat Yourself. 5( x8) 4( x) 6 5x40 4x4 6 x 50. 8( n) 786n7n 5. a.
13 Lesson. Seat Yourself 4 One way to think about this is that there are 4 corner tables that each seat people. All the other tables ( n 4 of them) seat person. So there are 4 ( n4) 8n4n 4 seats for n tables. c. Number of tables Number of chairs n n 4 You get the same general result, n 4, as was achieved by using the physical situation in part d. Yes. The number of tables in this arrangement must be a multiple of 4, and 0 is a multiple of 4. If 0 tables were used, 4 people could be seated. e. n 46 n tables would be needed to seat 6 people. 4. a. 9 You will meet at mile marker. c. B A d. e. f. g. ( ) B A A ( BA) A B A A B B ( BA) B B A A B A B ( A B) A B Yes, they are equivalent.
14 4 Cycle, Part Lesson. Punt, Pass, Kick.. (5 in.) (5 in.) hyp 5 in. 5 in. hyp 50 in. hyp hyp 50 in. hyp 7. in. (4 ft) (leg) (0 ft) 6 ft (leg ) 00 ft (leg ) 84 ft leg 9. ft. a. All are whole numbers and All are whole numbers and 6 0,56 4 4, 45, 5 c. d. The triangles are similar. 4. a. No. Since4 7, the lengths do not make a triangle. In order to make a triangle the sum of the lengths of the shorter sides must be greater than the length of the longest side.
15 Lesson. Punt, Pass, Kick 4 Yes. Since4 6, the lengths do make a triangle. No. Since 4 6, the lengths do not make a right triangle. c. Answers will vary. Some possible answers: 4 ft,5 ft, 6 ft ; in.,8 in., 0 in. 5. If the area of the square is 00 square inches, then each side is 0 inches long. (0 in.) (0 in.) hyp 00 in. 00 in. hyp 00 in. hyp hyp 00 in. hyp 4. in. So the diagonal of the square is about 4. inches long. 6. a distance 77, ,96 distance 96,5 distance 96,5 distance distance 957ft Yes. The crime was committed about 957 feet from a church, making it a felony.
16 44 Cycle, Part Lesson.4 Ramp Up. m The graph goes through the points (0,) and (5,0) 0 m Every time x increases by, y decreases by 5. So change in y 5 m 5. change in x 4. a. c. rise 70 inches 7 m run 0 inches rise 7 inches 7 m run inches (70 in.) (0 in.) hyp 4,900 in.,00 in. hyp 7,000 in. hyp hyp 7,000 in. hyp 0 in. 0 ft, 0 in. 5. For fractions with a numerator of, the larger the denominator, the smaller the fraction. So. The ramp with a slope of : is the steepest because it has the largest slope of the three 0 6 and the shortest run for the rise of. The ramp with a slope of :0 is the flattest because it has the smallest slope of the three and the longest run for a rise of.
17 Lesson.4 Ramp Up a. 50 ft m 50 ft/mi mi 500 ft m 50 ft/mi mi,000 ft m 50 ft/mi 4 mi We get the same slope regardless of which triangle is used. c. In order to write the slope as a percent, the units on the rise and run need to be the same. 50 ft m % 5,80 ft Yes. The truck can drive safely on these roads since the slope is less than 6%, 7. a. The student put the change in x on the top of the slope fraction and the change in y on the bottom of the slope fraction. The student subtracted in a different order in the numerator vs. the denominator of the slope fraction. c. The student did not simplify the final fraction to. 8. First triangle: (50 ft) (5, 80 ft) hyp 6,500 ft 7,878, 400 ft hyp 7,940,900 ft hyp Second triangle: miles 5,80 ft/mi 0,560 ft hyp 7,940,900 ft hyp 5,85.9 ft
18 46 Cycle, Part (500 ft) (0,560 ft) hyp 50,000 ft,5,600 ft hyp,76,600 ft hyp hyp,76,600 ft hyp 0,57.8 ft Third triangle: 4 miles 5, 80 ft/mi,0 ft (,000 ft) (,0 ft) hyp,000,000 ft 446, 054, 400 ft hyp 447,054,400 ft hyp Lesson.5 Shortest Distance hyp 447,054,400 ft hyp,4.7 ft. d ( x x ) ( y y ) () (8 6) d ( x x ) ( y y ) ( ) ( ) ( ) ( ) ( 4)
19 Lesson.5 Shortest Distance 47. Student #: This student forgot the square root. Student #: This student did not handle the negative number correctly when he subtracted the x-values. It should be ( ), not. Student #: This student did not do the operations in the correct order. He needed to square and add before taking the square root. d ( x x ) ( y y ) ( ) (68) ( ) ( ) a. d ( x x ) ( y y ) (4 ) ( 5) d ( x x ) ( y y ) ( 4) (5 ) ( 6) ( 8) c. When you square the differences in the distance formula, you get the same positive number regardless of the order of the subtraction. Changing the order of the subtraction changes the sign on the difference but does not affect the square of the difference. 5. The order of the subtraction does not matter in the distance formula, and the same answer will be obtained regardless of the order of the subtraction. The x-values do not have to be subtracted in the same order as the y-values to obtain the correct answer. The order of the subtraction does not matter in the slope formula, but the same order must be used in the numerator and denominator of the slope fraction.
20 48 Cycle, Part Cycle Part Recap. d ( x x ) ( y y ) ( ) (0 ) ( ) (0 ) y y m x x 0 ( ) ( ) 0 5 Concepts and Applications.. vertical distance slope horizontal distance distance (horizontal distance) (vertical distance)
21 Cycle, Part Recap 49 rise grade run 00 ft,640 ft % length of road (horizontal distance) (vertical distance) 00,640 40,000 6,969,600 7,009,600,647.6 ft
22 50 Cycle, Part Part Cycle : Why Does It Matter? Lesson.7 Parts of Speech. The multiplication in the numerator of the fraction should be performed first.. The squaring of the x-value under the square root should be done first.. a. 4 4( x y) c. x d. x 4 4. Jake is incorrect. The addition must be performed before the square root since the square root functions as a grouping symbol. The expression is correctly simplified as follows: 5. a x y x y x y Are the expressions equal? Yes.4 No 0 Yes No 4 0 Yes No Yes. Since there is at least one example in the table for which the expressions are not equal, that is enough to disprove the claim that x y x y. c. No. Even though there is at least one example in the table for which the expressions are equal, that is not enough to prove the claim that x y x y. d. No. There are examples in the table for which the two expressions are not equal. e. No. There are examples in the table for which the two expressions are not equal. 6. No. The expressions are not equivalent since, for example, (5 ) 9 but This one counterexample shows that the expressions are not equivalent.
23 Lesson.7 Parts of Speech 5 ( ab) ( ab)( ab) aa ( b) ba ( b) a ababb a abb 7. a. n square, multiply by, subtract 8. a. ( x ) (0 ) (9) 8 6 subtract, multiply by, divide by or subtract, divide by, multiply by. Lesson.8 In the Swing of Things. G x 7 9. a. square, then multiply by r (inches) A (square inches)
24 5 Cycle, Part c. square inches d. The formula represents a function since each value of the radius is matched with exactly one value of the area. The formula does not represent a linear function since the area does not increase by the same amount each time the radius goes up by one inch. e. The radius would need to be a little less than 5 inches to yield an area of 700 square inches. f. g. The data points might look like they fall in a line, depending on the scale used for the graph. We can be sure the data is not linear, however, by analyzing the table and noting that the area values do not increase by the same amount each time the radius increases by one inch. Lesson.9 Error and Estimation: Rounding. r APY n % n. a. divide i by n, add, raise to the n p power, subtract i p r n n %
25 Lesson.9 Error and Estimation: Rounding 5 c. i p r n n % Cycle Wrap-Up: Cycle Profile Write the slope of the line in two ways: a m ; b y y m x x Write two statements about the value of d: d a b ; d ( x x ) (y y ) Snapshots: Commutative Associative Distributive + Positive Negative Positive + depends Negative depends x x x a b ab ( x ) x a b a b Positive Negative Positive + Negative + Cycle Wrap-Up: Vocabulary Check. negative number. integers. opposite 4. absolute value 5. real numbers 6. mean 7. exponent, base 8. like terms, coefficients 9. polynomial 0. monomial, binomial, trinomial. degree. PEMDAS. commutative property 4. associative property 5. distributive property
26 54 Cycle, Part 6. Pythagorean theorem 7. hypotenuse, legs 8. Pythagorean triple 9. slope 0. distance formula. operation, objects. radical function Cycle Wrap-Up: Concepts and Applications Review. 8 ( 8) 6 8 ( 8) ( 8) 64 8 ( 8). a ( ) ( x ) 6 x c. ( x) 6 x 6 x x x x xx. a. Friday: $00 $00 $50 $5 $0 $0 $05 ; $05 $0 (overdraft fees of $5 per item) $5 Saturday: $5 $0 $5 $70 ; $70 $0 (overdraft fees of $5 per item) $5 (overdraft fee of $5 per day) $85
27 Cycle Wrap-up 55 Sunday: $85 $85 70 $70 $5 (overdraft fees of $5 per item) $5 (overdraft fee of $5 per day) $80 It would be better if the smaller charges cleared first on Friday. Since there is a charge based on the number of items once the account is overdrawn, the fee will be less if most of the smaller items clear first. If the book store charge was processed last, it would be the only one to incur a fee on Friday since the other items total to $55 and would be covered by the $00 balance. c. No. If you transfer $50 first thing Saturday, the balance will only be $5 and insufficient to cover both charges on Saturday. Transferring $50 on Saturday morning would avoid one of the overdraft fees on Saturday though. 4. a. c % S r rh ( ft) ( ft)(0 ft) 8 ft 40 ft 48 ft 50.8 ft 6. a. Yes, but with more than one variable. c. x and x are like terms. 4 x,5 x, and 9x are like terms. x 4xy y5xx 9xx y y 7. a. (5 4)( 4) ( 9)( ) 8 (5 4)( 4) ( 9)( 4)
28 56 Cycle, Part c. (5 4)( 4) 5( 4) 4( 4) (5) (00 )(5) 005 5,500 5, hyp 4 4 hyp 648 hyp 648 hyp hyp 5.5 in b 0 5 b 00 b 75 b 75 b 8.7 ft. a. 7 chairs n c. There is one seat for each table, plus two more seats on the ends.
29 . First, find the difference of the x-coordinates and the difference of the y-coordinates. Second, square each of those differences. Third, add the squared differences. Fourth, take the square root of that sum.. First, subtract the y-values. Second, subtract the x-values in the same order. Third, divide the difference in the y-values by the difference in the x-values. 4. Expression Translation x Take the square root of x and then add. x Take the square root of the quantity x plus. 5 Divide 5 by the sum of x and. x 5 x Divide 5 by x and then add. x Square x and then multiply the result by ( x ) Square the product of and x. x Take the absolute value of the difference of x and. x Take the absolute value of x and then subtract. Cycle Wrap-up Answers will vary. One possible answer is ( (,6) and (5,). 6. a inches 0 0 C r d 64.9 in. d 64.9 in. d 0.7 in. c. Take each circumference and divide by to produce the following set of diameters (each rounded to the nearest hundredth)
30 58 Cycle, Part Average diameter: in. 0 0 This produces the same result. 7. A steep line would have a large, positive value for the slope. Since there is no largest positive number, there is no steepest line. For any line, you can always draw one that is a little steeper because for any positive slope you can always find a slightly larger positive number. A vertical line may seem to be the steepest line, but by definition, it does not have a slope.
Using Proportions to Solve Percent Problems (page 562)
LESSON Name 81 Using Proportions to Solve Percent Problems (page 562) Percent problems can be solved using proportions. Make and complete a percent box. (The total is always 100.) 1. Write in the known
More informationPRE-ALGEBRA SUMMARY WHOLE NUMBERS
PRE-ALGEBRA SUMMARY WHOLE NUMBERS Introduction to Whole Numbers and Place Value Digits Digits are the basic symbols of the system 0,,,, 4,, 6, 7, 8, and 9 are digits Place Value The value of a digit in
More informationSummer Solutions Common Core Mathematics 8. Common Core. Mathematics. Help Pages
8 Common Core Mathematics 6 6 Vocabulary absolute value additive inverse property adjacent angles the distance between a number and zero on a number line. Example: the absolute value of negative seven
More informationMy Math Plan Assessment #1 Study Guide
My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.
More informationMultiplication and Division
UNIT 3 Multiplication and Division Skaters work as a pair to put on quite a show. Multiplication and division work as a pair to solve many types of problems. 82 UNIT 3 MULTIPLICATION AND DIVISION Isaac
More information8th Grade Final Test - Review Sheet
Class: Date: 8th Grade Final Test - Review Sheet 1. Which equation has a slope of 2 and passes through the point (5, 0)? A. y = 2x + 5 B. y = 2x + 10 C. y = 2x + 5 D. y = 2x + 10 2. Which of the following
More informationNew Rochelle High School Geometry Summer Assignment
NAME - New Rochelle High School Geometry Summer Assignment To all Geometry students, This assignment will help you refresh some of the necessary math skills you will need to be successful in Geometry and
More information= = =
. D - To evaluate the expression, we can regroup the numbers and the powers of ten, multiply, and adjust the decimal and exponent to put the answer in correct scientific notation format: 5 0 0 7 = 5 0
More informationMATH 080 Final-Exam Review
MATH 080 Final-Exam Review Can you simplify an expression using the order of operations? 1) Simplify 32(11-8) - 18 3 2-3 2) Simplify 5-3 3-3 6 + 3 A) 5 9 B) 19 9 C) - 25 9 D) 25 9 Can you evaluate an algebraic
More informationSolutions Key Exponents and Polynomials
CHAPTER 7 Solutions Key Exponents and Polynomials ARE YOU READY? PAGE 57. F. B. C. D 5. E 6. 7 7. 5 8. (-0 9. x 0. k 5. 9.. - -( - 5. 5. 5 6. 7. (- 6 (-(-(-(-(-(- 8 5 5 5 5 6 8. 0.06 9.,55 0. 5.6. 6 +
More informationVisit us at: for a wealth of information about college mathematics placement testing!
North Carolina Early Mathematics Placement Testing Program, 9--4. Multiply: A. 9 B. C. 9 9 9 D. 9 E. 9 Solution and Answer to Question # will be provided net Monday, 9-8-4 North Carolina Early Mathematics
More informationStudy Guide for Math 095
Study Guide for Math 095 David G. Radcliffe November 7, 1994 1 The Real Number System Writing a fraction in lowest terms. 1. Find the largest number that will divide into both the numerator and the denominator.
More informationRemember, you may not use a calculator when you take the assessment test.
Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.
More informationAlgebra I Part B. Help Pages & Who Knows
Algebra I Part B & Who Knows 83 Vocabulary General Absolute Value the distance between a number,, and zero on a number line; written as. Eample: 5 = 5 reads The absolute value of 5 is 5. -7 = 7 reads The
More informationTeacher: CORE Math Grade 7 Year: Greatest Common Factor (GCF) Factor 'T' Chart
Teacher: CORE Math Grade 7 Year: 2010-11 Course: Math Grade 7 Month: All Months S e p t e m b e r NUMBER SENSE AND OPERATIONS Place Value Greatest Common Factor Identify whole Decimal number place Notation
More informationMath 4 Review for Quarter 1 Cumulative Test
Math 4 Review for Quarter 1 Cumulative Test Name: I. Unit Conversion Units are important in describing the world around us To convert between units: o Method 1: Multiplication/Division Converting to a
More information1-1. Variables and Expressions. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
- Variables and Expressions Vocabulary Review What mathematical operation is shown in each equation? Write addition, subtraction, multiplication, or division.. 6? 2 5 2 2. 4 2 4 5 0. 27 4 5 9 4. 7 5 20
More informationCalifornia Content Standard. Essentials for Algebra (lesson.exercise) of Test Items. Grade 6 Statistics, Data Analysis, & Probability.
California Content Standard Grade 6 Statistics, Data Analysis, & Probability 1. Students compute & analyze statistical measurements for data sets: 1.1 Compute the mean, median & mode of data sets 1.2 Understand
More informationVariables and Expressions
Variables and Expressions A variable is a letter that represents a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic
More informationUnit 1 Foundations of Algebra
1 Unit 1 Foundations of Algebra Real Number System 2 A. Real Number System 1. Counting Numbers (Natural Numbers) {1,2,3,4, } 2. Whole Numbers { 0,1,2,3,4, } 3. Integers - Negative and Positive Whole Numbers
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II 1 st Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 1 st Nine Weeks, 2016-2017 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More informationName: Essential Skills Practice for students entering Geometry or Accelerated Geometry
Name: Essential Skills Practice for students entering Geometry or Accelerated Geometry Use this document to review the mathematics that you have learned previously. Completion of the Essential Skills Practice
More informationCorrelation: California State Curriculum Standards of Mathematics for Grade 6 SUCCESS IN MATH: BASIC ALGEBRA
Correlation: California State Curriculum Standards of Mathematics for Grade 6 To SUCCESS IN MATH: BASIC ALGEBRA 1 ALGEBRA AND FUNCTIONS 1.0 Students write verbal expressions and sentences as algebraic
More informationDividing in Scientific Notation Name (page 778)
LESSON 111 Dividing in Scientific Notation Name (page 778) To divide powers of 10, subtract the exponents. 10 7 10 4 = 10 7 4 = 10 3 To divide numbers in scientific notation: 1. Divide the decimal or whole
More informationAlgebra II Polynomials: Operations and Functions
Slide 1 / 276 Slide 2 / 276 Algebra II Polynomials: Operations and Functions 2014-10-22 www.njctl.org Slide 3 / 276 Table of Contents click on the topic to go to that section Properties of Exponents Review
More informationMA094 Part 2 - Beginning Algebra Summary
MA094 Part - Beginning Algebra Summary Page of 8/8/0 Big Picture Algebra is Solving Equations with Variables* Variable Variables Linear Equations x 0 MA090 Solution: Point 0 Linear Inequalities x < 0 page
More information4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1 1. Write the slope-intercept form of an equation of a. Write a definition of slope. 7 line with a slope of, and a y-intercept of 3. 11 3. You want
More informationWords 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 informationPart 2 - Beginning Algebra Summary
Part - Beginning Algebra Summary Page 1 of 4 1/1/01 1. Numbers... 1.1. Number Lines... 1.. Interval Notation.... Inequalities... 4.1. Linear with 1 Variable... 4. Linear Equations... 5.1. The Cartesian
More informationMAT 0022C/0028C Final Exam Review. BY: West Campus Math Center
MAT 0022C/0028C Final Exam Review BY: West Campus Math Center Factoring Topics #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 Problem Solving (Word Problems) #19, 20, 21, 22, 23, 24, 25,
More informationThe 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 informationReview for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.
LESSON 6- Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in
More informationNote-Taking Guides. How to use these documents for success
1 Note-Taking Guides How to use these documents for success Print all the pages for the module. Open the first lesson on the computer. Fill in the guide as you read. Do the practice problems on notebook
More information5.3. Polynomials and Polynomial Functions
5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a
More informationIn order to prepare for the final exam, you need to understand and be able to work problems involving the following topics:
MATH 080: Review for the Final Exam In order to prepare for the final exam, you need to understand and be able to work problems involving the following topics: I. Simplifying Expressions: Do you know how
More informationSimple Solutions Mathematics. Part A. Algebra I Part A. Help Pages & Who Knows
Simple Solutions Mathematics Algebra I Part A & Who Knows 83 Vocabulary General Absolute Value the distance between a number, x, and zero on a number line; written as x. Example: 5 = 5 reads The absolute
More informationAlgebra. Robert Taggart
Algebra Robert Taggart Table of Contents To the Student.............................................. v Unit : Algebra Basics Lesson : Negative and Positive Numbers....................... Lesson : Operations
More informationUsing the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles
Math 154 Chapter 9.6: Applications of Radical Equations Objectives: Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles Pythagorean
More informationUnit 8 Practice Problems Lesson 1
Unit 8 Practice Problems Lesson 1 Problem 1 Find the area of each square. Each grid square represents 1 square unit. 17 square units. 0 square units 3. 13 square units 4. 37 square units Problem Find the
More information2) If an athletic conference has 12 teams and each of the teams plays each of the other teams, how many games will there be?
Pre-Algebra Review Worksheet Final Exam Mr. Cierech Name: Date: Chapter 1: Number Patterns 1) Find the next three numbers in the sequence: a) 4, 9, 14, 19, 4... b) 16, 8, 4,, 1, ) If an athletic conference
More informationPearson Learning Solutions
Answers to Selected Exercises CHAPTER REVIEW OF REAL NUMBERS Section.. a. b. c.. a. True b. False c. True d. True. a. b. Ú c.. -0. a. b. c., -, - d.,, -, -, -.,., - e. f.,, -, -,, -.,., -. a. b. c. =.
More informationSimplifying Radicals. multiplication and division properties of square roots. Property Multiplication Property of Square Roots
10-2 Simplifying Radicals Content Standard Prepares for A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Objective To simplify
More informationChapter 5 Simplifying Formulas and Solving Equations
Chapter 5 Simplifying Formulas and Solving Equations Look at the geometry formula for Perimeter of a rectangle P = L W L W. Can this formula be written in a simpler way? If it is true, that we can simplify
More informationMathematics GRADE 8 Teacher Packet
COMMON CORE Standards Plus Mathematics GRADE 8 Teacher Packet Copyright 01 Learning Plus Associates All Rights Reserved; International Copyright Secured. Permission is hereby granted to teachers to reprint
More information8/15/2018, 8:31 PM. Assignment: Math 0410 Homework150bbbbtsiallnew123. Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 2018
of 3 8/15/018, 8:31 PM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework150bbbbtsiallnew13 1. Evaluate x y for the given replacement values. x=4and
More informationRatio Problems Involving Name Totals (page 528)
LESSON 101 Ratio Problems Involving Name Totals (page 528) In some ratio problems a total is needed in order to solve the problem. 1. Fill in the ratio box with things you know. 2. Write a proportion.
More informationGearing Up for Geometry!
Gearing Up for Geometry! Geometry is right around the corner and you need to make sure you are ready! Many of the concepts you learned in Algebra I will be used in Geometry and you will be epected to remember
More informationAre You Ready? Write each verbal expression as an algebraic expression more than m 2. r increased by 5
Are You Ready? Write each verbal expression as an algebraic expression. 1. 5 more than m 2. r increased by 5 3. 25 minus q 4. the difference of 20 and t 5. the sum of v and 8 6. the product of 4 and w
More informationMathwithsheppard.weebly.com
Unit #: Powers and Polynomials Unit Outline: Date Lesson Title Assignment Completed.1 Introduction to Algebra. Discovering the Exponent Laws Part 1. Discovering the Exponent Laws Part. Multiplying and
More informationMATH 60 Course Notebook Chapter #1
MATH 60 Course Notebook Chapter #1 Integers and Real Numbers Before we start the journey into Algebra, we need to understand more about the numbers and number concepts, which form the foundation of Algebra.
More informationIntroduction to Negative Numbers and Computing with Signed Numbers
Section 6. PRE-ACTIVITY PREPARATION Introduction to Negative Numbers and Computing with Signed Numbers In the previous five chapters of this book, your computations only involved zero and the whole numbers,
More informationWords 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 informationGive algebraic and numeric examples to support your answer. Which property is demonstrated when one combines like terms in an algebraic expression?
Big Idea(s): Algebra is distinguished from arithmetic by the systematic use of symbols for values. Writing and evaluating expressions with algebraic notation follows the same rules/properties as in arithmetic.
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
6 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compare and order positive and negative integers*, decimals, fractions, and mixed numbers. They find multiples*
More information2004 Washington State Math Championship. Individual Test - Grade 5
004 Washington State Math Championship Unless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Individual Test - Grade 5 The first 0 problems are multiple
More informationAlgebra vocabulary CARD SETS Frame Clip Art by Pixels & Ice Cream
Algebra vocabulary CARD SETS 1-7 www.lisatilmon.blogspot.com Frame Clip Art by Pixels & Ice Cream Algebra vocabulary Game Materials: one deck of Who has cards Objective: to match Who has words with definitions
More informationSolutions Math is Cool HS Championships Mental Math
Mental Math 9/11 Answer Solution 1 30 There are 5 such even numbers and the formula is n(n+1)=5(6)=30. 2 3 [ways] HHT, HTH, THH. 3 6 1x60, 2x30, 3x20, 4x15, 5x12, 6x10. 4 9 37 = 3x + 10, 27 = 3x, x = 9.
More informationSection 1 - Introduction to Integers
Pre Algebra Unit 1 Unit 1 Integers Objective Overview The following is a small subset of possible problems that could represent each objective. Refer to notes, homework and reviews for a more complete
More informationGrade 6. The Number System & Mathematical Operations.
1 Grade 6 The Number System & Mathematical Operations 2015 10 20 www.njctl.org 2 Table of Contents Addition, Natural Numbers & Whole Numbers Addition, Subtraction and Integers Multiplication, Division
More informationNOTES: Chapter 11. Radicals & Radical Equations. Algebra 1B COLYER Fall Student Name:
NOTES: Chapter 11 Radicals & Radical Equations Algebra 1B COLYER Fall 2016 Student Name: Page 2 Section 3.8 ~ Finding and Estimating Square Roots Radical: A symbol use to represent a. Radicand: The number
More informationCommon Core Algebra Regents Review
Common Core Algebra Regents Review Real numbers, properties, and operations: 1) The set of natural numbers is the set of counting numbers. 1,2,3,... { } symbol 2) The set of whole numbers is the set of
More informationReal Numbers and an Introduction to Algebra
ChaPter 1 Real Numbers and an Introduction to Algebra Objectives In this chapter you will learn how to do the following: 1. Read mathematical symbols. 2. Distinguish between different sets of numbers.
More informationChapter 8 RADICAL EXPRESSIONS AND EQUATIONS
Name: Instructor: Date: Section: Chapter 8 RADICAL EXPRESSIONS AND EQUATIONS 8.1 Introduction to Radical Expressions Learning Objectives a Find the principal square roots and their opposites of the whole
More information6 th Grade - TNREADY REVIEW Q3 Expressions, Equations, Functions, and Inequalities
6 th Grade - TNREADY REVIEW Q3 Expressions, Equations, Functions, and Inequalities INSTRUCTIONS: Read through the following notes. Fill in shaded areas and highlight important reminders. Then complete
More informationCollecting Like Terms
MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.
More informationReady To Go On? Skills Intervention 7-1 Integer Exponents
7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 7-1 Integer Exponents Negative Exponent:
More informationCorrelation of Moving with Math Grade 7 to HSEE Mathematics Blueprint
Correlation of Moving with Math Grade 7 to HSEE Mathematics Blueprint Number Sense 1.0 Students know the properties of, and compute with, rational numbers expressed n a variety of forms: 1.1 Read, write
More informationaddend angle composite number capacity Vocabulary Flash Cards Review Review Review Review Review Review
addend angle area bar graph capacity composite number cubic units difference A figure formed by two rays with the same endpoint A number to be added to another number. 2 or 3 in the sum 2 + 3. A graph
More informationVirginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning
BUI L T F O VIR R G INIA 2014 2015 Virginia -Specific Learning Pathways Grades 6-Algebra I: Standards of Learning Table of Contents Grade 6...3 Grade 7...6 Grade 8...9 Algebra I... 11 Grade 6 Virginia
More informationSecondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics
Secondary Math H Unit 3 Notes: Factoring and Solving Quadratics 3.1 Factoring out the Greatest Common Factor (GCF) Factoring: The reverse of multiplying. It means figuring out what you would multiply together
More informationPolynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together.
UNIT 10 Working with Polynomials The railcars are linked together. 370 UNIT 10 WORKING WITH POLYNOMIALS Just as a train is built from linking railcars together, a polynomial is built by bringing terms
More information7 th Grade MCA3 Standards, Benchmarks, Examples, Test Specifications & Sampler Questions
7 th Grade 3 Standards, Benchmarks, Examples, Test Specifications & Sampler Questions Strand Standard No. Benchmark (7 th Grade) Sampler Item Number & Operation 12-16 Items Modified 7-9 Items Read, write,
More informationBEMIDJI AREA SCHOOLS Outcomes in Mathematics Grade 7
Outcomes in Mathematics Grade Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that π is not rational, but.1.1.1 that it can
More informationThe Top 11 Keystones of Algebra 1
The Top 11 Keystones of Algebra 1 The Top Eleven Keystones of Algebra 1 You should be able to 1) Simplify a radical expression. 2) Solve an equation. 3) Solve and graph an inequality on a number line.
More informationName: Period: Unit 3 Modeling with Radical and Rational Functions
Name: Period: Unit Modeling with Radical and Rational Functions 1 Equivalent Forms of Exponential Expressions Before we begin today s lesson, how much do you remember about exponents? Use expanded form
More informationName Date Class. 5 y x + 7
Name Date Class 7.EE.1 SELECTED RESPONSE Select the correct answer. 1. What property allows the expression.7x + 10. + 15.3x 8.x + 15.6 to be simplified to the equivalent expression 0x + 10. 8.x + 15.6?
More informationMesa Public Schools. Q3 practice test. Assessment Summary: Powered by SchoolCity Inc. Page 1 of 44
Mesa Public Schools Assessment Summary: Q3 practice test Powered by SchoolCity Inc. www.schoolcity.com Page 1 of 44 Assessment Summary: Q3 practice test Year: 2016-2017 Subject: Math Total Items: 43 Total
More informationSection 2.2 Objectives
Section 2.2 Objectives Solve multi-step equations using algebra properties of equality. Solve equations that have no solution and equations that have infinitely many solutions. Solve equations with rational
More informationMath Review Packet. for Pre-Algebra to Algebra 1
Math Review Packet for Pre-Algebra to Algebra 1 Epressions, Equations, Eponents, Scientific Notation, Linear Functions, Proportions, Pythagorean Theorem 2016 Math in the Middle Evaluating Algebraic Epressions
More information= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:
Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations
More informationGrade 6 The Number System & Mathematical Operations
Slide 1 / 206 Slide 2 / 206 Grade 6 The Number System & Mathematical Operations 2015-10-20 www.njctl.org Slide 3 / 206 Table of Contents Addition, Natural Numbers & Whole Numbers Addition, Subtraction
More information( ) Chapter 7 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3.
Chapter 7 Exercise Set 7.1 1. A prime number is an integer greater than 1 that has exactly two factors, itself and 1. 3. To factor an expression means to write the expression as the product of factors.
More informationAlgebra 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 informationWhat students need to know for... Functions, Statistics & Trigonometry (FST)
What students need to know for... Functions, Statistics & Trigonometry (FST) 2018-2019 NAME: This is a MANDATORY assignment that will be GRADED. It is due the first day of the course. Your teacher will
More informationCongratulations! You ve completed Practice Test 1! You re now ready to check your
Practice Test 1: Answers and Explanations Congratulations! You ve completed Practice Test 1! You re now ready to check your answers to see how you fared. In this chapter, I provide the answers, including
More information7.2 Multiplying Polynomials
Locker LESSON 7. Multiplying Polynomials Teas Math Standards The student is epected to: A.7.B Add, subtract, and multiply polynomials. Mathematical Processes A.1.E Create and use representations to organize,
More informationAnswers Investigation 4
Answers Investigation Applications. a. 7 gallons are being pumped out each hour; students may make a table and notice the constant rate of change, which is - 7, or they may recognize that - 7 is the coefficient
More information2. Which of the following expressions represents the product of four less than three times x and two more than x?
Algebra Topics COMPASS Review You will be allowed to use a calculator on the COMPASS test. Acceptable calculators are: basic calculators, scientific calculators, and graphing calculators up through the
More informationAlgebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher
Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work
More informationLESSON 9.1 ROOTS AND RADICALS
LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical
More informationAlgebra I. Mathematics Curriculum Framework. Revised 2004 Amended 2006
Algebra I Mathematics Curriculum Framework Revised 2004 Amended 2006 Course Title: Algebra I Course/Unit Credit: 1 Course Number: Teacher Licensure: Secondary Mathematics Grades: 9-12 Algebra I These are
More informationDestination Math California Intervention
Destination Math California Intervention correlated to the California Intervention 4 7 s McDougal Littell Riverdeep STANDARDS MAPS for a Mathematics Intervention Program (Grades 4-7) The standards maps
More informationCHAPTER 5: ALGEBRA CHAPTER 5 CONTENTS
CHAPTER 5: ALGEBRA Image from www.coolmath.com CHAPTER 5 CONTENTS 5. Introduction to Algebra 5. Algebraic Properties 5. Distributive Property 5.4 Solving Equations Using the Addition Property of Equality
More information1 of 32 4/24/2018, 11:38 AM
1 of 3 4/4/018, 11:38 AM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework149aleks 1 Insert < or > between the pair of integers to make the statement
More informationThe Keystones of Algebra 1
The Keystones of Algebra 1 The Top Ten Keystones of Algebra 1 You should be able to 1) Simplify a radical expression. 2) Solve an equation. 3) Solve and graph an inequality on a number line. 4) Manipulate
More information6.2 Multiplying Polynomials
Locker LESSON 6. Multiplying Polynomials PAGE 7 BEGINS HERE Name Class Date 6. Multiplying Polynomials Essential Question: How do you multiply polynomials, and what type of epression is the result? Common
More informationFree Pre-Algebra Lesson 59! page 1
Free Pre-Algebra Lesson 59! page 1 Lesson 59: Review for Final Exam Section VII. Proportions and Percents Comprehensive Practice Lessons 37-42 Lesson 37: Scale and Proportion Skill: Write ratios of sides
More information8 th Grade Intensive Math
8 th Grade Intensive Math Ready Florida MAFS Student Edition August-September 2014 Lesson 1 Part 1: Introduction Properties of Integer Exponents Develop Skills and Strategies MAFS 8.EE.1.1 In the past,
More information5-7 The Pythagorean Theorem
5-7 The Pythagorean Theorem Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Classify each triangle by its angle measures. 1. 2. acute right 3. Simplify 12 4. If a = 6, b = 7, and c = 12, find
More informationLESSON 6.2 POLYNOMIAL OPERATIONS I
LESSON 6. POLYNOMIAL OPERATIONS I LESSON 6. POLYNOMIALS OPERATIONS I 63 OVERVIEW Here's what you'll learn in this lesson: Adding and Subtracting a. Definition of polynomial, term, and coefficient b. Evaluating
More information