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1 March 22, 2013 Mathe ematics s Re evie ew Note N es or Pa aren nts and d Sttude ents s fo Grad de 8 Mathe M ematiics 4thh Nine e Wee eks, Created by Julie A. Byrd 1

2 Grade 8 Mathematics Formula Sheet 2009 Mathematics Standards of Learning March 22, 2013 Geometric Formulas A h b bh = 1 2 s w s l p = 4s p = 2l + 2w A = s A= lw r d C = 2πr C = πd 2 A = πr b b 1 r h h h h b A = bh b 2 1 A = h ( b 1 + b 2) 2 l w V = lwh S. A. = 2lw + 2lh + 2wh 2 V = πr h 2 SA.. = 2πr + 2πrh B h V = Bh SA.. = hp+ 2B B h V = 1 Bh 3 SA 1.. = lp+ B 2 l 1 V = π 3 l h r 2 r h 2 SA.. = πr + πrl a b c a + b = c Abbreviations milligram mg gram g kilogram kg milliliter ml liter L kiloliter kl millimeter mm centimeter cm meter m kilometer km square centimeter cm 2 cubic centimeter cm 3 ounce pound quart gallon inch foot yard mile square inch square foot cubic inch cubic foot oz lb qt gal. in. ft yd mi. sq in. sq ft cu in. cu ft Area Area of Base Circumference Perimeter Surface Area Volume Pi π π 7 A B C p S.A. V Copyright 2011 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia All rights reserved. Except as permitted by law, this material may not be reproduced or used in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system, without written permission from the copyright owner. Commonwealth of Virginia public school educators may reproduce any portion of this mathematics formula sheet for non-commercial educational purposes without requesting permission. Created All by others Julie should A. Byrd direct their written requests to the Virginia Department of 2Education, Division of Student Assessment and School Improvement, at the above address or by to Student_Assessment@doe.virginia.gov.

Content Review: Standards of Learning in Detail Grade 8 Mathematics: Fourth Nine Weeks 2012-2013 This resource is intended to be a guide for parents and students to improve content knowledge and

3 Content Review: Standards of Learning in Detail Grade 8 Mathematics: Fourth Nine Weeks This resource is intended to be a guide for parents and students to improve content knowledge and understanding. The information below is detailed information about the Standards of Learning taught during the 4 th grading period and comes from the Mathematics Standards of Learning Curriculum Framework, Grade 8, issued by the Virginia Department of Education. The Curriculum Framework in its entirety can be found at the following website: math8.pdf SOL 8.13 The student will a) make comparisons, predictions, and inferences, using information displayed in graphs and b) construct and analyze scatterplots. Comparisons, predictions, and inferences are made by examining characteristics of a data set displayed in a variety of graphical representations to draw conclusions. The information displayed in different graphs may be examined to determine how data are or are not related, ascertaining differences between characteristics (comparisons), trends that suggest what new data might be like (predictions), and/or what could happen if (inferences). Below is an example of a frequency distribution table. A frequency distribution shows how often an item, a number, or a range of numbers occurs. Created by Julie A. Byrd 3

Below is an example of a line graph. According to the graph, it can be predicted that the decline in the number of U. S. farms will decrease at a slower rate during 1990 to 2000.

4 Below is an example of a line graph. According to the graph, it can be predicted that the decline in the number of U. S. farms will decrease at a slower rate during 1990 to A histogram is a form of bar graph in which the categories are consecutive and equal intervals. The length or height of each bar is determined by the number of data elements falling into a particular interval. This histogram shows the average 7 th grade math scores during each grading period. Created by Julie A. Byrd 4

5 A scatterplott illustrates the relationship between two sets of data. A scatter plot consists of points. The coordinates of the point represent the measures of the two attributes of the point. Scatterplots can be used to predict trends and estimate a line of best fit. The following are examples of scatterplots and the relationships demonstrated by each graph. This scatterplot shows a negative relationship between the distance traveled and the amount of gas remaining in the gas tank of a car. In other words, the more distance traveled, the less gas remains in the tank. This scatterplot shows a positive relationship between the husband s age and the wife s age. In other words, as the age of the husband increases, the age of the wife also increases. Created by Julie A. Byrd 5

6 This scatterplot shows that there is no relationship between the number of hours a person watches television and the height of a person. In a scatterplot, each point is represented by an independent and dependent variable. The independent variable is graphed on the horizontal axis and the dependent variable is graphed on the vertical axis. Scatterplots can be used to predict trends and estimate a line of best fit. This scatterplot shows how many total miles Caden has biked over the past several days. How many miles would you predict Caden will have biked by day 8? The pattern in the scatterplot shows that Caden is biking about 25 miles each day. To determine how many miles on Day 8, multiply 8 by = 200 miles Created by Julie A. Byrd 6

7 Released Test Items from the Virginia Standards of Learning, Grade 8 Mathematics Test Answers are located on the last page of the booklet. Comparisons, Predictions, & Inferences from Graphs, SOL Created by Julie A. Byrd 7

8 Comparisons, Predictions, & Inferences from Graphs, SOL Created by Julie A. Byrd 8

9 Comparisons, Predictions, & Inferences from Graphs, SOL Created by Julie A. Byrd 9

10 Comparisons, Predictions, & Inferences from Graphs, SOL Created by Julie A. Byrd 10

11 Comparisons, Predictions, & Inferences from Graphs, SOL Created by Julie A. Byrd 11

12 SOL 8.14 The student will make connections between any two representations (tables, graphs, words, and rules) for a given relationship. A relation is any set of ordered pairs. For each first member (domain), there may be many second members (range). The domain is the set of x values in a set of ordered pairs. The range is the set of y values in a set of ordered pairs. Example: The table below shows a relationship between d, the number of days a library book is overdue, and f, the amount of the fine. The function for this relationship is f = 0.05d. A function is a relation in which there is one and only one second member (range) for each first member (domain). Example: Which number replaces the? in the table? The value of n is given in the top row. The function is given in the second row. Replace the n in 3 n so that it reads 3-2 to determine the missing value. The correct answer is 9 1. Functions can be represented as tables, graphs, equations, physical models, or in words. As a graph, a function is any curve (including straight lines) such that any vertical line would pass through the curve only once. Created by Julie A. Byrd 12

Examples: These are examples of graphed functions.

variable (domain). Some relations are functions; all functions are relations. Graphs of functions can be discrete or continuous.

The points between the plotted points have no meaning and cannot be interpreted.

13 Examples: These are examples of graphed functions. y = x + 3 As a table of values, a function has a unique value assigned to the second variable (range) for each value of the first variable (domain). Some relations are functions; all functions are relations. Graphs of functions can be discrete or continuous. In a discrete function graph there are separate distinct points. You would not use a line to connect the points on the graph. The points between the plotted points have no meaning and cannot be interpreted. In a graph of a continuous function every point in the domain can be interpreted therefore it is possible to connect the points on the graph with a continuous line as every point on the line answers the original question being asked. (SOL ) Created by Julie A. Byrd 13

14 Released Test Items from the Virginia Standards of Learning, Grade 8 Mathematics Test Answers are located on the last page of the booklet. Relations and Functions, SOL March 22, 2013 Created by Julie A. Byrd 14

15 Created by Julie A. Byrd 15 March 22, 2013

16 Relations and Functions, SOL Created by Julie A. Byrd 16

17 Relations and Functions, SOL Created by Julie A. Byrd 17

18 Relations and Functions, SOL Created by Julie A. Byrd 18

19 Relations and Functions, SOL Created by Julie A. Byrd 19

20 Relations and Functions, SOL Created by Julie A. Byrd 20

21 Relations and Functions, SOL Created by Julie A. Byrd 21

22 SOL 8.16 The student will graph a linear equation in two variables. A linear equation is an equation in two variables whose graph is a straight line. Graphing a linear equation requires determining a table of ordered pairs by substituting into the equation values for one variable and solving for the other variable, plotting the ordered pairs in the coordinate plane, and connecting the points to form a straight line. The axes of a coordinate plane are generally labeled x and y; however, any letters may be used that are appropriate for the function. This is a list of ordered pairs. The ordered pairs are:(-1, 4), (0, 2), and (1, 0). When these points are plotted on a coordinate plane, they can be connected to form a line. This is the graph for the set of ordered pairs shown above. Created by Julie A. Byrd 22

23 Released Test Items from the Virginia Standards of Learning, Grade 8 Mathematics Test Answers are located on the last page of the booklet. Graphing Linear Equations in the Coordinate Plane, SOL 8.16 March 22, Created by Julie A. Byrd 23

24 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 24

25 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 25

26 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 26

27 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 27

28 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 28

29 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 29

30 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 30

31 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 31

32 Graphing Linear Equations in the Coordinate Plane, SOL Created by Julie A. Byrd 32

33 SOL 8.17 The student will identify the domain, range, independent variable, and dependent variable of a given situation. The domain is the possible set of all the input values for the independent variable in a given situation. The range is the possible set of all the output values for the dependent variable in a given situation. The independent variable is the input value. The dependent variable depends on the independent variable and is the output value. Example 1: Below is a table of values for finding the circumference of circles, C = πd, where the value of π is approximated as Diameter Circumference 1 in in. 2 in in. 3 in in. 4 in in. Independent Variable (input) = the diameter of the circle Domain = {1, 2, 3, 4} Dependent Variable (output) = the circumference of the circle Range = {3.14, 6.28, 9.42, 12.56} Example 2: The formula shows that c, the total cost of buying pizzas at Al s Restaurant depends on p, the number of pizzas ordered. c = 9p Independent Variable (input) = the number of pizzas Dependent Variable (output) = the total cost of buying the pizzas Using the domain {1, 2, 3, 4}, you can make a table and calculate the range. Number of Pizzas (p) Total Cost (c) Domain = {1, 2, 3, 4} Range = {9, 18, 27, 36} Created by Julie A. Byrd 33

34 Released Test Items from the Virginia Standards of Learning, Grade 8 Mathematics Test Answers are located on the last page of the booklet. Algebraic Terminology, SOL Created by Julie A. Byrd 34

35 Algebraic Terminology, SOL Created by Julie A. Byrd 35

36 Algebraic Terminology, SOL Created by Julie A. Byrd 36

37 Algebraic Terminology, SOL Created by Julie A. Byrd 37

38 Testing Information Midpoint Test, 4 th Nine Weeks The Midpoint Test will include questions from standards 8.13, 8.14, 8.16, and 8.17(included in this booklet), as well as questions from standards 8.6, 8.8, 8.3, and 8.12, which were taught and tested earlier in the school year. Use the 3 rd and 4 th Nine Weeks Review Notes for Parents and Students to prepare for this test. The 4 th Nine Weeks Midpoint Test will be administered May 2 nd through May 7 th, Check with your child s teacher for the specific testing date. 4 th Nine Weeks Test The 4 th Nine Weeks Test will include questions from standard 8.13, 8.14, 8.16, and 8.17 (included in this booklet) and standards 8.3 and 8.12 from the 3 rd nine weeks. Use the 3 rd and 4 th Nine Weeks Review Notes for Parents and Students to prepare for the 4 th Nine Weeks Test. The 4 th Nine Weeks Test will be administered the week of June 10 th, Check with your child s teacher for the specific testing date. Created by Julie A. Byrd 38

39 The following pages contain vocabulary sorts that can be used to review relevant math terms for this grading period. Cut out the sort and practice matching the vocabulary word with the matching description. Created by Julie A. Byrd 39

40 Created by Julie A. Byrd 40 March 22, 2013

41 SOL 8.13 histogram A bar chart representing a frequency distribution; heights of the bars represent observed frequencies circle graph A type of statistical graph used to compare parts of a whole. The entire represents the whole. bar graph A graphic form using bars to make comparisons of statistics picture graph A graphic form using pictures to make comparisons of statistics line graph frequency distribution scatterplot A type of statistical graph using lines to show how values change over a period of time. Shows how often an item, a number, or a range of numbers occurs Illustrates the relationship between two sets of data. It consists of points. Created by Julie A. Byrd 41

42 Created by Julie A. Byrd 42 March 22, 2013

43 SOL 8.14 function A relation in which there is one and only one second member (range) for each first member (domain) function table A table of values in which a unique value is assigned to the second variable (range) for each value of the first variable (domain.) nonlinear function A function that does not have a constant rate of change. The graph of a nonlinear function is not a straight line. quadratic function relation A function in the second degree; any function that an be described by an equation of the form y=ax 2 +bx+c, where a 0 Any set of ordered pairs discrete function Graph which has separate, distinct points that are not connected by a line continuous function In a graph of this function every point in the domain can be interpreted so it is possible to connect the points with a line. (A linear equation is an example of this type of function. Created by Julie A. Byrd 43

44 Created by Julie A. Byrd 44 March 22, 2013

45 SOL 8.16 input The independent (x) value of a function linear equation An equation in two variables whole graph is a line. (The independent variable is limited to the first power.) linear function Function in the first degree whose graph is a line ordered pair (x,y) A pair of numbers used to locate a point in the coordinate plane. The ordered pair is written in this form (x-coordinate, y-coordinate.) output The value of the dependent variable of a function x Variable commonly used for the domain, independent variable, or the input of a function y Variable commonly used for the range, dependent variable, or the output of a function Created by Julie A. Byrd 45

46 Created by Julie A. Byrd 46 March 22, 2013

47 SOL 8.16 (continued) coordinate plane Another name for the coordinate system which is formed by the intersection of two number lines that meet at right angles at their zero points SOL 8.17 domain The set of input values in a function range The set of output values in a function dependent variable The variable for the output of a function independent variable The variable for the input of a function. Created by Julie A. Byrd 47

48 Created by Julie A. Byrd 48 March 22, 2013

49 Released Test Answers (4 th Nine Weeks) March 22, 2013 SOL 8.13 (Data and Graphs) 1. J 2. H 3. H 4. C 5. J 6. C 7. J 8. A 9. G SOL 8.14 (Relations and Functions) 1. J 2. H 3. C 4. A 5. H 6. J 7. G 8. A 9. F 10. A 11. A 12. A 13. G 14. A 15. G SOL 8.16 (Graphing Linear Equations in the Coordinate Plane) 1. J 2. A 3. D 4. F 5. F 6. G 7. J 8. A 9. J 10. B SOL 8.17 (Algebraic Terminology) 1. J 2. A 3. H 4. B 5. A 6. F 7. A 8. A 9. J Created by Julie A. Byrd 49

50 Created by Julie A. Byrd 50 March 22, 2013

51 Math Smarts! Math + Smart Phone = Math Smarts! Need help with your homework? Wish that your teacher could explain the math concept to you one more time? This resource is for you! Use your smart phone and scan the QR code and instantly watch a 3 to 5 minute video clip to get that extra help. (These videos can also be viewed without the use of a smart phone. Click on the links included in this document.) Directions: Using your Android-based phone/tablet or iphone/ipad, download any QR barcode scanner. How do I do that? 1. Open Google Play (for Android devices) or itunes (for Apple devices). 2. Search for QR Scanner. 3. Download the app. After downloading, use the app to scan the QR code associated with the topic you need help with. You will be directed to a short video related to that specific topic! It s mobile math help when you need it! So next time you hear, You re always on that phone or Put that phone away! you can say It s homework!!! Access this document electronically on the STAR website through Suffolk Public Schools. ( PLEASE READ THE FOLLOWING: This resource is provided as a refresher for lessons learned in class. Each link will connect to a YouTube or TeacherTube video related to the specific skill noted under Concept. Please be aware that advertisements may exist at the beginning of each video. Created by Julie A. Byrd 51

52 Math 8 SOL Concept Link QR Code 8.1 Scientific Notation (negative exponents begin at 3:00) WwmJ5nMmigQ 8.2 Subsets of Real Numbers: 1bU0uY2XcJs 8.2 Subsets of Real Numbers (Music/Song/Rap) KKfoORhiSA0 8.3 Percent of a Number KewfKIXRRtI 8.3 Determining the percent increase and decrease for a given situation CLbRHY1YPK4 Created by Julie A. Byrd 52

53 Math 8 March 22, 2013 SOL Concept Link QR Code 8.4 Applying the order of operations oo5daho7nhy 8.4 Applying the order of operations SuivTXJmVPg 8.5 COMING SOON! 8.6 Describing angle relationships (starts at 5:55; advanced skills prior to 5:55) glh3svackpi 8.6 Describing relationships among complementary and supplementary angles (Rap) fsfgktxm6k Solving practical problems involving volume and surface area of prisms Solving practical problems involving volume and surface area of cylinders Solving practical problems involving volume and surface area of cones COMING SOON! COMING SOON! COMING SOON! Created by Julie A. Byrd 53

54 Math 8 SOL Concept Link QR Code 8.7 Solving practical problems involving volume and COMING SOON! surface area of pyramids 8.7 Solving practical problems involving volume and surface area of prisms, COMING SOON! cylinders, cones, and pyramids 8.8 Applying transformations COMING SOON! 8.9 Constructing threedimensional models COMING SOON! March 22, Applying the Pythagorean Theorem QNl_yb8doRk 8.10 Verifying the Pythagorean Theorem R=1&v=uaj0XcLtN5c&feature=endsc reen 8.11 Solving area and perimeter problems involving composite plane figures tfrcedydcek 8.12 Determining the probability of dependent and independent events COMING SOON! Created by Julie A. Byrd 54

55 Math 8 March 22, 2013 SOL Concept Link QR Code 8.13 Constructing scatterplots AXWtiVaOmPg 8.14 Analyzing scatterplots CWnfwZRAuaY 8.15? Solve/Graph Multi-step Inequalities (includes variables on both sides) 4lJNFxd_Ijg 8.15 Solving 2-step Equations variable on one side (starts at 0:00) and variable on both sides (starts at 6:45) f2ez0dbh1u Solving Equations with variables on both sides gqdh5pkwrpq Created by Julie A. Byrd 55

56 Math 8 March 22, 2013 SOL Concept Link QR Code 8.16 Representing Functions as Graphs Jggua4YtikY 8.16 Graphing Linear Equations 2UrcUfBizyw 8.16 Graphing Linear Equations m_mrqt7puuw 8.17 Identifying Domain/Range from Function RK2EM7lKmbw 8.17 Identifying Domain/Range from Function 934yReRW_LA Created by Julie A. Byrd 56

57 Math 8 March 22, 2013 SOL Concept Link QR Code 8.17 Identifying Independent and Dependent Variables okkzajyiona 8.17 Identifying Independent and Dependent Variables tbgtfz7gvse Created by Julie A. Byrd 57

STANDARDS OF LEARNING CONTENT REVIEW NOTES. Grade 6 Mathematics 3 rd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES Grade 6 Mathematics 3 rd Nine Weeks, 2016-2017 1 2 Content Review: Standards of Learning in Detail Grade 6 Mathematics: Third Nine Weeks 2016-2017 This resource