Outstanding Math Guide

Transcription

1 Outstanding Math Guide 6 th Grade Aligned to the Georgia Performance Standards Written by: Rhonda Davis, Leslie Hilderbrand, Darby Jochum and Robert Sheperd Graphic Design by: Sydney Hilderbrand ISBN: Outstanding Guides, LLC 1

2 2010 Outstanding Guides, LLC 2

3 We would like to extend our thanks and gratitude to our family, friends, co-workers and the Fairplay community for their support in this endeavor Outstanding Guides, LLC

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5 Table of Contents Page Introduction.. 7 Overview.. 9 Implementation Guide.. 11 GPS Alignment. 1 Suggested Layout. 15 Number and Operation Graphic Organizers Divisibility Rules Factor Slide Fundamentals of Fractions Fractions, Decimals & Percents Multiplication Table..... Prime Factorization.. 5 Types of Decimals 9 Measurement Graphic Organizers Formulas Measuring. 51 Metric... 5 Surface Area. 57 Volume. 61 Geometry Graphic Organizers Similar and Congruent (Scale). 65 Symmetry Algebra Graphic Organizer Proportions.. 75 Data Analysis and Probability Graphic Organizers Appendices Graphs.. 79 Probability 85 Vocabulary Template Vocabulary Grader... 9 File Box Labels 95 Parent Letter Outstanding Guides, LLC 5

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7 Outstanding Math Guide Introduction The Outstanding Math Guide (OMG) is packed with creative folded graphic organizers which contain steps and examples for each key concept encountered throughout the year. These graphic organizers are encased in a folded, standard -prong pocket folder. The OMG serves as a visual reference that students keep in their notebooks and use in class or at home when completing homework, studying, or working through spiraling material. This book contains differentiated graphic organizer templates that can be reproduced for your students to create. In addition to key concepts aligned to Georgia Performance Standards, and easily adaptable to Common Core, the OMG includes a section for vocabulary where students can record terms and examples as they are introduced in the classroom. Materials Needed Incorporating OMGs in your math instruction requires limited out of pocket expenses. Folders: Three prong folder with pockets for each student. Paper: Lightweight and colorful. Glue: Glue sticks only. Scissors: Classroom set. Heavy duty hole punch: To punch holes in folder. File Box: To store extra copies of graphic organizer templates. Disk (included): Can be used as an instructional guide when completing graphic organizers with students. Disk also includes videos for initial folder set-up and folding instructions for each graphic organizer Outstanding Guides, LLC 7

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9 Outstanding Math Guide Overview These reproducible graphic organizers can be used by your students to make an Outstanding Math Guide (OMG). The OMG is a work in progress; graphic organizers are constructed as an introduction or review of each topic. By the end of the year, your students will have an OMG that can be easily referenced for years to come. A standard - prong pocket folder is folded in half. Vocabulary sheets allow terms and examples to be recorded as they are introduced in class. Holes are punched so OMG will store in the front of a notebook Outstanding Guides, LLC 9

10 Pockets in folder are cut down each side so they will open up Outstanding Guides, LLC 10

11 Outstanding Math Guide IMPLEMENTATION To implement a successful OMG program you will need flexible and supportive co-workers. At our school, we have been blessed with a supportive administration and a flexible math team, so all students have their OMG in their math notebook at all times. Our principal has even been known to stop students in the hallway and ask to see their OMG. The following are the various components of the OMG implementation process: OMG: Every student in every grade creates an OMG. The OMG will only be as valuable as you make it. The way to make it valuable and your students more independent is to require them to reference previously taught material as the need arises. We suggest that students have OMG s out during class time. You must get them in the habit of looking up questions in their OMG. As students have increased ownership in the OMG, they will begin to see its value beyond a place to glue graphic organizers. Folder Set-up: For logistic purposes we recommend each grade level use a different color folder for their OMGs. To help minimize your costs, we suggest adding a specific color folder to your back-to-school supplies list, and some students will actually get their own folder (stress a prong folder with pockets is needed). One of the first few days of school should be used to set up the OMG. See included disk for a video of folder set-up instructions. Graphic Organizers: Each graphic organizer can be used as unit introduction or review. Three types of graphic organizer templates are offered in this book: Completed notes and examples - targeting students with special needs. Fill in the blank - targeting students on grade level. Blank - targeting accelerated students or deviation from the provided material. Graphic Organizer Placement: Reference the layout placement guide to ensure that all the created graphic organizers fit inside the OMG. Vocabulary Sheets: Copies of the vocabulary sheets will be needed for each OMG. As a suggestion have the vocabulary template accessible on your website and request that students download copies for their OMG. See Appendix A for vocabulary template and Appendix B for vocabulary grading rubric Outstanding Guides, LLC 11

12 Outstanding Math Guide Absent Students: If a student is absent on the a day a graphic organizer is made, have another trusted student make one for them. New Students: To help new students create an OMG, delegate the responsibility to a classmate. It is helpful to make additional graphic organizers as you go to provide new students with an up-to-date OMG. Lost OMG: Explain the consequences of losing your OMG. If the inevitable happens and a student loses his OMG, give the student a time frame in which the graphic organizers should be recreated. You will be amazed when students realize they will have to remake the OMG on their own time they become much more protective of it! File Box: A file crate can be used to store extra copies of each graphic organizer template. Print labels have been provided in Appendix C. Parents: It is helpful for parents to be familiar with the OMG purpose. When students need help with homework, an informed parent can suggest they reference their OMG. A sample parent letter is provided in Appendix D Outstanding Guides, LLC 12

13 GEORGIA PERFORMANCE STANDARDS Graphic Organizer Number and Operations: Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will apply these concepts and associated skills in real world situations. Students will understand the meaning of the four arithmetic operations as M6N1 related to positive rational numbers and will use these concepts to solve problems. a. Apply factors and multiples. Factor Slide b. Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic). Prime Factorization c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers. Factor Slide d. Add and subtract fractions and mixed numbers with unlike denominators. Fractions e. Multiply and divide fractions and mixed numbers. Fractions f. Use fractions, decimals, and percents interchangeably. Fraction/Decimal/% g. Solve problems involving fractions, decimals, and percents. Fraction/Decimal/% Measurement: Students will understand how to determine the volume and surface area of solid figures. They will understand and use the customary and metric systems of measurement to measure quantities efficiently and to represent volume and surface area appropriately. M6M1 Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships. Metric M6M2 Students will use appropriate units of measure for finding length, perimeter, area, and volume and will express each quantity using the appropriate unit. a. Measure length to the nearest half, fourth, eighth, and sixteenth of an inch. Measuring b. Select and use units of appropriate size and type to measure length, perimeter, area, and volume. Surface Area/Volume c. Compare and contrast units of measure for perimeter, area, and volume. Surface Area/Volume M6M Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders, pyramids, and cones). a. Determine the formula for finding the volume of fundamental solid figures. Formulas b. Compute the volumes of fundamental solid figures, using appropriate units of measure. Volume c. Estimate the volumes of simple geometric solids. Volume d. Solve application problems involving the volume of fundamental solid Volume M6M4 Students will determine the surface area of solid figures (right rectangular prisms and cylinders). Find the surface area of right rectangular prisms and cylinders using a. manipulatives and constructing nets. Surface Area Compute the surface area of right rectangular prisms and cylinders using b. formulae. Surface Area c. Estimate the surface areas of simple geometric solids. Surface Area d. Solve application problems involving surface area of right rectangular prisms and cylinders. Surface Area Geometry: Students will further develop their understanding of plane and solid geometric figures, incorporating the use of appropriate technology and using this knowledge to solve authentic problems. M6G1 Students will further develop their understanding of plane figures. a. Determine and use lines of symmetry. Symmetry b. Investigate rotational symmetry, including degree of rotation. Symmetry c. Use the concepts of ratio, proportion, and scale factor to demonstrate the relationship between similar plane figures. Proportion d. Interpret and sketch simple scale drawings. Proportion 2010 Outstanding Guides, LLC 1

14 e. Solve problems involving scale drawings. Proportion M6G2 Students will further develop their understanding of solid figures. a. Compare and contrast right prisms and pyramids. Surface Area/Volume b. Compare and contrast cylinders and cones. Surface Area/Volume c. Interpret and sketch front, back, top bottom, and side views of solid figures. Surface Area/Volume d. Construct nets for prisms, cylinders, pyramids, and cones. Surface Area/Volume Algebra: Students will investigate relationships between two quantities. They will write and solve proportions and simple one-step equations that result from problem situations. M6A1 Students will understand the concept of ratio and use it to represent Proportion M6A2 Students will consider relationships between varying quantities. a. Analyze and describe patterns arising from mathematical rules, tables, and graphs. b. Use manipulatives or draw pictures to solve problems involving proportional Proportion relationships. c. Use proportions (a/b= c/d) to describe relationships and solve problems, including percent problems. Proportion d. Describe proportional relationships mathematically using y = kx, where k is the constant of proportionality. e. Graph proportional relationships in the form y = kx and describe characteristics of the graphs. In a proportional relationship expressed as y = kx, solve for one quantity f. given values of the other two. Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship y = kx. g. Use proportional reasoning (a/b= c/d and y =kx) to solve problems. Proportion M6A Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations. Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. They will represent, investigate, and use data to answer those questions. Students will understand experimental and theoretical probability. M6D1 a. Students will pose questions, collect data, represent and analyze the data, and interpret results. Formulate questions that can be answered by data. Students should collect data by using samples from a larger population (surveys), or by conducting experiments. Graphs b. Using data, construct frequency distributions, frequency tables, and graphs. Graphs c. Choose appropriate graphs to be consistent with the nature of the data (categorical or numerical). Graphs should include pictographs, histograms, Graphs bar graphs, line graphs, circle graphs, and line plots. d. Use tables and graphs to examine variation that occurs within a group and variation that occurs between groups. Graphs e. Relate the data analysis to the context of the questions posed. Graphs M6D2 a. b. c. Students will use experimental and simple theoretical probability and understand the nature of sampling. They will also make predictions from investigations. Predict the probability of a given event through trials/simulations (experimental probability), and represent the probability as a ratio. Determine and use a ratio to represent the theoretical probability of a given event. Discover that experimental probability approaches theoretical probability when the number of trials is large. Probability Probability Probability 2010 Outstanding Guides, LLC 14

15 Fundamentals of Fractions Probability 2010 Outstanding Guides, LLC 15 Volume Surface Area Proportions Measuring with a Ruler Metric Multiplication Chart Folded Flap 6th Grade GPS Suggested Lay out for Graphic Organizers Folded Flap Fractions Decimals Percents Types of Decimals Types of Graphs Factor Slide Divisibility Rules Folded Flap SCALE Symmetry Formulas Prime Factorization Back of Folder

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17 2010 Outstanding Guides, LLC Divisibility Rules Numbers and Operations Divisibility rules for numbers 2,, 5, 6, 9, and 10 6 Vocabulary even multiple sum

18 2010 Outstanding Guides, LLC 18 Divisibility Memorize Examples: Rules 2 A number is divisible by two if the number is evenends in 0, 2, 4, 6, or 8. 24, 48, 70, 108 Even A number is divisible by three if the sum of the digits adds up to a multiple of three., 9, 96, 102 Add 5 A number is divisible by five if the number ends in a five or a zero , 155, 215 Ends in 5 or 0 6 A number is divisible by six if the number is divisible by both two and three. 24, 48, 90, 120 Two and Three 9 A number is divisible by nine if the sum of the digits adds up to a multiple of nine. 6, 81, 99, 15 Add 10 A number is divisible by ten if the number ends in a zero. 100, 200, 00, 400 Ends in 0

19 2010 Outstanding Guides, LLC 19 Divisibility Memorize Examples: Rules 2 A number is divisible by two if is it ends in 0, 2, 4, 6, or 8 Even A number is divisible by three if the. A number is divisible by five is it ends in a or a. A number is divisible by six if it is divisible by both and. A number is divisible by nine if the sum of the digits adds up to a multiple of A number is divisible by ten if it in a. Add Ends in 5 or 0 Two and Three Add Ends in 0

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21 2010 Outstanding Guides, LLC Factor Slide Numbers and Operations Using the slide method to identify GCF and LCM 6 Vocabulary common factor divisor factor Greatest Common Factor (GCF) Least Common Multiple (LCM) prime factor quotient

22 2010 Outstanding Guides, LLC 22 Write the first number here. 12 Write the second number here. 18 Write first common prime factor 2 Write the quotient here. 6 Write the quotient here. 9 Divide Another common prime factor? Continue to choose divisors until the only remaining divisor is 1. 1 GCF LCM Write the quotient here. 2 Write the quotient here. 2 Write the quotient here. Write the quotient here. To find the GCF multiply all the divisors. 2 1 = 6 To find the LCM, multiply the GCF and the numbers left on the bottom of the slide. 6 2 = 6 Divide If the only common factor is 1, you are done! Multiply everything on the outside. Multiple everything in the L Factor Slide

23 2010 Outstanding Guides, LLC 2 Write first common prime factor 2 Another common prime factor? Continue to choose divisors until the only remaining divisor is 1. 1 GCF LCM Write the first number here. 12 Write the second number here. 18 Write the quotient here. Write the quotient here. Divide Write the quotient here. Write the quotient here. Divide Write the quotient here. Write the quotient here. If the only common factor is 1, you are done! To find the GCF multiply all the divisors. To find the LCM, multiply the GCF and the numbers left on the bottom of the slide. Multiply everything on the outside. Multiple everything in the L Factor Slide

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25 2010 Outstanding Guides, LLC Fractions Numbers and Operations Add/Subtract/Multiple/Divide Fractions 6 Vocabulary common factors denominator dividend divisor improper fraction mixed number numerator reciprocal

26 + Adding Fractions - Subtraction Fractions Multiplying Fractions Dividing Fractions Step 1 Do the fractions have like denominators? If necessary, rewrite the fractions with like denominators Example: Step 1 Do the fractions have like denominators? If necessary, rewrite the fractions with like denominators Example: Step 1 Are the factors in fraction form? If necessary, rewrite mixed numbers in fraction form. Step 1 Are the divisor and dividend in fraction form? If necessary, rewrite mixed numbers in fraction form. = Step 2 Add the fractions. Can the answer be simplified by finding common factors? Step 2 Subtract the fractions. Can the answer be simplified by finding common factors? If so, divide both numerator and denominator by the common factor. Step 2 Multiply the numerators and multiply the denominators. Can the answer be simplified by finding common factors? Step 2 Multiply by the reciprocal. Multiply the numerators and multiply the denominators. Can the answer be simplified by finding common factors? Step Is the answer an improper fraction? If so, change improper to mixed number. Step Is the answer an improper fraction? If so, change improper to mixed number. Step Is the answer an improper fraction? If so, change improper to mixed number. Step Is the answer an improper fraction? If so, change improper to mixed number. Additional Example Additional Example Additional Example Additional Example Outstanding Guides, LLC

27 + Adding Fractions - Subtraction Fractions Multiplying Fractions Dividing Fractions Step 1 Do the fractions have like denominators? If necessary, rewrite the fractions with like denominators Example: Step 1 Do the fractions have like denominators? If necessary, rewrite the fractions with like denominators Example: Step 1 Are the factors in fraction form? If necessary, rewrite mixed numbers in fraction form. Step 1 Are the divisor and dividend in fraction form? If necessary, rewrite mixed numbers in fraction form. Step 2 Add the fractions. Can the answer be simplified by finding common factors? Step 2 Subtract the fractions. Can the answer be simplified by finding common factors? If so, divide both numerator and denominator by the common factor. Step 2 Multiply the numerators and multiply the denominators. Can the answer be simplified by finding common factors? Step 2 Multiply by the reciprocal. Multiply the numerators and multiply the denominators. Can the answer be simplified by finding common factors? Step Is the answer an improper fraction? If so, change improper to mixed number. Step Is the answer an improper fraction? If so, change improper to mixed number. Step Is the answer an improper fraction? If so, change improper to mixed number. Step Is the answer an improper fraction? If so, change improper to mixed number. Additional Example Additional Example Additional Example Additional Example Outstanding Guides, LLC

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29 2010 Outstanding Guides, LLC Fractions, Decimals, and Percents Numbers and Operations Use fractions, decimals, and percents interchangeably 6 Vocabulary denominator equivalent numerator repeating decimal terminating decimal

30 2010 Outstanding Guides, LLC 0 Fraction Decimal Percent Fractions, Decimals, and Percents Operation Explanation Example Divide the numerator by the Decimal denominator. 8 Percent Decimal Move the decimal 2 places to the right, add a % sign. Move the decimal two places to the left. Decimal Fraction Read it, Write it, Reduce it! Percent Fraction Fraction Percent Turn into decimal. Read it, Write it, Reduce it! Divide the numerator by the denominator, move the decimal 2 places to the right and write the % sign. 6% % 45.6% % 9 25 Practice Fraction Decimal Percent 1 0..% % % % % %

31 2010 Outstanding Guides, LLC 1 Fraction Decimal Percent Fractions, Decimals, and Percents Operation Explanation Example Divide the numerator by the Decimal denominator. 8 Percent Decimal Move the decimal 2 places to the right, add a % sign. Move the decimal two places to the left. Decimal Fraction Read it, Write it, Reduce it! Percent Fraction Fraction Percent Turn into decimal. Read it, Write it, Reduce it! Divide the numerator by the denominator, move the decimal 2 places to the right and write the % sign. 6% % 45.6% % 9 25 Practice Fraction Decimal Percent % % 100 4

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33 2010 Outstanding Guides, LLC 6.5 Multiplication Table Numbers and Operations 6

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35 2010 Outstanding Guides, LLC Prime Factorization Numbers and Operations 6 Vocabulary factor Fundamental Theorem of Arithmetic prime factorization prime number

36 2010 Outstanding Guides, LLC = ² 7 Fundamental Theorem of Arithmetic: Every counting number greater than 1 is either prime or can be written as a product of prime numbers. Factor Tree = 2² ² 48 Prime Number: A number that has only two factors, 1 and itself. Examples: 7, 1, 17 Prime Factorization = 2 4

37 2010 Outstanding Guides, LLC = Fundamental Theorem of Arithmetic: Every counting number greater than 1 is either prime or can be written as a product of numbers. Factor Tree 6 6 = 48 Prime Number: A number that has only two factors,. Examples: Prime Factorization 48 =

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39 2010 Outstanding Guides, LLC Types of Decimals Numbers and Operations Terminating/Repeating/Non-terminating/Non-repeating 6 Vocabulary bar notation irrational number non-repeating non-terminating repeating decimal terminating decimal

40 2010 Outstanding Guides, LLC 40 Terminating Types of Decimals Repeating Non-terminating Non-repeating

41 2010 Outstanding Guides, LLC 41 Terminating Decimal A decimal number in which the digits stop, or terminate. Repeating Decimal A decimal number in which a digit or group of digits repeats without end. Only digits under the bar notation are repeated. Non-terminating Non-repeating A decimal number that does not have repeating digits and never terminates. These are called irrational numbers π These decimals can not be written as a fraction.

42 2010 Outstanding Guides, LLC 42 Terminating Decimal A decimal number in which the digits, or. Repeating Decimal A decimal number in which a digit or group of digits. Only digits under the are repeated. Non-terminating Non-repeating A decimal number that and. These are called numbers π These decimals be written as a fraction.

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45 2010 Outstanding Guides, LLC Formulas Measurement Area/Perimeter/Volume/Circumference 6 Vocabulary area circumference perimeter volume

46 2010 Outstanding Guides, LLC 46 Formulas Area Perimeter Volume Circumference

47 2010 Outstanding Guides, LLC 47 A side 2 A 2 1 base height P 4 side A length width A radius 2 P 2 length 2 width V side V radius 2 height C 2 radius V 1 2 ( height) C diameter V length width height

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51 2010 Outstanding Guides, LLC Measuring Length Measurement Measuring length to the nearest inch, ,,, and inch

52 2010 Outstanding Guides, LLC 52 Measuring Length to the Nearest Half, Fourth, Eighth and Sixteenth of an Inch 1 inch inch inch inch inch This is an enlarged inch. Label the correct fraction of an inch 0 1

53 2010 Outstanding Guides, LLC Metric Measurement Converting between metric units 6

54 2010 Outstanding Guides, LLC 54 k kilo h hecto dk deka BASE UNIT d deci c centi m milli kg kl km hg hl hm dkg dkl dkm g L m dg dl dm cg cl cm mg ml mm kilogram kiloliter kilometer 1000 hectogram hectoliter hectometer 100 dekagram dekaliter dekameter 10 gram Liter meter decigram deciliter decimeter 0.10 centigram centiliter centimeter 0.01 milligram milliliter millimeter King Henry Died Unexpectedly Drinking Chocolate Milk

55 2010 Outstanding Guides, LLC 55 k kilo h hecto dk deka BASE UNIT d deci c centi m milli King Henry Died Unexpectedly Drinking Chocolate Milk

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57 2010 Outstanding Guides, LLC Surface Area Measurement Calculating surface area of a cube, rectangular prism, and cylinder 6 Vocabulary area base circumference congruent faces net

58 58 Cube Rectangular Prism Cylinder Net of a cube cm Surface Area Side = cm 6cm 2cm Net of a rectangular prism 20 cm 0cm Surface Area Step 1 Find the area of the first rectangle. A = lw = 9 cm² Find the area of the top and bottom faces. These faces are congruent. A = lw 2 = 6 cm² Combined area 2(6) = 12 cm² Find the area of the top and bottom base. A = πr².14 20² = A 1256 cm² A cm² Think: How do I find area? Step 2 Since there are 6 sides and all the sides are the same, you can multiply the area by = 54cm². The surface area of this cube is 54cm². Find the area of the front and back faces. These faces are congruent. 6 = 18 cm² Combined areas 2 (18) = 6 cm² Find the circumference of the base. C = 2πr C C cm Think: Did I find the area of all of the sides? Step No step for cube! Find the area of the two side faces. These faces are congruent. 2 6 = 12cm² Combined area 2(12) = 24 cm² Multiple the height times the circumference. A A 768 cm² Think: What am I adding? Step 4 Remember: The units for area/surface area are ALWAYS SQUARED! Add to find the total surface area. SA = = 72 cm² Add the areas of the two bases and the rectangle. SA cm² Think: Did I put square units on my final answer? 2010 Outstanding Guides, LLC

59 59 Cube Rectangular Prism Cylinder Net of a cube cm Surface Area Side = cm 6cm 2cm Net of a rectangular prism 20 cm 0cm Surface Area Step 1 Find the area of the first rectangle. Find the area of the top and bottom faces. These faces are congruent. Find the area of the top and bottom base A = πr². Think: How do I find area? Step 2 Since there are 6 sides and all the sides are the same you can multiply the area by 6. Find the area of the front and back faces. These faces are congruent. Find the circumference of the base. Think: Did I find the area of all of the sides? Step No step for cube! Find the area of the two side faces. These faces are congruent. Multiple the height times the circumference. Think: What am I adding? Step 4 Remember: The units for area/surface area are ALWAYS! Add to find the total surface area. Add the areas of the two bases and the rectangle. Think: Did I put square units on my final answer? 2010 Outstanding Guides, LLC

60 60 Cube Rectangular Prism Cylinder Surface Area Side = cm Net of a cube cm 6cm 2cm Net of a rectangular prism 20 cm 0cm Surface Area 2010 Outstanding Guides, LLC

61 2010 Outstanding Guides, LLC Volume Measurement Calculating volume of solid figures 6 Vocabulary cubed net

62 62 Cube Rectangular Prism Cylinder Triangular Prism Net of a cube cm Volume Side = cm 6cm 2cm Net of a rectangular prism 20 cm 0cm 2cm 5cm 12 cm Step 1 Pick the correct formula Volume of cube = s³ Volume of a rectangular prism = lwh Volume of cylinder = πr²h Volume of Triangular prism = ½ bhl Step 2 Substitute the values into the formula V = s³ V = ³ V = lwh V = 2 6 V= πr²h V = π(20)²(0) V = ½ bhl V = ½ Step Calculate the volume. V = s³ V = ³ = 27 V = lwh V = = 6 V= πr²h V = π(20)²(0) V = π(400)(0) V = π(12,000) V = 7,680 V = ½ bhl V = ½ V = 60 Step 4 Make sure you have the right units! V = 27 cm³ Units in volume are always CUBED! V = 6 cm³ Units in volume are always CUBED! V = 7,680 cm³ Units in volume are always CUBED! V = 60 cm³ Units in volume are always CUBED! 2010 Outstanding Guides, LLC

63 6 Cube Rectangular Prism Cylinder Triangular Prism Volume Side = cm Net of a cube cm Net of a rectangular prism 6cm 2cm 20 cm 0cm 2cm 5cm 12 cm Step 1 Pick the correct formula Volume of cube = s³ Volume of a rectangular prism = lwh Volume of cylinder = πr²h Volume of Triangular prism = ½ bhl Step 2 Substitute the values into the formula Step Calculate the volume. V = s³ V = lwh V= πr²h V = ½ bhl V = s³ V = lwh V= πr²h V = ½ bhl Step 4 Make sure you have the right units! V = Units in volume are always CUBED! V = Units in volume are always CUBED! V = Units in volume are always CUBED! V = Units in volume are always CUBED! 2010 Outstanding Guides, LLC

64 64 Cube Rectangular Prism Cylinder Triangular Prism Net of a cube cm Net of a rectangular prism 6cm 20 cm Side = cm 2cm 0cm 2cm 5cm 12 cm 2010 Outstanding Guides, LLC

65 2010 Outstanding Guides, LLC Similar and Congruent Figures Numbers and Operations Comparing similarity and congruency 6 Vocabulary congruent corresponding side similar

66 D Triangle D is congruent to Triangle C. The relationship of Triangle D to Triangle B is 2:1. If the side length of Triangle D is 8 in, the corresponding side length on B is 4 in Outstanding Guides, LLC 66 p C m Triangles A and B are congruent because they have the same shape and size. Triangle C is similar to Triangles A and B. (That means they are the same shape but different sizes.) The relationship of Triangle A to Triangle C is 1:2. If the side length of Triangle A is in, then the corresponding side on Triangle C is 6 inches. Copy page or 68 front to back. A R Similar and Congruent SCALE If a side length on Triangle A is 2 in, the corresponding side length on Triangle B is 2 in as well! B m R p

67 2010 Outstanding Guides, LLC 67 Scale factor <1 then size of the picture is reduced Scale factor =1 then size never changes Scale factor >1 then size of the picture is enlarged The distances between two cities cannot be shown on a piece of paper. It can be scaled down to be represented on a map. 2 in For example, the distance between Vero beach and Boynton Beach is 77 miles. That distance cannot be drawn on a map, but using a 1in = 22 mile scale, the distance can be represented with a line that is.5 in long. 6 in On a map of Florida, the scale is 1 in = 22 miles. If the distance between Vero Beach and Boynton Beach is.5 in, what is the actual length? 21 in RECTANGLE Y 1in =.5 in x = 77 miles 22miles x miles Corresponding sides change by the same scale factor meaning all the sides of the small figure are multiplied by the same number to obtain the lengths of the corresponding sides of the large figure. 7 in RECTANGLE X Copy page or 68 front to back. Scale factor from rectangle x to rectangle y is 1:.

68 2010 Outstanding Guides, LLC 68 Scale factor <1 then size of the picture is Scale factor =1 then size Scale factor >1 then size of the picture is The distances between two cities cannot be shown on a piece of paper. It can be scaled down to be represented on a map. 2 in For example, the distance between Vero beach and Boynton Beach is 77 miles. That distance cannot be drawn on a map, but using a 1in = 22 mile scale, the distance can be represented with a line that is.5 in long. 6 in On a map of Florida, the scale is 1 in = 22 miles. If the distance between Vero Beach and Boynton Beach is.5 in, what is the actual length? 21 in RECTANGLE Y 1in =.5 in x = 77 miles 22miles x miles Corresponding sides change by the same scale factor meaning all the sides of the small figure are multiplied by the same number to obtain the lengths of the corresponding sides of the large figure. 7 in RECTANGLE X Scale factor from rectangle x to rectangle y is 1:.

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71 2010 Outstanding Guides, LLC Symmetry Geometry Identifying Line and Rotational Symmetry 6 Vocabulary angle of rotation line of symmetry rotational symmetry

72 2010 Outstanding Guides, LLC 72 Symmetry Line Symmetry Rotational Symmetry A figure has reflection symmetry or line symmetry if a line drawn creates identical halves. If the object can be rotated less than 180 around its center and appears unchanged, the figure has rotational symmetry. The line drawn through the figure is the line of symmetry. A shape can have more than one line of symmetry. The smallest angle a figure can be rotated and appears unchanged is called the angle of rotation. This figure has rotation symmetry of 72. Determine the lines of symmetry. Determine the degree of rotational symmetry.

73 2010 Outstanding Guides, LLC 7 Line Symmetry Rotational Symmetry A figure has or line symmetry if a line drawn creates identical halves. If the object can be rotated less than 180 around its center and appears unchanged, the figure has. The line drawn through the figure is the. A shape can have more than one line of symmetry. The smallest angle a figure can be rotated and appears unchanged is called the. This figure has rotation symmetry of 72. Determine the lines of symmetry. Determine the degree of rotational symmetry.

74 2010 Outstanding Guides, LLC 74 Determine the lines of symmetry. Determine the degree of rotational symmetry.

75 2010 Outstanding Guides, LLC Proportions Algebra Set up and solve proportional relationships 6 Vocabulary equation ratio

76 76 Propo Examples Examples rtion An equation states ratios x x 1 9 One mango costs $2. How many mangos can you buy for $6? A map has a scale of cm: 18 km. If Mobile and Biloxi are 54 km apart, they are how far apart on the map? which that two are equal Long Side Large Triangle Short Side Large Triangle Long Side Large Triangle Short Side Large Triangle Mango Mango cm cm Same Unit 14 x 9 1 x x Same Unit Other Unit 2 1 x Other Unit Long Side Short Side Long Side Short Side Dollars Dollars km km Small Triangle Small Triangle Small Triangle Small Triangle 2010 Outstanding Guides, LLC

77 77 Propo Examples Examples rtion An equation states ratios x x 1 9 One mango costs $2. How many mangos can you buy for $6? A map has a scale of cm: 18 km. If Mobile and Biloxi are 54 km apart, they are how far apart on the map? which that two are equal Long Side Large Triangle Short Side Large Triangle Long Side Large Triangle Short Side Large Triangle Mango Mango cm cm Same Unit Same Unit Other Unit Other Unit Long Side Short Side Long Side Short Side Dollars Dollars km km Small Triangle Small Triangle Small Triangle Small Triangle 2010 Outstanding Guides, LLC

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79 2010 Outstanding Guides, LLC Graphs Data Analysis and Probability Line Plot/Bar Graph/Line Graph/Circle Graph/Histogram/Stem-and-Leaf Plot 6 Vocabulary bar graph histogram line plot stem-and-leaf plot

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81 2010 Outstanding Guides, LLC 81 Number of Books Number of books Frequency.. Number of Students Line Plot X XX X XX X Pizza Choices Black Olives 10% Pepperoni 0% Cheese 60% Circle Graph , 4, 4, 5, 5, 5, 8 Bar Graph Daily Temperature MON TUES WED THURS FRI SAT SUN Day Number of Students in Math Club Over 26 Age Histogram Line Graph Book Collection Month Series1 Number of Sit-Ups STEM LEAVES Key 6 = 6 Stem -and- Leaf Plot

82 2010 Outstanding Guides, LLC 82 Line Plot Circle Graph Bar Graph Histogram Line Graph Stem -and- Leaf Plot

83 2010 Outstanding Guides, LLC 8 Temperature Number Number of of books Books Number of Students Number of Students in Math Club Number of Sit-Ups X XX X XX X STEM LEAVES Over 26 Age Key 6 = 6 0, 4, 4, 5, 5, 5, 8 Daily Temperature Pizza Choices Book Collection MON TUES WED THURS FRI SAT SUN Day Black Olives 10% Cheese 60% Pepperoni 0% Month Series1

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85 2010 Outstanding Guides, LLC Probability Data Analysis and Probability Experimental and Theoretical Probability 6 Vocabulary experimental probability theoretical probability

86 2010 Outstanding Guides, LLC 86 Experimental Theoretical Experimental Probability: favorable outcome. number of trials conducted Theoretical Probability: favorable outcomes. total possible outcomes What does happen? What should happen? Example: You toss a die 10 times. You record the number. You want to find the experimental probability of getting a. If a occurred 6 times, the probability is Example: Probability There are 6 numbers on a die. You want to find the theoretical probability of getting a. Probability of rolling a = When you toss a die, you should get a one sixth of the time. 1 6.

87 2010 Outstanding Guides, LLC 87 Experimental Theoretical Experimental Probability: Theoretical Probability: Example: You toss a die 10 times. You record the number. You want to find the experimental probability of getting a. Example: There are 6 numbers on a die. The theoretical probability of getting a on a die is. Probability

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89 Appendices 2010 Outstanding Guides, LLC 89

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91 VOCABULARY VOCABULARY Example Example Definition Definition Example Example Definition Definition Example Example Definition Definition VOCABULARY Definition Example VOCABULARY Definition Example Definition Example Definition Example Definition Example Definition Example 2010 Outstanding Guides, LLC 91

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93 Vocabulary Rubric Owner of OMG: Student Grader: Date: Vocabulary Grade: Vocabulary Definition is Given Example is Given Yes No Yes No 2010 Outstanding Guides, LLC 9

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95 Graphic Organizer Labels for File Box Divisibility Rules Surface Area Factor Slide Volume Fundamentals of Fractions Similar and Congruent (Scale) Fractions, Decimals & Percents Symmetry Multiplication Table Proportions Prime Factorization Graphs Types of Decimals Probability Formulas Measuring Metric 2010 Outstanding Guides, LLC 95

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97 Dear Parents/Guardian: This letter is to inform you about a quick reference that students create and use to review math concepts we have covered in class - an Outstanding Math Guide (OMG). The OMG consists of brightly colored graphic organizers for each unit of study that are encased in a standard, -prong pocket folder that s been folded. Each graphic organizer contains notes and examples of key concepts. Your student can use the OMG as a visual reference as they work on homework and review material. The OMG also contains vocabulary terms. As the terms are introduced in class, students are required to record a definition and example. The OMG s will be collected and vocabulary assignments will be graded periodically. The OMG is a valuable asset for your student. It should be in their notebook at all times. You are encouraged to look through it now and watch it take shape with each unit of study! Sincerely, Math Team 2010 Outstanding Guides, LLC 97