Wednesday, May 4, Proportions
|
|
- Ashley Cain
- 5 years ago
- Views:
Transcription
1 Proportions
2 Proportions
3 Proportions What are proportions?
4 Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures = 1:3 = 3:9 8
5 Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures = 1:3 = 3:9 8
6 Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures. What do we mean by similar? = 1:3 = 3:9 8
7 Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures. What do we mean by similar? - Similar describes things which have the same shape but are not the same size = 1:3 = 3:9 8
8 Examples These two stick figures are similar. As you can see both are the same shape. However, the bigger stick figure s dimensions are exactly twice the smaller. 8 feet So the ratio of the smaller figure to the larger figure is 1:2 (said one to two ). This can also be written as a fraction of ½. 4 feet 2 feet A proportion can be made relating the height and the width of the smaller figure to the larger figure: 4 ft 2 ft = 8 ft 4 ft 4 feet
9 Solving Proportional Problems So how do we use proportions and similar figures? 8 feet Using the previous example we can show how to solve for an unknown dimension. 4 feet 2 feet? feet
10 Solving Proportion Problems First, designate the unknown side as x. Then, set up an equation using proportions. What does the numerator represent? What does the denominator represent? 4 ft 2 ft = 8 ft x ft 4 feet 8 feet Then solve for x by cross multiplying: 4x = 16 X = 4 2 feet? feet
11 Try One Yourself 8 feet 12 feet 4 feet x feet
12 Try One Yourself 8 feet 12 feet 4 feet x feet
13 Try One Yourself 8 feet 12 feet Knowing these two stick figures are similar to each other, what is the ratio between the smaller figure to the larger figure? 4 feet x feet
14 Try One Yourself 8 feet 12 feet Knowing these two stick figures are similar to each other, what is the ratio between the smaller figure to the larger figure? 4 feet x feet
15 Try One Yourself 8 feet 12 feet 4 feet x feet Knowing these two stick figures are similar to each other, what is the ratio between the smaller figure to the larger figure? Set up a proportion. What is the width of the larger stick figure?
16 Similar Shapes In geometry similar shapes are very important. This is because if we know the dimensions of one shape and one of the dimensions of another shape similar to it, we can figure out the unknown dimensions.
17 Similar Shapes In geometry similar shapes are very important. This is because if we know the dimensions of one shape and one of the dimensions of another shape similar to it, we can figure out the unknown dimensions.
18 Triangle and Angle Review Today we will be working with right triangles. Recall that one of the angles in a right triangle equals 90 o. This angle is represented by a square in the corner. To designate equal angles we will use the same symbol for both angles. equal angles 90 o angle
19 Proportions and Triangles 16 m What are the unknown values on these triangles? 20 m First, write proportions relating the two triangles. x m 4 m y m 3 m
20 Proportions and Triangles What are the unknown values on these triangles? First, write proportions relating the two triangles. 16 m 20 m 4 m 16 m = 3 m x m 4 m 16 m = y m 20 m x m 4 m y m 3 m
21 Proportions and Triangles What are the unknown values on these triangles? First, write proportions relating the two triangles. 16 m 20 m 4 m 16 m = 3 m x m 4 m 16 m = y m 20 m x m Solve for the unknown by cross multiplying. 4 m y m 3 m
22 Proportions and Triangles What are the unknown values on these triangles? First, write proportions relating the two triangles. 16 m 20 m 4 m 16 m = 3 m x m 4 m 16 m = y m 20 m 4 m 3 m x m y m Solve for the unknown by cross multiplying. 4x = 48 x = 12 16y = 80 y = 5
23 Triangles in the Real World Do you know how tall your school building is? There is an easy way to find out using right triangles. To do this create two similar triangles using the building, its shadow, a smaller object with a known height (like a yardstick), and its shadow. The two shadows can be measured, and you know the height of the yard stick. So you can set up similar triangles and solve for the height of the building.
24 Solving for the Building s Height Here is a sample calculation for the height of a building: building x feet yardstick 48 feet 3 feet 4 feet
25 Solving for the Building s Height Here is a sample calculation for the height of a building: building x ft 3 ft = 48 ft 4 ft x feet 48 feet yardstick 3 feet 4 feet
26 Solving for the Building s Height Here is a sample calculation for the height of a building: building x ft 3 ft = 48 ft 4 ft x feet 4x = 144 x = 36 3 feet yardstick 48 feet 4 feet
27 Solving for the Building s Height Here is a sample calculation for the height of a building: building x ft 3 ft = 48 ft 4 ft 4x = 144 x = 36 x feet The height of the building is 36 feet. 3 feet yardstick 4 feet 48 feet
28 Accuracy and Error Do you think using proportions to calculate the height of the building is better or worse than actually measuring the height of the building? Determine your height by the same technique used to determine the height of the building. Now measure your actual height and compare your answers. Were they the same? Why would there be a difference?
PART I: NO CALCULATOR (115 points)
Prealgebra Practice Midterm Math 40 OER (Ch. 1-4) PART I: NO CALCULATOR (115 points) (1.) 1. Find the difference. a) 578 80 480 b) 10 165 51 (1.). Multiply the given numbers. 684 9. Divide the given numbers.
More informationSimilar Figures 2.5. ACTIVITY: Reducing Photographs. How can you use proportions to help make decisions in art, design, and magazine layouts?
.5 Similar Figures How can you use proportions to help make decisions in art, design, and magazine layouts? In a computer art program, when you click and drag on a side of a photograph, you distort it.
More informationDay 1 p.2-3 SS 3.1/3.2: Rep-Tile Quadrilaterals & Triangles
Stretching and Shrinking Unit: Understanding Similarity Name: Per: Investigation 3: Scaling Perimeter and Area and Investigation 4: Similarity and Ratios Date Learning Target/s Classwork (Check Off Completed/
More informationThird Grade Mathematics
Standard 1: Number & Operation 3.M.1.1.1 Read, write, compare, and order whole numbers to 10,000. (287.01.a) and use numbers 38-40% and use numbers Content Limit: When comparing numbers between 1,000 and
More informationChapter 7 Math Guide
I can write fractions as a sum Write as unit fractions This means the fractions are broken into each individual unit/1 single piece. The fraction is /6. The model shows that pieces are shaded in. If you
More informationEssential Mathematics Practice Problems for Exam 5 Chapter 8
Math 254B Essential Mathematics Practice Problems for Eam 5 Chapter 8 Name Date This eam is closed book and closed notes, ecept for the Geometry Formula sheet that is provided by the instructor. You can
More informationCommon Core State Standard I Can Statements 2 nd Grade
CCSS Key: Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Measurement and Data (MD) Geometry (G) Common Core State Standard 2 nd Grade Common Core State Standards for Mathematics
More informationName: Class: Date: Practice Problems
Unit 3: Stretching and Shrinking Investigation 4: Similarity and Ratios Practice Problems Directions: Please complete the necessary problems to earn a maximum of 11 points according to the chart below.
More information5.1, 5.2, 5.3 Properites of Exponents last revised 12/4/2010
48 5.1, 5.2, 5.3 Properites of Exponents last revised 12/4/2010 Properites of Exponents 1. *Simplify each of the following: a. b. 2. c. d. 3. e. 4. f. g. 5. h. i. j. Negative exponents are NOT considered
More informationOutcome 7 Review. *Recall that -1 (-5) means
Outcome 7 Review Level 2 Determine the slope of a line that passes through A(3, -5) and B(-2, -1). Step 1: Remember that ordered pairs are in the form (x, y). Label the points so you can substitute into
More informationAW Math 10 UNIT 6 SIMILARITY OF FIGURES
AW Math 10 UNIT 6 SIMILARITY OF FIGURES Assignment Title Work to complete Complete 1 Review Proportional Reasoning Cross Multiply and Divide 2 Similar Figures Similar Figures 3 4 Determining Sides in Similar
More informationMathematics Success Level F
T598 [OBJECTIVE] The student will find the perimeter and area of rectangles and triangles. [MATERIALS] Student pages S204 S212 Transparencies T612, T614, T616, T618, T620, T622 Ruler Scissors Gridded index
More informationGrade 2 Arkansas Mathematics Standards. Represent and solve problems involving addition and subtraction
Grade 2 Arkansas Mathematics Standards Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction AR.Math.Content.2.OA.A.1 Use addition and subtraction within 100
More informationLesson 1 Area of Parallelograms
NAME DATE PERIOD Lesson 1 Area of Parallelograms Words Formula The area A of a parallelogram is the product of any b and its h. Model Step 1: Write the Step 2: Replace letters with information from picture
More informationProportions and Similar Figures
Proportions and Similar Figures Learning Targets Learning Targets I can find missing lengths in similar figures. I can use similar figures when measuring indirectly. Vocabulary Similar Figures Scale Drawing
More informationGrade 7, Unit 1 Practice Problems - Open Up Resources
Grade 7, Unit 1 Practice Problems - Open Up Resources Scale Drawings Lesson 1 Here is a gure that looks like the letter A, along with several other gures. Which gures are scaled copies of the original
More informationBuilding Concepts: Connecting Ratios and Scaling
Lesson Overview In this TI-Nspire lesson, students investigate ratios and scale factors. Scale factors are ratios that can be used to make a figure smaller or larger, depending on whether the scale factor
More informationHillhead High School. Fractions. What you need to know. S.O Grady 1
Fractions What you need to know S.O Grady What is a fraction? A fraction is a part of a whole (). Fractions consist of two numbers, a numerator and a denominator. Top number How many parts we have Bottom
More informationUNIT 6 SIMILARITY OF FIGURES
UNIT 6 SIMILARITY OF FIGURES Assignment Title Work to complete Complete Complete the vocabulary words on Vocabulary the attached handout with information from the booklet or text. 1 Review Proportional
More informationRounding Mixed Numbers
LESSON 0 Rounding Mixed Numbers Power Up facts mental math Power Up J a. Estimation: Andrea estimated that each story of the tall building was feet tall. Andrea counted 30 stories in the building. What
More informationML # 1: Similar Figures and Scale Drawings (Unit 7 Math 7 PLUS) SCALE FACTOR: SIMILAR FIGURES:
ML # 1: Similar Figures and Scale Drawings (Unit 7 Math 7 PLUS) SCALE FACTOR: SIMILAR FIGURES: Corresponding Sides and Angles Corresponding Sides and Angles: Sides or angles that lie in the same location
More informationCopyright 2014 Edmentum - All rights reserved.
Study Island Copyright 2014 Edmentum - All rights reserved. Generation Date: 03/05/2014 Generated By: Brian Leslie Unit Rates 1. Tanya is training a turtle for a turtle race. For every of an hour that
More informationInclined Plane, Wedge, Screw PRE-TEST. DIRECTIONS: Answer the following questions in the space provided.
1 PRE-TEST DIRECTIONS: Answer the following questions in the space provided. 1. Name the six simple machines. 2. Describe how a wedge is related to an inclined plane? 3. Give a definition for the term
More informationI can use the four operations (+, -, x, ) to help me understand math.
I Can Common Core! 4 th Grade Math I can use the four operations (+, -, x, ) to help me understand math. Page 1 I can understand that multiplication fact problems can be seen as comparisons of groups (e.g.,
More information2nd Grade Math Curriculum Map
Standards Quarter 1 2.OA.2. Fluently add and subtract within 20 using mental strategies.* By end of Grade 2, know from memory all sums of two one-digit numbers. 2.OA.3. Determine whether a group of objects
More informationa. by measuring the angle of elevation to the top of the pole from a point on the ground
Trigonometry Right Triangle Lab: Measuring Height Teacher Instructions This project will take two class parts (two days or two parts of one block). The first part is for planning and building your sighting
More informationMath Problem Set 5. Name: Neal Nelson. Show Scored View #1 Points possible: 1. Total attempts: 2
Math Problem Set 5 Show Scored View #1 Points possible: 1. Total attempts: (a) The angle between 0 and 60 that is coterminal with the 69 angle is degrees. (b) The angle between 0 and 60 that is coterminal
More informationPercentage means, a 'number over 100'. For example: 16% = 16 5% = 5 12% = 12 35% =
Q1. [0.2 0.2 = 0.04] The skill you need here is multiplications of decimal numbers. Count the total number of decimal places in the two numbers. Your answer should also have the same number of decimal
More informationStudent Outcomes. Lesson Notes. Classwork. Example 1 (7 minutes) Students use properties of similar triangles to solve real world problems.
Student Outcomes Students use properties of similar triangles to solve real world problems. MP.4 Lesson Notes This lesson is the first opportunity for students to see how the mathematics they have learned
More informationLesson 16: The Computation of the Slope of a Non Vertical Line
++ Lesson 16: The Computation of the Slope of a Non Vertical Line Student Outcomes Students use similar triangles to explain why the slope is the same between any two distinct points on a non vertical
More informationSimple Solutions Mathematics Level 3. Level 3. Help Pages & Who Knows Drill
Level 3 & Who Knows Drill 283 Vocabulary Arithmetic Operations Difference the result or answer to a subtraction problem. Example: The difference of 5 and 1 is 4. Product the result or answer to a multiplication
More informationGrade 2 Mathematics Scope and Sequence
Grade 2 Mathematics Scope and Sequence Common Core Standards 2.OA.1 I Can Statements Curriculum Materials & (Knowledge & Skills) Resources /Comments Sums and Differences to 20: (Module 1 Engage NY) 100
More informationSelected Answers for Core Connections, Course 2
Selected Answers for Core Connections, Course 2 Lesson 6.1.1 6-6. x x + 1 3 = 2 b: 2x 2 + 4x x + 2 3 = 2x 2 + 3x 1 6-7. Parts a, c, and d match the perimeter. 6-8. a: 23 20 or 1 3 20 d: 19 15 or 1 4 15
More informationSample test problems for Mathematics for Elementary Teachers by Sybilla Beckmann, copyright c Addison-Wesley, 2003.
Sample test problems for Mathematics for Elementary Teachers by Sybilla eckmann, copyright c ddison-wesley, 2003. 1 1 Sample Test Problems for Chapter 8 1. Draw a design that is made with copies of the
More informationMeasurement of perimeter and area is a topic traditionally
SHOW 113 PROGRAM SYNOPSIS Segment 1 (1:20) OOPS! PERIMETER A careless draftsman mistakenly calculates the perimeter of a rectangle by adding its length and width. He realizes too late that the perimeter
More informationSummer Solutions Problem Solving Level 4. Level 4. Problem Solving. Help Pages
Level Problem Solving 6 General Terms acute angle an angle measuring less than 90 addend a number being added angle formed by two rays that share a common endpoint area the size of a surface; always expressed
More informationPhoto Scale The photo scale and representative fraction may be calculated as follows: PS = f / H Variables: PS - Photo Scale, f - camera focal
Scale Scale is the ratio of a distance on an aerial photograph to that same distance on the ground in the real world. It can be expressed in unit equivalents like 1 inch = 1,000 feet (or 12,000 inches)
More information2-6 Ratios and Proportions. Determine whether each pair of ratios are equivalent ratios. Write yes or no. SOLUTION: No, the ratios are not equivalent.
Determine whether each pair of ratios are equivalent ratios. Write yes or no. 5. 1. No, the ratios are not equivalent. 6. 2. Yes, the ratios are equivalent. 3. 7. RACE Jennie ran the first 6 miles of a
More informationDCSD Common Core State Standards Math Pacing Guide 2nd Grade Trimester 1
Trimester 1 OA: Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 100 to solve oneand two-step word problems involving
More informationProblem Solving with Length, Money, and Data
Grade 2 Module 7 Problem Solving with Length, Money, and Data OVERVIEW Module 7 presents an opportunity for students to practice addition and subtraction strategies within 100 and problem-solving skills
More informationMath Mammoth Grade 4. Class Description:
Math Mammoth Grade 4 Class Description: In the fourth grade, students focus on multi-digit multiplication and division, and a start to studying fractions and decimals, accompanied by studies in geometry
More information5.1 Congruent Triangles 99 Mastery Practice Squares Square Roots Cubes Cube Roots 15 Mastery Practice 21
Chapter - Squares, Square Roots, Cubes and Cube Roots. Squares. Square Roots 7. Cubes. Cube Roots 5 Mastery Practice Chapter - Rational and Irrational Numbers. Rational Numbers. Real Numbers 7. Operations
More informationGEOMETRY CHAPTER 8 TEST
GEOMETRY CHAPTER 8 TEST NAME BLOCK DATE I,, hereby affirm that I neither gave nor received any help on this test. Furthermore, I used no sources of information to answer questions other than those explicitly
More informationCovering and Surrounding Practice Answers
Investigation Additional Practice. a. units, Area 8 square units b. 8 units, Area 33 square units c. 3 units, Area 33 square units d. units, 7 Area 7 square units 8. a. Students should draw and label a
More informationNotes 1.2. Notes 1.3
Notes 1.2 Comparing Similar Figures * image: A. Complete the instructions for Stretching a Figure on page 8 using Labsheet 1.2. Tell how the original figure and the image are alike and how are they different.
More informationLEVEL 9 Mathematics Observation
LEVEL 9 Mathematics Observation Student: Assessment Date: Grade in School: Concepts Evaluated Score Notes. Applying the concept of slope to determine rate of change Equation of a line: slope-intercept
More informationRight Triangle Trigonometry (Section 4-3)
Right Triangle Trigonometry (Section 4-3) Essential Question: How does the Pythagorean Theorem apply to right triangle trigonometry? Students will write a summary describing the relationship between the
More informationFoundations of Math 11: Unit 2 Proportions. The scale factor can be written as a ratio, fraction, decimal, or percentage
Lesson 2.3 Scale Name: Definitions 1) Scale: 2) Scale Factor: The scale factor can be written as a ratio, fraction, decimal, or percentage Formula: Formula: Example #1: A small electronic part measures
More informationCOWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Pre-Algebra - Level 1
COWLEY COUNTY COMMUNITY COLLEGE REVIEW GUIDE Compass Pre-Algebra - Level This study guide is for students trying to test into Pre-Algebra or Beginning Algebra. There are three levels of math study guides..
More informationFind the value of the expressions. 3 x = 3 x = = ( ) 9 = 60 (12 + 8) 9 = = 3 9 = 27
PreAlgebra Concepts Important Concepts exponent In a power, the number of times a base number is used as a factor order of operations The rules which tell which operation to perform first when more than
More informationCOMMON CORE STATE STANDARDS FOR MATHEMATICS K-2 DOMAIN PROGRESSIONS
COMMON CORE STATE STANDARDS FOR MATHEMATICS K-2 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Domain: Counting and Cardinality Know number names and the count
More informationLesson 17: The Unit Rate as the Scale Factor
Student Outcomes Students recognize that the enlarged or reduced distances in a scale drawing are proportional to the corresponding distance in the original picture. Students recognize the scale factor
More information5.3. Area of Polygons and Circles Play Area. My Notes ACTIVITY
Area of Polygons and Circles SUGGESTED LEARNING STRATEGIES: Think/Pair/Share ACTIVITY 5.3 Pictured below is an aerial view of a playground. An aerial view is the view from above something. Decide what
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1316 Ch.1-2 Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Find the supplement of an angle whose
More information+ 4 ~ You divided 24 by 6 which equals x = 41. 5th Grade Math Notes. **Hint: Zero can NEVER be a denominator.**
Basic Fraction numerator - (the # of pieces shaded or unshaded) denominator - (the total number of pieces) 5th Grade Math Notes Mixed Numbers and Improper Fractions When converting a mixed number into
More informationHonors Geometry Summer Math Packet
Honors Geometry Summer Math Packet Dear students, The problems in this packet will give you a chance to practice geometry-related skills from Grades 6 and 7. Do your best to complete each problem so that
More informationStudy Guide and Review
Complete each sentence with the correct term. Choose from the list below. congruent constant of proportionality corresponding parts cross products dilation dimensional analysis indirect measurement inverse
More informationConstruction. Student Handbook
Construction Essential Math Skills for the Apprentice Student Handbook Theory 2 Measurement In all trades the most commonly used tool is the tape measure. Understanding units of measurement is vital to
More informationGeometry. Practice Pack
Geometry Practice Pack WALCH PUBLISHING Table of Contents Unit 1: Lines and Angles Practice 1.1 What Is Geometry?........................ 1 Practice 1.2 What Is Geometry?........................ 2 Practice
More informationMth 075: Applied Geometry (Individualized Sections) MODULE THREE STUDY GUIDE
Mth 075: Applied Geometry (Individualized Sections) MODULE THREE STUDY GUIDE INTRODUCTION TO GEOMETRY Assignment Seven: Problems Involving Right Triangles A. Read pages 35-38 in your textbook. Study examples
More informationThe CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Galois Contest. Thursday, April 18, 2013
The CENTRE for EDUCATION in MATHEMATIC and COMUTING cemc.uwaterloo.ca 201 Galois Contest Thursday, April 18, 201 (in North America and outh America) Friday, April 19, 201 (outside of North America and
More informationSecond Grade Mathematics Goals
Second Grade Mathematics Goals Operations & Algebraic Thinking 2.OA.1 within 100 to solve one- and twostep word problems involving situations of adding to, taking from, putting together, taking apart,
More informationa. The probability of getting a yellow marble or P(yellow) is 2/3. What is P(blue or green)?
Chapter 1 Practice Exam Name: A bag of marbles contains only the colors blue, yellow and green. a. The probability of getting a yellow marble or P(yellow) is 2/3. What is P(blue or green)? b. P(green)
More informationWelcome to Norwalk High School!
Welcome to Norwalk High School! You are about to embark on the next journey in your educational career. We are looking forward to a year-long adventure with you in Algebra. There are a team of teachers
More informationPearson's Ramp-Up Mathematics
Introducing Slope L E S S O N CONCEPT BOOK See pages 7 8 in the Concept Book. PURPOSE To introduce slope as a graphical form of the constant of proportionality, k. The lesson identifies k as the ratio
More informationSection 1.4 Fractions LAWS & PROCESSES. Addition of Fractions DEFINITIONS & BASICS. 1. Common Denominator 2. Add numerators 3. Carry by denominator
34 Fractions DEFINITIONS & BASICS 1) Numerator the top of a fraction 2) Denominator the bottom of the fraction 3) Simplify Fractions are simplified when the numerator and have no factors in common. 4)
More informationGrade 8 Module 3 Lessons 1 14
Eureka Math 2015 2016 Grade 8 Module 3 Lessons 1 14 Eureka Math, A Story of R a t i o s Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced, distributed,
More informationIntermediate A. Help Pages & Who Knows
& Who Knows 83 Vocabulary Arithmetic Operations Difference the result or answer to a subtraction problem. Example: The difference of 5 and is 4. Product the result or answer to a multiplication problem.
More informationMath Grade 2. Understand that three non-zero digits of a 3-digit number represent amounts of hundreds, tens and ones.
Number Sense Place value Counting Skip counting Other names for numbers Comparing numbers Using properties or place value to add and subtract Standards to be addressed in Number Sense Standard Topic Term
More informationUnit Rates, and Proportions
Unit Rates, and Proportions Multiple hoice Identify the choice that best completes the statement or answers the question. 1. The scale used to create a blueprint of a new house is 0.25 inches = 1 foot.
More informationSkill Builder 8.1 Rational Expressions and Their Simplification
Skill Builder 1 Rational Epressions and Their Simplification Simplif each rational epression. State all numbers for which each ration epression is undefined. If the rational epression cannot be simplified
More information5.4 You Nailed It! A Practice Understanding Task
SECONDARY MATHEMATICS III // MODULE 5 MODELING WITH GEOMETRY 5.4 Tatiana is helping her father purchase supplies for a deck he is building in their back yard. Based on her measurements for the area of
More informationNumber Line: Comparing and Ordering Integers (page 6)
LESSON Name 1 Number Line: Comparing and Ordering Integers (page 6) A number line shows numbers in order from least to greatest. The number line has zero at the center. Numbers to the right of zero are
More informationLesson 6 ~ Write and Solve Proportions
Lesson 6 ~ Write and Solve Proportions Solve each proportion. 3 x 1. = 2. 4 20 5 25 8 a = 3. = 7 y 28 7 4. x 32 = 3 16 5. 6 12 = y 48 6. 3 5 = 15 b 7. 11 14 = x 28 8. 26 30 = x 15 9. 5 = 20 4 y Determine
More informationThe Real Number System and Pythagorean Theorem Unit 9 Part B
The Real Number System and Pythagorean Theorem Unit 9 Part B Standards: 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion;
More informationSlope-Intercept Form. Find the x- and y-intercepts. 1. y 3x 6 2. y 2x 8. Graph each equation. 3. y 1 x 3 4. y 5x 5 5. y x 4
Practice A Slope-Intercept Form Find the x- and y-intercepts. 1. y 3x 6. y x 8 _ Graph each equation. 3. y 1 x 3 4. y 5x 5 5. y x 4 Write the equation of the line in slope-intercept form. 6. 7. _ Practice
More informationUnit 9 Notes: Proportions. A proportion is an equation stating that two ratios (fractions) are equal.
Name: Block: Date: MATH 6/7 NOTES & PRACTICE Unit 9 Notes: Proportions A proportion is an equation stating that two ratios (fractions) are equal. If the cross products are equivalent, the two ratios form
More informationThird Grade Mathematics Scope and Sequence
Third Grade Mathematics Scope and Sequence Quarter 1 Domain Operations & Algebraic Thinking Numbers & Operation in Base Ten Standard 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as
More information7.G.1 Scale Drawings and Scale Models Created By: Melissa Forsyth
Bell Ringers 1. 15% of 45 2. 30 is what percent of 75 3. 10 is 20% of what number 4. What is the percent increase from 10 to 15. 5. What is the percent decrease from 30 to 24 7.G.1 Scale Drawings and Scale
More informationMeet #5 March Intermediate Mathematics League of Eastern Massachusetts
Meet #5 March 2008 Intermediate Mathematics League of Eastern Massachusetts Meet #5 March 2008 Category 1 Mystery 1. In the diagram to the right, each nonoverlapping section of the large rectangle is
More informationCore Connections, Course 2 Checkpoint Materials
Core Connections, Course Checkpoint Materials Notes to Students (and their Teachers) Students master different skills at different speeds. No two students learn exactly the same way at the same time. At
More informationMathematics in your head the secrets of mental math
Mathematics in your head the secrets of mental math 1. Fundamentals: mental addition, subtraction, multiplication and division, and gestimation. Addition: 42 + 3 = 45 42 + 30 = 72 42 + 300 = 342 42 + 3000
More information3.1 Solving Systems by Graphing. In consistent systems, Independent systems consist of. Three Cases: A. consistent and independent
3.1 Solving Systems by Graphing In consistent systems, 2. y Independent systems consist of Three Cases: x A. consistent and independent B. inconsistent and independent 3. y C. consistent and dependent
More informationSolving Linear & Graphing Inequalities
Solving Linear & Graphing Inequalities Sep 7 11:06 PM 1 Open circle on the graph means that the inequality will be greater than or less than. > or < Closed circle on the graph means that the inequality
More informationStudy Guide: Slope and Linear Equations
Rates and Unit Rates A rate is a proportional relationship between two quantities. Unit rate is a rate where the second quantity is 1. Example: Pauline can mow 35 square feet of lawn is 2.5 minutes. (this
More informationBook 10: Slope & Elevation
Math 21 Home Book 10: Slope & Elevation Name: Start Date: Completion Date: Year Overview: Earning and Spending Money Home Travel and Transportation Recreation and Wellness 1. Budget 2. Personal Banking
More informationSimilarity and Ratios
" Similarity and Ratios You can enhance a report or story by adding photographs, drawings, or diagrams. Once you place a graphic in an electronic document, you can enlarge, reduce, or move it. In most
More information5.1, 5.2, 5.3 Properites of Exponents last revised 12/28/2010
48 5.1, 5.2, 5.3 Properites of Exponents last revised 12/28/2010 Properites of Exponents 1. *Simplify each of the following: a. b. 2. c. d. 3. e. 4. f. g. 5. h. i. j. Negative exponents are NOT considered
More informationCourse Syllabus - Online Prealgebra
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 1.1 Whole Numbers, Place Value Practice Problems for section 1.1 HW 1A 1.2 Adding Whole Numbers Practice Problems for section 1.2 HW 1B 1.3 Subtracting Whole Numbers
More informationMath 520 Practice Test 2 (Ch3 and Ch4) Name. Find the perimeter of the given square or rectangle. 1) 5 in. Find the perimeter. 6) 46 m.
Math 5 Practice Test 2 (Ch and Ch4) Name Find the perimeter of the given square or rectangle. ) 5 in. 8 in. 8 in. Find the perimeter. 6) 4 m 46 m 5 in. 26 in. B) in. 6 in. D) in. 26 m B) 4 m 80 m D) 60
More informationLesson 12: Modeling Using Similarity
Classwork Example 1 Not all flagpoles are perfectly upright (i.e., perpendicular to the ground). Some are oblique (i.e., neither parallel nor at a right angle, slanted). Imagine an oblique flagpole in
More informationMultiplying Three Factors and Missing Factors
LESSON 18 Multiplying Three Factors and Missing Factors Power Up facts count aloud Power Up C Count up and down by 5s between 1 and 51. Count up and down by 200s between 0 and 2000. mental math a. Number
More informationCore Focus on Proportions & Probability Block 2 Test ~ Proportions and Similarity
Form A Part I Selected Response 1. What is the value of x in the proportion 9 6 =? 12 x A. 8 B. 10 C. 12 D. 18 2. Trevor bought 5 packages of cake mix for $22.50. How much would 8 packages of cake mix
More informationPre-Algebra Unit 1: Number Sense Unit 1 Review Packet
Pre-Algebra Unit 1: Number Sense Unit 1 Review Packet Target 1: Writing Repeating Decimals in Rational Form Remember the goal is to get rid of the repeating decimal so we can write the number in rational
More informationAIMS Common Core Math Standards Alignment
AIMS Common Core Math Standards Alignment Third Grade Operations and Algebraic Thinking (.OA) 1. Interpret products of whole numbers, e.g., interpret 7 as the total number of objects in groups of 7 objects
More informationxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopa Grade 2 Math Crook County School District # 1 Curriculum Guide
qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjkl zxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiop asdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmq wertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklz Crook County School District
More informationTriangles, Rectangles, Squares, and Circles
LESSON Name 2 Teacher Notes: page 27 Triangles, Rectangles, Squares, and Circles Refer students to Circle on page 4 in the Student Reference Guide. Post Reference Chart Circle. Use the compasses from the
More informationI.G.C.S.E. Solving Linear Equations. You can access the solutions from the end of each question
I.G.C.S.E. Solving Linear Equations Inde: Please click on the question number you want Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 You can access the solutions
More informationMath Review Questions
Math Review Questions Working with Feet and Inches A foot is broken up into twelve equal parts called inches. On a tape measure, each inch is divided into sixteenths. To add or subtract, arrange the feet
More information2 A rectangle 3 cm long and. Find the perimeter and area of each figure. Remember to include the correct units in your answers.
5- Homework Draw each rectangle on the dot paper. Find the perimeter and area. A rectangle 5 cm long and cm wide A rectangle cm long and cm wide Perimeter = Area = Perimeter = Area = Find the perimeter
More information