Introduction to Geometry
|
|
- Dortha Ford
- 6 years ago
- Views:
Transcription
1 Introduction to Geometry What is Geometry Why do we use Geometry What is Geometry? Geometry is a branch of mathematics that concerns itself with the questions of shape, size, position of figures, and the properties of space. Geometry became a useful study of mathematics when Rene Descartes introduced coordinates on the Cartesian plane. This allowed shapes to be graphically represented and allowed algebra to graphically represent equations and functions. Recall how we graphed linear equations in Algebra I. The study of geometry rose from the need to understand the concepts of length, area, and volume. As the formulas to describe length, area, and volume via the Pythagorean theorem, circumference and area of a circle, area of a triangle, volume of a cylinder, sphere, and pyramid, inaccessible measurements were able to be calculated based on similarity.
2 Introduction to Geometry What is Geometry Why do we use Geometry This lead to the development of trigonometry in astronomy. What is the size of the moon or sun? When the use of coordinates became common place, analytic geometry and algebraic geometry began to look at three dimensional curves on the Cartesian plane. This study developed into Calculus. For those interested, Einstein used geometry to explain his theories of relativity which incorporates gravitation, force, electro-magnetism, and lots and lots of mathematics. I would encourage all of you to spend a little time reading Einstein s theories, even if you do not understand the math or science behind the theories.
3 Introduction to Geometry What will we study in Geometry Developing reasoning skills in Geometry Problem solving steps Coordinate Graphing Angles Parallels Triangles and their uses Quadrilaterals and the types of quadrilaterals Circles
4 Chapter 1.1 Patterns and Inductive Reasoning Develop Inductive Reasoning skills When you see dark, towering clouds approaching, would you think a storm is coming? Sure, your past experience with weather tells you that a thunderstorm is likely to happen. You have made a conclusion based on past experiences or recognized patterns. When you make these conclusions, you are using inductive reasoning. Using inductive reasoning, we can find the next three terms of the sequence 33, 39, 45, Each consecutive term is 6 more than the previous; therefore, the next three terms are 51, 57, and 63. What is the next shape? First, the pattern is Triangle-Triangle-Square-Square-Triangle-Triangle. Second, the pattern is Blue-Red-Blue-Red-Blue-Red. Answer: Blue Square
5 Chapter 1.1 Patterns and Inductive Reasoning Develop Inductive Reasoning skills A conclusion based on inductive reasoning is known as a conjecture. A conjecture is an educated guess, which can be true or sometimes false. How can a conjecture, which is based on inductive reasoning, be false? When we test a conjecture and find an example where the conjecture is false. This false example is known as a counterexample. A student studies a table of data and forms the following conjecture The product of two positive numbers is always greater than either factor. Is there a counterexample? Yes, if a factor is a positive fraction, then the conjecture is false. Bookwork: page 8; problems Factors Product
6 Chapter 1.2 Points, Lines, and Planes Define and determine characteristics of points, lines, and planes. Has anyone ever seen Sunday Afternoon on the Island of La Grande Jatte by George Seurat in ? The dot, known as a point in geometry is the basic unit of geometry. A point has no size. A point is named by a capital letter. A line is made up of an infinite number of points. Arrows at the end of a line indicate that the line extends without end. A line can be named by a single lowercase script letter or by two points on the line A Ḃ This line is named line AB or line BA, or line l. The symbol for line AB is AB. l Three points that lie on the same line are said to be collinear. Points that do not lie on the same line are noncollinear. A
7 Chapter 1.2 Points, Lines, and Planes Define and determine characteristics of points, lines, and planes. A ray has a definite starting point and extends into infinity in one direction. A ray is named using the endpoint first, then a second point on the ray. The symbol for a ray is CD. A line segment is part of a line with two endpoints. A line segment is named using the endpoints. The symbol for a line segment is EF. A plane is a flat surface that extends into infinity in all directions. At least three points make up a plane. G J A plane can be named with a single uppercase script letter H or by three noncollinear points. Plane GHJ or plane M. M Points that lie in the same plane are coplanar. Points that do not lie in the same plane are noncoplanar. Bookwork: page 16; problems E C D F
8 Chapter 1.3 Postulates Identify and use postulates about points, lines, and planes. In order to use geometry, we must accept certain truths and build on these truths. The truths in geometry that are used to build geometric thought are called postulates. A postulate is a statement in geometry that is accepted to be true. Postulate 1-1 states that two points determine a unique line. There is only one line that contains points E and F. E F Postulate 1-2 states that two distinct lines intersect at one point. Lines l and m intersect at point T. Postulate 1-3 states that three noncollinear points determine a plane. There is only one plane that contains points G, H, and J. l G T H J m
9 Chapter 1.3 Postulates Identify and use postulates about points, lines, and planes. Postulate 1-4 states that if two planes intersect, then their intersection is a line. Use construction paper exercise to show the intersection. These postulates allow us to draw figures. Postulate 1-3 states that at least three points make up a plane. We could define a plane using four points. Bookwork: page 21, problems 9-30.
10 Chapter 1.4 Conditional Statements and Converses Write if-then statements and converse statements. If a number is an even number, then the number is divisible by two. This is an example of an if-then statement. If-then statements join two statements that state a condition. If-then statements are also called conditional statements. Conditional statements have two parts: the hypothesis, if a number is an even number, and the conclusion, then the number is divisible by two. How can we determine if a conditional statement is true? If a figure is a triangle, then it has three angles? Is this true? Yes! One way to test a conditional statement is to state the converse. By testing the conclusion. The converse of a conditional statement is formed by exchanging the hypothesis and the conclusion. If a figure has three angles, then the figure is a triangle. Is this true? Maybe! It could have four angles.
11 Chapter 1.4 Conditional Statements and Converses Write if-then statements and converse statements. State the hypothesis and conclusion in the following statement. If it is raining, then we will read a book. Write two other statements that mean the same as, if two lines are parallel, then they never intersect. All parallel lines never intersect. Lines never intersect if they are parallel. Write the converse of the following statement. If today is Saturday, then there is no school. Is this always true? Bookwork: page 27, problems and emphasis on problem 31.
12 l Geometry Chapter 1.6 Problem Solving Develop and use the four step plan to solve problems. Determine the formulas for perimeter and area. A formula is an equation that shows the relationship of the certain quantities identified in the equation. Like equations, formulas allow us to fine unknown information from known information. Lets look at a couple of useful formulas. When a rancher rides the fence line looking for breaks, the rancher is travelling along the perimeter.. The perimeter of an object or figure, is the distance around the object or figure. Perimeter can be expressed as the sum of the sides of a figure. Perimeter of a rectangle, P = l + w + l + w, or P = 2l + 2w w
13 Chapter 1.6 Problem Solving Develop and use the four step plan to solve problems. Determine the formulas for perimeter and area. The area of a figure is the number of square units needed to cover the figure s surface. The area of a rectangle, A = l w Notice by definition, the figure must be divided into square units. Also, the unit chosen will determine the magnitude of the area measurement, cm, ft, in, etc. This means the calculated number must have squared units or unit 2 because feet times feet is equal to feet 2. Count the number of squares for the area of this rectangle, 20. And four times five equals twenty.
14 Chapter 1.6 Problem Solving Develop and use the four step plan to solve problems. Determine the formulas for perimeter and area. A parallelogram is a figure that has two pairs of opposite sides that are parallel. We will show later that opposite sides are congruent or equal in length. The area of a parallelogram, A = b h; where b is the base length and h is the height. h b
15 Chapter 1.6 Problem Solving Develop and use the four step plan to solve problems. Determine the formulas for perimeter and area. Some math problems can be solved using a formula, like perimeter and area. Other problems can be solved using patterns or models. All problems need to use a four-step plan. Step 1: Explore the problem. Step 2: Plan the solution. Step 3: Solve the problem. Step 4: Examine the solution. Lets look at example 4 on page 37. Bookwork: page 39, problems
CMA Geometry Unit 1 Introduction Week 2 Notes
CMA Geometry Unit 1 Introduction Week 2 Notes Assignment: 9. Defined Terms: Definitions betweenness of points collinear points coplanar points space bisector of a segment length of a segment line segment
More informationChapter 2. Reasoning and Proof
Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9
More informationChapter 2. Reasoning and Proof
Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9
More informationUNIT 1. Basics of Geometry. What is a pattern? Aug 20 11:14 AM. Jun 8 2:09 PM. Aug 20 10:46 AM. Aug 20 11:08 AM. 1.1 Finding and Describing Patterns
UNIT 1 Basics of Geometry 1.1 Finding and Describing Patterns What is a pattern? Jun 8 2:09 PM Aug 20 11:00 AM Aug 20 10:46 AM Aug 20 11:04 AM Let's Practice! Making predictions! Describe a pattern. 3.
More information1.2 Inductive Reasoning
1.2 Inductive Reasoning Goal Use inductive reasoning to make conjectures. Key Words conjecture inductive reasoning counterexample Scientists and mathematicians look for patterns and try to draw conclusions
More informationGeometry First Semester Exam Review
Geometry First Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name three points that are collinear. a. points T, Q, and R c. points
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
8 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students know the properties of rational* and irrational* numbers expressed in a variety of forms. They understand and use
More informationAlgebra 1 Math Year at a Glance
Real Operations Equations/Inequalities Relations/Graphing Systems Exponents/Polynomials Quadratics ISTEP+ Radicals Algebra 1 Math Year at a Glance KEY According to the Indiana Department of Education +
More informationDISCOVERING GEOMETRY Over 6000 years ago, geometry consisted primarily of practical rules for measuring land and for
Name Period GEOMETRY Chapter One BASICS OF GEOMETRY Geometry, like much of mathematics and science, developed when people began recognizing and describing patterns. In this course, you will study many
More informationGeometry. Unit 2- Reasoning and Proof. Name:
Geometry Unit 2- Reasoning and Proof Name: 1 Geometry Chapter 2 Reasoning and Proof ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (2-1)
More informationChapter Review #1-3. Choose the best answer.
Chapter Review #1- Choose the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew.
More information(b) Follow-up visits: December, May, October, March. (c ) 10, 4, -2, -8,..
Geometry Honors - Chapter 2 Reasoning and Proof Section 2-1 Inductive Reasoning and Conjecture I can explore inductive and deductive reasoning. I can find counterexamples to disprove conjectures. I can
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
7 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students understand and use scientific notation* and square roots. They convert between fractions and decimals. MA.7.1.1
More informationCorrelation of Moving with Math Grade 7 to HSEE Mathematics Blueprint
Correlation of Moving with Math Grade 7 to HSEE Mathematics Blueprint Number Sense 1.0 Students know the properties of, and compute with, rational numbers expressed n a variety of forms: 1.1 Read, write
More informationNational Benchmark Test 1. 1 Which three-dimensional figure does this net produce? Name: Date: Copyright by Pearson Education Page 1 of 13
National enchmark Test 1 Name: ate: 1 Which three-dimensional figure does this net produce? opyright 2005-2006 by Pearson Education Page 1 of 13 National enchmark Test 1 2 Which of the following is a net
More informationJANE LONG ACADEMY HIGH SCHOOL MATH SUMMER PREVIEW PACKET SCHOOL YEAR. Geometry
JANE LONG ACADEMY HIGH SCHOOL MATH SUMMER PREVIEW PACKET 2015-2016 SCHOOL YEAR Geometry STUDENT NAME: THE PARTS BELOW WILL BE COMPLETED ON THE FIRST DAY OF SCHOOL: DUE DATE: MATH TEACHER: PERIOD: Algebra
More information4 The Cartesian Coordinate System- Pictures of Equations
4 The Cartesian Coordinate System- Pictures of Equations Concepts: The Cartesian Coordinate System Graphs of Equations in Two Variables x-intercepts and y-intercepts Distance in Two Dimensions and the
More informationParallel and Perpendicular Lines
Cumulative Test Choose the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew. D A
More information9-12 Mathematics Vertical Alignment ( )
Algebra I Algebra II Geometry Pre- Calculus U1: translate between words and algebra -add and subtract real numbers -multiply and divide real numbers -evaluate containing exponents -evaluate containing
More informationAlgebra II Crosswalk. Red font indicates a passage that is not addressed in the compared sets of standards.
The chart below includes the assessed on the Algebra II California Test, the Mathematics ), the the, the Competencies in Mathematics from the Intersegmental Committee of the Academic Senate (ICAS), and
More informationCorrelation of 2012 Texas Essential Knowledge and Skills (TEKS) for Algebra I and Geometry to Moving with Math SUMS Moving with Math SUMS Algebra 1
Correlation of 2012 Texas Essential Knowledge and Skills (TEKS) for Algebra I and Geometry to Moving with Math SUMS Moving with Math SUMS Algebra 1 ALGEBRA I A.1 Mathematical process standards. The student
More informationGeometry Study Guide. Name: Class: Date: Matching
Name: Class: Date: ID: A Geometry Study Guide Matching Match each vocabulary term with its definition. a. conjecture e. biconditional statement b. inductive reasoning f. hypothesis c. deductive reasoning
More informationGeometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems
Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary
More information1.4 Reasoning and Proof
Name Class Date 1.4 Reasoning and Proof Essential Question: How do you go about proving a statement? Explore Exploring Inductive and Deductive Reasoning Resource Locker A conjecture is a statement that
More informationDistance in the Plane
Distance in the Plane The absolute value function is defined as { x if x 0; and x = x if x < 0. If the number a is positive or zero, then a = a. If a is negative, then a is the number you d get by erasing
More informationGeometry - Chapter 2 Corrective 1
Name: Class: Date: Geometry - Chapter 2 Corrective 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Make a table of values for the rule x 2 16x + 64 when
More informationSuccessful completion of the core function transformations unit. Algebra manipulation skills with squares and square roots.
Extension A: Circles and Ellipses Algebra ; Pre-Calculus Time required: 35 50 min. Learning Objectives Math Objectives Students will write the general forms of Cartesian equations for circles and ellipses,
More informationSolutions to Exercises in Chapter 1
Solutions to Exercises in hapter 1 1.6.1 heck that the formula 1 a c b d works for rectangles but not for 4 parallelograms. b a c a d d b c FIGURE S1.1: Exercise 1.6.1. rectangle and a parallelogram For
More informationOhio Department of Education Academic Content Standards Mathematics Detailed Checklist ~Grade 9~
Ohio Department of Education Academic Content Standards Mathematics Detailed Checklist ~Grade 9~ Number, Number Sense and Operations Standard Students demonstrate number sense, including an understanding
More informationPre-Algebra Chapter 9 Spatial Thinking
Pre-Algebra Chapter 9 Spatial Thinking SOME NUMBERED QUESTIONS HAVE BEEN DELETED OR REMOVED. YOU WILL NOT BE USING A CALCULATOR FOR PART I MULTIPLE-CHOICE QUESTIONS, AND THEREFORE YOU SHOULD NOT USE ONE
More informationGTPS Curriculum 6 th Grade Math. Topic: Topic 1- Numeration
9 days / September Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm
More informationGeometry Unit 2 Notes Logic, Reasoning and Proof
Geometry Unit Notes Logic, Reasoning and Proof Review Vocab.: Complementary, Supplementary and Vertical angles. Syllabus Objective:. - The student will justify conjectures and solve problem using inductive
More informationCN#4 Biconditional Statements and Definitions
CN#4 s and Definitions OBJECTIVES: STUDENTS WILL BE ABLE TO WRITE AND ANALYZE BICONDITIONAL STATEMENTS. Vocabulary biconditional statement definition polygon triangle quadrilateral When you combine a conditional
More informationNumber Sets 1,0,1,2,3,... } 3. Rational Numbers ( Q) 1. Natural Numbers ( N) A number is a rational number if. it can be written as where a and
Number Sets 1. Natural Numbers ( N) N { 0,1,,,... } This set is often referred to as the counting numbers that include zero.. Integers ( Z) Z {...,,, 1,0,1,,,... }. Rational Numbers ( Q) A number is a
More informationMATHEMATICS (IX-X) (CODE NO. 041) Session
MATHEMATICS (IX-X) (CODE NO. 041) Session 2018-19 The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society.
More informationA. 180 B. 108 C. 360 D. 540
Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior
More informationNORTH MAC MIDDLE SCHOOL CURRICULUM GUIDE
Teacher Sara Floyd Grade Level 7 th and 8 th Grade Course Pre-Algebra Course Aims To prepare students for Algebra I. Course Description This course is designed for students who need the basic skills required
More informationEscondido Union School District Office of Assessment and Staff Development DRAFT Pre-Algebra (including Advanced) Pacing Guide
See cover page for notes on pacing guide structure. 2010-2011 Pre-Algebra (including Advanced) Pacing Guide Big Idea(s): Algebra is distinguished from arithmetic by the systematic use of symbols for values.
More informationWarm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
2-4 Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Write a conditional statement from each of the following. 1. The intersection of two lines is a point. If two lines intersect, then they intersect
More informationGeometry Summer Assignment
2018-2019 Geometry Summer Assignment You must show all work to earn full credit. This assignment will be due Friday, August 24, 2018. It will be worth 50 points. All of these skills are necessary to be
More informationGeometry GENERAL GEOMETRY
Geometry GENERAL GEOMETRY Essential Vocabulary: point, line, plane, segment, segment bisector, midpoint, congruence I can use the distance formula to determine the area and perimeters of triangles and
More informationSection 2-1. Chapter 2. Make Conjectures. Example 1. Reasoning and Proof. Inductive Reasoning and Conjecture
Chapter 2 Reasoning and Proof Section 2-1 Inductive Reasoning and Conjecture Make Conjectures Inductive reasoning - reasoning that uses a number of specific examples to arrive at a conclusion Conjecture
More informationCalifornia Content Standard. Essentials for Algebra (lesson.exercise) of Test Items. Grade 6 Statistics, Data Analysis, & Probability.
California Content Standard Grade 6 Statistics, Data Analysis, & Probability 1. Students compute & analyze statistical measurements for data sets: 1.1 Compute the mean, median & mode of data sets 1.2 Understand
More informationTest Review: Geometry L2 Period 1 and 3 Test Date: Friday November 6
Test Review: Geometry L2 Period 1 and 3 Test Date: Friday November 6 Things it would be a good idea to know: 1) All terms, definitions, properties, postulates, theorems from Unit 1 and Unit 2 2) How to
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More informationStepping stones for Number systems. 1) Concept of a number line : Marking using sticks on the floor. (1 stick length = 1 unit)
Quality for Equality Stepping stones for Number systems 1) Concept of a number line : Marking using sticks on the floor. (1 stick length = 1 unit) 2) Counting numbers: 1,2,3,... Natural numbers Represent
More informationGeometry Summer Review Packet Page 1
June 017 Dear Geometry Students and Parents: Welcome to Geometry! For the 017-018 school year, we would like to focus your attention to the fact that many concepts from Algebra I are infused into Geometry.
More informationSTAAR STANDARDS ALGEBRA I ALGEBRA II GEOMETRY
STANDARDS ALGEBRA I ALGEBRA II GEOMETRY STANDARDS ALGEBRA I TEKS Snapshot Algebra I (New TEKS 2015-16) Mathematical Process Standards A.1 Mathematical process standards. The student uses mathematical processes
More informationOBJECTIVES UNIT 1. Lesson 1.0
OBJECTIVES UNIT 1 Lesson 1.0 1. Define "set," "element," "finite set," and "infinite set," "empty set," and "null set" and give two examples of each term. 2. Define "subset," "universal set," and "disjoint
More informationChapter 2: Reasoning and Proof
Name: Chapter 2: Reasoning and Proof Guided Notes Geometry Fall Semester 2.1 Use Inductive Reasoning CH. 2 Guided Notes, page 2 Term Definition Example conjecture An unproven statement that is based on
More informationConditional Statements
2-2 Conditional Statements Common Core State Standards Prepares for G-CO.C.9 Prove theorems about lines and angles. Also Prepares for G-CO.C.10, G-CO.C.11 MP 3, MP 6, MP 7 Objectives To recognize conditional
More informationCorrelation: California State Curriculum Standards of Mathematics for Grade 6 SUCCESS IN MATH: BASIC ALGEBRA
Correlation: California State Curriculum Standards of Mathematics for Grade 6 To SUCCESS IN MATH: BASIC ALGEBRA 1 ALGEBRA AND FUNCTIONS 1.0 Students write verbal expressions and sentences as algebraic
More informationNAME DATE PERIOD. Inductive Reasoning and Conjecture. Make a conjecture based on the given information. Draw a figure to illustrate your conjecture.
2-1 NAME DATE PERIOD Skills Practice Inductive Reasoning and Conjecture Make a conjecture about the next item in each sequence. 1. 2. 4, 1, 2, 5, 8 3. 6, 1 1, 5, 9 2 2,4 4. 2, 4, 8, 16, 32 Make a conjecture
More informationREQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS
REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study
More informationIntegrated Math 3 Math 3 Course Description:
Course Description: Integrated Math 3 Math 3 Course Description: Integrated strands include algebra, functions, geometry, trigonometry, statistics, probability and discrete math. Scope and sequence includes
More informationGeometric Formulas (page 474) Name
LESSON 91 Geometric Formulas (page 474) Name Figure Perimeter Area Square P = 4s A = s 2 Rectangle P = 2I + 2w A = Iw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1_ 2 bh Teacher Note:
More informationTable of contents. Jakayla Robbins & Beth Kelly (UK) Precalculus Notes Fall / 53
Table of contents The Cartesian Coordinate System - Pictures of Equations Your Personal Review Graphs of Equations with Two Variables Distance Equations of Circles Midpoints Quantifying the Steepness of
More informationT a b l e o f C o n t e n t s
T a b l e o f C o n t e n t s C O M P E T E N C Y 1 KNOWLEDGE OF ALGEBRA... 1 SKILL 1.1: Apply the properties of real numbers: closure, commutative, associative, distributive, transitive, identities, and
More informationCalifornia. Performance Indicator. Form B Teacher s Guide and Answer Key. Mathematics. Continental Press
California Performance Indicator Mathematics Form B Teacher s Guide and Answer Key Continental Press Contents Introduction to California Mathematics Performance Indicators........ 3 Answer Key Section
More informationCommon Core Georgia Performance Standards Mathematics Grades Adopted Reason quantitatively and use units to solve problems.
, VersaTiles (R), High School Level, Book 2, VersaTiles (R), High School Level, Book 3,, VersaTiles (R), High School Level, Book 5 Grades: 9, 10, 11, 12 State: Georgia Common Core Standards Subject: Mathematics
More informationChapter 2. Reasoning and Proof
Chapter 2 Reasoning and Proof 2.1 Inductive Reasoning 2.2 Analyze Conditional Statements 2.3 Apply Deductive Reasoning 2.4 Use Postulates and Diagrams 2.5 Algebraic Proofs 2.6 Segments and Angles Proofs
More informationChapter 2 Test Review. Complete each truth table.
1. Complete each truth table. 2. SCHOOL The Venn diagram shows the number of students in the band who work after school or on the weekends. 3. How many students work after school and on weekends? 4. How
More informationFind the next item in the pattern below. The red square moves in the counterclockwise direction. The next figure is.
CHAPTER 2 Study Guide: Review Organizer Objective: Help students organize and review key concepts and skills presented in Chapter 2. Online Edition Multilingual Glossary Countdown Week 4 Vocabulary biconditional
More informationAlgebra II/Geometry Curriculum Guide Dunmore School District Dunmore, PA
Algebra II/Geometry Dunmore School District Dunmore, PA Algebra II/Geometry Prerequisite: Successful completion of Algebra 1 Part 2 K Algebra II/Geometry is intended for students who have successfully
More informationGeometry - Chapter 2 Earn-A-Try Test
Name: Geometry - Chapter 2 Earn-A-Try Test Multiple Choice Identify the choice that best completes the statement or answers the question. Use CAPITAL letters only!! Ex: A,B,C,D; Not a,b,c,d. 1. Write a
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
6 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compare and order positive and negative integers*, decimals, fractions, and mixed numbers. They find multiples*
More informationConditional Statements
2.1 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G.4.B Conditional Statements Essential Question When is a conditional statement true or false? A conditional statement, symbolized by p q, can be written as an
More informationPhysics 2A Chapter 1: Introduction and Mathematical Concepts
Physics 2A Chapter 1: Introduction and Mathematical Concepts Anyone who has never made a mistake has never tried anything new. Albert Einstein Experience is the name that everyone gives to his mistakes.
More informationPre-AP Geometry. True or False: 1. Points A, B, and D are collinear. 2. Points B, F, and H are coplanar. 3. Points H, B, D, and A are coplanar.
Pre-AP Geometry Unit 1 Test Review Name: Date: Period: True or False: 1. Points A, B, and D are collinear. 2. Points B, F, and H are coplanar.. Points H, B, D, and A are coplanar. 4. XV is the same as
More informationCOURSE STRUCTURE CLASS IX Maths
COURSE STRUCTURE CLASS IX Maths Units Unit Name Marks I NUMBER SYSTEMS 08 II ALGEBRA 17 III COORDINATE GEOMETRY 04 IV GEOMETRY 28 V MENSURATION 13 VI STATISTICS & PROBABILITY 10 Total 80 UNIT I: NUMBER
More informationMath Requirements for applicants by Innopolis University
Math Requirements for applicants by Innopolis University Contents 1: Algebra... 2 1.1 Numbers, roots and exponents... 2 1.2 Basics of trigonometry... 2 1.3 Logarithms... 2 1.4 Transformations of expressions...
More informationNew Jersey Center for Teaching and Learning. Progressive Mathematics Initiative
Slide 1 / 150 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
More informationI can translate between a number line graph, an inequality, and interval notation.
Unit 1: Absolute Value 2 I can translate between a number line graph, an inequality, and interval notation. 2 2 I can translate between absolute value expressions and English statements about numbers on
More informationBENCHMARKS GRADE LEVEL INDICATORS STRATEGIES/RESOURCES
GRADE OHIO ACADEMIC CONTENT STANDARDS MATHEMATICS CURRICULUM GUIDE Tenth Grade Number, Number Sense and Operations Standard Students demonstrate number sense, including an understanding of number systems
More information2-4. Holt McDougal Geometry
Warm Up Write a conditional statement from each of the following. 1. The intersection of two lines is a point. If two lines intersect, then they intersect in a point. 2. An odd number is one more than
More informationContent Guidelines Overview
Content Guidelines Overview The Pearson Video Challenge is open to all students, but all video submissions must relate to set of predetermined curriculum areas and topics. In the following pages the selected
More informationTheorems About Roots of Polynomial Equations. Theorem Rational Root Theorem
- Theorems About Roots of Polynomial Equations Content Standards N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. Also N.CN.8 Objectives To solve equations using the
More informationCircles and Volume. Circle Theorems. Essential Questions. Module Minute. Key Words. What To Expect. Analytical Geometry Circles and Volume
Analytical Geometry Circles and Volume Circles and Volume There is something so special about a circle. It is a very efficient shape. There is no beginning, no end. Every point on the edge is the same
More informationTERMWISE SYLLABUS SESSION CLASS-IX SUBJECT : MATHEMATICS. Course Structure. Schedule for Periodic Assessments and CASExam. of Session
TERMWISE SYLLABUS SESSION-2018-19 CLASS-IX SUBJECT : MATHEMATICS Course Structure Units Unit Name Marks I NUMBER SYSTEMS 08 II ALGEBRA 17 III COORDINATE GEOMETRY 04 IV GEOMETRY 28 V MENSURATION 13 VI STATISTICS
More informationContents. Test-Taking Tips... 8
Contents Test-Taking Tips... 8 Unit 1 Number and Number Relations... 9 Lesson 1: Number Concepts...10 Computing with Real Numbers 2 Effects of Computations on Real Numbers 2 Evaluating Radical Expressions
More informationMath 8 Notes Unit 8: Area and Perimeter
Math 8 Notes Unit 8: Area and Perimeter Syllabus Objective: (6.) The student will compute the perimeter and area of rectangles and parallelograms. Perimeter is defined as the distance around the outside
More informationCOURSE STRUCTURE CLASS -IX
environment, observance of small family norms, removal of social barriers, elimination of gender biases; mathematical softwares. its beautiful structures and patterns, etc. COURSE STRUCTURE CLASS -IX Units
More informationGranite School District Parent Guides Utah Core State Standards for Mathematics Grades K-6
Granite School District Parent Guides Grades K-6 GSD Parents Guide for Kindergarten The addresses Standards for Mathematical Practice and Standards for Mathematical Content. The standards stress not only
More informationFLORIDA STANDARDS TO BOOK CORRELATION FOR GRADE 7 ADVANCED
FLORIDA STANDARDS TO BOOK CORRELATION FOR GRADE 7 ADVANCED After a standard is introduced, it is revisited many times in subsequent activities, lessons, and exercises. Domain: The Number System 8.NS.1.1
More informationCME Project, Geometry 2009 Correlated to: Kentucky Core Content for Mathematics Assessment 4.1 (High School, Grade 11)
Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. This becomes the foundation
More informationConditional Statements
Conditional Statements nalyze statements in if-then form. Write the converse, inverse, and contrapositive of if-then statements. Vocabulary conditional statement if-then statement hypothesis conclusion
More informationMathematics (Core - Level: 08) Pre-Algebra Course Outline
Crossings Christian School Academic Guide Middle School Division Grades 5-8 Mathematics (Core - Level: 08) Course Outline Exponents and Exponential Functions s will simplify expressions with zero and negative
More informationGH Chapter 2 Test Review-includes Constructions
Name: Class: Date: Show All Work. Test will include 2 proofs from the proof practice worksheet assigned week of 9/8. GH Chapter 2 Test Review-includes Constructions ID: A 1. What is the value of x? State
More information6 th Grade Math Connects
6 th Grade Math Connects Chapter 1: Multiply and Divide Decimals Multi-Part Lesson 1: Multiply Decimals A: Estimate Products B: Explore Multiply Decimals by Whole Numbers C: Multiply Decimals by Whole
More informationPlease allow yourself one to two hours to complete the following sections of the packet. College Integrated Geometry Honors Integrated Geometry
Incoming Integrated Geometry Summer Work Dear Incoming Integrated Geometry Students, To better prepare for your high school mathematics entry process, summer work is assigned to ensure an easier transition
More informationALGEBRA I: State Standards, MPS Objectives and Essential Learnings
ALGEBRA I: s, s and s MA 12.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. MA
More informationPrecalculus, Quarter 4, Unit 4.1. Matrices. Overview
Precalculus, Quarter 4, Unit 4.1 Matrices Overview Number of instructional days: 11 (1 day = 45 60 minutes) Content to be learned Add, subtract, and use scalar multiplication with matrices and equivalent
More informationTRIPURA BOARD OF SECONDARY EDUCATION. SYLLABUS (effective from 2016) SUBJECT : MATHEMATICS (Class IX)
TRIPURA BOARD OF SECONDARY EDUCATION SYLLABUS (effective from 2016) SUBJECT : MATHEMATICS (Class IX) Total Page- 10 MATHEMATICS COURSE STRUCTURE Class IX HALF YEARLY One Paper Time: 3 Hours Marks: 90 Unit
More informationChapter 2-Reasoning and Proof
Chapter 2-Reasoning and Proof Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the hypothesis and conclusion of this conditional statement: If
More informationPrentice Hall PreCalculus, 3rd Edition 2007, (Blitzer)
Prentice Hall PreCalculus, 3rd Edition 2007, (Blitzer) C O R R E L A T E D T O Number Properties and Operations High school students should enter high school with a strong background in rational numbers
More informationPrentice Hall Intermediate Algebra, 5th Edition 2009 (Martin-Gay)
Prentice Hall Intermediate Algebra, 5th Edition 2009 (Martin-Gay) C O R R E L A T E D T O Number Properties and Operations High school students should enter high school with a strong background in rational
More informationSection 1: Sets and Interval Notation
PART 1 From Sets to Functions Section 1: Sets and Interval Notation Introduction Set concepts offer the means for understanding many different aspects of mathematics and its applications to other branches
More informationChapter 2 Test Review 1. Based on the pattern, what are the next two terms of the sequence? 8, 15, 22, 29,...
Number of Customers Geometry Honors Name: Chapter 2 Test Review 1. Based on the pattern, what are the next two terms of the sequence? 8, 15, 22, 29,... 2. Based on the pattern, what is the next figure
More information8 th Grade Essential Learnings
8 th Grade Essential Learnings Subject: Math Grade/Course: 8 th Grade AG1 EL # Ex 1 Essential Learning Benchmark (framed by Standard) Learning Goal Topic (Report Card) NCTM Focal Points (Grade Level and/or
More informationMILLIS PUBLIC SCHOOLS
MILLIS PUBLIC SCHOOLS Curriculum Guide High School Math The Millis Public Schools Curriculum Guide highlights the Power Standards for each grade level, Grade 9 through Grade 12 for the Math department.
More information