Lesson 2: Solving for Unknown Angles Using Equations
|
|
|
- Shonda Barber
- 6 years ago
- Views:
Transcription
1 Classwork Opening Exercise Two lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Find the values of r, s, and t. r 25 s t Example 1 Two lines meet at the vertex of a ray. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of p and r. r 28 p 16 Exercise 1 Three lines meet at a point. In a complete sentence, describe the relevant angle relationship in the diagram. Set up and solve an equation to find the value of a. 144 a a Date: 3/19/15 S.7
2 Example 2 Three lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of z. 19 z Exercise 2 Three lines meet at a point; AOF = 144. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to determine the value of c. E c C A 144 O F D Example 3 Two lines meet at the vertex of a ray. The ray is perpendicular to one of the lines as shown. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of t. 26 t Date: 3/19/15 S.8
3 Exercise 3 Two lines meet at the vertex of a ray. The ray is perpendicular to one of the lines as shown. In a complete sentence, describe the relevant angle relationships in the diagram. You may add labels to the diagram to help with your description of the angle relationship. Set up and solve an equation to find the value of v. 46 v Example 4 Three lines meet at a point. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Is your answer reasonable? x 8 Exercise 4 Two lines meet at the common vertex of two rays. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Find the measurements of AO and OC. A 2x O 25 3x C Date: 3/19/15 S.9
4 Exercise 5 a. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of x. Find the measurements of AO and OC. A O 5x (2x+20) C b. Katrina was solving the problem above and wrote the equation 7x + 20 = 90. Then she rewrote this as 7x + 20 = Why did she rewrite the equation in this way? How does this help her to find the value of x? Date: 3/19/15 S.10
5 Problem Set 1. Two lines meet at the vertex of a ray. Set up and solve an equation to find the value of c. c Two lines meet at the vertex of a ray. Set up and solve an equation to find the value of a. Explain why your answer is reasonable a 3. Two lines meet at the vertex of a ray. Set up and solve an equation to find the value of w. 125 w 4. Two lines meet at the common vertex of two rays. Set up and solve an equation to find the value of m. m Three lines meet at a point. Set up and solve an equation to find the value of r. 34 r 122 Date: 3/19/15 S.11
6 6. Three lines meet at the vertex of a ray. Set up and solve an equation to find the value of each variable in the diagram v w x z y 7. Set up and solve an equation to find the value of x. Find the measurement of AO and of OC. 8. Set up and solve an equation to find the value of x. Find the measurement of AO and of OC. 9. Set up and solve an equation to find the value of x. Find the measurement of AO and of OC. (4x+5) (5x+22) A O C 10. Write a verbal problem that models the following diagram. Then solve for the two angles. 10x 2x Date: 3/19/15 S.12
Lesson 3: Solving for Unknown Angles using Equations
Classwork Opening Exercise Two lines meet at the common vertex of two rays; the measurement of. Set up and solve an equation to find the value of and. Example 1 Set up and solve an equation to find the
Exercise 2 (4 minutes) Example 3 (4 minutes)
Student Outcomes Students solve for unknown angles in word problems and in diagrams involving complementary, supplementary, ical, and adjacent angles. Classwork Opening Exercise (5 minutes) Opening Exercise
Draw, construct, and describe geometrical figures and describe the relationships between them.
Focus Standards Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.A.2 7.G.A.3 Draw (freehand, with ruler and protractor, and with technology) geometric
Eureka Math. Grade 7, Module 6. Student File_A. Contains copy-ready classwork and homework
A Story of Ratios Eureka Math Grade 7, Module 6 Student File_A Contains copy-ready classwork and homework Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be
Lesson 1: Complementary and Supplementary Angles
lasswork Opening As we begin our study of unknown angles, let us review key definitions. Term Definition Two angles and, with a common side, are angles if is in the interior of. When two lines intersect,
Lesson 1 Complementary and Supplementary Angles
Lesson 1 Complementary and Supplementary Angles Essential Questions: Term Definition Two angles AAAAAA and CCCCCC, with a common side OOOO, are angles if CC is in the interior of AAAAAA. When two lines
Lesson 9: Decimal Expansions of Fractions, Part 1
Classwork Opening Exercises 1 2 1. a. We know that the fraction can be written as a finite decimal because its denominator is a product of 2 s. Which power of 10 will allow us to easily write the fraction
Unit 14 Angles. Name. Period. Teacher
Unit 14 Angles Name Period Teacher Defining Angles/Adjacent Angles Day 1 Classwork Review: Angle Vocabulary Definition Picture Acute angle Obtuse angle Right angle Straight angle New Definitions Vocabulary
Lesson 5: Graphs of Functions and Equations
Classwork Exploratory Challenge/Exercises 1 3 1. The distance that Giselle can run is a function of the amount of time she spends running. Giselle runs 3 miles in 21 minutes. Assume she runs at a constant
Eureka Math. Grade 7, Module 6. Teacher Edition
A Story of Units Eureka Math Grade 7, Module 6 Teacher Edition Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced, sold, or commercialized, in whole
Section 8.3 Vector, Parametric, and Symmetric Equations of a Line in
Section 8.3 Vector, Parametric, and Symmetric Equations of a Line in R 3 In Section 8.1, we discussed vector and parametric equations of a line in. In this section, we will continue our discussion, but,
Classwork. Exercises Use long division to determine the decimal expansion of. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 6 8 7
Classwork Exercises 1 5 1. Use long division to determine the decimal expansion of. 2. Use long division to determine the decimal expansion of. 3. Use long division to determine the decimal expansion of.
Classwork. Opening Exercise. Example 1. Which prism will hold more 1 in. 1 in. 1 in. cubes? 12 in. 6 in. 4 in. 5 in. 10 in. 8 in.
Classwork Opening Exercise Which prism will hold more 1 in. 1 in. 1 in. cubes? 6 in. 12 in. 10 in. 4 in. 8 in. 5 in. How many more cubes will the prism hold? Example 1 A box with the same dimensions as
Lesson 20: Every Line is a Graph of a Linear Equation
Student Outcomes Students know that any non vertical line is the graph of a linear equation in the form of, where is a constant. Students write the equation that represents the graph of a line. Lesson
Lesson 10.1 Parallel and Perpendicular
Lesson 10.1 Parallel and Perpendicular 1. Find the slope of each line. a. y 4x 7 b. y 2x 7 0 c. 3x y 4 d. 2x 3y 11 e. y 4 3 (x 1) 5 f. 1 3 x 3 4 y 1 2 0 g. 1.2x 4.8y 7.3 h. y x i. y 2 x 2. Give the slope
Coefficient Constant Equivalent expressions Equation. 3 A mathematical sentence containing an equal sign
8.4.0 Lesson Date Algebra Vocabulary and Generating Equivalent s Student Objectives I can identify how many terms an expression has and what the coefficients, constants, and like terms of that expression
Lesson 19. Opening Discussion
Opening Discussion 1. Think about the forms of the quadratic equations you ve written throughout this module. We have gone from vertex form to standard form and from factored form to standard form. Draw
Lesson 11: Conditions on Measurements that Determine a Triangle
Lesson 11: Conditions on Measurements that Determine a Triangle Classwork Exploratory Challenge 1 a. Can any three side lengths form a triangle? Why or why not? b. Draw a triangle according to these instructions:
Module 1 Topic C Lesson 14 Reflections
Geometry Module 1 Topic C Lesson 14 Reflections The purpose of lesson 14 is for students to identify the properties of reflection, to use constructions to find line of reflection, get familiar with notations
Angles. Problems: A.! Name the vertex of the angle. What rays are the sides of the angle? C.! Give three other names of LJK.
ngles page # Problems:. ngles. Name the vertex of the angle.. What rays are the sides of the angle? J. Give three other names of LJK.. Name the following angles with three letters: = = N M The remaining
Lesson 19: The Graph of a Linear Equation in Two Variables is a Line
Lesson 19: The Graph of a Linear Equation in Two Variables is a Line Classwork Exercises Theorem: The graph of a linear equation y = mx + b is a non-vertical line with slope m and passing through (0, b),
Absolute Value Function. Some properties of Absolute value: 1. ex. because
Absolute Value Function The absolute value of a number considers only the magnitude of the number and not the sign. Examples: and Some properties of Absolute value: 1. ex. because 2. ex. 3. ex. and 4.
GEOMETRY R Unit 2: Angles and Parallel Lines
GEOMETRY R Unit 2: Angles and Parallel Lines Day Classwork Homework Friday 9/15 Unit 1 Test Monday 9/18 Tuesday 9/19 Angle Relationships HW 2.1 Angle Relationships with Transversals HW 2.2 Wednesday 9/20
Unit 10 Angles. Name: Teacher: Grade:
Unit 10 Angles Name: Teacher: Grade: 1 Lesson 1 Classwork Complementary Angles Complementary Angles: ** Using the above definition, the word sum tells us that we are using addition to set up an equation.
Name Core Date Accentuate the Negative
Name Core Date Accentuate the Negative Investigation 2 Additional Practice Problem 1 Extending Addition to Rational Numbers FOCUS QUESTION: How can you predict whether the results of addition of two numbers
Use the Associative Property of Multiplication to find the product.
3-1 1. The Associative Property of Multiplication states factors can be grouped differently and the product remains the same. Changing the grouping of the factors changes the factors that are multiplied
Lesson 10: Representing, Naming, and Evaluating Functions
: Representing, Naming, and Evaluation Functions Classwork Opening Exercise Study the 4 representations of a function below. How are these representations alike? How are they different? TABLE: Input 0
Lesson 16: Applying the Properties of Operations to Multiply and Divide Rational Numbers
Lesson 16: Applying the Properties of Operations to Multiply and Divide Rational Student Outcomes Students use properties of operations to multiply and divide rational numbers without the use of a calculator.
Lesson 5: Investigating Quadratic Functions in the Standard Form, ff(xx) = aaxx 2 + bbxx + cc
: Investigating Quadratic Functions in the Standard Form, ff(xx) = aaxx 22 + bbxx + cc Opening Exercise 1. Marshall had the equation y = (x 2) 2 + 4 and knew that he could easily find the vertex. Sarah
Lesson 22: Congruence Criteria for Triangles SAS
Student Outcomes Students learn why any two triangles that satisfy the SAS congruence criterion must be congruent. Lesson Notes In, we begin to investigate criteria, or the indicators, of triangle congruence.
Lesson 2: Generating Equivalent Expressions
Lesson 2: Generating Equivalent Expressions Classwork Opening Exercise Additive inverses have a sum of zero. Multiplicative inverses have a product of 1. Fill in the center column of the table with the
Student Outcomes. Classwork. Opening Exercise (3 minutes) Example 1 (8 minutes)
Student Outcomes Students model and write equivalent expressions using the distributive property. They move from a factored form to an expanded form of an expression. Classwork Opening Exercise (3 minutes)
Study Guide and Review
Fill in the blank in each sentence with the vocabulary term that best completes the sentence 1 A is a flat surface made up of points that extends infinitely in all directions A plane is a flat surface
Lesson 2: The Area of Right Triangles
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 6 5 Lesson : The Area of Right Triangles Student Outcomes Students justify the area formula for a right triangle by viewing the right triangle as part of a
Problems of Plane analytic geometry
1) Consider the vectors u(16, 1) and v( 1, 1). Find out a vector w perpendicular (orthogonal) to v and verifies u w = 0. 2) Consider the vectors u( 6, p) and v(10, 2). Find out the value(s) of parameter
Lesson 2: Using the Number Line to Model the Addition of Integers
: Using the Number Line to Model the Addition of Integers Classwork Exercise 1: Real-World Introduction to Integer Addition Answer the questions below. a. Suppose you received $10 from your grandmother
The x-intercept can be found by setting y = 0 and solving for x: 16 3, 0
y=-3/4x+4 and y=2 x I need to graph the functions so I can clearly describe the graphs Specifically mention any key points on the graphs, including intercepts, vertex, or start/end points. What is the
Focus Questions How does the new shape compare to the old shape? How do the coordinates of the new shape compare to the coordinates of the old shape?
Learning Target: Extend their techniques for using integer expressions to record movement on a number line to using expressions to represent movement on the coordinate graph. Practice identifying whether
Lesson 2: The Area of Right Triangles
NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 6 5 Lesson : Student Outcomes Students justify the area formula for a right triangle by viewing the right triangle as part of a rectangle composed of two right
Did You Find a Parking Space?
Lesson.4 Skills Practice Name Date Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane Vocabulary Complete the sentence. 1. The point-slope form of the equation of the
Module Four: Connecting Algebra and Geometry Through Coordinates
NAME: Period: Module Four: Connecting Algebra and Geometry Through Coordinates Topic A: Rectangular and Triangular Regions Defined by Inequalities Lesson 1: Searching a Region in the Plane Lesson 2: Finding
Which function is represented by the graph below?
Read each question carefully. 1) Which function is represented by the graph below? 1 2) Algebra 1 Final Exam 15-16 Review Part 2 (short) (Demo Version) Which function is represented by the graph below?
3x 2 + 7x + 2. A 8-6 Factor. Step 1. Step 3 Step 4. Step 2. Step 1 Step 2 Step 3 Step 4
A 8-6 Factor. Step 1 3x 2 + 7x + 2 Step 2 Step 3 Step 4 3x 2 + 7x + 2 3x 2 + 7x + 2 Step 1 Step 2 Step 3 Step 4 Factor. 1. 3x 2 + 4x +1 = 2. 3x 2 +10x + 3 = 3. 3x 2 +13x + 4 = A 8-6 Name BDFM? Why? Factor.
Lesson 21: Solution Sets to Inequalities with Two Variables
Student Outcomes Students recognize and identify solutions to two variable inequalities. They represent the solution set graphically. They create two variable inequalities to represent a situation. Students
Performance Tasks. Chapter 1. Task 1
Performance Tasks Chapter 1 Task 1 Draw and label a figure that meets the following characteristics: Plane R contains points S, M, and Y. Plane Z intersects with plane R at * SM ). * AY ) intersects plane
HFCC Math Lab Intermediate Algebra 1 SLOPE INTERCEPT AND POINT-SLOPE FORMS OF THE LINE
HFCC Math Lab Intermediate Algebra SLOPE INTERCEPT AND POINT-SLOPE FORMS OF THE LINE THE EQUATION OF A LINE Goal I. Use the slope-intercept form of the line to write the equation of a non-vertical line
Review Exercise. 1. Determine vector and parametric equations of the plane that contains the
Review Exercise 1. Determine vector and parametric equations of the plane that contains the points A11, 2, 12, B12, 1, 12, and C13, 1, 42. 2. In question 1, there are a variety of different answers possible,
Lesson 2: Basic Concepts of Geometry
: Basic Concepts of Geometry Learning Target I can identify the difference between a figure notation and its measurements I can list collinear and non collinear points I can find the distance / length
slope rise run Definition of Slope
The Slope of a Line Mathematicians have developed a useful measure of the steepness of a line, called the slope of the line. Slope compares the vertical change (the rise) to the horizontal change (the
Lesson 12: Angles Associated with Parallel Lines
Lesson 12 Lesson 12: Angles Associated with Parallel Lines Classwork Exploratory Challenge 1 In the figure below, LL 1 is not parallel to LL 2, and mm is a transversal. Use a protractor to measure angles
OpenStax-CNX module: m Quadratic Functions. OpenStax OpenStax Precalculus. Abstract
OpenStax-CNX module: m49337 1 Quadratic Functions OpenStax OpenStax Precalculus This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 In this section, you
4th Grade Critical Areas
Q2 Q1 4.OA.3: Solve multistep word problems, using equations with variables, posed with whole numbers and having whole-number answers 4.NBT.4: Fluently add and subtract multi-digit whole numbers using
Understanding Quadrilaterals
Understanding Quadrilaterals Parallelogram: A quadrilateral with each pair of opposite sides parallel. Properties: (1) Opposite sides are equal. (2) Opposite angles are equal. (3) Diagonals bisect one
Unit 10 Circles 10-1 Properties of Circles Circle - the set of all points equidistant from the center of a circle. Chord - A line segment with
Unit 10 Circles 10-1 Properties of Circles Circle - the set of all points equidistant from the center of a circle. Chord - A line segment with endpoints on the circle. Diameter - A chord which passes through
Student Outcomes. Lesson Notes. Classwork. Discussion (4 minutes)
Student Outcomes Students write mathematical statements using symbols to represent numbers. Students know that written statements can be written as more than one correct mathematical sentence. Lesson Notes
Commutative property. Associative property. Distributive property
Math 4. Class work 4. Algebra Addition Multiplication a+b=b+a Commutative a b=b a a+(b+c)=(a+b)+c Associative a (b c)=(a b) c Distributive a (b+c)=a b + a c a (b c)=a b a c Commutative and associative
7-2 Complementary and Supplementary Angles. Identify the pair of angles as complementary, supplementary, or neither. 1. ANSWER: neither ANSWER:
Identify the pair of angles as complementary,, or neither. 1. 6. A and B are complementary angles. The measure of B is (4x), and the measure of A is 50. What is the value of x? 10 neither 7. A skateboard
Lesson 3: Rectangles Inscribed in Circles
Classwork Opening Exercise Using only a compass and straightedge, find the location of the center of the circle below. Follow the steps provided. Draw chord. AAAA Construct a chord perpendicular to AAAA
GRADE 4 MATH COMPETENCY STATEMENTS / PERFORMANCE INDICATORS
Common Core State Standards Alignment Codes Everyday Math Strands & Goals Alignment Codes OA; Operations and Algebraic Thinking NBT; Number and Operations in Base Ten NOF; Number and Operations - Fractions
1. Solve the following system of equations below. What does the solution represent? 5x + 2y = 10 3x + 5y = 2
1. Solve the following system of equations below. What does the solution represent? 5x + 2y = 10 3x + 5y = 2 2. Given the function: f(x) = a. Find f (6) b. State the domain of this function in interval
Name Period Date GRADE 7: MATHEMATICS COMMON CORE SUPPLEMENT ANGLES, DRAWINGS, AND ALGEBRAIC CONNECTIONS
Name Period Date 7-CORE3.1 Geometric Figures Measure and draw angles using a protractor. Review facts about interior angles of triangles and quadrilaterals. Find missing angle measures in geometric diagrams.
Introduction to Geometry
Introduction to Geometry Objective A: Problems involving lines and angles Three basic concepts of Geometry are: Points are a single place represented by a dot A Lines are a collection of points that continue
7.1 Start Thinking. 7.1 Warm Up. 7.1 Cumulative Review Warm Up
7.1 Start Thinking The polygon in the diagram has been formed by adjoining triangles. Use your knowledge of the sum of the measures of the interior angles of a triangle to determine the sum of the measures
Mathematics (www.tiwariacademy.com)
() Miscellaneous Exercise on Chapter 10 Question 1: Find the values of k for which the line is (a) Parallel to the x-axis, (b) Parallel to the y-axis, (c) Passing through the origin. Answer 1: The given
Engage NY Lesson 15: Representing Three-Dimensional Figures Using Nets
Name: Surface Area & Volume Packet Engage NY Lesson 15: Representing Three-Dimensional Figures Using Nets Classwork Cereal Box Similarities: Cereal Box Differences: Exercise 1 1. Some of the drawings below
Secondary Strategies that Sustain Sense-Making
Secondary Strategies that Sustain Sense-Making NCTM April 15, 2016 Session #328 9:30-10:30 Victoria Miles victoria.miles1@gmail.com Shephali Chokshi-Fox shepcfox@gmail.com Essential Question Which elementary
If you place one vertical and cross at the 0 point, then the intersection forms a coordinate system. So, the statement is true.
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. 2. A coordinate system is formed by the intersection of two number lines. A coordinate system
Standard 1 Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals.
Stretch Standard 1 Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals. Objective 1: Represent whole numbers and decimals from
Lesson 19: The Graph of a Linear Equation in Two Variables Is a Line
The Graph of a Linear Equation in Two Variables Is a Line Classwork Exercises THEOREM: The graph of a linear equation yy = mmmm + bb is a non-vertical line with slope mm and passing through (0, bb), where
Lesson 9 Reflections Learning Targets :
Reflections Learning Targets : I can construct the line of reflection using the compass and a straightedge I can draw the reflected figure using a compass and a straightedge and on coordinate grid Opening
Parabolas have a, a middle point. For
Key Ideas: 3.1A Investigating Quadratic Functions in Vertex Form: y = a(x ± p) ± q Date: Graph y x using the count method. Quick way to graph: Use a basic count: Start at vertex: in this case (0,0) Graph
GEOMETRY IN THREE DIMENSIONS
1 CHAPTER 5. GEOMETRY IN THREE DIMENSIONS 1 INSTITIÚID TEICNEOLAÍOCHTA CHEATHARLACH INSTITUTE OF TECHNOLOGY CARLOW GEOMETRY IN THREE DIMENSIONS Contents 1 Geometry in R 3 2 1.1 Lines...............................................
Lesson ( 1 = + ALGEBRA. Use Properties of Addition Essential Question How can properties help you add fractions with unlike denominators?
Name Use Properties of Addition Essential Question How can properties help you add fractions with unlike denominators? connect You can use properties of addition to help you add fractions with unlike denominators.
Lesson 5: Definition of Rotation and Basic Properties
Student Outcomes Students know how to rotate a figure a given degree around a given center. Students know that rotations move lines to lines, rays to rays, segments to segments, and angles to angles. Students
Geometry 5-1 Bisector of Triangles- Live lesson
Geometry 5-1 Bisector of Triangles- Live lesson Draw a Line Segment Bisector: Draw an Angle Bisectors: Perpendicular Bisector A perpendicular bisector is a line, segment, or ray that is perpendicular to
Determine whether the dilation from A to B is an enlargement or a reduction. Then find the scale factor of the dilation.
Determine whether the dilation from A to B is an enlargement or a reduction. Then find the scale factor of the dilation. 1. Triangle B is larger than triangle A, so the dilation is an enlargement. The
A Quick Review of Trigonometry
A Quick Review of Trigonometry As a starting point, we consider a ray with vertex located at the origin whose head is pointing in the direction of the positive real numbers. By rotating the given ray (initial
Test Name: Chapter 3 Review
Test Name: Chapter 3 Review 1. For the following equation, determine the values of the missing entries. If needed, write your answer as a fraction reduced to lowest terms. 10x - 8y = 18 Note: Each column
Multiply the dividend by the reciprocal of the divisor.
Domain Lesson 6 Complex Fractions Common Core Standards: 7.RP., 7.RP. Getting the Idea To divide fractions, first find the reciprocal of the divisor. Then multiply the dividend by the reciprocal of the
Maintaining Mathematical Proficiency
Chapter 3 Maintaining Mathematical Proficiency Find the slope of the line.. y. y 3. ( 3, 3) y (, ) (, ) x x (, ) x (, ) ( 3, 3)... (, ) y (0, 0) 8 8 x x 8 8 y (, ) (, ) y (, ) (, 0) x Write an equation
Honors Geometry Sections
Honors Geometry Sections 14.3 14.4 Name Determine whether the figure has rotational symmetry. If so, describe the rotations that map the figure onto itself. 1. 2. 3. Use the diagram to complete each sentence.
6.1.3 How can I describe it?
Name: Date: Per: A# 6.1.3 How can I describe it? Describing Transformations In Lesson 6.1.2, you used words and coordinate points to describe how a triangle moved on a graph. These expressions described
Finding the axis of symmetry, vertex, and roots of a parabola
Finding the axis of symmetry, vertex, and roots of a parabola 1) Find the Axis of Symmetry of y = x 2-4x + 3 (The AOS is the vertical line that splits the parabola in 2 equal parts) Axis of Symmetry Axis
Student Outcomes. Classwork. Opening Exercises 1 2 (5 minutes)
Student Outcomes Students use the Pythagorean Theorem to determine an unknown dimension of a cone or a sphere. Students know that a pyramid is a special type of cone with triangular faces and a rectangular
Lesson 6: Solve for Unknown Angles Angles and Lines at a Point
: Solve for Unknown Angles Angles and Lines at a Point Student Outcomes Students review formerly learned geometry facts and practice citing the geometric justifications in anticipation of unknown angle
2.2 Transformers: More Than Meets the y s
10 SECONDARY MATH II // MODULE 2 STRUCTURES OF EXPRESSIONS 2.2 Transformers: More Than Meets the y s A Solidify Understanding Task Writetheequationforeachproblembelow.Useasecond representationtocheckyourequation.
1.6 Start Thinking. 1.6 Warm Up. 1.6 Cumulative Review Warm Up
.6 Start Thinking In Section.5, you learned that a straight angle is an angle with a measure of 0. Imagine the straight angle you are measuring is the x-axis of a coordinate plane and the origin is the
2006 Fryer Contest. Solutions
Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 006 Fryer Contest Thursday, April 0, 006 Solutions c 006
Lesson 15. Student Outcomes. Lesson Notes. Classwork. Opening (2 minutes) Opening Exercise (3 minutes) (optional)
Lesson 5 Lesson 5: Piecewise Functions Student Outcomes Students examine the features of piecewise functions including the absolute value function and step functions. Students understand that the graph
Lesson 9: An Application of Linear Equations
Classwork Exercises 1. Write the equation for the 15 th step. 2. How many people would see the photo after 15 steps? Use a calculator if needed. S.30 3. Marvin paid an entrance fee of $5 plus an additional
A square centimeter is 1 centimeter by 1 centimeter. It has an area of 1 square centimeter. Sketch a square centimeter such as the one here.
3 Measuring Triangles You can find the area of a figure by drawing it on a grid (or covering it with a transparent grid) and counting squares, but this can be very time consuming. In Investigation, you
Lesson 17: Graphing Quadratic Functions from the Standard Form,
: Graphing Quadratic Functions from the Standard Form, Student Outcomes Students graph a variety of quadratic functions using the form 2 (standard form). Students analyze and draw conclusions about contextual
An angle that has a measure less than a right angle.
Unit 1 Study Strategies: Two-Dimensional Figures Lesson Vocab Word Definition Example Formed by two rays or line segments that have the same 1 Angle endpoint. The shared endpoint is called the vertex.
Mathematics Assessment Anchor Glossary Grades 3 & 4
Mathematics Assessment Anchor Glossary Grades 3 & 4 The definitions for this glossary were taken from one or more of the following sources: Webster s Dictionary, various mathematics dictionaries, the PA
S.W.B.A.T: Identify the independent and dependent variable in sentence. Write a function rule for a table and a situation.
Lesson 31 Date: Mr. Jones S.W.B.A.T: Identify the independent and dependent variable in sentence. Write a function rule for a table and a situation. DO NOW 1. If ( ), find f(3). 2. If f(x) = 2x -1, what
THIS IS AN EXAMPLE. READ IT CLOSELY TO LEARN HOW TO GRAPH POLYGONS (closed sided figures) ON THE COORDINATE PLANE AND THEN FIND THE AREA.
THIS IS AN EXAMPLE. READ IT CLOSELY TO LEARN HOW TO GRAPH POLYGONS (closed sided figures) ON THE COORDINATE PLANE AND THEN FIND THE AREA. NOW TRY THE PROBLEMS BELOW ON YOUR OWN. DO THESE ON A SEPARATE
Assignment Assignment for Lesson 11.1
Assignment Assignment for Lesson.1 Name Date Conics? Conics as Cross Sections Determine the conic section that results from the intersection of the double-napped cone shown and each plane described. 1.
( )! 1! 3 = x + 1. ( ) =! x + 2
7.5 Graphing Parabolas 1. First complete the square: y = x 2 + 2x! 3 = x 2 + 2x + 1 ( )! 1! 3 = x + 1 ( ) 2! 4 The x-intercepts are 3,1 and the vertex is ( 1, 4). Graphing the parabola: 3. First complete
Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets
Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of the way along each median
Mth 60 Module 2 Section Signed Numbers All numbers,, and
Section 2.1 - Adding Signed Numbers Signed Numbers All numbers,, and The Number Line is used to display positive and negative numbers. Graph -7, 5, -3/4, and 1.5. Where are the positive numbers always