The Pythagorean Theorem and Right Triangles

Size: px
Start display at page:

Download "The Pythagorean Theorem and Right Triangles"

Transcription

1 The Pythagorean Theorem and Right Triangles Student Probe Triangle ABC is a right triangle, with right angle C. If the length of and the length of, find the length of. Answer: the length of, since and Lesson Description Students will do a hands- on activity to verify the Pythagorean Theorem for a right triangle. They will then use the theorem to solve for the length of the hypotenuse and for the length of a leg in two additional examples. All triangles used in this lesson have sides of integral length. Students should then proceed to applying the theorem in problem situations and with triangles that do not necessarily have integral side lengths. Rationale The Pythagorean Theorem is perhaps the most At a Glance What: Pythagorean Theorem and Right Triangles Common Core Standard: CC.8.G.7 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real- world and mathematical problems in two and three dimensions. Matched Arkansas Standard:AR.9-2.T.G.2.4 (T.2.G.4) Apply the Pythagorean Theorem and its converse in solving practical problems Mathematical Practices: Make sense of problems and persevere in solving them. Model with mathematics. Who: Students who cannot apply the Pythagorean Theorem. Grade Level: 8 Prerequisite Vocabulary: leg, square root, hypotenuse, right angle, right triangle Prerequisite Skills: finding squares and square roots of numbers, solving numeric and algebraic equations involving squares and square roots Delivery Format: Small groups Lesson Length: 30 minutes Materials, Resources, Technology: scissors, tape or glue stick, calculators (optional) Student Worksheets: Pythagorean Theorem Puzzle important theorem in school mathematics. Equations of circles, the distance formula, many principles of trigonometry, resolution of vectors, and applications of perimeter, area, and volume are derived from it. Not only is a student s ability to correctly use and apply the Pythagorean Theorem is necessary for success in subsequent mathematics courses, many practical applications require its use. These include construction projects such as tiling or carpeting and determining if walls and corners are square or perpendicular.

2 Preparation Prepare copies of Pythagorean Theorem Puzzle for each student. Provide each student with a pair of scissors, tape or glue stick, and a calculator (optional). Lesson The teacher says or does 1. Look at the Pythagorean Theorem Puzzle. Do you see a triangle? What kind of triangle is it? How do you know it is a right triangle? 2. We are going to investigate a very important property of all right triangles, but only of right triangles. Expect students to say or do Yes. Right triangle. It has one right angle. If students do not, then the teacher says or does Point out the triangle. Review the properties of a right triangle. Review that the legs are the sides of the triangle that form the right angle. What are the lengths of the legs of the right triangle? 3, 4 3. Can you count to find the length of the hypotenuse of the right triangle? Why not? Let s find a way to determine its length. 4. How many squares do you see drawn on the grid? 5. Find the area of each of the smaller squares. No, because it is not a vertical or horizontal line segment. Count the lengths of the legs, if necessary. If students try to count the length (perhaps they will say a length of 6), use a piece of the grid to show that is not an accurate answer. 3 Make sure that students see the drawn squares, not the grid itself. 9 and 16 Review how to find the area of a square. Some students may need to count the number of unit squares in each of the squares.

3 The teacher says or does 6. Cut the squares with area 9 and area 16 away from the triangle. Cut them into individual unit squares. How many unit squares do you have? 7. Cover the big square attached to the hypotenuse with the unit squares. What do you notice? 8. Can we make a conjecture that is true for this triangle? 9. What is the length of the hypotenuse? 10. Let s see if this works for other right triangles. Suppose that a right triangle has legs of length 6 and 8. What is the length of its hypotenuse? Expect students to say or do 25, because. They fit perfectly. 5 Because. If students do not, then the teacher says or does Can you count the unit squares? Assist students as they place and secure the unit squares on the paper. Guide students from to. 10 Sketch the triangle and assist students as they label the diagram.

4 The teacher says or does Expect students to say or do If students do not, then the teacher says or does 11. This is a very important mathematical property called the Pythagorean Theorem. It states that for every right triangle ABC, Students should write this in their notebooks and/or math journals. where is the right angle,. (Note: Draw this diagram to illustrate the theorem. Emphasize that c must be the length of the hypotenuse.) 12. Let s use the Pythagorean Theorem in a different way. Suppose that a right triangle has a leg with length 12, and a hypotenuse with length 13. What is the length of the other leg? Prompt students as they draw the diagram and solve the equation. Students may use a calculator if they wish. Draw a diagram and find the length of the missing leg. 13. The Pythagorean Theorem can help us find the length of either leg or the hypotenuse of a right triangle if we know the lengths of two of the other sides.

5 Teacher Notes 1. When stating the Pythagorean Theorem as, emphasize that the hypotenuse must have length c. 2. Students may need to be reminded that either leg can be considered as having length a or b. 3. Students will need additional practice. Practice problems should include right triangles with non- integral lengths, triangles with the length of the hypotenuse missing, and triangles with the length of one leg missing. 4. The purpose of this lesson is for students to become familiar with and apply the Pythagorean Theorem correctly. Students may experience numerical and algebra difficulties that are best addressed in another lesson. 5. The Converse of the Pythagorean Theorem (If, then the triangle is a right triangle.) leads to an interesting relationship: If, then the triangle is acute. If If, then the triangle is right., then the triangle is obtuse. Variations Additional problems should include right triangles with non- integral lengths, triangles with the length of the hypotenuse missing, and triangles with the length of one leg missing. Formative Assessment Triangle ABC is a right triangle, with right angle C. If the length of, find the length of. and the length of Answer: 17

6 Resources Mathematics Preparation for Algebra. (n.d.). Retrieved 1 14, 2011, from Doing What Works: Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide - Response to Intervention in Mathematics. Retrieved August 16, 2011, from rti4sucess: on.pdf

The Pythagorean Theorem

The Pythagorean Theorem . The Pythagorean Theorem Goals Draw squares on the legs of the triangle. Deduce the Pythagorean Theorem through exploration Use the Pythagorean Theorem to find unknown side lengths of right triangles

More information

SPIRIT 2.0 Lesson: How Far Am I Traveling?

SPIRIT 2.0 Lesson: How Far Am I Traveling? SPIRIT 2.0 Lesson: How Far Am I Traveling? ===============================Lesson Header ============================ Lesson Title: How Far Am I Traveling? Draft Date: June 12, 2008 1st Author (Writer):

More information

Understanding Similarity

Understanding Similarity Understanding Similarity Student Probe In Quadrilateral ABCD, m A 90, m B 140, andm C 60. In Quadrilateral WXYZ, m W 90, m X 140, andm Y 60. Is Quadrilateral ABCD similar to Quadrilateral WXYZ? Explain

More information

Exploring the Pythagorean Theorem

Exploring the Pythagorean Theorem Exploring the Pythagorean Theorem Lesson 11 Mathematics Objectives Students will analyze relationships to develop the Pythagorean Theorem. Students will find missing sides in right triangles using the

More information

Part to Part Relationships

Part to Part Relationships Part to Part Relationships Student Probe Jerry has a set of 10 marbles pictured below. He needs some help describing the amount of marbles he has in his collection. Use the picture below to help Jerry

More information

Part to Part Relationships

Part to Part Relationships Part to Part Relationships Student Probe Jerry has a set of 10 marbles pictured below. He needs some help describing the amount of marbles he has in his collection. Use the picture below to help Jerry

More information

Measurement Using Standard Units

Measurement Using Standard Units Student Probe Measurement Using Standard Units 6 7 8 9 List the length of each colored line segment: blue, red, green. Explain how you found your answers. Lesson Description The lesson is intended to help

More information

Fraction Values and Changing Wholes

Fraction Values and Changing Wholes Fraction Values and Changing Wholes Student Probe Figure A Name the fractional part of Figure A for each of the following colored pattern blocks: blue rhombus, green triangle, red trapezoid. Name the fractional

More information

Deriving the General Equation of a Circle

Deriving the General Equation of a Circle Deriving the General Equation of a Circle Standard Addressed in this Task MGSE9-12.G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square

More information

Looking for Pythagoras An Investigation of the Pythagorean Theorem

Looking for Pythagoras An Investigation of the Pythagorean Theorem Looking for Pythagoras An Investigation of the Pythagorean Theorem I2t2 2006 Stephen Walczyk Grade 8 7-Day Unit Plan Tools Used: Overhead Projector Overhead markers TI-83 Graphing Calculator (& class set)

More information

Square Roots and the Pythagorean Theorem

Square Roots and the Pythagorean Theorem UNIT 1 Square Roots and the Pythagorean Theorem Just for Fun What Do You Notice? Follow the steps. An example is given. Example 1. Pick a 4-digit number with different digits. 3078 2. Find the greatest

More information

Geometer s Sketchpad Version 4

Geometer s Sketchpad Version 4 Geometer s Sketchpad Version 4 For PC Name: Date: INVESTIGATION: The Pythagorean Theorem Directions: Use the steps below to lead you through the investigation. After each step, be sure to click in the

More information

THE PYTHAGOREAN SPIRAL PROJECT

THE PYTHAGOREAN SPIRAL PROJECT THE PYTHAGOREAN SPIRAL PROJECT A Pythagorean Spiral is a series of right triangles arranged in a spiral configuration such that the hypotenuse of one right triangle is a leg of the next right triangle.

More information

Set 6: Understanding the Pythagorean Theorem Instruction

Set 6: Understanding the Pythagorean Theorem Instruction Instruction Goal: To provide opportunities for students to develop concepts and skills related to understanding that the Pythagorean theorem is a statement about areas of squares on the sides of a right

More information

Representing Square Numbers. Use materials to represent square numbers. A. Calculate the number of counters in this square array.

Representing Square Numbers. Use materials to represent square numbers. A. Calculate the number of counters in this square array. 1.1 Student book page 4 Representing Square Numbers You will need counters a calculator Use materials to represent square numbers. A. Calculate the number of counters in this square array. 5 5 25 number

More information

Concept: Pythagorean Theorem Name:

Concept: Pythagorean Theorem Name: Concept: Pythagorean Theorem Name: Interesting Fact: The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and

More information

How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr.

How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr. Common Core Standard: 8.G.6, 8.G.7 How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.2.2 What Is Special

More information

The Basics: Geometric Structure

The Basics: Geometric Structure Trinity University Digital Commons @ Trinity Understanding by Design: Complete Collection Understanding by Design Summer 6-2015 The Basics: Geometric Structure Danielle Kendrick Trinity University Follow

More information

UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet

UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet Name Period Date UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet 24.1 The Pythagorean Theorem Explore the Pythagorean theorem numerically, algebraically, and geometrically. Understand a proof

More information

1.1 The Pythagorean Theorem

1.1 The Pythagorean Theorem 1.1 The Pythagorean Theorem Strand Measurement and Geometry Overall Expectations MGV.02: solve problems involving the measurements of two-dimensional shapes and the volumes of three-dimensional figures;

More information

Challenging Students to Discover the Pythagorean Relationship

Challenging Students to Discover the Pythagorean Relationship Brought to you by YouthBuild USA Teacher Fellows! Challenging Students to Discover the Pythagorean Relationship A Common Core-Aligned Lesson Plan to use in your Classroom Author Richard Singer, St. Louis

More information

Geometry. Teacher s Guide

Geometry. Teacher s Guide Geometry Teacher s Guide WALCH PUBLISHING Table of Contents To the Teacher.......................................................... vi Classroom Management..................................................

More information

Addition and Subtraction of Polynomials

Addition and Subtraction of Polynomials Student Probe What is 10x 2 2y x + 4y 6x 2? Addition and Subtraction of Polynomials Answer: 4x 2 x + 2y The terms 10x 2 and - 6x 2 should be combined because they are like bases and the terms - 2y and

More information

8.2 Slippery Slopes. A Solidify Understanding Task

8.2 Slippery Slopes. A Solidify Understanding Task SECONDARY MATH I // MODULE 8 7 8.2 Slippery Slopes A Solidify Understanding Task CC BY https://flic.kr/p/kfus4x While working on Is It Right? in the previous module you looked at several examples that

More information

Pythagorean Theorem Unit

Pythagorean Theorem Unit Pythagorean Theorem Unit TEKS covered: ~ Square roots and modeling square roots, 8.1(C); 7.1(C) ~ Real number system, 8.1(A), 8.1(C); 7.1(A) ~ Pythagorean Theorem and Pythagorean Theorem Applications,

More information

Investigation. Triangle, Triangle, Triangle. Work with a partner.

Investigation. Triangle, Triangle, Triangle. Work with a partner. Investigation Triangle, Triangle, Triangle Work with a partner. Materials: centimetre ruler 1-cm grid paper scissors Part 1 On grid paper, draw a large right triangle. Make sure its base is along a grid

More information

8.2 Slippery Slopes. A Solidify Understanding Task

8.2 Slippery Slopes. A Solidify Understanding Task 7 8.2 Slippery Slopes A Solidify Understanding Task CC BY https://flic.kr/p/kfus4x While working on Is It Right? in the previous module you looked at several examples that lead to the conclusion that the

More information

2016 Geometry Honors Summer Packet

2016 Geometry Honors Summer Packet Name: 2016 Geometry Honors Summer Packet This packet is due the first day of school. It will be graded for completion and effort shown. There will be an assessment on these concepts the first week of school.

More information

Day 1. Last Night s Homework Angle Worksheet (11 problems) Bellwork Angle quiz.

Day 1. Last Night s Homework Angle Worksheet (11 problems) Bellwork Angle quiz. Course: 7 th Grade Math DETAIL LESSON PLAN Wednesday, January 25 / Thursday, January 26 Student Objective (Obj. 3e) TSW use the Pythagorean Theorem to find the missing length of a side of a right triangle.

More information

Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.

Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions. Student Outcomes Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions. Lesson Notes It is recommended that students have access to a calculator as they work

More information

1. 1 Square Numbers and Area Models (pp. 6-10)

1. 1 Square Numbers and Area Models (pp. 6-10) Math 8 Unit 1 Notes Name: 1. 1 Square Numbers and Area Models (pp. 6-10) square number: the product of a number multiplied by itself; for example, 25 is the square of 5 perfect square: a number that is

More information

Catty Corner. Side Lengths in Two and. Three Dimensions

Catty Corner. Side Lengths in Two and. Three Dimensions Catty Corner Side Lengths in Two and 4 Three Dimensions WARM UP A 1. Imagine that the rectangular solid is a room. An ant is on the floor situated at point A. Describe the shortest path the ant can crawl

More information

ACT Coordinate Geometry Review

ACT Coordinate Geometry Review ACT Coordinate Geometry Review Here is a brief review of the coordinate geometry concepts tested on the ACT. Note: there is no review of how to graph an equation on this worksheet. Questions testing this

More information

Getting Triggy With It

Getting Triggy With It Getting Triggy With It Date: 15 May 2013 Topic: Pythagorean Theorem and Trigonometric Ratios Class: Grade 9 Ability Level: Mixed Ability Teacher: Mr. Cyrus Alvarez LESSON OBJECTIVES: At the end of the

More information

Concept: Pythagorean Theorem Name:

Concept: Pythagorean Theorem Name: Concept: Pythagorean Theorem Name: Interesting Fact: The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and

More information

E G 2 3. MATH 1012 Section 8.1 Basic Geometric Terms Bland

E G 2 3. MATH 1012 Section 8.1 Basic Geometric Terms Bland MATH 1012 Section 8.1 Basic Geometric Terms Bland Point A point is a location in space. It has no length or width. A point is represented by a dot and is named by writing a capital letter next to the dot.

More information

Identify Non-linear Functions from Data

Identify Non-linear Functions from Data Identify Non-linear Functions from Data Student Probe Identify which data sets display linear, exponential, or quadratic behavior. x -1 0 1 2 3 y -3-4 -3 0 5 x -2 0 2 4 6 y 9 4-1 -6-11 x -1 0 1 2 3 y ¼

More information

The Pythagorean Theorem 8.6.C

The Pythagorean Theorem 8.6.C ? LESSON 8.1 The Pythagorean Theorem ESSENTIAL QUESTION Expressions, equations, and relationships 8.6.C Use models and diagrams to explain the Pythagorean Theorem. 8.7.C Use the Pythagorean Theorem...

More information

During What could you do to the angles to reliably compare their measures?

During What could you do to the angles to reliably compare their measures? Measuring Angles LAUNCH (9 MIN) Before What does the measure of an angle tell you? Can you compare the angles just by looking at them? During What could you do to the angles to reliably compare their measures?

More information

Construction. Student Handbook

Construction. 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 information

Angle Measure and Plane Figures

Angle Measure and Plane Figures Grade 4 Module 4 Angle Measure and Plane Figures OVERVIEW This module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize,

More information

Geometer s Skethchpad 8th Grade Guide to Learning Geometry

Geometer s Skethchpad 8th Grade Guide to Learning Geometry Geometer s Skethchpad 8th Grade Guide to Learning Geometry This Guide Belongs to: Date: Table of Contents Using Sketchpad - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

More information

Special Right Triangles and Right Triangle Trigonometry

Special Right Triangles and Right Triangle Trigonometry Special Right Triangles and Right Triangle Trigonometry Reporting Category Topic Triangles Investigating special right triangles and right triangle trigonometry Primary SOL G.8 The student will solve real-world

More information

The Pythagorean Theorem

The Pythagorean Theorem ! The Pythagorean Theorem Recall that a right triangle is a triangle with a right, or 90, angle. The longest side of a right triangle is the side opposite the right angle. We call this side the hypotenuse

More information

Lesson 16: The Computation of the Slope of a Non Vertical Line

Lesson 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 information

Course: Math Grade: 7. Unit Plan: Geometry. Length of Unit:

Course: Math Grade: 7. Unit Plan: Geometry. Length of Unit: Course: Math Grade: 7 Unit Plan: Geometry Length of Unit: Enduring Understanding(s): Geometry is found in the visual world in two and three dimension. We use geometry daily in problem solving. Essential

More information

Your Task. Unit 3 (Chapter 1): Number Relationships. The 5 Goals of Chapter 1

Your Task. Unit 3 (Chapter 1): Number Relationships. The 5 Goals of Chapter 1 Unit 3 (Chapter 1): Number Relationships The 5 Goals of Chapter 1 I will be able to: model perfect squares and square roots use a variety of strategies to recognize perfect squares use a variety of strategies

More information

Lesson 4: Fundamental Theorem of Similarity (FTS)

Lesson 4: Fundamental Theorem of Similarity (FTS) Student Outcomes Students experimentally verify the properties related to the Fundamental Theorem of Similarity (FTS). Lesson Notes The goal of this activity is to show students the properties of the Fundamental

More information

TIalgebra.com Algebra 1

TIalgebra.com Algebra 1 Perpendicular Slopes ID: 8973 Time required 45 minutes Topic: Linear Functions Graph lines whose slopes are negative reciprocals and measure the angles to verify they are perpendicular. Activity Overview

More information

Building Concepts: Fractions and Unit Squares

Building Concepts: Fractions and Unit Squares Lesson Overview This TI-Nspire lesson, essentially a dynamic geoboard, is intended to extend the concept of fraction to unit squares, where the unit fraction b is a portion of the area of a unit square.

More information

Grade 4 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print

Grade 4 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 4 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology

More information

Pearson's Ramp-Up Mathematics

Pearson'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 information

LAB 9.2 The Pythagorean Theorem

LAB 9.2 The Pythagorean Theorem LAB 9.2 The Pythagorean Theorem Equipment: Geoboards, dot paper 1. The figure above shows a right triangle with a square on each side. Find the areas of the squares. 2. Make your own right triangles on

More information

Chapter 1 and Section 2.1

Chapter 1 and Section 2.1 Chapter 1 and Section 2.1 Diana Pell Section 1.1: Angles, Degrees, and Special Triangles Angles Degree Measure Angles that measure 90 are called right angles. Angles that measure between 0 and 90 are called

More information

Problem of the Month: Between the Lines

Problem of the Month: Between the Lines Problem of the Month: Between the Lines Overview: In the Problem of the Month Between the Lines, students use polygons to solve problems involving area. The mathematical topics that underlie this POM are

More information

Lesson 6.1 Linear Equation Review

Lesson 6.1 Linear Equation Review Name: Lesson 6.1 Linear Equation Review Vocabulary Equation: a math sentence that contains Linear: makes a straight line (no Variables: quantities represented by (often x and y) Function: equations can

More information

Building Concepts: Ratios Within and Between Scaled Shapes

Building Concepts: Ratios Within and Between Scaled Shapes Lesson Overview In this TI-Nspire lesson, students learn that ratios are connected to geometry in multiple ways. When one figure is an enlarged or reduced copy of another by some scale factor, the ratios

More information

Geometry Vocabulary Book

Geometry Vocabulary Book Geometry Vocabulary Book Units 2-4 Page 1 Unit 2 General Geometry Point Characteristics: Line Characteristics: Plane Characteristics: RELATED POSTULATES: Through any two points there exists exactly one

More information

Area of Composite Figures. ESSENTIAL QUESTION do you find the area of composite figures? 7.9.C

Area of Composite Figures. ESSENTIAL QUESTION do you find the area of composite figures? 7.9.C ? LESSON 9.4 Area of Composite Figures ESSENTIAL QUESTION How do you find the area of composite figures? Equations, expressions, and relationships Determine the area of composite figures containing combinations

More information

Chapter 5. Drawing a cube. 5.1 One and two-point perspective. Math 4520, Spring 2015

Chapter 5. Drawing a cube. 5.1 One and two-point perspective. Math 4520, Spring 2015 Chapter 5 Drawing a cube Math 4520, Spring 2015 5.1 One and two-point perspective In Chapter 5 we saw how to calculate the center of vision and the viewing distance for a square in one or two-point perspective.

More information

Lesson 6.1 Skills Practice

Lesson 6.1 Skills Practice Lesson 6.1 Skills Practice Name Date Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Vocabulary Match each definition to its corresponding term. 1. A mathematical statement

More information

. line segment. 1. Draw a line segment to connect the word to its picture. ray. line. point. angle. 2. How is a line different from a line segment?

. line segment. 1. Draw a line segment to connect the word to its picture. ray. line. point. angle. 2. How is a line different from a line segment? COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Exit Ticket 4 1. Draw a line segment to connect the word to its picture. ray line. line segment point angle 2. How is a line different from a line segment? Lesson

More information

2. Where might you find an example of a right angle in your home? How could you check that it is a right angle?

2. Where might you find an example of a right angle in your home? How could you check that it is a right angle? Master 4.22 Extra Practice 1 Lesson 1: Naming Angles 1. Look at the angles in each of the shapes below. Which angles are acute, right, or obtuse angles? How do you know? 2. Where might you find an example

More information

Anthony Chan. September, Georgia Adult Education Conference

Anthony Chan. September, Georgia Adult Education Conference Anthony Chan September, 2018 1 2018 Georgia Adult Education Conference Attendees will be able to: Make difficult math concepts simple and help their students discover math principles on their own. This

More information

1 Version 2.0. Related Below-Grade and Above-Grade Standards for Purposes of Planning for Vertical Scaling:

1 Version 2.0. Related Below-Grade and Above-Grade Standards for Purposes of Planning for Vertical Scaling: Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Geometry Target E [a]: Draw, construct,

More information

Please bring a laptop or tablet next week! Upcoming Assignment Measurement Investigations Patterns & Algebraic Thinking Investigations Break A Few

Please bring a laptop or tablet next week! Upcoming Assignment Measurement Investigations Patterns & Algebraic Thinking Investigations Break A Few Please bring a laptop or tablet next week! Upcoming Assignment Measurement Investigations Patterns & Algebraic Thinking Investigations Break A Few More Investigations Literature Circles Final Lesson Plan

More information

Angles and. Learning Goals U N I T

Angles and. Learning Goals U N I T U N I T Angles and Learning Goals name, describe, and classify angles estimate and determine angle measures draw and label angles provide examples of angles in the environment investigate the sum of angles

More information

6.00 Trigonometry Geometry/Circles Basics for the ACT. Name Period Date

6.00 Trigonometry Geometry/Circles Basics for the ACT. Name Period Date 6.00 Trigonometry Geometry/Circles Basics for the ACT Name Period Date Perimeter and Area of Triangles and Rectangles The perimeter is the continuous line forming the boundary of a closed geometric figure.

More information

and Transitional Comprehensive Curriculum. Geometry Unit 3: Parallel and Perpendicular Relationships

and Transitional Comprehensive Curriculum. Geometry Unit 3: Parallel and Perpendicular Relationships Geometry Unit 3: Parallel and Perpendicular Relationships Time Frame: Approximately three weeks Unit Description This unit demonstrates the basic role played by Euclid s fifth postulate in geometry. Euclid

More information

HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934)

HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934) HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.1a

More information

Deconstructing Prisms

Deconstructing Prisms Using Patterns, Write Expressions That Determine the Number of Unit Cubes With Any Given Number of Exposed Faces Based on the work of Linda S. West, Center for Integrative Natural Science and Mathematics

More information

1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw.

1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Homework 4 Name Date 1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw. c.

More information

B. Examples: 1. At NVHS, there are 104 teachers and 2204 students. What is the approximate teacher to student ratio?

B. Examples: 1. At NVHS, there are 104 teachers and 2204 students. What is the approximate teacher to student ratio? Name Date Period Notes Formal Geometry Chapter 7 Similar Polygons 7.1 Ratios and Proportions A. Definitions: 1. Ratio: 2. Proportion: 3. Cross Products Property: 4. Equivalent Proportions: B. Examples:

More information

Problem of the Month: Between the Lines

Problem of the Month: Between the Lines Problem of the Month: Between the Lines The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common

More information

( for 2 lessons) Key vocabulary: triangle, square, root, hypotenuse, leg, angle, side, length, equation

( for 2 lessons) Key vocabulary: triangle, square, root, hypotenuse, leg, angle, side, length, equation LESSON: Pythagoras Theorem ( for 2 lessons) Level: Pre-intermediate, intermediate Learning objectives: to understand the relationship between the sides of right angled-triangle to solve problems using

More information

Reflect & Share. Here is the same parallelogram. This is a parallelogram. The height is perpendicular to the base. Work with a partner.

Reflect & Share. Here is the same parallelogram. This is a parallelogram. The height is perpendicular to the base. Work with a partner. 6.1 Area of a Parallelogram Focus Use a formula to find the area of a parallelogram. This is a parallelogram. How would you describe it? Here is the same parallelogram. Any side of the parallelogram is

More information

Number Relationships. Chapter GOAL

Number Relationships. Chapter GOAL Chapter 1 Number Relationships GOAL You will be able to model perfect squares and square roots use a variety of strategies to recognize perfect squares use a variety of strategies to estimate and calculate

More information

Pythagorean Theorem Worksheet And Answer Key

Pythagorean Theorem Worksheet And Answer Key PYTHAGOREAN THEOREM WORKSHEET AND ANSWER KEY PDF - Are you looking for pythagorean theorem worksheet and answer key Books? Now, you will be happy that at this time pythagorean theorem worksheet and answer

More information

Volumes of Revolution

Volumes of Revolution Connecting Geometry to Advanced Placement* Mathematics A Resource and Strategy Guide Updated: 0/7/ Volumes of Revolution Objective: Students will visualize the volume of a geometric solid generated by

More information

Connected Mathematics 2, 6 th and 7th Grade Units 2009 Correlated to: Washington Mathematics Standards for Grade 5

Connected Mathematics 2, 6 th and 7th Grade Units 2009 Correlated to: Washington Mathematics Standards for Grade 5 Grade 5 5.1. Core Content: Multi-digit division (Operations, Algebra) 5.1.A Represent multi-digit division using place value models and connect the representation to the related equation. 5.1.B Determine

More information

Lesson Idea by: Van McPhail, Okanagan Mission Secondary

Lesson Idea by: Van McPhail, Okanagan Mission Secondary Click to Print This Page Fit by Design or Design to Fit Mechanical Drafter Designer Lesson Idea by: Van McPhail, Okanagan Mission Secondary There's hardly any object in your home or school that hasn't

More information

Paper Folding: Maximizing the Area of a Triangle Algebra 2

Paper Folding: Maximizing the Area of a Triangle Algebra 2 Paper Folding: Maximizing the Area of a Triangle Algebra (This lesson was developed by Jan Baysden of Hoggard High School and Julie Fonvielle of Whiteville High School during the Leading to Success in

More information

2005 Galois Contest Wednesday, April 20, 2005

2005 Galois Contest Wednesday, April 20, 2005 Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 2005 Galois Contest Wednesday, April 20, 2005 Solutions

More information

1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw.

1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Problem Set 4 Name Date 1. Use the following directions to draw a figure in the box to the right. a. Draw two points: and. b. Use a straightedge to draw.

More information

Lesson 12: Unique Triangles Two Sides and a Non- Included Angle

Lesson 12: Unique Triangles Two Sides and a Non- Included Angle Lesson 12: Unique Triangles Two Sides and a Non- Included Angle Student Outcomes Students understand that two sides of a triangle and an acute angle, not included between the two sides, may not determine

More information

2016 Summer Break Packet for Students Entering Geometry Common Core

2016 Summer Break Packet for Students Entering Geometry Common Core 2016 Summer Break Packet for Students Entering Geometry Common Core Name: Note to the Student: In middle school, you worked with a variety of geometric measures, such as: length, area, volume, angle, surface

More information

Lesson 3 Pre-Visit Perimeter and Area

Lesson 3 Pre-Visit Perimeter and Area Lesson 3 Pre-Visit Perimeter and Area Objective: Students will be able to: Distinguish between area and perimeter. Calculate the perimeter of a polygon whose side lengths are given or can be determined.

More information

6. True or false? Shapes that have no right angles also have no perpendicular segments. Draw some figures to help explain your thinking.

6. True or false? Shapes that have no right angles also have no perpendicular segments. Draw some figures to help explain your thinking. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 3 Homework 4 4 5. Use your right angle template as a guide and mark each right angle in the following figure with a small square. (Note that a right angle

More information

Mathematics Geometry Grade 6AB

Mathematics Geometry Grade 6AB Mathematics Geometry Grade 6AB It s the Right Thing Subject: Mathematics: Geometry: Ratio and Proportion Level: Grade 7 Abstract: Students will learn the six types of triangles and the characteristics

More information

Sample test questions All questions

Sample test questions All questions Ma KEY STAGE 3 LEVELS 3 8 Sample test questions All questions 2003 Contents Question Level Attainment target Page Completing calculations 3 Number and algebra 3 Odd one out 3 Number and algebra 4 Hexagon

More information

Pythagorean Theorem. 2.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem... 45

Pythagorean Theorem. 2.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem... 45 Pythagorean Theorem What is the distance from the Earth to the Moon? Don't let drawings or even photos fool you. A lot of them can be misleading, making the Moon appear closer than it really is, which

More information

GAP CLOSING. Powers and Roots. Intermediate / Senior Facilitator Guide

GAP CLOSING. Powers and Roots. Intermediate / Senior Facilitator Guide GAP CLOSING Powers and Roots Intermediate / Senior Facilitator Guide Powers and Roots Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5 Solutions...5

More information

Count By Tens and Hundreds

Count By Tens and Hundreds Count By Tens and Hundreds Student Probe Sarah had 70 stickers. Then she got 30 more stickers. How many stickers does Lesson Description This lesson helps students develop an understanding of counting

More information

Student Book SAMPLE CHAPTERS

Student Book SAMPLE CHAPTERS Student Book SAMPLE CHAPTERS Nelson Student Book Nelson Math Focus... Eas Each lesson starts with a Lesson Goal. Chapter 6 You will need base ten blocks GOAL Multiply using a simpler, related question.

More information

AREA & PERIMETER LESSON 1 OBJ ECTIVE: OBJECTIVE: INVESTIGATE AND USE THE FORMULAS FOR AREA AND PERIMETER OF RECTANGLES.

AREA & PERIMETER LESSON 1 OBJ ECTIVE: OBJECTIVE: INVESTIGATE AND USE THE FORMULAS FOR AREA AND PERIMETER OF RECTANGLES. AREA & PERIMETER LESSON 1 OBJ ECTIVE: OBJECTIVE: INVESTIGATE AND USE THE FORMULAS FOR AREA AND PERIMETER OF RECTANGLES. Learning Goal By the end of the unit... students will apply the area and perimeter

More information

Mathematics Success Level F

Mathematics 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 information

Sample. Do Not Copy. Chapter 5: Geometry. Introduction. Study Skills. 5.1 Angles. 5.2 Perimeter. 5.3 Area. 5.4 Circles. 5.5 Volume and Surface Area

Sample. Do Not Copy. Chapter 5: Geometry. Introduction. Study Skills. 5.1 Angles. 5.2 Perimeter. 5.3 Area. 5.4 Circles. 5.5 Volume and Surface Area Chapter 5: Geometry Study Skills 5.1 Angles 5.2 Perimeter 5.3 Area 5.4 Circles 5.5 Volume and Surface Area 5.6 Triangles 5.7 Square Roots and the Pythagorean Theorem Chapter 5 Projects Math@Work Foundations

More information

II. UNIT AUTHOR: Hannah Holmes, Falling Creek Middle School, Chesterfield County Sue Jenkins, St. Catherine s School, Private School

II. UNIT AUTHOR: Hannah Holmes, Falling Creek Middle School, Chesterfield County Sue Jenkins, St. Catherine s School, Private School Google Earth Trip I. UNIT OVERVIEW & PURPOSE: will use pictorial representations of real life objects to investigate geometric formulas, relationships, symmetry and transformations. II. UNIT AUTHOR: Hannah

More information

Grade 4. COMMON CORE STATE STANDARDS FOR MATHEMATICS Correlations

Grade 4. COMMON CORE STATE STANDARDS FOR MATHEMATICS Correlations COMMON CORE STATE STANDARDS FOR MATHEMATICS Standards for Mathematical Practices CC.K 12.MP.1 Make sense of problems and persevere in solving them. In most Student Edition lessons. Some examples are: 50

More information

Student Instruction Sheet: Unit 4 Lesson 1. Pythagorean Theorem

Student Instruction Sheet: Unit 4 Lesson 1. Pythagorean Theorem Student Instruction Sheet: Unit 4 Lesson 1 Suggested time: 75 minutes Pythagorean Theorem What s important in this lesson: In this lesson you will learn the Pythagorean Theorem and how to apply the theorem

More information