Challenging Students to Discover the Pythagorean Relationship

Size: px
Start display at page:

Download "Challenging Students to Discover the Pythagorean Relationship"

Transcription

1 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 YouthBuild The lesson Students will be able to determine the length of the hypotenuse of a right triangle if given the lengths of the two legs by implementing the Pythagorean Theorem. Students will be able to prove the theorem by drawing squares on all three sides of a right triangle. Students will see the relationship of the three squares of their triangle drawings, and come to the conclusion that the sum of the squares of the two legs equals the square of the hypotenuse. Objective: Having knowledge of the Pythagorean Theorem and right angles is useful and applicable in the trade of carpentry. This knowledge is also very applicable to those who go on to post-secondary training (mathematics courses, engineering majors.) Students will be able to CCSS: Math 8.G.B.7 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions. Instructional Shifts: Rigor "Pursuing conceptual understanding, procedural skill and fluency, and application all with equal intensity." Rigor includes more than how to get the answer. Rigor calls for using key concepts in a variety of contexts, including calculations related to geometrical figures. Visit to access more classroom activity ideas 1

2 Here s what you do Resources needed: Dot paper (available here ot for drawing triangles. Printed table with the length of two sides of right triangles listed Problem related to carpentry in which they must calculate length of hypotenuse of a right triangle on a roof truss. Rulers with centimeter scales Time: 1 hour + Instructions Academic Vocabulary: Right triangle terminology: legs, sides A, B, and C, hypotenuse, centimeter, roof truss, Pythagorean Theorem or relationship, squares and square roots, dot paper. 1) Activity: (Discuss as a large group, or use pair share and report answers to the class): a) On an overhead transparency, or computer projector, students will be shown an example of a triangle drawn on ¼ inch graph paper. They will then be shown the same triangle with the squares drawn on it. See examples.

3 b) After obtaining rulers and graph paper, students should use the inch side of the ruler to measure the hypotenuse and then draw their square on the hypotenuse. Be sure to explain how to make sure that two sides of the square are perpendicular to the hypotenuse. An inexpensive transparent T-square would be perfect for making sure that the sides are perpendicular to the hypotenuse. c) Students will then be given a printed table containing facts about three right triangles. The table will show the lengths of the two legs of the right triangles, but not the length of the hypotenuse. d) Students will also be given three pieces (or more if needed) of dot paper. Switching from graph to dot paper makes the lesson a bit more challenging, since the students must now measure in centimeters. The students will draw the two legs of the right triangles, one on each dot paper, and then connect the two legs by drawing the hypotenuse. (See examples at the end of this document.) Students will then draw a square on all three sides of the triangles by measuring each side and creating the square from their measurements. Students will fill in their tables with the areas of each side. 2) Wrap up: Students will be given a real-life, work-related problem involving a roof truss which contains a right triangle. Using what they learned, students will calculate the length of the hypotenuse of the right triangle on the roof truss, as follows:

4 Problem A: You are new on the job as an apprentice carpenter, working in a new housing subdivision. You are with your boss, working on roof trusses. Your boss gives you the below drawing and asks you to figure out the length of side C, which happens to be the hypotenuse of a right triangle. Your boss is counting on you to be accurate. Based on what you know, what is the length of side C? Examples of Triangles Drawn on Dot Paper 3) Differentiated Instruction: What are ways that you will adapt the lesson for students with different skill levels? How could you stretch the lesson for more advanced learners? How might you make the lesson more accessible for struggling/reluctant learners? Student pairs can be assigned by levels of ability; one higher level with one lower level. This would address struggling/reluctant learners because the higher level student in the paid will aid the understanding of the lower level partner. More advanced learners could be given more triangles in which they are given the length of the hypotenuse and one leg and must calculate length of the remaining leg, using an algebraic formula. Manipulative (tiles) could be used as another method of proving the theorem.

5 Success Tips What specific tips could you offer educators adopting this lesson? What are potential student misconceptions or struggles with the lesson? It is assumed that at this level, the students have already been exposed to right triangles and their terminology, but have not yet learned the Pythagorean theorem/relationship. Even if they have learned the theorem, it is unlikely that they have seen the actual proof by drawing squares on all three legs of a right triangle and seeing the theorem proven in a clear illustration. Students may need some guided practice to understand the measuring and drawing of the squares, and drawing the small squares inside the large squares. Because of this, the example of a drawn triangle given at the beginning of the lesson is very important. During guided instruction, do not take the pencil out of a student s hand. Explain the correction, and let the student make it. Put the objective on the board: What is the relationship among the squares of the legs and hypotenuse of a right triangle? Encourage students to answer each other s questions. Evidence of Success By the end of the lesson, students will be able to apply the Pythagorean theorem without drawing squares, and will understand the meaning of the Pythagorean theorem. Mastery will be demonstrated when students understand the relationship of the legs and hypotenuse of the right triangle. Outsiders should be able to see that the students have a deep understanding once the relationship is clear.

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

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

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

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

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

The Pythagorean Theorem and Right Triangles

The Pythagorean Theorem and Right Triangles 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

More information

IM 8 Ch Does It Always Work. Common Core Standard: Is the triangle a right triangle? Who is Pythagoras? CPM Materials modified by Mr.

IM 8 Ch Does It Always Work. Common Core Standard: Is the triangle a right triangle? Who is Pythagoras? CPM Materials modified by Mr. Common Core Standard: 8.G.6 Is the triangle a right triangle? Who is Pythagoras? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.2.7 Does It Always Work? Date: Learning Target By the end of the period,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

INTERMEDIATE LEVEL MEASUREMENT

INTERMEDIATE LEVEL MEASUREMENT INTERMEDIATE LEVEL MEASUREMENT TABLE OF CONTENTS Format & Background Information...3-6 Learning Experience 1- Getting Started...6-7 Learning Experience 2 - Cube and Rectangular Prisms...8 Learning Experience

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

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

SFUSD Mathematics Core Curriculum Development Project

SFUSD Mathematics Core Curriculum Development Project 1 SFUSD Mathematics Core Curriculum Development Project 2014 2015 Creating meaningful transformation in mathematics education Developing learners who are independent, assertive constructors of their own

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

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

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

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

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

7.3B STUDENT ACTIVITY #1

7.3B STUDENT ACTIVITY #1 E MAT I CS 7.3B STUDENT ACTIVITY #1 PROBLEM: Right triangles MNP and DEF are similar. Find the length in inches of side EF. D M 6 in. P 9 in. N 24 in. F x E Since the triangles are similar, their corresponding

More information

13-1 Trigonometric Identities. Find the exact value of each expression if 0 < θ < If cot θ = 2, find tan θ. ANSWER: 2. If, find cos θ.

13-1 Trigonometric Identities. Find the exact value of each expression if 0 < θ < If cot θ = 2, find tan θ. ANSWER: 2. If, find cos θ. Find the exact value of each expression if 0 < θ < 90 1. If cot θ = 2, find tan θ. 8. CCSS PERSEVERANCE When unpolarized light passes through polarized sunglass lenses, the intensity of the light is cut

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

Assignment. Visiting Washington, D.C. Transversals and Parallel Lines

Assignment. Visiting Washington, D.C. Transversals and Parallel Lines Assignment Assignment for Lesson.1 Name Date Visiting Washington, D.C. Transversals and Parallel Lines Do not use a protractor in this assignment. Rely only on the measurements given in each problem. 1.

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

13-1 Trigonometric Identities. Find the exact value of each expression if 0 < θ < If cot θ = 2, find tan θ. SOLUTION: 2. If, find cos θ.

13-1 Trigonometric Identities. Find the exact value of each expression if 0 < θ < If cot θ = 2, find tan θ. SOLUTION: 2. If, find cos θ. Find the exact value of each expression if 0 < θ < 90 1. If cot θ = 2, find tan θ. 2. If, find cos θ. Since is in the first quadrant, is positive. Thus,. 3. If, find sin θ. Since is in the first quadrant,

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

Objective: Use varied protractors to distinguish angle measure from length

Objective: Use varied protractors to distinguish angle measure from length NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 6 4 Lesson 6 Objective: Use varied protractors to distinguish angle measure from length Suggested Lesson Structure Fluency Practice Application Problem Concept

More information

Lesson 3: Identify, define, and draw perpendicular lines.

Lesson 3: Identify, define, and draw perpendicular lines. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 3 4 4 Lesson 3 Objective: Identify, define, and draw perpendicular lines. Suggested Lesson Structure Fluency Practice Application Problem Concept Development

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

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

Standard Indicator The Logic Behind the Formula

Standard Indicator The Logic Behind the Formula Standard Indicator 5.5.1 The Logic Behind the Formula Purpose Students will understand the formulas for the area of a triangle, parallelogram, and trapezoid by comparing them to the area of a related rectangle

More information

Multiplication and Area

Multiplication and Area Grade 3 Module 4 Multiplication and Area OVERVIEW In this 20-day module students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. In

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

Objective: Draw polygons with specified attributes to solve problems. (3 minutes) (5 minutes) (60 minutes)

Objective: Draw polygons with specified attributes to solve problems. (3 minutes) (5 minutes) (60 minutes) Lesson 6 3 7 Lesson 6 Objective: Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (12 minutes) (8 minutes) (30 minutes) (10 minutes) (60 minutes)

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

Analytic Geometry/ Trigonometry

Analytic Geometry/ Trigonometry Analytic Geometry/ Trigonometry Course Numbers 1206330, 1211300 Lake County School Curriculum Map Released 2010-2011 Page 1 of 33 PREFACE Teams of Lake County teachers created the curriculum maps in order

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

The Real Number System and Pythagorean Theorem Unit 9 Part B

The Real Number System and Pythagorean Theorem Unit 9 Part B The Real Number System and Pythagorean Theorem Unit 9 Part B Standards: 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion;

More information

a. Sketch a wrapper like the one described above, using the actual size of your cone. Ignore any overlap required for assembly.

a. Sketch a wrapper like the one described above, using the actual size of your cone. Ignore any overlap required for assembly. Illustrative Mathematics G-MG Ice Cream Cone Alignment : G-MG.A.3 You have been hired by the owner of a local ice cream parlor to assist in his company s new venture. The company will soon sell its ice

More information

SESSION ONE GEOMETRY WITH TANGRAMS AND PAPER

SESSION ONE GEOMETRY WITH TANGRAMS AND PAPER SESSION ONE GEOMETRY WITH TANGRAMS AND PAPER Outcomes Develop confidence in working with geometrical shapes such as right triangles, squares, and parallelograms represented by concrete pieces made of cardboard,

More information

Design Your Own Dream Home! Michael Daniels Olive Grove Charter School Grade Levels: 9-12 Subject: Mathematics

Design Your Own Dream Home! Michael Daniels Olive Grove Charter School Grade Levels: 9-12 Subject: Mathematics Design Your Own Dream Home! Michael Daniels Olive Grove Charter School Grade Levels: 9-12 Subject: Mathematics Project Summary: Using Free CAD, a computer aided drafting software program, students design

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

Day 2: Tangram Tune Up Grade 7

Day 2: Tangram Tune Up Grade 7 Day 2: Tangram Tune Up Grade 7 Minds On... Action! Description Review geometric language. Introduce new geometric terminology. Construct tangram pieces and create 2-D composite shapes. Whole Class Reflection

More information

6.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Can That Be Right? 6.3 Pythagoras to the Rescue

6.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Can That Be Right? 6.3 Pythagoras to the Rescue 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

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

Lesson 5: Area of Composite Shape Subject: Math Unit: Area Time needed: 60 minutes Grade: 6 th Date: 2 nd

Lesson 5: Area of Composite Shape Subject: Math Unit: Area Time needed: 60 minutes Grade: 6 th Date: 2 nd Lesson 5: Area of Composite Shape Subject: Math Unit: Area Time needed: 60 minutes Grade: 6 th Date: 2 nd Materials, Texts Needed, or advanced preparation: Lap tops or computer with Geogebra if possible

More information

(60 minutes) (5 minutes)

(60 minutes) (5 minutes) Lesson 13 2 6 Lesson 13 Objective: Suggested Lesson Structure Fluency Practice Concept Development Application Problem Student Debrief Total Time (10 minutes) (33 minutes) (7 minutes) (10 minutes) (60

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

QaD Teacher Support Materials

QaD Teacher Support Materials QaD Teacher Support Materials Focus: Develop skills at interpreting geometric diagrams and using them to solve problems. Instructions Remember to download the Weekly Class Report and use it to help plan

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

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

MAT.HS.PT.4.CANSB.A.051

MAT.HS.PT.4.CANSB.A.051 MAT.HS.PT.4.CANSB.A.051 Sample Item ID: MAT.HS.PT.4.CANSB.A.051 Title: Packaging Cans Grade: HS Primary Claim: Claim 4: Modeling and Data Analysis Students can analyze complex, real-world scenarios and

More information

Construction Junction, What s your Function?

Construction Junction, What s your Function? Construction Junction, What s your Function? Brian Shay Teacher and Department Chair Canyon Crest Academy Brian.Shay@sduhsd.net @MrBrianShay Session Goals Familiarize ourselves with CCSS and the GSE Geometry

More information

Classroom Tips and Techniques: Applying the Epsilon-Delta Definition of a Limit

Classroom Tips and Techniques: Applying the Epsilon-Delta Definition of a Limit Classroom Tips and Techniques: Applying the Epsilon-Delta Definition of a Limit Introduction Robert J. Lopez Emeritus Professor of Mathematics and Maple Fellow Maplesoft My experience in teaching calculus

More information

Brain-on! A Trio of Puzzles

Brain-on! A Trio of Puzzles Hands Hands-on = Brain-on! A Trio of Puzzles "I hear and I forget, I see and I remember, I do and I understand." - Chinese proverb Manipulatives and hands-on activities can be the key to creating concrete

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

Objective: Use the addition of adjacent angle measures to solve problems using a symbol for the unknown angle measure.

Objective: Use the addition of adjacent angle measures to solve problems using a symbol for the unknown angle measure. Lesson 10 Objective: Use the addition of adjacent angle measures to solve problems using a Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time

More information

Irrational Numbers Can In-Spiral You

Irrational Numbers Can In-Spiral You L e s l i e D. L e w i s Irrational Numbers Can In-Spiral You Introducing students to the Pytha - gorean theorem presents a natural context for investigating what irrational numbers are and how they differ

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

The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2.

The area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2. ALGEBRA Find each missing length. 21. A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base? The area A of a trapezoid

More information

HANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273)

HANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273) HANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.3 8.G.4

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

Chapter 12. A Cheerful Fact The Pythagorean Theorem

Chapter 12. A Cheerful Fact The Pythagorean Theorem Chapter 12 A Cheerful Fact The Pythagorean Theorem Outline Brief History Map Pythagoreans Algebraic Square Proof Geometric Square Proof Proof without Words More Proofs Euclid s Elements Triples Coordinate

More information

Georgia Standards of Excellence Frameworks. Mathematics. Accelerated GSE Pre-Calculus Unit 4: Trigonometric Identities

Georgia Standards of Excellence Frameworks. Mathematics. Accelerated GSE Pre-Calculus Unit 4: Trigonometric Identities Georgia Standards of Excellence Frameworks Mathematics Accelerated GSE Pre-Calculus Unit 4: Trigonometric Identities These materials are for nonprofit educational purposes only. Any other use may constitute

More information

Number Models for Area

Number Models for Area Number Models for Area Objectives To guide children as they develop the concept of area by measuring with identical squares; and to demonstrate how to calculate the area of rectangles using number models.

More information

COMPOUND ROOFS WORKSHOP - Introduction Complex roof geometry is a challenge most framers face eventually. These problems can be solved either

COMPOUND ROOFS WORKSHOP - Introduction Complex roof geometry is a challenge most framers face eventually. These problems can be solved either COMPOUND ROOFS WORKSHOP - Introduction Complex roof geometry is a challenge most framers face eventually. These problems can be solved either mathematically or visually, but the complete carpenter will

More information

Measurement and Data Core Guide Grade 4

Measurement and Data Core Guide Grade 4 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit (Standards 4.MD.1 2) Standard 4.MD.1 Know relative sizes of measurement units within each system

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

Teaching Time: Two 50-minute periods

Teaching Time: Two 50-minute periods Lesson Summary In this lesson, students will build an open spectrograph to calculate the angle the light is transmitted through a holographic diffraction grating. After finding the desired angles, the

More information

One of the classes that I have taught over the past few years is a technology course for

One of the classes that I have taught over the past few years is a technology course for Trigonometric Functions through Right Triangle Similarities Todd O. Moyer, Towson University Abstract: This article presents an introduction to the trigonometric functions tangent, cosecant, secant, and

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

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

Unit 1 Foundations of Geometry: Vocabulary, Reasoning and Tools

Unit 1 Foundations of Geometry: Vocabulary, Reasoning and Tools Number of Days: 34 9/5/17-10/20/17 Unit Goals Stage 1 Unit Description: Using building blocks from Algebra 1, students will use a variety of tools and techniques to construct, understand, and prove geometric

More information

Grade 2 Arkansas Mathematics Standards. Represent and solve problems involving addition and subtraction

Grade 2 Arkansas Mathematics Standards. Represent and solve problems involving addition and subtraction Grade 2 Arkansas Mathematics Standards Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction AR.Math.Content.2.OA.A.1 Use addition and subtraction within 100

More 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

Constructions. Unit 9 Lesson 7

Constructions. Unit 9 Lesson 7 Constructions Unit 9 Lesson 7 CONSTRUCTIONS Students will be able to: Understand the meanings of Constructions Key Vocabulary: Constructions Tools of Constructions Basic geometric constructions CONSTRUCTIONS

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

3.9. Pythagorean Theorem Stop the Presses. My Notes ACTIVITY

3.9. Pythagorean Theorem Stop the Presses. My Notes ACTIVITY Pythagorean Theorem SUGGESTED LEARNING STRATEGIES: Marking the Text, Predict and Confirm, Shared Reading Jayla and Sidney are co-editors-in-chief of the school yearbook. They have just finished the final

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

MAT 1160 Mathematics, A Human Endeavor

MAT 1160 Mathematics, A Human Endeavor MAT 1160 Mathematics, A Human Endeavor Syllabus: office hours, grading Schedule (note exam dates) Academic Integrity Guidelines Homework & Quizzes Course Web Site : www.eiu.edu/ mathcs/mat1160/ 2005 09,

More information

The Texas Education Agency and the Texas Higher Education Coordinating Board Geometry Module Pre-/Post-Test. U x T'

The Texas Education Agency and the Texas Higher Education Coordinating Board Geometry Module Pre-/Post-Test. U x T' Pre-/Post-Test The Texas Education Agency and the Texas Higher Education Coordinating Board Geometry Module Pre-/Post-Test 1. Triangle STU is rotated 180 clockwise to form image STU ' ' '. Determine the

More information

3.3. You wouldn t think that grasshoppers could be dangerous. But they can damage

3.3. You wouldn t think that grasshoppers could be dangerous. But they can damage Grasshoppers Everywhere! Area and Perimeter of Parallelograms on the Coordinate Plane. LEARNING GOALS In this lesson, you will: Determine the perimeter of parallelograms on a coordinate plane. Determine

More information

Visualizing Integers TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System

Visualizing Integers TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System Math Objectives Students will identify expressions that balance an equation. Students will find values that satisfy integer equalities. Students will recognize and use the additive inverse property. Students

More information

2nd Grade Math 2007 Standards, Benchmarks, Examples & Vocabulary

2nd Grade Math 2007 Standards, Benchmarks, Examples & Vocabulary 2nd Grade Math 2007 Stards, Benchmarks, s & Vocabulary Str Stard No. Benchmark (2nd Grade) 2.1.1.1 Read, write represent whole numbers up to 1000. Representations may include numerals, addition, subtraction,

More information

Ultimatum. Robotics Unit Lesson 5. Overview

Ultimatum. Robotics Unit Lesson 5. Overview Robotics Unit Lesson 5 Ultimatum Overview In this final challenge the students will deploy their TETRIX rescue robot up the mountain to rescue the stranded mountain climbers. First the rescue robot has

More information