Activities. for building. geometric connections. MCTM Conference Cheryl Tucker

Size: px
Start display at page:

Download "Activities. for building. geometric connections. MCTM Conference Cheryl Tucker"

Transcription

1 Activities for building geometric connections (handout) MCTM Conference 2013 Cheryl Tucker Minneapolis Public Schools (Many materials are from Geometry Connections, CPM, used with permission)

2 Kaleidoscope: Each team will need hinged mirrors and a piece of colored paper. Your Task: Place a hinged mirror on a piece of paper so that its sides intersect the edge of the paper. Explore what shapes you see when you look directly at the mirror, and how those shapes change when you change the angle of the mirror. Discuss the following questions with your team. Be ready to share your responses with the class. Team Questions: 1. What happens to the shape you see as the angle formed by the mirror gets bigger (wider)? What happens as the angle gets smaller? 2. Does it matter if the sides of the mirror intersect the edge of the paper the same distance from the point where the mirrors are hinged? 3. What happens to the shapes if they are not equal? What is the smallest number of sides the shape you see in the mirror can have? What is the largest? 4. Find a way to form a regular hexagon (a shape with 6 equal sides and equal angles). 5. Describe how you set the mirrors to form a hexagon.

3 Next, try this with the class: Use a protractor to measure the angle at the hinge. Put the protractor on the top of the hinge so it does not interfere with what you see. Specific shapes may be formed with specific angle measures. Some students may note that the product of the angle measure and the number of the sides is always 360 degrees!

4 Height Lab Materials: small weight or washer, string - one piece 3 ft., another 1 ft., tape - 2 pieces per team, rulers - 1 per team Objective: I will investigate heights of triangles. 1. Tape a 15 cm section of the long string along the edge of a desk or table. Be sure to leave long ends of string hanging off each side. 2. Tie one end of the short string to the weight and the other to the end of a pencil. Mark a distance 14 cm from the pencil toward the weight by placing a piece of tape on the string. 3. Bring the loose ends of string up from the table and cross them. Put the pencil with the weight over the crossing of the string. Cross the strings again on top of the pencil. Now, with your team, build and sketch triangles that meet these 3 conditions: Student jobs are: *Hold the pen with the weight. *Make sure that the height stays the same and all strings stay taught. *draw accurate sketches. *hold the strings that make the sides of the triangles. Find and draw a picture of: 1. The height of the triangle is inside the triangle. 2. The height of the triangle is a side of the triangle. 3. The height of the triangle is outside of the triangle. Questions: Do all three triangles have the same base and height? Do they look the same? Do they have the same area? What follows? Use index cards to find height of triangles, finding areas of triangles.

5 Heights For figures (a) through (d), draw a height to the side labeled base. One possible way to do this (there are many more!) is shown below. 2-89, part (b)

6 Pantograph Lesson Intro: Before computer and copy machines existed it sometimes took hours o enlarge documents or to shrink text on items such as jewelry. A pantograph device was once used to duplicate written documents and rtistic drawings. You will now employ the same geometric principles by using rubber bands to draw enlarged copies of a design. 1. Draw a simple shape. 2. Take either the 2 or 3 rubber band chain, putting a pencil in 1 end and placing it on the stretch point.. 3. Stretch until the first knot is on the design. Keep knot on the design while using marker to draw the new shape. Marker is in the other end of the rubber band chain. Questions to ask: 1. What do the shapes have in common? 2. What is different about the shapes? The teacher is leading to: Figures will have the same shape if their angles are equal in measure and their sides grow in a common pattern.

7 You are getting sleepy Prior learning consists of triangle similarity. This can be used as an assessment to determine understanding of sides being proportional and similarity relationships. Legend has it that if you stare into a person s eyes in a special way, you can hypnotize them into squawking like a chicken! Here is how it works. Place a mirror on the floor. Your victim has to stand exactly 200 cm away from the mirror and stare into it. The only tricky part is that you need to figure out where you have to stand so that when you stare into the mirror, you are also staring into your victim s eyes. If your calculations are correct and you stand at the EXACT distance, your victim will squawk like a chicken! Directions: 1. Choose a member of your team to hypnotize. 2. Measure heights of both yourself and your victim (eye height) 3. Draw a diagram to represent this situation. 4. Label all lengths you can on the diagram. (Remember - victim stands 200 cm from mirror!) 5. Find any equal angle pairs(remember what you know about how images reflect off mirrors.) 6. What is the relationship between the 2 triangles? How do you know? 7. Moment of truth check it out! Squawk!!

8 Making Predictions and Investigation Results Today you will investigate what happens when you change the attributes of a Möbius strip. As you investigate, you will record data in a table. You will then analyze this data and use your results to brainstorm further experiments. As you look back at your data, you may start to consider other related questions that can help you understand a pattern and learn more about what is happening. This Way of Thinking, called investigating, includes not only generating new questions, but also rethinking when the results are not what you expected On a piece of paper provided by your teacher, make a "bracelet" by taping the two ends securely together. Putting tape on both sides of the bracelet will help to make sure the bracelet is secure. In the diagram of the rectangular strip shown at right, you would tape the ends together so that point A would attach to point C, and point B would attach to point D. Now predict what you think would happen if you were to cut the bracelet down the middle, as shown in the diagram at right. Record your prediction in a table like the one shown below. Experiment Prediction 1-9 Cut bracelet in half as shown in the diagram a 1-12b 1-12c 1-12d Now cut your strip as described above and record your result in the first row of your table. Make sure to include a short description of your result.

9 1-10. On a second strip of paper, label a point X in the center of the strip at least one inch away from one end. Now turn this strip into a Möbius strip by attaching the ends together securely after making one twist. For the strip shown in the diagram above, the paper would be twisted once so that point A would attach to point D. The result should look like the diagram at right. A Möbius Strip Predict what would happen if you were to draw a line down the center of the strip from point X until you ran out of paper. Record your prediction, conduct the experiment, and record your result What do you think would happen if you were to cut your Möbius strip along the central line you drew in problem 1-10? Record your prediction in your table.cut just one of your team's Möbius strips. Record your result in your table. Consider the original strip of paper drawn in problem 1-9 to help you explain why cutting the Möbius strip had this result What else can you learn about Möbius strips? For each experiment below, first record your expectation. Then record your result in your table after conducting the experiment. Use a new Möbius strip for each experiment. What if the result from problem 1-11 is cut in half down the middle again? What would happen if the Möbius strip is cut one-third of the way from one of the sides of the strip? Be sure to cut a constant distance from the side of the strip. What if a strip is formed by 2 twists instead of one? What would happen if it were cut down the middle? If time allows, make up your own experiment. You might

10 change how many twists you make, where you make your cuts, etc. Try to generalize your findings as you conduct your experiment. Be prepared to share your results with the class LEARNING REFLECTION Think over how you and your study team worked today, and what you learned about Möbius strips. What questions did you or your teammates ask that helped move the team forward? What questions do you still have about Möbius strips? What would you like to know more about?

11 Final Exam Circle Fold 1. Make a circle with a 3- inch radius. Cut it out 2. How can you find the center if you don t know it? a. 2 quarter folds b. If you can t fold it? Fold on any chord. Bisect it and crease. Repeat and the point of intersection is the center O. Why: diameter is perpendicular to a chord at its midpoint 3. Fold any point A on the circle to the center of the circle. Crease. Label the endpoints of the crease (chord) AB. 4. Fold chord AC where C is determined by folding this section down so another point on the chord intersects (touches) the center O. You now have 2 chords equal in length with a common endpoint and 2 points on the circle intersecting at the center 5. Do this same procedure a third time, creating an equilateral triangle. a. Questions should be asked at this time what are the angle measures? Is it regular? Etc 6. Bisect 1 side by folding it in half. Make a small crease at the midpoint. a. If folded completely, what kind of a triangle do you have? Special Leg lengths, area 7. Fold the vertex of the side opposite down to the midpoint. Crease. a. What shape do you have? Area? Base angles? Characteristics? Etc 8. Fold the 2 single triangles on top of the others to form 1 single smaller triangle. Open it up. a. Questions regarding similar shapes, areas, ratio of sides, perimeters, area 9. Next, with 1 triangle folded down and 1 folded over, what shape do you have? a. Trapezoid questions are next! 10. Make a 3 dimensional shape. What is it a triangular pyramid? Or a tetrahedron. a. Ask a few volume questions. 11. Open up so you have the original triangle. Fold 1 vertex to the center of the circle. Crease. Repeat with the other 2 vertices. What shape? Hexagon a. Questions regarding hexagon, symmetry, central angles, area, area of regular polygons. 12. Gently squeeze the shape so that the 3 small triangles of each side overlap (on top of each other). a. What shape is this? A truncated tetrahedron! Why is it not a pyramid? Similarities? Differences? 13. Lastly, I have my students autograph the large triangle (the base). I use a small amount of tape and then collect them. I have a couple of volunteers put 20 of them together to make an icosahedron. Then I hang it from my ceiling, recalling their class forever!!

is formed where the diameters intersect? Label the center.

is formed where the diameters intersect? Label the center. E 26 Get Into Shape Hints or notes: A circle will be folded into a variety of geometric shapes. This activity provides the opportunity to assess the concepts, vocabulary and knowledge of relationships

More information

Measuring and Drawing Angles and Triangles

Measuring and Drawing Angles and Triangles NME DTE Measuring and Drawing ngles and Triangles Measuring an angle 30 arm origin base line 0 180 0 If the arms are too short to reach the protractor scale, lengthen them. Step 1: lace the origin of the

More information

You need to be really accurate at this before trying the next task. Keep practicing until you can draw a perfect regular hexagon.

You need to be really accurate at this before trying the next task. Keep practicing until you can draw a perfect regular hexagon. Starter 1: On plain paper practice constructing equilateral triangles using a ruler and a pair of compasses. Use a base of length 7cm. Measure all the sides and all the angles to check they are all the

More information

UNIT PLAN. Grade Level: Unit #: 7 Unit Name: Circles

UNIT PLAN. Grade Level: Unit #: 7 Unit Name: Circles UNIT PLAN Subject: Geometry Grade Level: 10-12 Unit #: 7 Unit Name: Circles Big Idea/Theme: The understanding of properties of circles, the lines that intersect them, and the use of their special segments

More information

1 st Subject: 2D Geometric Shape Construction and Division

1 st Subject: 2D Geometric Shape Construction and Division Joint Beginning and Intermediate Engineering Graphics 2 nd Week 1st Meeting Lecture Notes Instructor: Edward N. Locke Topic: Geometric Construction 1 st Subject: 2D Geometric Shape Construction and Division

More information

Geometry 2001 part 1

Geometry 2001 part 1 Geometry 2001 part 1 1. Point is the center of a circle with a radius of 20 inches. square is drawn with two vertices on the circle and a side containing. What is the area of the square in square inches?

More information

Sec Geometry - Constructions

Sec Geometry - Constructions Sec 2.2 - Geometry - Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have

More information

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 3: Constructing Polygons Instruction

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 3: Constructing Polygons Instruction rerequisite Skills This lesson requires the use of the following skills: using a compass copying and bisecting line segments constructing perpendicular lines constructing circles of a given radius Introduction

More information

5.3. Area of Polygons and Circles Play Area. My Notes ACTIVITY

5.3. Area of Polygons and Circles Play Area. My Notes ACTIVITY Area of Polygons and Circles SUGGESTED LEARNING STRATEGIES: Think/Pair/Share ACTIVITY 5.3 Pictured below is an aerial view of a playground. An aerial view is the view from above something. Decide what

More 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

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

LIST OF HANDS-ON ACTIVITIES IN MATHEMATICS FOR CLASSES III TO VIII. Mathematics Laboratory

LIST OF HANDS-ON ACTIVITIES IN MATHEMATICS FOR CLASSES III TO VIII. Mathematics Laboratory LIST OF HANDS-ON ACTIVITIES IN MATHEMATICS FOR CLASSES III TO VIII Mathematics Laboratory The concept of Mathematics Laboratory has been introduced by the Board in its affiliated schools with the objective

More information

The Grade 6 Common Core State Standards for Geometry specify that students should

The Grade 6 Common Core State Standards for Geometry specify that students should The focus for students in geometry at this level is reasoning about area, surface area, and volume. Students also learn to work with visual tools for representing shapes, such as graphs in the coordinate

More information

Cross Sections of Three-Dimensional Figures

Cross Sections of Three-Dimensional Figures Domain 4 Lesson 22 Cross Sections of Three-Dimensional Figures Common Core Standard: 7.G.3 Getting the Idea A three-dimensional figure (also called a solid figure) has length, width, and height. It is

More information

What You ll Learn. Why It s Important

What You ll Learn. Why It s Important Many artists use geometric concepts in their work. Think about what you have learned in geometry. How do these examples of First Nations art and architecture show geometry ideas? What You ll Learn Identify

More information

Worksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics

Worksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics Worksheet 10 Memorandum: Construction of Geometric Figures Grade 9 Mathematics For each of the answers below, we give the steps to complete the task given. We ve used the following resources if you would

More information

Middle School Geometry. Session 2

Middle School Geometry. Session 2 Middle School Geometry Session 2 Topic Activity Name Page Number Related SOL Spatial Square It 52 6.10, 6.13, Relationships 7.7, 8.11 Tangrams Soma Cubes Activity Sheets Square It Pick Up the Toothpicks

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

How to Design a Geometric Stained Glass Lamp Shade

How to Design a Geometric Stained Glass Lamp Shade This technique requires no calculation tables, math, or angle computation. Instead you can use paper & pencil with basic tech drawing skills to design any size or shape spherical lamp with any number of

More information

Challenges from Ancient Greece

Challenges from Ancient Greece Challenges from ncient Greece Mathematical goals Make formal geometric constructions with a variety of tools and methods. Use congruent triangles to justify geometric constructions. Common Core State Standards

More information

Objective: Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes.

Objective: Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 5 5 Lesson 18 Objective: Draw rectangles and rhombuses to clarify their attributes, and define Suggested Lesson Structure Fluency Practice Application Problem

More information

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 2: Constructing Lines, Segments, and Angles Instruction

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 2: Constructing Lines, Segments, and Angles Instruction Prerequisite Skills This lesson requires the use of the following skills: using a compass understanding the geometry terms line, segment, ray, and angle Introduction Two basic instruments used in geometry

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

Session 1 What Is Geometry?

Session 1 What Is Geometry? Key Terms for This Session Session 1 What Is Geometry? New in This Session altitude angle bisector concurrent line line segment median midline perpendicular bisector plane point ray Introduction In this

More information

6.1 Justifying Constructions

6.1 Justifying Constructions Name lass ate 6.1 Justifying onstructions Essential Question: How can you be sure that the result of a construction is valid? Resource Locker Explore 1 Using a Reflective evice to onstruct a erpendicular

More information

Kansas City Area Teachers of Mathematics 2017 KCATM Contest

Kansas City Area Teachers of Mathematics 2017 KCATM Contest Kansas City Area Teachers of Mathematics 2017 KCATM Contest GEOMETRY AND MEASUREMENT TEST GRADE 4 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 15 minutes You may use calculators

More information

use properties and relationships in geometry.

use properties and relationships in geometry. The learner will understand and 3 use properties and relationships in geometry. 3.01 Using three-dimensional figures: a) Identify, describe, and draw from various views (top, side, front, corner). A. Going

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

4 th Grade Mathematics Instructional Week 30 Geometry Concepts Paced Standards: 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and

4 th Grade Mathematics Instructional Week 30 Geometry Concepts Paced Standards: 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and 4 th Grade Mathematics Instructional Week 30 Geometry Concepts Paced Standards: 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge

More information

Standards of Learning Guided Practice Suggestions. For use with the Mathematics Tools Practice in TestNav TM 8

Standards of Learning Guided Practice Suggestions. For use with the Mathematics Tools Practice in TestNav TM 8 Standards of Learning Guided Practice Suggestions For use with the Mathematics Tools Practice in TestNav TM 8 Table of Contents Change Log... 2 Introduction to TestNav TM 8: MC/TEI Document... 3 Guided

More information

Objective: Use a compass and straight edge to construct congruent segments and angles.

Objective: Use a compass and straight edge to construct congruent segments and angles. CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Introduction to Constructions Constructions: The drawing of various shapes using only a pair of compasses

More information

7th Grade Drawing Geometric Figures

7th Grade Drawing Geometric Figures Slide 1 / 53 Slide 2 / 53 7th Grade Drawing Geometric Figures 2015-11-23 www.njctl.org Slide 3 / 53 Topics Table of Contents Determining if a Triangle is Possible Click on a topic to go to that section

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

Copying a Line Segment

Copying a Line Segment Copying a Line Segment Steps 1 4 below show you how to copy a line segment. Step 1 You are given line segment AB to copy. A B Step 2 Draw a line segment that is longer than line segment AB. Label one of

More information

Daily Warmup. - x 2 + x x 2 + x Questions from HW?? (7x - 39) (3x + 17) 1. BD bisects ABC. Find the m ABC.

Daily Warmup. - x 2 + x x 2 + x Questions from HW?? (7x - 39) (3x + 17) 1. BD bisects ABC. Find the m ABC. Daily Warmup Questions from HW?? B 1. BD bisects ABC. Find the m ABC. (3x + 17) (7x - 39) C 2. The figure below is a regular polygon. Find the value of x. - x 2 + x + 43 A D 4x 2 + x - 37 3. The measure

More information

Objective: Use a compass and straight edge to construct congruent segments and angles.

Objective: Use a compass and straight edge to construct congruent segments and angles. CONSTRUCTIONS Objective: Use a compass and straight edge to construct congruent segments and angles. Oct 1 8:33 AM Oct 2 7:42 AM 1 Introduction to Constructions Constructions: The drawing of various shapes

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

Honors Geometry Summer Math Packet

Honors Geometry Summer Math Packet Honors Geometry Summer Math Packet Dear students, The problems in this packet will give you a chance to practice geometry-related skills from Grades 6 and 7. Do your best to complete each problem so that

More information

1. Geometry/Measurement Grade 9 Angles, Lines & Line Segments G/M-1e

1. Geometry/Measurement Grade 9 Angles, Lines & Line Segments G/M-1e 1. Geometry/Measurement Grade 9 Angles, Lines & Line Segments G/M-1e small rectangle or square of colored paper mira Geometry Set cardboard strips Your friend call you over the telephone and says, How

More information

S. Stirling Page 1 of 14

S. Stirling Page 1 of 14 3.1 Duplicating Segments and ngles [and riangles] hese notes replace pages 144 146 in the book. You can read these pages for extra clarifications. Instructions for making geometric figures: You can sketch

More information

June 2016 Regents GEOMETRY COMMON CORE

June 2016 Regents GEOMETRY COMMON CORE 1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation? 4) 2

More information

b. Draw a line and a circle that intersect at exactly one point. When this happens, the line is called a tangent.

b. Draw a line and a circle that intersect at exactly one point. When this happens, the line is called a tangent. 6-1. Circles can be folded to create many different shapes. Today, you will work with a circle and use properties of other shapes to develop a three-dimensional shape. Be sure to have reasons for each

More information

Chapter 11: Constructions and Loci

Chapter 11: Constructions and Loci Chapter 11: Section 11.1a Constructing a Triangle given 3 sides (sss) Leave enough room above the line to complete the shape. Do not rub out your construction lines. They show your method. 1 Section 11.1b

More information

Basic Mathematics Review 5232

Basic Mathematics Review 5232 Basic Mathematics Review 5232 Symmetry A geometric figure has a line of symmetry if you can draw a line so that if you fold your paper along the line the two sides of the figure coincide. In other words,

More information

Name. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0

Name. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 Name FRIDAY, FEBRUARY 24 Due on: Per: TH Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume

More information

ENGINEERING DRAWING. UNIT III - Part A

ENGINEERING DRAWING. UNIT III - Part A DEVELOPMENT OF SURFACES: ENGINEERING DRAWING UNIT III - Part A 1. What is meant by development of surfaces? 2. Development of surfaces of an object is also known as flat pattern of the object. (True/ False)

More information

Principles of Technology DUE one week from your lab day. Lab 2: Measuring Forces

Principles of Technology DUE one week from your lab day. Lab 2: Measuring Forces Lab 2: Measuring Forces Principles of Technology DUE one week from your lab day Lab Objectives When you ve finished this lab, you should be able to do the following: Measure forces by using appropriate

More information

New Jersey Center for Teaching and Learning. Progressive Mathematics Initiative

New Jersey Center for Teaching and Learning. Progressive Mathematics Initiative Slide 1 / 126 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students

More information

Folding Activity 3. Compass Colored paper Tape or glue stick

Folding Activity 3. Compass Colored paper Tape or glue stick Folding Activity 3 Part 1 You re not done until everyone in your group is done! If you finish before someone else, help them finish before starting on the next part. You ll need: Patty paper Ruler Sharpie

More information

Developing geometric thinking. A developmental series of classroom activities for Gr. 1-9

Developing geometric thinking. A developmental series of classroom activities for Gr. 1-9 Developing geometric thinking A developmental series of classroom activities for Gr. 1-9 Developing geometric thinking ii Contents Van Hiele: Developing Geometric Thinking... 1 Sorting objects using Geostacks...

More information

PENNSYLVANIA. List properties, classify, draw, and identify geometric figures in two dimensions.

PENNSYLVANIA. List properties, classify, draw, and identify geometric figures in two dimensions. Know: Understand: Do: CC.2.3.4.A.1 -- Draw lines and angles and identify these in two-dimensional figures. CC.2.3.4.A.2 -- Classify twodimensional figures by properties of their lines and angles. CC.2.3.4.A.3

More information

UNIT 1 GEOMETRY. (revision from 1 st ESO) Unit 8 in our books

UNIT 1 GEOMETRY. (revision from 1 st ESO) Unit 8 in our books UNIT 1 GEOMETRY (revision from 1 st ESO) Unit 8 in our books WHAT'S GEOMETRY? Geometry is the study of the size, shape and position of 2 dimensional shapes and 3 dimensional figures. In geometry, one explores

More information

Refer to Blackboard for Activities and/or Resources

Refer to Blackboard for Activities and/or Resources Lafayette Parish School System Curriculum Map Mathematics: Grade 5 Unit 4: Properties in Geometry (LCC Unit 5) Time frame: 16 Instructional Days Assess2know Testing Date: March 23, 2012 Refer to Blackboard

More information

Activity: Fold Four Boxes

Activity: Fold Four Boxes ctivity: Fold Four Boxes 1. Cut out your copy of the crease pattern for the square-base twist box but only cut along the solid lines. 2. Look at this key: mountain crease valley crease When folded, a mountain

More information

All About That Base... and Height

All About That Base... and Height All About That Base... and Height Area of Triangles and Quadrilaterals 2 WARM UP Write 3 different expressions to describe the total area of this rectangle. LEARNING GOALS State and compare the attributes

More information

Unit 1, Lesson 1: What are Scaled Copies?

Unit 1, Lesson 1: What are Scaled Copies? Unit 1, Lesson 1: What are Scaled Copies? Let s explore scaled copies. 1.1: Printing Portraits m.openup.org/1/7-1-1-1 Here is a portrait of a student. 1. Look at Portraits A E. How is each one the same

More information

Shelf, Treasure Chest, Tub. Math and Quiet!! Center, A. Quiet Dice for Make. (Talk! = Walk!) A. Warm Up or Lesson, CONTINUE ON!! B.

Shelf, Treasure Chest, Tub. Math and Quiet!! Center, A. Quiet Dice for Make. (Talk! = Walk!) A. Warm Up or Lesson, CONTINUE ON!! B. Sandra White - snannyw@aol.com - CAMT 2012 No Wasted Time 9 12 1 12 1 11 10 11 2 10 11 2 3 9 3 8 4 8 4 7 6 5 7 6 5 from Beginningto End Procedures Traveling / Waiting Unexpected Visitors Finishing Early

More information

Class : VI - Mathematics

Class : VI - Mathematics O. P. JINDAL SCHOOL, RAIGARH (CG) 496 001 Phone : 07762-227042, 227293, (Extn. 227001-49801, 02, 04, 06); Fax : 07762-262613; e-mail: opjsraigarh@jspl.com; website : www.opjsrgh.in Class : VI - Mathematics

More information

CONSTRUCTION #1: Segment Copy

CONSTRUCTION #1: Segment Copy CONSTRUCTION #1: Segment Copy Objective: Given a line segment, construct a line segment congruent to the given one. Procedure: After doing this Your work should look like this Start with a line segment

More information

Student Name: Teacher: Date: District: Rowan. Assessment: 9_12 T and I IC61 - Drafting I Test 1. Form: 501

Student Name: Teacher: Date: District: Rowan. Assessment: 9_12 T and I IC61 - Drafting I Test 1. Form: 501 Student Name: Teacher: Date: District: Rowan Assessment: 9_12 T and I IC61 - Drafting I Test 1 Description: Test 4 A (Diagrams) Form: 501 Please use the following figure for this question. 1. In the GEOMETRIC

More information

ILLUSION CONFUSION! - MEASURING LINES -

ILLUSION CONFUSION! - MEASURING LINES - ILLUSION CONFUSION! - MEASURING LINES - WHAT TO DO: 1. Look at the line drawings below. 2. Without using a ruler, which long upright or vertical line looks the longest or do they look the same length?

More information

Elementary Geometric Drawings Angles. Angle Bisector. Perpendicular Bisector

Elementary Geometric Drawings Angles. Angle Bisector. Perpendicular Bisector Lessons and Activities GEOMETRY Elementary Geometric Drawings Angles Angle Bisector Perpendicular Bisector 1 Lessons and Activities POLYGONS are PLANE SHAPES (figures) with at least 3 STRAIGHT sides and

More information

Problem Set #4 Due 5/3 or 5/4 Pd

Problem Set #4 Due 5/3 or 5/4 Pd Geometry Name Problem Set #4 Due 5/3 or 5/4 Pd Directions: To receive full credit, show all required work. Questions may have multiple correct answers. Clearly indicate the answers chosen. For multiple

More information

Find the area and perimeter of any enlargement of the original rug above. Your work must include the following:

Find the area and perimeter of any enlargement of the original rug above. Your work must include the following: 7-1.Your friend Alonzo owns a rug manufacturing company, which is famous for its unique designs. Each rug design has an original size as well as enlargements that are exactly the same shape. Find the area

More information

Geometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1

Geometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1 Postulates and Theorems from Chapter 1 Postulate 1: The Ruler Postulate 1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. 2. Once

More information

Constructing Perpendiculars to a Line. Finding the Right Line. Draw a line and a point labeled P not on the line, as shown above.

Constructing Perpendiculars to a Line. Finding the Right Line. Draw a line and a point labeled P not on the line, as shown above. Page 1 of 5 3.3 Intelligence plus character that is the goal of true education. MARTIN LUTHER KING, JR. Constructing Perpendiculars to a Line If you are in a room, look over at one of the walls. What is

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

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

Look carefully at the dimensions on each shape and find the perimeter. Express your answers in cm: 3 cm. Length, Perimeter and Area

Look carefully at the dimensions on each shape and find the perimeter. Express your answers in cm: 3 cm. Length, Perimeter and Area Perimeter measure perimeters Perimeter is the length around a shape. The word originates from Greek and literally means around measure. The boundary of this shape is the perimeter. Choose classroom objects.

More information

Fair Game Review. Chapter 4. Name Date. Find the area of the square or rectangle Find the area of the patio.

Fair Game Review. Chapter 4. Name Date. Find the area of the square or rectangle Find the area of the patio. Name Date Chapter Fair Game Review Find the area of the square or rectangle... ft cm 0 ft cm.. in. d in. d. Find the area of the patio. ft 0 ft Copright Big Ideas Learning, LLC Big Ideas Math Green Name

More information

Lesson 1 Pre-Visit Ballpark Figures Part 1

Lesson 1 Pre-Visit Ballpark Figures Part 1 Lesson 1 Pre-Visit Ballpark Figures Part 1 Objective: Students will be able to: Estimate, measure, and calculate length, perimeter, and area of various rectangles. Time Requirement: 1 class period, longer

More information

.VP CREATING AN INVENTED ONE POINT PERSPECTIVE SPACE

.VP CREATING AN INVENTED ONE POINT PERSPECTIVE SPACE PAGE ONE Organize an invented 1 point perspective drawing in the following order: 1 Establish an eye level 2 Establish a Center Line Vision eye level vision Remember that the vanishing point () in one

More information

h r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.

h r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck. ACT Plane Geometry Review Let s first take a look at the common formulas you need for the ACT. Then we ll review the rules for the tested shapes. There are also some practice problems at the end of this

More information

Geometry For Technical Drawing Chapter 4

Geometry For Technical Drawing Chapter 4 Geometry For Technical Drawing Chapter 4 Sacramento City College EDT 300/ENGR 306 EDT 300/ENGR 306 1 Objectives Identify and describe geometric shapes and constructions used by drafters. Construct various

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

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

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

STRAND H: Angle Geometry

STRAND H: Angle Geometry Mathematics SKE, Strand H UNIT H3 onstructions and Loci: Text STRND H: ngle Geometry H3 onstructions and Loci Text ontents Section H3.1 Drawing and Symmetry H3.2 onstructing Triangles and ther Shapes H3.3

More information

Abstract. Introduction

Abstract. Introduction BRIDGES Mathematical Connections in Art, Music, and Science Folding the Circle as Both Whole and Part Bradford Hansen-Smith 4606 N. Elston #3 Chicago IL 60630, USA bradhs@interaccess.com Abstract This

More information

Geometry. Learning Goals U N I T

Geometry. Learning Goals U N I T U N I T Geometry Building Castles Learning Goals describe, name, and sort prisms construct prisms from their nets construct models of prisms identify, create, and sort symmetrical and non-symmetrical shapes

More information

4th Grade. Geometry. Slide 2 / 126. Slide 1 / 126. Slide 4 / 126. Slide 3 / 126. Slide 5 / 126. Slide 6 / 126. Geometry Unit Topics.

4th Grade. Geometry. Slide 2 / 126. Slide 1 / 126. Slide 4 / 126. Slide 3 / 126. Slide 5 / 126. Slide 6 / 126. Geometry Unit Topics. Slide 1 / 126 Slide 2 / 126 New Jersey enter for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial

More information

Inclusion of a regular tetrahedron in a cube

Inclusion of a regular tetrahedron in a cube Inclusion of a regular tetrahedron in a cube Teaching suggestions for a math laboratory activities with paper folding Antonio Criscuolo Centro MatNet Università di Bergamo (Italy) Francesco Decio CDO Bergamo

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

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

Squares Multiplication Facts: Square Numbers

Squares Multiplication Facts: Square Numbers LESSON 61 page 328 Squares Multiplication Facts: Square Numbers Name Teacher Notes: Introduce Hint #21 Multiplication/ Division Fact Families. Review Multiplication Table on page 5 and Quadrilaterals on

More information

9.3 Properties of Chords

9.3 Properties of Chords 9.3. Properties of Chords www.ck12.org 9.3 Properties of Chords Learning Objectives Find the lengths of chords in a circle. Discover properties of chords and arcs. Review Queue 1. Draw a chord in a circle.

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

1. If one side of a regular hexagon is 2 inches, what is the perimeter of the hexagon?

1. If one side of a regular hexagon is 2 inches, what is the perimeter of the hexagon? Geometry Grade 4 1. If one side of a regular hexagon is 2 inches, what is the perimeter of the hexagon? 2. If your room is twelve feet wide and twenty feet long, what is the perimeter of your room? 3.

More information

Big Ideas Math: A Common Core Curriculum Geometry 2015 Correlated to Common Core State Standards for High School Geometry

Big Ideas Math: A Common Core Curriculum Geometry 2015 Correlated to Common Core State Standards for High School Geometry Common Core State s for High School Geometry Conceptual Category: Geometry Domain: The Number System G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,

More information

3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm.

3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify

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

Period: Date Lesson 2: Common 3-Dimensional Shapes and Their Cross- Sections

Period: Date Lesson 2: Common 3-Dimensional Shapes and Their Cross- Sections : Common 3-Dimensional Shapes and Their Cross- Sections Learning Target: I can understand the definitions of a general prism and a cylinder and the distinction between a cross-section and a slice. Warm

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

3 Kevin s work for deriving the equation of a circle is shown below.

3 Kevin s work for deriving the equation of a circle is shown below. June 2016 1. A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation?

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, :15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

Paper 2. Mathematics test. Calculator allowed. First name. Last name. School KEY STAGE TIER

Paper 2. Mathematics test. Calculator allowed. First name. Last name. School KEY STAGE TIER Ma KEY STAGE 3 TIER 6 8 2004 Mathematics test Paper 2 Calculator allowed Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your

More information

Lesson 4: General Pyramids and Cones and Their Cross-Sections

Lesson 4: General Pyramids and Cones and Their Cross-Sections : General Pyramids and Cones and Their Cross-Sections Learning Target 1. I can state the definition of a general pyramid and cone, and that their respective cross-sections are similar to the base. 2. I

More information

Downloaded from

Downloaded from Understanding Elementary Shapes 1 1.In the given figure, lines l and m are.. to each other. (A) perpendicular (B) parallel (C) intersect (D) None of them. 2.a) If a clock hand starts from 12 and stops

More information

Student Teacher School. Mathematics Assesslet. Geometry

Student Teacher School. Mathematics Assesslet. Geometry Student Teacher School 6GRADE Mathematics Assesslet Geometry All items contained in this assesslet are the property of the. Items may be used for formative purposes by the customer within their school

More information

Unit 5 Shape and space

Unit 5 Shape and space Unit 5 Shape and space Five daily lessons Year 4 Summer term Unit Objectives Year 4 Sketch the reflection of a simple shape in a mirror line parallel to Page 106 one side (all sides parallel or perpendicular

More information