Relating Math to the Real World: A Study of Platonic Solids and Tessellations

Size: px
Start display at page:

Download "Relating Math to the Real World: A Study of Platonic Solids and Tessellations"

Transcription

1 Sheila Green Professor Dyrness ED200: Analyzing Schools Curriculum Project December 15, 2010 Relating Math to the Real World: A Study of Platonic Solids and Tessellations

2 Introduction The study of Platonic solids and tessellations at the middle school level allows the students to explore, analyze and question mathematics on their own. The student will be lead to the concept of duality as he analyzes patterns which emerge. The instructor will present models of all Platonic solids, point out intrinsic similarities, and provide examples of tessellations for the students to examine. Through the creation of a unique and original tessellation, the student is involved in a new design which would support symmetry. The objectives reflect guidelines presented in the State of Connecticut Frameworks. Through this curriculum unit, the student experiences mathematics through nontraditional means, using visual and hands-on manipulation. Inductive reasoning is utilized as the student compares two separate type die. Gardner s Theory of Multiple Intelligences played a part in the inception of this unit, as varied approaches to learning are used to augment the students information processing. The curriculum involves the student with research presented in a final paper, an accurate representation of Platonic solids and tessellations, and a justification on choice of die. Context This unit is targeted for seventh graders at Hartford Magnet Middle School. I observed in my seventh grade placement that although the students frequently worked in 2

3 pairs or three s, they did not work on a project together. I have also witnessed that the students became enlivened and engrossed in their work when they had had brief tactile and visual occurrences. This project was chosen for its hands-on manipulation, as well as its ability to encourage critical thinking and creative design. This unit is for students enrolled at the prealgebra level. A detracked environment is appropriate, and diversity of culture is not a factor. This is a classroom of twenty students, and groups of four are formed, totaling five groups. The project will last four days, with each session having a duration of sixty minutes. The middle school years is an ideal time to involve students in this type learning. During these years, students begin to develop the cognitive structures to allow them to reason within a linear deductive system of thought. Simultaneously, they continue informally to observe the boundless activity of their environment, tapping into native curiosities and intuitions that can, if nurtured, provide the foundation for inductive discoveries and reinventions of many of our fundamental mathematical concepts. (Navigating Through Geometry in Grades 6-8, p.vii) Overall Objective Students will find coincidences and patterns that can reveal underlying structures. This will take place when working on the chart which involves counting vertices, edges, and faces. Students will experience the two highest levels of Bloom s Taxonomy, synthesis and evaluation, as they think critically and create designs of their own. This will take place through the exercise involving the dice, and the session of group creations 3

4 of tessellations. The students, through working in the capacity of the group, will further their experience of working cooperatively and effectively with one another. The students will also enhance their ability to master mathematical vocabulary. Objectives The group will construct representations of the tetrahedron and the cube; the group will also design a tessellation. The group will determine congruence, similarity, symmetry, and tessellation through the handling of models, which are provided by the instructor. The relationship between the duals (as taught by the instructor) will be observed and discussed by the group. A drawing will be made of one set of duals, with precision in mind. All observations and determinations concerning the solids will be recorded by the group. This objective relates to the Common Core State Standards for Mathematics, Grade 7. The Connecticut State Standards to District Curriculum, CT C.2a states Apply transformations to plane figures to determine congruence, similarity, symmetry, and tessellation. The students will examine each Platonic solis by carefully counting the edges, faces and vertices. The group will compare and categorize this data by formulating a chart. Relationships between the sides and perimeters (edges), the congruency and similarity will be noted on chart. Students will compare the data (the numbers counted) among each solid, and focus on equal numbers. They must also look for relationships among the numbers. Can you devise a way of calculating the number of vertices of a regular solid 4

5 once you know how many faces it has, how many sides each face has, and how many faces come together at each vertex? After you have devised the method, use it to check your entries for the number of vertices for each figure. (The Heart of Mathematics, p. 305). These objectives are supported by CT State Standard to District Curriculum, CT which states, Classify two- and three- dimensional geometric figures based on their properties including relationship of sides and angles and symmetry (line and/or rotational) and apply this information to solve problems. The group will differentiate between a cube-shaped die and a tetrahedron-shaped die, and solve the problem of which die will better enhance their chances. The group will compare and contrast by actual throw of the dice, and record their findings. This objective reflects and expands upon CT State Standard to District Curriculum, CT which states, Classify two- and three- dimensional geometric figures based on their properties including relationship of sides and angles and symmetry (line and/or rotational) and apply this information to solve problems. The student will use his/her unique skills (ie., drawing, paper construction of solids, writing skills, spelling skills, computer skills) in the group. This will work toward receiving the optimum grade for the group. This objective is supported by Slavin s cooperative learning strategy, incorporating the Jigsaw method. A key element of Jigsaw and other task-specialization methods is the assignment of a unique subtask to each group member. (An Introduction to Cooperative Learning, p.13). 5

6 However, in this curriculum, students are not assigned tasks, rather they assume or head tasks as they see fit, due to their abilities. This unit involves lectures by the instructor, and each group will present one final paper (two pages) and hand-made representations of a cube, a tetrahedron, and a tessellation. There will also be an additional page turned in, justifying which die was chosen. Activities Day 1. The instructor will begin b defining five Platonic solids and present several examples of these solids made of wood, plastic, sugar cube, miniature pyramid, dice. The instructor will encourage discussion of additional examples which exist in life, perhaps even world reknown structures. The instructor will give a short (10 min.) lecture on the five solids, informing the students to research why we say, Platonic solids, and will introduce two dice into the talk. The instructor will ask the students to consider two Platonic solid die shapes. The question presented to the class is Which die would better increase your chances (or would it make a difference), a cube-shaped die of a tetrahedron-shaped die? The instructor will then divide the students into groups of four, and go over instructions about what would be expected of them in order to complete their project. They will find out that they are to carry on independent research via the computer s in the classroom, and they would be given a few suggestions for relevant websites. They would take notes on observations of the solids which they handle 6

7 (models) and be responsible to complete the handout which compares the number of vertices, sides, and faces of the solids. The instructor also mentions that they would be covering a set of new concepts the next day, but that they would be related to the topic. It is at this time that the class is informed that a two- page paper would be expected from each group, which would show an understanding of the topics covered represented by excellent choices of expression. The instructor informs the class that they will have the opportunity to show their design and precision skills when they construct two Platonic solids, and what is known as tessellations. The students will be told by the instructor that all these tasks would be completed within four days, and would be presented as a group, and the group would share in a common grade for the project. The groups now formed, they get started on filling out their charts which have been handed out, and they mark the edges, faces, and vertices with erasable markers which have been handed out (to avoid mistakes in counting). They also discuss a strategy in figuring out the answer to the die question, studying each die in detail (faces, roll possibilities, etc.) Day 2. In addition to the group having models that they are studying closely, there are additional models on display in the classroom to which all groups may refer. The instructor lectures on congruence, similarity, symmetry and tessellation. The instructor shows floor tile, wallpaper, and fabric designs, and wall tiles as example showing tessellation. Again, the instructor encourages the class to offer their own examples of tessellations that they notice in their environment. The instructor points out the materials which are set up in order that the group may create their own tessellations. The students are informed that each new word introduced in the unit should be made familiar through 7

8 its meaning and its spelling. The students would be provided a list of the key words, which would be used when writing their final paper. After the lecture (which has lasted 20 min.) the students are free to begin making their cubes, tetrahedrons, and tessellations. Materials include various colorful construction type paper, colored markers rulers for precise measurements, invisible tape, scissors. Mindful of the ancient pyramids, the students are instructed to be as precise as possible. Day3. The instructor discusses duality of: the octahedron/cube, the dodecahedron/icosahedron, and the tetrahedron/tetrahedron. The group will now focus on any two duals, and recreate on paper what they have learned about duality. Along with the drawing will be the group interpretation of how duality manifests itself (resulting from research). Again, precision is the key to the drawing. The group members will designate who will se the computer to begin search for information which the instructor provided on all topics. Those gathering research information will note their sources, as the instructor has informed them to do. Day 4. This day is used for whatever purpose the group deems necessary in order to complete their project to perfection. Perhaps they have decided to remake their solids, or change their tessellation. They may need additional justification fr answering the question on the dice, or they may need to use the computer again. Their final paper is typed and printed, and they present it along with their two solids, tessellation example, and duality rendition/writing exercise. 8

9 Evaluation The teaching strategy is designed to open the door for learning the unit material by the student. The student plays the greater pert in thinking critically: he has compared data, he has evaluated two die, he has group-discussed, and he has created an actual example of what he has gained knowledge, therefore applying his understanding. The student has reached the highest goals (Bloom s Taxonomy) of learning in that he has evaluated, criticized, justified, and made a choice. Rubric The group has full understanding of material covered in the unit, have presented precise renditions of two Platonic solids, tessellations, and dual solids. Final paper shows excellent for expression of information. Sound justification for the die choice expressed. 5 Points Group shows an understanding of the material covered, and two other categories show strength. But one remaining category is lacking. 4 Points Group shows an understanding of material covered, and one other category shows strength. 3 Points 9

10 Group shows no understanding of the material covered. Remaining categories may show strength. 2 Points Group shows no understanding of the material covered. Remaining categories show little strength. 1 Point 10

11 Bibliography Robert Slavin, Cooperative Learning : Theory, Research Practice 2 nd edition (Boston: Allyn and Bacon, 1995) chapters 1 and 2. Navigating Through Geometry in Grades 6-8. Reston VA: National Council of Teachers in Mathematics, Edward Burger and Michael Starbird, The Heart of Mathematics (John Wiley & Sons, 2010) chap.4.5 YouTube, Platonic Solids by Peter Wetherall Tessellations.org Bloom s Taxonomy Howard Gardner s theory of Multiple Intelligences 11

12 Key Words Platonic Solids Cube Tetrahedron Octahedron Dodecahedron Icosahedron Vertex (Vertices) Tessellations Congruence Similarity Symmetry Duals 12

Curriculum Design Project with Virtual Manipulatives. Gwenanne Salkind. George Mason University EDCI 856. Dr. Patricia Moyer-Packenham

Curriculum Design Project with Virtual Manipulatives. Gwenanne Salkind. George Mason University EDCI 856. Dr. Patricia Moyer-Packenham Curriculum Design Project with Virtual Manipulatives Gwenanne Salkind George Mason University EDCI 856 Dr. Patricia Moyer-Packenham Spring 2006 Curriculum Design Project with Virtual Manipulatives Table

More information

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic

More information

Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice

Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Title: Considering Coordinate Geometry Common Core State Standards

More information

End-of-Module Assessment Task K 2

End-of-Module Assessment Task K 2 Student Name Topic A: Two-Dimensional Flat Shapes Date 1 Date 2 Date 3 Rubric Score: Time Elapsed: Topic A Topic B Materials: (S) Paper cutouts of typical triangles, squares, Topic C rectangles, hexagons,

More information

Dublin City Schools Mathematics Graded Course of Study GRADE 4

Dublin City Schools Mathematics Graded Course of Study GRADE 4 I. Content Standard: Number, Number Sense and Operations Standard Students demonstrate number sense, including an understanding of number systems and reasonable estimates using paper and pencil, technology-supported

More information

Grade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand

Grade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand Grade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand Texas Essential Knowledge and Skills (TEKS): (2.1) Number, operation, and quantitative reasoning. The student

More information

Missouri Mathematics Grade-Level Expectations

Missouri Mathematics Grade-Level Expectations A Correlation of to the Grades K - 6 G/M-223 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley Mathematics in meeting the

More information

Montana Content Standards for Mathematics Grade 3. Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011

Montana Content Standards for Mathematics Grade 3. Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011 Montana Content Standards for Mathematics Grade 3 Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011 Contents Standards for Mathematical Practice: Grade

More information

LLD MATH. Student Eligibility: Grades 6-8. Credit Value: Date Approved: 8/24/15

LLD MATH. Student Eligibility: Grades 6-8. Credit Value: Date Approved: 8/24/15 PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION LLD MATH Length of Course: Elective/Required: School: Full Year Required Middle Schools Student Eligibility: Grades 6-8 Credit Value:

More information

KS1 Transport Objectives

KS1 Transport Objectives KS1 Transport Y1: Number and Place Value Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Count, read and write numbers to 100 in numerals; count in multiples

More information

Mathematics subject curriculum

Mathematics subject curriculum Mathematics subject curriculum Dette er ei omsetjing av den fastsette læreplanteksten. Læreplanen er fastsett på Nynorsk Established as a Regulation by the Ministry of Education and Research on 24 June

More information

Arizona s College and Career Ready Standards Mathematics

Arizona s College and Career Ready Standards Mathematics Arizona s College and Career Ready Mathematics Mathematical Practices Explanations and Examples First Grade ARIZONA DEPARTMENT OF EDUCATION HIGH ACADEMIC STANDARDS FOR STUDENTS State Board Approved June

More information

7. Stepping Back. 7.1 Related Work Systems that Generate Folding Nets. The problem of unfolding three-dimensional models is not a new one (c.f.

7. Stepping Back. 7.1 Related Work Systems that Generate Folding Nets. The problem of unfolding three-dimensional models is not a new one (c.f. 112 7. Stepping Back 7.1 Related Work 7.1.1 Systems that Generate Folding Nets The problem of unfolding three-dimensional models is not a new one (c.f. Samek, et al. 1986), nor is it one limited to the

More information

Hardhatting in a Geo-World

Hardhatting in a Geo-World Hardhatting in a Geo-World TM Developed and Published by AIMS Education Foundation This book contains materials developed by the AIMS Education Foundation. AIMS (Activities Integrating Mathematics and

More information

PRIMARY ASSESSMENT GRIDS FOR STAFFORDSHIRE MATHEMATICS GRIDS. Inspiring Futures

PRIMARY ASSESSMENT GRIDS FOR STAFFORDSHIRE MATHEMATICS GRIDS. Inspiring Futures PRIMARY ASSESSMENT GRIDS FOR STAFFORDSHIRE MATHEMATICS GRIDS Inspiring Futures ASSESSMENT WITHOUT LEVELS The Entrust Mathematics Assessment Without Levels documentation has been developed by a group of

More information

Grade 6: Correlated to AGS Basic Math Skills

Grade 6: Correlated to AGS Basic Math Skills Grade 6: Correlated to AGS Basic Math Skills Grade 6: Standard 1 Number Sense Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and

More information

Create A City: An Urban Planning Exercise Students learn the process of planning a community, while reinforcing their writing and speaking skills.

Create A City: An Urban Planning Exercise Students learn the process of planning a community, while reinforcing their writing and speaking skills. Create A City: An Urban Planning Exercise Students learn the process of planning a community, while reinforcing their writing and speaking skills. Author Gale Ekiss Grade Level 4-8 Duration 3 class periods

More information

SPATIAL SENSE : TRANSLATING CURRICULUM INNOVATION INTO CLASSROOM PRACTICE

SPATIAL SENSE : TRANSLATING CURRICULUM INNOVATION INTO CLASSROOM PRACTICE SPATIAL SENSE : TRANSLATING CURRICULUM INNOVATION INTO CLASSROOM PRACTICE Kate Bennie Mathematics Learning and Teaching Initiative (MALATI) Sarie Smit Centre for Education Development, University of Stellenbosch

More information

LESSON PLANS: AUSTRALIA Year 6: Patterns and Algebra Patterns 50 MINS 10 MINS. Introduction to Lesson. powered by

LESSON PLANS: AUSTRALIA Year 6: Patterns and Algebra Patterns 50 MINS 10 MINS. Introduction to Lesson. powered by Year 6: Patterns and Algebra Patterns 50 MINS Strand: Number and Algebra Substrand: Patterns and Algebra Outcome: Continue and create sequences involving whole numbers, fractions and decimals. Describe

More information

ASSESSMENT TASK OVERVIEW & PURPOSE:

ASSESSMENT TASK OVERVIEW & PURPOSE: Performance Based Learning and Assessment Task A Place at the Table I. ASSESSMENT TASK OVERVIEW & PURPOSE: Students will create a blueprint for a decorative, non rectangular picnic table (top only), and

More information

2 nd grade Task 5 Half and Half

2 nd grade Task 5 Half and Half 2 nd grade Task 5 Half and Half Student Task Core Idea Number Properties Core Idea 4 Geometry and Measurement Draw and represent halves of geometric shapes. Describe how to know when a shape will show

More information

TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system

TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system Curriculum Overview Mathematics 1 st term 5º grade - 2010 TOPICS LEARNING OUTCOMES ACTIVITES ASSESSMENT Numbers and the number system Multiplies and divides decimals by 10 or 100. Multiplies and divide

More information

Paper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 1 (Non-Calculator) Foundation Tier. Monday 6 June 2011 Afternoon Time: 1 hour 30 minutes

Paper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 1 (Non-Calculator) Foundation Tier. Monday 6 June 2011 Afternoon Time: 1 hour 30 minutes Centre No. Candidate No. Paper Reference 1 3 8 0 1 F Paper Reference(s) 1380/1F Edexcel GCSE Mathematics (Linear) 1380 Paper 1 (Non-Calculator) Foundation Tier Monday 6 June 2011 Afternoon Time: 1 hour

More information

AP Statistics Summer Assignment 17-18

AP Statistics Summer Assignment 17-18 AP Statistics Summer Assignment 17-18 Welcome to AP Statistics. This course will be unlike any other math class you have ever taken before! Before taking this course you will need to be competent in basic

More information

Learning Disability Functional Capacity Evaluation. Dear Doctor,

Learning Disability Functional Capacity Evaluation. Dear Doctor, Dear Doctor, I have been asked to formulate a vocational opinion regarding NAME s employability in light of his/her learning disability. To assist me with this evaluation I would appreciate if you can

More information

Math Grade 3 Assessment Anchors and Eligible Content

Math Grade 3 Assessment Anchors and Eligible Content Math Grade 3 Assessment Anchors and Eligible Content www.pde.state.pa.us 2007 M3.A Numbers and Operations M3.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among

More information

(I couldn t find a Smartie Book) NEW Grade 5/6 Mathematics: (Number, Statistics and Probability) Title Smartie Mathematics

(I couldn t find a Smartie Book) NEW Grade 5/6 Mathematics: (Number, Statistics and Probability) Title Smartie Mathematics (I couldn t find a Smartie Book) NEW Grade 5/6 Mathematics: (Number, Statistics and Probability) Title Smartie Mathematics Lesson/ Unit Description Questions: How many Smarties are in a box? Is it the

More information

Assessment Requirements: November 2017 Grade 5

Assessment Requirements: November 2017 Grade 5 1 Assessment Requirements: November 2017 Grade 5 Your son starts his exams on 15 November 2017 Please ensure that he has the following at school EVERY DAY during the assessment week: A complete pencil

More information

QUICK START GUIDE. your kit BOXES 1 & 2 BRIDGES. Teachers Guides

QUICK START GUIDE. your kit BOXES 1 & 2 BRIDGES. Teachers Guides QUICK START GUIDE BOXES 1 & 2 BRIDGES Teachers Guides your kit Your Teachers Guides are divided into eight units, each of which includes a unit introduction, 20 lessons, and the ancillary pages you ll

More information

Stafford Beer's Syntegration as a Renascence of the Ancient Greek Agora in Present-day Organizations

Stafford Beer's Syntegration as a Renascence of the Ancient Greek Agora in Present-day Organizations Journal of Universal Knowledge Management, vol. 0, no. 1 (2005), 59-66 submitted: 7/2/05, accepted: 18/4/05, appeared: 28/6/05 J.UKM Stafford Beer's Syntegration as a Renascence of the Ancient Greek Agora

More information

First Grade Standards

First Grade Standards These are the standards for what is taught throughout the year in First Grade. It is the expectation that these skills will be reinforced after they have been taught. Mathematical Practice Standards Taught

More information

Answer Key For The California Mathematics Standards Grade 1

Answer Key For The California Mathematics Standards Grade 1 Introduction: Summary of Goals GRADE ONE By the end of grade one, students learn to understand and use the concept of ones and tens in the place value number system. Students add and subtract small numbers

More information

Answers: Year 4 Textbook 3 Pages 4 10

Answers: Year 4 Textbook 3 Pages 4 10 Answers: Year 4 Textbook Pages 4 Page 4 1. 729 2. 8947. 6502 4. 2067 5. 480 6. 7521 > 860 7. 85 > 699 8. 9442< 9852 9. 4725 > 4572. 8244 < 9241 11. 026 < 211 12. A number between 20 and 4800 1. A number

More information

Standard 1: Number and Computation

Standard 1: Number and Computation Standard 1: Number and Computation Standard 1: Number and Computation The student uses numerical and computational concepts and procedures in a variety of situations. Benchmark 1: Number Sense The student

More information

Measurement. When Smaller Is Better. Activity:

Measurement. When Smaller Is Better. Activity: Measurement Activity: TEKS: When Smaller Is Better (6.8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and

More information

Activities for School

Activities for School Activities for School Label the School Label the school in the target language and then do a hide-n-seek activity using the directions in the target language. Label the Classroom I label my room (these

More information

This scope and sequence assumes 160 days for instruction, divided among 15 units.

This scope and sequence assumes 160 days for instruction, divided among 15 units. In previous grades, students learned strategies for multiplication and division, developed understanding of structure of the place value system, and applied understanding of fractions to addition and subtraction

More information

End-of-Module Assessment Task

End-of-Module Assessment Task Student Name Date 1 Date 2 Date 3 Topic E: Decompositions of 9 and 10 into Number Pairs Topic E Rubric Score: Time Elapsed: Topic F Topic G Topic H Materials: (S) Personal white board, number bond mat,

More information

Pre-AP Geometry Course Syllabus Page 1

Pre-AP Geometry Course Syllabus Page 1 Pre-AP Geometry Course Syllabus 2015-2016 Welcome to my Pre-AP Geometry class. I hope you find this course to be a positive experience and I am certain that you will learn a great deal during the next

More information

Extending Place Value with Whole Numbers to 1,000,000

Extending Place Value with Whole Numbers to 1,000,000 Grade 4 Mathematics, Quarter 1, Unit 1.1 Extending Place Value with Whole Numbers to 1,000,000 Overview Number of Instructional Days: 10 (1 day = 45 minutes) Content to Be Learned Recognize that a digit

More information

Characteristics of Functions

Characteristics of Functions Characteristics of Functions Unit: 01 Lesson: 01 Suggested Duration: 10 days Lesson Synopsis Students will collect and organize data using various representations. They will identify the characteristics

More information

Unit 3 Ratios and Rates Math 6

Unit 3 Ratios and Rates Math 6 Number of Days: 20 11/27/17 12/22/17 Unit Goals Stage 1 Unit Description: Students study the concepts and language of ratios and unit rates. They use proportional reasoning to solve problems. In particular,

More information

TabletClass Math Geometry Course Guidebook

TabletClass Math Geometry Course Guidebook TabletClass Math Geometry Course Guidebook Includes Final Exam/Key, Course Grade Calculation Worksheet and Course Certificate Student Name Parent Name School Name Date Started Course Date Completed Course

More information

Economics Unit: Beatrice s Goat Teacher: David Suits

Economics Unit: Beatrice s Goat Teacher: David Suits Economics Unit: Beatrice s Goat Teacher: David Suits Overview: Beatrice s Goat by Page McBrier tells the story of how the gift of a goat changed a young Ugandan s life. This story is used to introduce

More information

TEKS Resource System. Effective Planning from the IFD & Assessment. Presented by: Kristin Arterbury, ESC Region 12

TEKS Resource System. Effective Planning from the IFD & Assessment. Presented by: Kristin Arterbury, ESC Region 12 TEKS Resource System Effective Planning from the IFD & Assessments Presented by: Kristin Arterbury, ESC Region 12 karterbury@esc12.net, 254-297-1115 Assessment Curriculum Instruction planwithifd.wikispaces.com

More information

Introducing the New Iowa Assessments Mathematics Levels 12 14

Introducing the New Iowa Assessments Mathematics Levels 12 14 Introducing the New Iowa Assessments Mathematics Levels 12 14 ITP Assessment Tools Math Interim Assessments: Grades 3 8 Administered online Constructed Response Supplements Reading, Language Arts, Mathematics

More information

EDUC-E328 Science in the Elementary Schools

EDUC-E328 Science in the Elementary Schools 1 INDIANA UNIVERSITY NORTHWEST School of Education EDUC-E328 Science in the Elementary Schools Time: Monday 9 a.m. to 3:45 Place: Instructor: Matthew Benus, Ph.D. Office: Hawthorn Hall 337 E-mail: mbenus@iun.edu

More information

Primary National Curriculum Alignment for Wales

Primary National Curriculum Alignment for Wales Mathletics and the Welsh Curriculum This alignment document lists all Mathletics curriculum activities associated with each Wales course, and demonstrates how these fit within the National Curriculum Programme

More information

Robot manipulations and development of spatial imagery

Robot manipulations and development of spatial imagery Robot manipulations and development of spatial imagery Author: Igor M. Verner, Technion Israel Institute of Technology, Haifa, 32000, ISRAEL ttrigor@tx.technion.ac.il Abstract This paper considers spatial

More information

Mathematics process categories

Mathematics process categories Mathematics process categories All of the UK curricula define multiple categories of mathematical proficiency that require students to be able to use and apply mathematics, beyond simple recall of facts

More information

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade The third grade standards primarily address multiplication and division, which are covered in Math-U-See

More information

Analysis: Evaluation: Knowledge: Comprehension: Synthesis: Application:

Analysis: Evaluation: Knowledge: Comprehension: Synthesis: Application: In 1956, Benjamin Bloom headed a group of educational psychologists who developed a classification of levels of intellectual behavior important in learning. Bloom found that over 95 % of the test questions

More information

TEACHING Simple Tools Set II

TEACHING Simple Tools Set II TEACHING GUIDE TEACHING Simple Tools Set II Kindergarten Reading Level ISBN-10: 0-8225-6880-2 Green ISBN-13: 978-0-8225-6880-3 2 TEACHING SIMPLE TOOLS SET II Standards Science Mathematics Language Arts

More information

Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified

Page 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General Grade(s): None specified Unit: Creating a Community of Mathematical Thinkers Timeline: Week 1 The purpose of the Establishing a Community

More information

Florida Mathematics Standards for Geometry Honors (CPalms # )

Florida Mathematics Standards for Geometry Honors (CPalms # ) A Correlation of Florida Geometry Honors 2011 to the for Geometry Honors (CPalms #1206320) Geometry Honors (#1206320) Course Standards MAFS.912.G-CO.1.1: Know precise definitions of angle, circle, perpendicular

More information

Zoo Math Activities For 5th Grade

Zoo Math Activities For 5th Grade Zoo Math 5th Grade Free PDF ebook Download: Zoo Math 5th Grade Download or Read Online ebook zoo math activities for 5th grade in PDF Format From The Best User Guide Database Successful completion of Algebra

More information

CAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4-Year Subgroup: none Test Date: Spring 2011

CAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4-Year Subgroup: none Test Date: Spring 2011 CAAP Content Analysis Report Institution Code: 911 Institution Type: 4-Year Normative Group: 4-year Colleges Introduction This report provides information intended to help postsecondary institutions better

More information

Bittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2012). Prealgebra (6th ed.). Boston, MA: Addison-Wesley.

Bittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2012). Prealgebra (6th ed.). Boston, MA: Addison-Wesley. Course Syllabus Course Description Explores the basic fundamentals of college-level mathematics. (Note: This course is for institutional credit only and will not be used in meeting degree requirements.

More information

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in

More information

An NWO Hands-On STEM Activity Mathematics and Language Arts with The Mitten by Jan Brett

An NWO Hands-On STEM Activity Mathematics and Language Arts with The Mitten by Jan Brett An NWO Hands-On STEM Activity Mathematics and Language Arts with The Mitten by Jan Brett Suggested Grade Levels: prek-3 Standards Alignment: Geometry K, 1, & 2. Measurement and Data K, 1, 2, & 3 Materials:

More information

May To print or download your own copies of this document visit Name Date Eurovision Numeracy Assignment

May To print or download your own copies of this document visit  Name Date Eurovision Numeracy Assignment 1. An estimated one hundred and twenty five million people across the world watch the Eurovision Song Contest every year. Write this number in figures. 2. Complete the table below. 2004 2005 2006 2007

More information

Lesson Plan. Preliminary Planning

Lesson Plan. Preliminary Planning Lesson Plan Date: 01.20.15 Subject: Social Studies Grade Level: 7th Time Needed: 20 Mins. Preliminary Planning Topic/Central Focus: Examining the history and significance of the Day of the Dead Mexican

More information

Working with Rich Mathematical Tasks

Working with Rich Mathematical Tasks Working with Rich Mathematical Tasks being good at mathematics involves many different ways of working it involves asking questions, drawing pictures and graphs, rephrasing problems, justifying methods,

More information

Fourth Grade. Reporting Student Progress. Libertyville School District 70. Fourth Grade

Fourth Grade. Reporting Student Progress. Libertyville School District 70. Fourth Grade Fourth Grade Libertyville School District 70 Reporting Student Progress Fourth Grade A Message to Parents/Guardians: Libertyville Elementary District 70 teachers of students in kindergarten-5 utilize a

More information

THEORETICAL CONSIDERATIONS

THEORETICAL CONSIDERATIONS Cite as: Jones, K. and Fujita, T. (2002), The Design Of Geometry Teaching: learning from the geometry textbooks of Godfrey and Siddons, Proceedings of the British Society for Research into Learning Mathematics,

More information

Multiple Intelligences 1

Multiple Intelligences 1 Multiple Intelligences 1 Reflections on an ASCD Multiple Intelligences Online Course Bo Green Plymouth State University ED 5500 Multiple Intelligences: Strengthening Your Teaching July 2010 Multiple Intelligences

More information

Teacher Action Research Multiple Intelligence Theory in the Foreign Language Classroom. By Melissa S. Ferro George Mason University

Teacher Action Research Multiple Intelligence Theory in the Foreign Language Classroom. By Melissa S. Ferro George Mason University Teacher Action Research Multiple Intelligence Theory in the Foreign Language Classroom By Melissa S. Ferro George Mason University mferro@gmu.edu Melissa S. Ferro mferro@gmu.edu I am a doctoral student

More information

2 nd Grade Math Curriculum Map

2 nd Grade Math Curriculum Map .A.,.M.6,.M.8,.N.5,.N.7 Organizing Data in a Table Working with multiples of 5, 0, and 5 Using Patterns in data tables to make predictions and solve problems. Solving problems involving money. Using a

More information

Seventh Grade Course Catalog

Seventh Grade Course Catalog 2017-2018 Seventh Grade Course Catalog Any information parents want to give the school which would be helpful for the student s educational placement needs to be addressed to the grade level counselor.

More information

1.11 I Know What Do You Know?

1.11 I Know What Do You Know? 50 SECONDARY MATH 1 // MODULE 1 1.11 I Know What Do You Know? A Practice Understanding Task CC BY Jim Larrison https://flic.kr/p/9mp2c9 In each of the problems below I share some of the information that

More information

Cal s Dinner Card Deals

Cal s Dinner Card Deals Cal s Dinner Card Deals Overview: In this lesson students compare three linear functions in the context of Dinner Card Deals. Students are required to interpret a graph for each Dinner Card Deal to help

More information

Similar Triangles. Developed by: M. Fahy, J. O Keeffe, J. Cooper

Similar Triangles. Developed by: M. Fahy, J. O Keeffe, J. Cooper Similar Triangles Developed by: M. Fahy, J. O Keeffe, J. Cooper For the lesson on 1/3/2016 At Chanel College, Coolock Teacher: M. Fahy Lesson plan developed by: M. Fahy, J. O Keeffe, J. Cooper. 1. Title

More information

Sample Performance Assessment

Sample Performance Assessment Page 1 Content Area: Mathematics Grade Level: Six (6) Sample Performance Assessment Instructional Unit Sample: Go Figure! Colorado Academic Standard(s): MA10-GR.6-S.1-GLE.3; MA10-GR.6-S.4-GLE.1 Concepts

More information

Content Language Objectives (CLOs) August 2012, H. Butts & G. De Anda

Content Language Objectives (CLOs) August 2012, H. Butts & G. De Anda Content Language Objectives (CLOs) Outcomes Identify the evolution of the CLO Identify the components of the CLO Understand how the CLO helps provide all students the opportunity to access the rigor of

More information

Topic: Making A Colorado Brochure Grade : 4 to adult An integrated lesson plan covering three sessions of approximately 50 minutes each.

Topic: Making A Colorado Brochure Grade : 4 to adult An integrated lesson plan covering three sessions of approximately 50 minutes each. Lesson-Planning Approach Topic: Making A Colorado Brochure Grade : 4 to adult An integrated lesson plan covering three sessions of approximately 50 minutes each. Some learners perceive their world as a

More information

PART C: ENERGIZERS & TEAM-BUILDING ACTIVITIES TO SUPPORT YOUTH-ADULT PARTNERSHIPS

PART C: ENERGIZERS & TEAM-BUILDING ACTIVITIES TO SUPPORT YOUTH-ADULT PARTNERSHIPS PART C: ENERGIZERS & TEAM-BUILDING ACTIVITIES TO SUPPORT YOUTH-ADULT PARTNERSHIPS The following energizers and team-building activities can help strengthen the core team and help the participants get to

More information

Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology. Michael L. Connell University of Houston - Downtown

Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology. Michael L. Connell University of Houston - Downtown Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology Michael L. Connell University of Houston - Downtown Sergei Abramovich State University of New York at Potsdam Introduction

More information

Radius STEM Readiness TM

Radius STEM Readiness TM Curriculum Guide Radius STEM Readiness TM While today s teens are surrounded by technology, we face a stark and imminent shortage of graduates pursuing careers in Science, Technology, Engineering, and

More information

AGENDA LEARNING THEORIES LEARNING THEORIES. Advanced Learning Theories 2/22/2016

AGENDA LEARNING THEORIES LEARNING THEORIES. Advanced Learning Theories 2/22/2016 AGENDA Advanced Learning Theories Alejandra J. Magana, Ph.D. admagana@purdue.edu Introduction to Learning Theories Role of Learning Theories and Frameworks Learning Design Research Design Dual Coding Theory

More information

Instructional Supports for Common Core and Beyond: FORMATIVE ASSESMENT

Instructional Supports for Common Core and Beyond: FORMATIVE ASSESMENT Instructional Supports for Common Core and Beyond: FORMATIVE ASSESMENT Defining Date Guiding Question: Why is it important for everyone to have a common understanding of data and how they are used? Importance

More information

Why Pay Attention to Race?

Why Pay Attention to Race? Why Pay Attention to Race? Witnessing Whiteness Chapter 1 Workshop 1.1 1.1-1 Dear Facilitator(s), This workshop series was carefully crafted, reviewed (by a multiracial team), and revised with several

More information

Building Community Online

Building Community Online LESSON PLAN Building Community Online UNIT 2 Essential Question How can websites foster community online? Lesson Overview Students examine websites that foster positive community. They explore the factors

More information

Using Calculators for Students in Grades 9-12: Geometry. Re-published with permission from American Institutes for Research

Using Calculators for Students in Grades 9-12: Geometry. Re-published with permission from American Institutes for Research Using Calculators for Students in Grades 9-12: Geometry Re-published with permission from American Institutes for Research Using Calculators for Students in Grades 9-12: Geometry By: Center for Implementing

More information

Becoming Herodotus. Objectives: Task Description: Background or Instructional Context/Curriculum Connections: Time:

Becoming Herodotus. Objectives: Task Description: Background or Instructional Context/Curriculum Connections: Time: Becoming Herodotus Content Area: : Visual Arts Grades: 9-12 Advanced Task Description: Students are to be introduced to the life and histories of Herodotus, giving specific attention to his recollections

More information

Tutoring First-Year Writing Students at UNM

Tutoring First-Year Writing Students at UNM Tutoring First-Year Writing Students at UNM A Guide for Students, Mentors, Family, Friends, and Others Written by Ashley Carlson, Rachel Liberatore, and Rachel Harmon Contents Introduction: For Students

More information

PHYSICS 40S - COURSE OUTLINE AND REQUIREMENTS Welcome to Physics 40S for !! Mr. Bryan Doiron

PHYSICS 40S - COURSE OUTLINE AND REQUIREMENTS Welcome to Physics 40S for !! Mr. Bryan Doiron PHYSICS 40S - COURSE OUTLINE AND REQUIREMENTS Welcome to Physics 40S for 2016-2017!! Mr. Bryan Doiron The course covers the following topics (time permitting): Unit 1 Kinematics: Special Equations, Relative

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 259574_P2 5-7_KS3_Ma.qxd 1/4/04 4:14 PM Page 1 Ma KEY STAGE 3 TIER 5 7 2004 Mathematics test Paper 2 Calculator allowed Please read this page, but do not open your booklet until your teacher tells you

More information

Module 12. Machine Learning. Version 2 CSE IIT, Kharagpur

Module 12. Machine Learning. Version 2 CSE IIT, Kharagpur Module 12 Machine Learning 12.1 Instructional Objective The students should understand the concept of learning systems Students should learn about different aspects of a learning system Students should

More information

Longman English Interactive

Longman English Interactive Longman English Interactive Level 3 Orientation Quick Start 2 Microphone for Speaking Activities 2 Course Navigation 3 Course Home Page 3 Course Overview 4 Course Outline 5 Navigating the Course Page 6

More information

George Mason University College of Education and Human Development Secondary Education Program. EDCI 790 Secondary Education Internship

George Mason University College of Education and Human Development Secondary Education Program. EDCI 790 Secondary Education Internship George Mason University College of Education and Human Development Secondary Education Program EDCI 790 Secondary Education Internship Len Annetta, Secondary Education Academic Program Coordinator lannetta@gmu.edu

More information

UNIT ONE Tools of Algebra

UNIT ONE Tools of Algebra UNIT ONE Tools of Algebra Subject: Algebra 1 Grade: 9 th 10 th Standards and Benchmarks: 1 a, b,e; 3 a, b; 4 a, b; Overview My Lessons are following the first unit from Prentice Hall Algebra 1 1. Students

More information

2.B.4 Balancing Crane. The Engineering Design Process in the classroom. Summary

2.B.4 Balancing Crane. The Engineering Design Process in the classroom. Summary 2.B.4 Balancing Crane The Engineering Design Process in the classroom Grade Level 2 Sessions 1 40 minutes 2 30 minutes Seasonality None Instructional Mode(s) Whole class, groups of 4 5 students, individual

More information

Plenary Session The School as a Home for the Mind. Presenters Angela Salmon, FIU Erskine Dottin, FIU

Plenary Session The School as a Home for the Mind. Presenters Angela Salmon, FIU Erskine Dottin, FIU Plenary Session The School as a Home for the Mind Presenters Angela Salmon, FIU Erskine Dottin, FIU Noting Important Advice Give the pupils something to do, not something to learn; and the doing is of

More information

Unit: Human Impact Differentiated (Tiered) Task How Does Human Activity Impact Soil Erosion?

Unit: Human Impact Differentiated (Tiered) Task How Does Human Activity Impact Soil Erosion? The following instructional plan is part of a GaDOE collection of Unit Frameworks, Performance Tasks, examples of Student Work, and Teacher Commentary. Many more GaDOE approved instructional plans are

More information

Notetaking Directions

Notetaking Directions Porter Notetaking Directions 1 Notetaking Directions Simplified Cornell-Bullet System Research indicates that hand writing notes is more beneficial to students learning than typing notes, unless there

More information

RIGHTSTART MATHEMATICS

RIGHTSTART MATHEMATICS Activities for Learning, Inc. RIGHTSTART MATHEMATICS by Joan A. Cotter, Ph.D. LEVEL B LESSONS FOR HOME EDUCATORS FIRST EDITION Copyright 2001 Special thanks to Sharalyn Colvin, who converted RightStart

More information

Observing Teachers: The Mathematics Pedagogy of Quebec Francophone and Anglophone Teachers

Observing Teachers: The Mathematics Pedagogy of Quebec Francophone and Anglophone Teachers Observing Teachers: The Mathematics Pedagogy of Quebec Francophone and Anglophone Teachers Dominic Manuel, McGill University, Canada Annie Savard, McGill University, Canada David Reid, Acadia University,

More information

Table of Contents. Introduction Choral Reading How to Use This Book...5. Cloze Activities Correlation to TESOL Standards...

Table of Contents. Introduction Choral Reading How to Use This Book...5. Cloze Activities Correlation to TESOL Standards... Table of Contents Introduction.... 4 How to Use This Book.....................5 Correlation to TESOL Standards... 6 ESL Terms.... 8 Levels of English Language Proficiency... 9 The Four Language Domains.............

More information

Technical Manual Supplement

Technical Manual Supplement VERSION 1.0 Technical Manual Supplement The ACT Contents Preface....................................................................... iii Introduction....................................................................

More information

ARTS IMPACT INSTITUTE LESSON PLAN Core Program Year 1 Arts Foundations VISUAL ARTS LESSON Unity and Variety in a Textural Collage

ARTS IMPACT INSTITUTE LESSON PLAN Core Program Year 1 Arts Foundations VISUAL ARTS LESSON Unity and Variety in a Textural Collage ARTS IMPACT INSTITUTE LESSON PLAN Core Program Year 1 Arts Foundations Artist-Mentor: Maria Grade Grade Levels: Second Fifth Grade Examples: Enduring Understanding Repeating elements for unity and adding

More information