2. InTech “Students and teachers collaborating to learn mathematics using the tools of our time”

3. Presentation and resources found at: http://intechone.wikispaces.com

4. Contact Information Camille Baker (Jordan District): camille.baker@jordan.k12.ut.us camille.baker@jordan.k12.ut.us Robyn Hussey (Mont Harmon JH—Price): husseyr@dtc.carbon.k12.ut.us husseyr@dtc.carbon.k12.ut.us Walter Lewis (Oquirrh Hills Middle—Jordan): wlewis3736@msn.com wlewis3736@msn.com Heather Riddle (Granite District): heather.riddle@granite.k12.ut.us heather.riddle@granite.k12.ut.us Diana Suddreth ( Utah State Office of Education ): diana.suddreth@schools.utah.gov diana.suddreth@schools.utah.gov

5. InTech: How should we think about integrating technology in mathematics teaching?

6. Professional Development The practice of training teachers on skills rather than on how to use technology to enhance student learning handicaps the potential to promote higher- order thinking.

7. InTech Goals 1. Improve student academic achievement in secondary mathematics. 2. Provide opportunities for teachers to improve their practice by integrating technology and collaborating with teachers throughout the state (in person and electronically). 3. Effectively integrate technology to teach and learn mathematics.

8. Technology Hardware  Computers  Printers  Calculators  CBL / CBR  Probes  TI-Navigator  TI-Nspire  IPODs  Mimio / Smartboard  Student Response Systems

9. Technology Software  TI-Interactive  TI-Connect  TI-Smartview  Geometer’s Sketchpad  Cabri Geometry  HandyGraph  MathType  Microsoft Office PowerPoint Word Publisher Excel  Inspirations

10. Technology Internet  Email  Websites http://nlvm.usu.edu/en/nav/vlibrary.html http://nsdl.org http://ia.usu.edu http://www.pbs.org/teachers http://illuminations.nctm.org www.shodor.org/interactive/activities www.amathsdictionaryforkids.com http://teachertube.com  E-portfolios  UTIPS  E-desk

11. In the math classroom, how can we integrate engaging activities from students’ lives outside of school?

12. InTech Teacher Summer Collaboration in Price and Riverton Utah CollaborationTimeline Day 1 Getting to know you. Select the big idea focuses for teacher pairs. Intro sample units and assessments. Examine the possible technologies. Set up teacher wikispaces. Day 2 Develop unit criteria. Select and learn the technology for the big idea focus. Plan the lesson activities, connections with other resources, and sequence. Beginning project and assessment preparation. Update wikispaces. Day 3 Continue lesson/assessment preparation. Evaluate and revise. Update wikispaces. Day 4 Project and assessment preparation. Trial run with students and teachers. Evaluate and revise as a group. Upload to SEUTIPS InTech Website.

13. InTech SEUTIPS Web Page InTech 1. Units 2. Unit Overviews and Lesson Plan 3. Student Testing 4. Other Resources 5. Student Zone http://www.seutips.org/~intech/

14. Units 1 Number Sense with Real Numbers 1 Number Sense with Real Numbers_1 2 Solve Linear Equations and Inequalities 3 Proportional and Linear Relationships 4 Analyzing real world linear data 5 Solve Systems of Equations and Inequalities 6 Polynomials and solving quadratic equations

15. Unit 2

16. Unit 2 Curriculum Map Big Idea Utah Core Obj ecti ves Time FrameUnit Learning Activities Literacy/ Technology/ Collaboration Text -book Linear Equations and Inequalities 7. Solve and interpret linear equations and inequalities in various situations including real-world problems. For this year, plan on about 3 weeks. Next year you may wish to condense this section on solving equations. (By the new core, students should come to algebra able to solve linear equations) Unit Outline Launch: 1) Graphic organizer 2) Discussion about balance (A Balancing Act PowerPoint) Explore: 3) Build and Solve Equations (Virtual Manipulatives) Summarize and Discuss: 4) Solving equations foldable Apply and Solidify: (students solve with pencil and paper, then solidify using TI Interactive) 1.5) Equation Stories and Solutions, 2.6) Thinking Backwards — Writing Word Problems from Equations 3.7) Writing Equations from Word-problems, Writing Equations from Stories 4.8) I Love a Parade 5.9) Textbook practice (Also use your textbook to solve inequalities and the 6. worksheet Graphing Inequalities to have them practice graphing 7. inequalities on a number line. ) Assessment: 12) Solving Equations and Inequalities Multiple Choice Test 11) Solving Multi-step Equations and Inequalities Assessment 12) Create a Story Problem (email groups for peer-editing) Daily Outline (Lesson Plan details are found in the “ Solve Equations and Inequalities Lesson Plan ” document.) Literacy:  Writing stories from equations and equations from stories  Writing components on lessons and assessments  Create a Story Problem Assessment Student Collaboration  In class: Preparing and presenting equation stories  Online: Solving Multi-step Equations Technology:  Power Point  Virtual manipulatives http://nlvm.usu.edu/en/nav/ vlibrary.htmlhttp://nlvm.usu.edu/en/nav/ vlibrary.html (go to 6-8 algebra, balance scale)  TI Interactive  Calculators

17. Unit 2 Overview Course: Algebra Unit: Solving Equations Focal Point: Developing an understanding of solving equations. Essential Questions: 1.What are equations? Why are they so important in algebra? 2. Explain why the idea of balance is so important in solving equations? Skill Focus: Solving basic one step and multi step equations. Connections: variable, expression, equation, inverse operation, balance, like terms, sides of the equation, coefficient, constant terms Materials:  Internet permission slips  Precision School Balance (if possible). Some kind model for a balance scale to place manipulative on.  Computers  Online Virtual Manipulatives [If you use “ Hands-On ” Equations ®, students should have balance scale mats, one baggie containing 4 number cubes (2 cubes numbered from 0-5 and 2 cubes numbered from 5-10) and 8 to 10 triangles to represent the variable (the green triangles from pattern blocks would work well).]  TI Interactive  Calculators  Email groups  Worksheets and Homework (Attached) Technology:  PowerPoint  Virtual Manipulatives  TI-Interactive  Calculators UNIT OUTLINE Launch: Graphic organizer, Discussion about balance (A Balancing Act PowerPoint) Explore: Build and Solve Equations (Virtual Manipulatives) Summarize and Discuss: Solving equations foldable Apply and Solidify: (TI Interactive — students solve with pencil and paper, then solidify using TI Interactive) 1.Equation Stories and Solutions 2.Thinking Backwards — Writing Word Problems from Equations 3.Writing Equations from Word-problems, Writing Equations from Stories 4.I Love a Parade 5.Textbook practice (Use your textbook to have students practice solving inequalities and the worksheet “ Graphing Inequalities ” to have them practice graphing inequalities on a number line) Assessment: 1.Solving Multi-Step Equations and Inequalities 2.Create a Story Problem (email groups for peer-editing) 3.Solving Equations and Inequalities Multiple Choice Assessment

18. Unit 2 Lesson Plans Build and Solve Equations If you do not have access to NLVM you may use Hands-On-Equations to do this activity or create your own. Instructions for this are found below. To create number cubes, use unnumbered dice or plain 1inch wooden cubes. Prepare 4 cubes for each student, 2 cubes with the numbers 0-5 written on and 2 cubes with the numbers 5-10 written on. In all the worksheets, have students check their answers by substituting in to the original problem or the equation. They can write the numbers above the symbols. Introduce the idea of a balance scale. Show the balance scale using grams weights. Set the scale so that both sides are balanced. Put a 2 gram weight on both sides. The scale is still in balance because the same thing happened to both sides. Put two 5 gram weights on one side and one 10gram weight on the other. The scale is still in balance because even though each side looks different, each side has the same value. Model taking the same thing off both sides and maintaining the balance. Demonstrate the use of manipulatives to represent variables and numbers. Place equivalent blocks on both sides of the balance scale model. Then use a triangle to balance a 5, then a 3 etc. The variable varies. Show these others: with a 7, a 2, two triangles with an 8, three triangles with a 12. How can we find out what one triangle is equal to? What can you do to both sides so that you are left with = ____ State the rule: Each side of the balance must always equal the other. Your job is to find out the value of one of the triangles Have students complete the worksheet using manipulates and writing down the solving actions they used to find the value of x. Do not have them solve algebraically until after the first few lessons. (If students are still struggling with the idea of balance, you may want to do all of the lessons before you start solving algebraically.) After the first lesson you may want them to start demonstrating what they are doing by drawing it on their paper and using arrows to show what they are removing from each side. Teacher moves around the room to listen and assess progress. Have students present different problems in front of the class and discuss how they solved them using hands-on- equations. Have another student draw what the other student did with the manipulatives. If students were able to solve them algebraically, have another student show this process as well.

19. Student Testing

20. Other Resources

21. Individual Teacher http://lewisinmath.wikispaces.com/ Student Links Assignments InTech Lesson Plans Textbook Links District, School, and Teacher Links

22. Student Links

23. Assignments

24. InTech

25. Lesson Plans-Pre-Algebra

26. Lesson Plans-Algebra

27. Textbook Links

28. Links to the district, school, PowerSchool, and other teachers

29. We continue our collaboration each month through video conferences. Price is on screen and Riverton is sitting in the room.

31. Carnegie Learning’s computerized math program was used with students that traditionally struggled with learning mathematics.

33. Each school purchased a mobile lab, using computers for instruction, review, math games and explorations, and assessments.

36. By: Natalie H. Samantha T. Tessa T.

37. Mayans North of Peru, centered on Yucatan Peninsula in Central and South America Mayans had as many as twenty states The Mayan civilization existed 3,000 years It had written language, architecture, a well- ordered social class system, agriculture, art, the development of a calendar, trade and a well- developed religious system. They had 30 different languages.

38. Mayan Number System Had 3 symbols instead of our 10 Shell represents 0 Dot represents 1 Bar represents 5 Ex. 3 bars and 1 dot would be 16

39. For Unit One-The Real Number System students used graphing calculators to support their learning about numbers.

41. Unit 3 Proportional and Linear Relationships CBRs are used as a tool to help student develop understanding about linear graphs.

43. Unit 4-Analyzing real world linear data Oquirrh Hills Middle School-InTech Algebra Unit 3 Assessment-Create Your Own Constellation Name ________________________________ Date __________________Period ____ Due Date_____________ Student Directions: Create a picture on a coordinate grid that represents something about you. Choose at least seven dominant points. Points must be in each of the four quadrants. Connect those points with straight lines to create a constellation. At least four lines must not be horizontal or vertical. Write the equation for each line, at least six equations – use the attached worksheet. Equations must be written in red ink. After you have your equations complete, have your teacher’s initial your work. You will then open the Geometer’s Sketchpad (GSP) and draw your constellation in it. Save your work on the desktop. You will use GSP to check your constellation equations. You must write the correct equation from the GSP in blue ink below your red inked answer. Write a paragraph (at least five sentences) that explains the constellation and your story behind it. You will be graded on neatness and accuracy of your picture (20 points), linear equations (60 points), and paragraph (20 points). The entire project is worth 50 points. Project Title: ____________________________________________________________________ ______________________________________________________________________________________________________ NumberSlope, Point, or Points used to determine the EquationShow WorkEquation/Equation Check 1 2

44. Sample constellation: The constellation below represents the bull which was a significant figure in a town that I lived for many years. The bull was honored for its courage and strength. It was celebrated each weekend in Mexicali, a Mexican city across the border from where I lived. The bullring was festive with excitement at each of the bullfights. The courage of the bullfighter and the bull were both tested.

48. Unit 5 Solve Systems of Equations and Inequalities-Students used graphing calculators, GSP, and a SmartBoard to find solutions using systems of equations and inequalities.

52. Changes: John DeSandre in Price, shortly before school began, had his assignment changed to teaching science and geometry. He adapted his plans quickly to continue integrating technology as a tool for instruction, Here are student works on GSP on constructing Parallel lines and parallelograms.

53. 30-60-90 triangles and polygon interiors

54. 1918 Spanish flu By Sarah

55. Some Facts about the flu The Spanish flu occurred in 1918- 1919 about 25 million people died including about 800,000 Americans! In India the rate was extremely high at around 50 deaths from influenza per 1,000 people! Science reveals another US team has successfully recreated the 1918 virus in mice.

56. How Many People died It Started just as 40 to 50 million people Then 50 to 100 million people world wide The infection rate was 50%

57. E-Portfolios What are the advantages to students having e- portfolios? What are the issues that challenge you in setting up e-portfolios for all of your students?

58. Student e portfolios January 19, 2008 Dear Parent(s)/Guardian(s), The Internet provides a unique opportunity for students to display, share, and communicate about their school work with their family and other students. As part of an ongoing collaboration with the Carbon School District through Project InTech, my Algebra I classes at OHMS will be creating an individual web page for each student. Project InTech is a pilot for future teacher professional development as established by the Utah Office of Education. This project focuses on helping teachers use technological tools to enhance mathematics instruction. Student e-portfolios is one part of this project. For more information on InTech please access InTech’s web page at http://www.seutips.org/~intech/. My webhttp://www.seutips.org/~intech/ page may also be accessed at www.lewisinmath.wikispaces.com.www.lewisinmath.wikispaces.com Student web pages will allow students to create electronic web portfolios to display student work for viewing by other students and their parents. These web pages will be set up through the Southeastern Utah Test Item Pool Service (SEUTIPS) and are free for students to use as part of Project InTech. SEUTIPS is part of a statewide network that teachers use for testing and for teacher web pages. Important information to know about SEUTIPS includes: The site is secure and password protected; Students will use their intials to protect their name; All student work may be viewed by parents and students using a password to access the portfolio; Students may publish specific projects that will be viewable on the open web or keep their site viewable only through a password; Each math teacher will be able to access each site to score student work and review the site for proper; Each student will own the copyright on all materials they create and then post to their portfolio or publish on the Internet; Students may not post photos of themselves without the approval of parents indicated on the goldenrod permission slip; Student web sites will be the property of each student and their parents with parents deciding on the continuation of the web page after June 10, 2008. All guidelines of the Jordan School District Student Information Network Acceptable Use Policy must be adhered to. Each student is not required to create a web portfolio. They must have the goldenrod Jordan School District permission slip signed by students and parents to have their own web portfolio. Students that do not create a web portfolio will create a portfolio saved on a CD.

59. InTech Revamped 08-09 Six big curriculum ideas per course, per year One technology poject or lesson series per big idea High priorities for students  Online collaboration  E-portfolios Teacher Collaboration  Three summer days (rural schools to Wasatch front)  Online collaboration (each teacher with a web-cam)

60. InTech: How should we think about integrating technology in mathematics teaching?

61. Presentation and resources found at: http://intechone.wikispaces.com