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MATH 90 CURRICULUM RENEWAL & MATH MAKES SENSE 9 WORKSHOP June 24th, 2009 Math 90 Workshop All the information you receive today will be available to you on the GSCS High School Math Support Website: http://blog.scs.sk.ca/hayes/ Once you subscribe to this blog, you will receive an email update each time the website is updated with more information & resources. Math 90 Course Outline Unit 2 – Powers and Exponent Laws (Sections 2.1 – 2.5) Unit 3 - Rational Numbers (Sections 3.1 – 3.6) Unit 1 - Square Roots & Surface Area (Sections 1.1–1.4) Unit 5 – Polynomials (Sections 5.1 – 5.6) Unit 6 – Linear Equations & Inequalities (Sections 6.1-6.5) Unit 4 – Linear Relations (Sections 4.1 – 4.5) Unit 8 – Circles Geometry (Sections 8.1 – 8.4) Math 90 Course Outline Math 90 Plus Unit 9 – Probability & Statistics (9.1 – 9.5) Unit 7 – Similarity & Transformations (7.1 – 7.7) Year-Long Math 90 will cover all 9 units. Math Makes Sense Overview Possible Timeline for Semestered Math 90 (based on 85 teaching days) Unit 2 – 12 days Unit 3 – 14 days Unit 1 - 10 days Unit 5 – 14 days Unit 6 – 12 days Unit 4 – 12 days Unit 8 – 8 days Cumulative Reviews – 3 days Future Workshops For Semester One Math 90 Teachers: Math 90 Plus (Units 7 & 9): Thursday, August 27th,1 – 4pm Math 90 (Units 3 & 1): Tuesday, September 15th, 1 – 4pm Math 90 (Units 5 & 6): Wednesday, October 21st, 1 – 4pm th Math 90 (Unit 4 & 8): Thursday, November 26 , 1- 4pm For Second Semester Math 90 Teachers: Math 90 Plus (Units 7 & 9): Friday, January 29th, 1 – 4pm Other workshops are TBA Why the change? Development of a Common Curriculum Framework: Western & Northern Canadian Protocal (WNCP, 2006) According to the WNCP, the critical components students must encounter in a mathematics program are: communication, connection, mental math and estimation, problem solving, reasoning, technology, & visualization. Resource Selection Process The department heads met in March to look at the new Math 90 curriculum and resource options. Only two textbooks are WNCP approved: Math Links and Make Makes Sense The two texts are very similar Math Makes Sense was chosen to be consistent with the elementary schools. We also decided to purchase one copy of the Math Links text for each teacher as additional resource. Math Makes Sense Overview Resource Components: Student Textbook Manipulative Kits Printed ProGuide (teacher resource) ProGuide DVD (e-book format, PD video clips, unit prep talk videos, classroom videos, virtual manipulatives) ProGuide CD (editable word files – extra practice sheet and sample tests) Practice and Homework Book (teacher edition and reproducible copy) Test Generator Solutions CD – fully worked solutions Math Makes Sense 9 Overview Unit Components: Launch (includes key words, unit objectives, & purpose) Lessons Mid-Unit Review Game Study Guide Unit Review Practice Test Unit Problem Math Makes Sense 9 Overview Extras: Cumulative Reviews (Units 1-3, Units 1–6, Units 1–9) Projects (before Unit 1, after Unit 9) Start where you are – encourages different learning styles Math Link- to highlight cross-curricular, mathematical or real-world connections Technology – to explore ways of using computers and calculators to do math Glossary The Lesson Model Investigate l Reflect & Share Connect Discuss the Ideas Practice The Lesson Model 1. Investigate – brief problem-solving activity designed to draw out prior knowledge and stimulate student interest Reflect and Share – allows students to make connections and develop mathematical reasoning skills The Lesson Model 2. Connect – presents new problems and instruction to teach the math concepts. Involves a range of examples. Discuss the ideas – opportunity for students to communicate their understanding of the concepts The Lesson Model 3. Practice – progressively challenging range of problems Assessment Focus Question – allows students to demonstrate their level of achievement Take it Further – extension questions Reflect – opportunity for students to communicate/summarize their understanding Math Makes Sense 9 Overview ProGuide Components: Overview Booklet Planning and Assessment Support (program masters) Unit Modules: Background – big ideas explained (video option), curriculum overview, curriculum across the grades, additional activities, planning for instruction and assessment, lesson organizers, mental math, reaching all learners, etc Math Makes Sense 9 Overview ProGuide Structure to Support Teachers: Before – Getting Started: Teachers should activate prior knowledge using the introduction to the lesson and key questions. Present the problem in the investigate and ensure expectations are clear. During – Investigate: Teachers should listen carefully, observe and assess, and ask questions to facilitate learning. After – Connect: Review responses from the reflect and share. Use the connect and examples to complete the lesson. Math Makes Sense 9 Overview To help you implement the new resource, Math Makes Sense offers online Orientation Sessions: http://www.pearsoned.ca/school/math/elementarym ath/pearsonwncp/implement.html Items to consider Importance of a positive attitude Classroom organization Manipulative organization Parent Communication (i.e. newsletters, parent nights) Use of Calculators Assessment Focus Questions Word Walls – highlights key words in each unit Support for Teachers – How can I help? UNIT 2 – POWERS AND EXPONENT LAWS 2.1 What is a Power? What is the area of this square? 4 units What is the volume of this cube? 3 units 2.1 What is a Power? Investigate: Use the square tiles to make as many different larger squares as you can. Write the area as a product. Record your results in the table provided. Use the cubes to make as many different larger cubes as you can. Write the volume as a product. Record your results in the table provided. Reflect and Share 2.1 What is a Power? Connect: Your lesson http://www.scs.sk.ca/hch/harbidge/ For students who need to review prior concepts there will be “Activating Prior Knowledge Masters”on the CD-ROM (see page 66 – 67). Use of Calculators 2.1 What is a Power? Discuss the Ideas: #1 – 3 Assignment: #4 – 16 Assessment Focus Question #17 (see rubric) For students who struggle with the AFQ, there are step-by-step masters at the back of the Unit 2 ProGuide – see pages 56 - 61) Reflect: What is a Power? Why are brackets used when there is a negative base? Section 2.2 Powers of Ten and the Zero Exponent Nuclear reactions in the core of the sun create solar energy. For these reactions to take place, extreme temperatures and pressure are needed. The temperature of the sun’s core is about 10^7 °C. What is the temperature in millions of degrees Celsius? Section 2.2 Powers of Ten and the Zero Exponent Exponent Power Repeated Standard Form Multiplication 5 (2)^5 (2)(2)(2)(2)(2) 32 4 (2)^4 (2)(2)(2)(2) 16 3 (2)^3 (2)(2)(2) 8 2 (2)^2 (2)(2) 4 1 (2)^1 (2) 2 Section 2.3 Order of Operations with Powers Skill testing question: 6 x ( 3 + 2) – 10 ÷ 2 Which answer is correct? 5, 10, 15, or 20 Section 2.3 Order of Operations with Powers Skill testing question: 6 x ( 3 + 2) – 10 ÷ 2 = 6 x 5 – 10 ÷ 2 = 6 x 5 – 10 ÷ 2 = 30 – 10 ÷ 2 = 30 – 10 ÷ 2 = 20 ÷ 2 = 30 – 5 = 10 = 25 = 18 + 2 – 10 ÷ 2 = 20 – 10 ÷ 2 = 20 – 5 = 15 2.4 Exponent Laws I When we multiply numbers the order in which we multiply does not matter: (2 x 2) x 2 = 2 x (2 x 2) = 2 x 2 x 2 How would you write this product as a power? What does the word product mean? What does the word quotient mean? 2.4 Exponent Laws I Product of Powers Product as Repeated Product as Power Multiplication 5^4 x 5^2 (5x5x5x5)(5x5) 5^6 3^3 x 3^1 (3x3x3)(3) 3^4 6^2 x 6^2 (6x6)(6x6) 6^4 4^2 x 4^5 (4x4)(4x4x4x4x4) 4^7 1^2 x 1^4 (1x1)(1x1x1x1) 1^6 2.4 Exponent Laws I Quotient of Powers Quotient as Repeated Quotient as Power Multiplication 5^4 ÷ 5^2 (5x5x5x5)/(5x5) 5^2 2^6 ÷ 2^1 (2x2x2x2x2x2)/(2) 2^5 3^5 ÷ 3^2 (3x3x3x3x3)/(3x3) 3^3 2^4 ÷ 2^3 (2x2x2x2)/(2x2x2) 2^1 2.5 Exponent Laws II A power indicates repeated multiplication. What is the standard form of (2^3)^2? How did you find out? (2^3)^2 is called a power of a power. Why? The base of a power might be a product. For example: (2 x 3)^4. (2^3)^2 is called a power of a product. Why? 2.5 Exponent Laws II Power As Repeated As a Product of Factors As a As a Multiplication Power Product of Powers (2^4)^3 2^4 x 2^4 x2^4 (2)(2)(2)(2) x (2)(2)(2)(2) 2^12 x (2)(2)(2)(2) [(-4)^3]^2 (-4)^3 x (-4)^3 (-4)(-4)(-4) x(-4)(-4)(-4) (-4)^6 (2 x 5)^3 (2 x 5) x (2 x 5) x 2x2x2x5x5x5 2^3 x 5^3 (2 x 5) (3 x 4)^2 (3 x 4) x (3 x 4) 3x3x4x4 3^2 x 4^2 Math Makes Sense Overview Back of Unit 2 ProGuide: Masters (Rubrics, Sample Tests, etc) Questions? Please fill out feedback form. Thanks for coming! Have a great summer!