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. Following today’s workshop, I will email you with this link so that you can get signed up.

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) We decided to start with Unit 2 because we thought it would be the easiest transition for teachers and students. It is important to note that some Grade 8’s have been doing Math Makes Sense for one year, some have never been exposed. We may want to change the order in the future, but for this year we want to be consistent at all the schools. Makes sense for workshop purposes . . .

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 We’ll talk about the Math 90 Plus time-line at the workshop in the fall. Math 90 Year-long can follow the time line in the Proguide.

Future Workshops Other workshops are TBA 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 Math 90 (Unit 4 & 8): Thursday, November 26th, 1- 4pm For Second Semester Math 90 Teachers: Math 90 Plus (Units 7 & 9): Friday, January 29th, 1 – 4pm Other workshops are TBA We will offer Math 90 and Math 90 Plus workshops both semesters. The workshops are designed for semestered Math 90/Plus but we will work out a plan for the Year long Math 90 teachers. You can attend sessions in both semesters depending on where you are . . . Subs will be covered when the workshops are during class time. Some of the workshops are during turn around days. Locations are still to be determined . . . Board office/STA building

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. Alignment with other provinces and territories (AB, BC, MB, SK, NT, NU, YT) . . . Consistency, development of a common resource, etc

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. No textbook is perfect . . . Each have pros and cons. The curriculum has changes and so has the approach to learning . . . Both text books follow the similar lesson formats . . . In Math Links, the lesson format is called “Explore, Reflect and Check, Link the Ideas . . .”

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 Teacher support unlike never seen before! You have the Proguides now to start preparing over the summer. Student texts and manipulative kits will arrive by the fall. The rest has been ordered and are expected sometime in the fall . . . Once they are ready.

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 Look at the sample text book you have in front of you . . . Take a flip through one of the units and find the following components. Since we are starting with Unit 2 – turn to page 50 to start . . .

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 l Investigate Connect Practice Reflect & Share Discuss the Ideas l Consistent three-part lesson model . . . New approach to learning.

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 Investigate – an idea/problem - often done in groups/pairs with use of materials/manipulatives – hands-on, student-centered learning Reflect and share their results with other students

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 Connect – connects the idea to the mathematical concepts behind it. Summarizes the math and uses examples to demonstrate different ways to approach the question. Discuss the ideas – can be verbal or written

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 Assignments – will want to assign up to and including the assessment focus question. If too much, suggestion is to assign every numbered question but have students do every second part. May want to take up questions before doing assessment focus and reflect. Assessment focus – struggling students can be supported by the “step by step” black—line masters at back of the Proguide. Taking it further – for students who need/want to be challenged. Reflect – could be used as a classroom discussion, lesson summary, or math journal entry . . . Goal is to encourage students to think about the big ideas of the lesson, as well as their own learning style and strategies.

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 Teachers will find valuable support and embedded Professional Learning in a comprehensive ProGuide package that includes print materials, a CD-ROM, and a DVD. Let’s look at the Proguide binder . . . and specifically the Unit Module for Unit 2. Assessment For Learning supports teaching with What to Look For and What to Do If You Don’t See It Answers and Sample Solutions are provided for Practice and Reflect questions Reaching All Learners may include an alternative explore, extension activity, common misconceptions, ESL strategies. Planning and Assessment Support (program masters) – column charts, grid paper, student self assessment sheets, etc. Unit Modules - We will go through this more thoroughly as we plan for Unit 2. Overview

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. In the blue shaded area of the Proguide, there is a step by step guide for teachers to use to teach the lesson. Includes key questions and other important tips. We will walk through some parts of the Unit 2 Guide after the break . . . Comprehensive Teaching Notes support teachers Before, During and After, corresponding to the student lesson model of Explore, Connect, and Practice.

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? Classroom organization – how you structure, organize and manage your classroom. Setting up investigate, getting student in groups, pairs – should to change group members on a regular basis. Use of Calculators – see “mental math” section of proguide. Assessment Focus Question – in elementary some teachers use a duotang for student to complete these questions and reflect on the lesson. We will design rubrics for you to use to assess the questions. Take them in after each section, once a week, at the end of the unit, etc. Can use mark as part of homework/assignments, math journal, etc . . .

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 BEFORE: Activating Prior Knowledge . . . Review of Area and Volume . . . Preparing for the investigate. How can you use the side length of a cube to calculate its volume? ow can you use the side length of a square to calculate its area?

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 Connect to investigate – volume of a cube that 2 units by 2units by 2 units = (2)(2)(2) = 2^3

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? #165 – need to use calculators

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 Repeated Multiplication Standard Form 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) 1 (2)^1 (2) Describe any patterns in the table. Continue the pattern to complete the last row. Compare with other students.

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 BEFORE: Predict which answer is correct . . . Do not share your predictions! How were these answers derived?

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 Are all the answers correct? How do you know that some of the answers are not correct? Which operation should be performed first? Why is it important that everyone follows the same order of operations? Investigate Assessment Focus Questio

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? BEFORE: Multiplication is commutative Investigate: Groups of 4, one pair does multiplying powers, the other does dividing. Reflect and Share: share results and rules for multiplying and dividing of powers.

2.4 Exponent Laws I 5^4 x 5^2 (5x5x5x5)(5x5) 5^6 3^3 x 3^1 (3x3x3)(3) Product of Powers Product as Repeated Multiplication Product as Power 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 Here are some examples of what students will have in the chart. Describe the patterns in the table . . . Use the patterns to describe a way to multiply two powers with the same bases.

2.4 Exponent Laws I Quotient of Powers Quotient as Repeated Multiplication Quotient as Power 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 Describe the patterns in the table . . . Use the patterns to describe a way to divide two powers with the same bases.

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? Before Investigate – fill in chart in pairs. Look for patterns. Record a rule for each scenario. In the connect you still need to introduce the power of the quotient!!

As Repeated Multiplication 2.5 Exponent Laws II Power As Repeated Multiplication As a Product of Factors As a Power As a Product of Powers (2^4)^3 2^4 x 2^4 x2^4 (2)(2)(2)(2) x (2)(2)(2)(2) x (2)(2)(2)(2) 2^12 [(-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 (2 x 5) 2 x 2 x 2 x 5 x 5 x 5 2^3 x 5^3 (3 x 4)^2 (3 x 4) x (3 x 4) 3 x 3 x 4 x 4 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!