1. Math 90 Curriculum Renewal & Math Makes Sense 9 Workshop
June 24th, 2009

2. Math 90 Workshop
All the information you receive today will be available to you on the GSCS High School Math Support Website:
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Following today’s workshop, I will you with this link so that you can get signed up.

4. 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 )
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 . . .

5. 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.

6. Math Makes Sense Overview
Possible Timeline for Semestered Math 90
(based on 85 teaching days)
Unit 2 – 12 days
Unit 3 – 14 days
Unit 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.

7. 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

8. 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

9. 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 . . .”

10. 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.

11. 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 . . .

12. 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

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

14. 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

15. 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

16. 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.

17. 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

18. 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.

19. Math Makes Sense 9 Overview
To help you implement the new resource, Math Makes Sense offers online Orientation Sessions: ath/pearsonwncp/implement.html

20. 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 . . .

21. Unit 2 – Powers and Exponent Laws

22. 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?

23. 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

24. 2.1 What is a Power? Connect: Your lesson
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

25. 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 )
Reflect: What is a Power? Why are brackets used when there is a negative base?
#165 – need to use calculators

26. 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?

27. 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.

28. 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?

29. 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
= = 25
= – 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

30. 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.

31. 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.

32. 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.

33. 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!!

34. 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

35. Math Makes Sense Overview
Back of Unit 2 ProGuide:
Masters (Rubrics, Sample Tests, etc)
Questions?
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Thanks for coming! Have a great summer!