MATH 90 CURRICULUM RENEWAL& MATH MAKES SENSE 9 WORKSHOP

June 24th, 2009

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Math 90 Workshop

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 OverviewPossible 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 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

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 OverviewResource 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 OverviewUnit 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 OverviewExtras: 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

lInvestigate

Connect

Practice

Reflect & Share

Discuss the Ideas

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 OverviewProGuide 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 OverviewProGuide 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/elementarymath/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 lessonhttp://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 Multiplicatio

n

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) 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 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

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

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 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)

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