math 90 curriculum renewal & math makes sense 9 workshop june 24 th, 2009
TRANSCRIPT
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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
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?
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