Post on 16-Jan-2016
Mathematics
Sept. 14, 2012
Invitation to the Spirit of the Day
Enjoy the activities.
Engage in the mathematics.
Be an active participantlisten, talk, question, explore, persist, wonder, predict, summarize, synthesize
Introductions
Please introduce yourselfname, school, SD, FN
position, role, responsibility
Overview
Foundations of Mathematics 30Course InformationThe Foundations of Mathematics pathway is designed to provide students with the mathematical knowledge, skills and understandings required for post secondary studies. Content in this pathway will meet the needs of students intending to pursue careers in areas that typically require a university degree, but are not math intensive, such as humanities, fine arts, and social sciences. Students who successfully complete this course will be granted a grade 12 credit. Students must successfully complete the common course, Foundations of Mathematics 20, prior to taking this course.Topics Include: financial decision making inductive and deductive reasoning set theory and its applications odds and probability probability of two events combinatorics representation and analysis of data
Workplace and Apprenticeship 30
Course InformationThe Workplace and Apprenticeship pathway is designed to provide students with the mathematical knowledge, skills and understandings required entry into some trades-related courses and for direct entry into t he work force Students who successfully complete this course will be granted a grade 12 credit. Students must successfully complete Workplace and Apprenticeship 20 prior to taking this course.
Topics Include: limitations of measuring instruments sine and cosine laws properties of triangles, quadrilaterals, and regular polygons transformations options for acquiring a vehicle viability of a small business linear relations measures of central tendency percentiles odds and probability
Pre-Calculus 30Course InformationThe Pre-calculus pathway is designed to provide students with the mathematical knowledge, skills and understandings required for post secondary studies. Content in this pathway will meet the needs of students intending to pursue careers that will require a university degree with a math intensive focus. Students who successfully complete this course will be granted a grade 12 credit. Students must successfully complete the common course, Pre-Calculus 20, prior to taking this course. This course is a prerequisite to Calculus 30.
Topics Include: angles in standard position the unit circle and the six trig ratios graphs of primary trig ratios first and second degree trigonometric equations trigonometric identities operations and compositions of functions transformations functions, relations, and inverses logarithms polynomial functions of greater than degree 2 radical and rational functions permutations and fundamental counting principle combinations and the binomial theorem
About the Pathways
• not based on perceived ability, but on destination• cover different content for different reasons-just like
Biology, Chemistry, and Physics• students to construct understanding with the same
level of rigour• Sk students can take more than one pathway for
credit• There is no hierarchy between the pathways• changing pathways requires the necessary pre-
requisite
Workplace & Apprenticeship
• NOT “math for those who can’t do math”
• mathematics content needed for apprenticeship and trades
• meets needs of 30%-40% of students
Pre-Calculus
• NOT “math for the mathematically gifted”
• mathematical content needed for math and science-related areas
• meets needs of 10%-20% of students
Foundations of Mathematics
• NOT “math for those who can do math but would rather not”
• mathematics content needed for non-mathematics and non-science based university programs
• meets the needs of 40%-60% of students
Recognize any of the following?
Lifelong Learners, Engaged CitizensSense of self, community and Place
Developing thinking, identity, interdependence,social responsibility, and literacies
Logical Thinking, Number Sense, Spatial Sense,Mathematics as a Human Endeavour
Communication, connections, visualization, technology, problem solving, reasoning, mental math and estimation
Warm Up
A woman is on a diet and goes into a shop to buy some turkey slices. She is given 3 slices which together weight 1/3 of a pound, but her diet says that she is only allowed to eat ¼ of a pound. How much of the 3 slices she bought can she eat while staying true to her diet?
Strategies?
If 3 slices is 1/3 of a pound, then 9 slices is a pound. I can eat ¼ of a pound, and ¼ of 9 slices is 9/4 slices.
“What is the point of knowing procedures if students don’t know when they should use them, or how to apply them to complex problems?”
Jo Boaler pg 87 What’s Math Got to Do With It?
http://www.curriculum.gov.sk.ca/index.jsp
www.joboaler.com
http://lisaebe.wikispaces.com/
Tangles
Tangles
Zero State:
Twist
A lifts and B goes underneath: Number associated with the tangle is 1
Rotate
Rotate one spot in a clockwise direction
Perform:
UnTwists are not admitted.
t(x) = x + 1
r(x)=?
r(r(r(r(x)))) = x
r(r(x)) = x
Perform:
T T R How do we get back to a zero configuration?
What is the numerical operation performed by a rotate?
Magic
T2RT3RT
FM30.2 Demonstrate understanding of inductive and deductive reasoning including: • analysis of conditional statements • analysis of puzzles and games involving numerical and logical reasoning • making and justifying decisions • solving problems.
[C, CN, ME, PS, R]
Role of Homework
“students should be given unique problems and tasks that consolidate new learning with prior knowledge, explore possible solutions, and apply learning to new situation.”
We will be exploring global population until October 20th, 2012.
What will the global population be at that exact time?
This was the population at 3:00 p.m. on Saturday, March 31st, 2012.
This was the population March 31st, 2002
• What will the population be in 2022?
Population clock:http://galen.metapath.org/popclk.html
• Doing Mathematics Bloghttp://www.doingmathematics.com/2/category/doing%20mathematics/1.html
Differentiation is..
• “A flexible approach to teaching in which the teacher plans and carries out varied approaches to content, process, and product in anticipation of and in response to student differences in readiness, interests, and learning needs”.
Carol Ann Tomlinson
• Effective differentiated instruction involves:– Knowing your students & their individual needs– Understanding the curriculum– Providing multiple pathways for learning– Sharing responsibility for learning with students– Taking a flexible and reflective approach.
• …”an appropriate teacher response to learners’ needs.”
A Russian Fable• Take three blades of grass, folded in two,
and hold them in your hand so that the six ends are hanging down.
• Tie the ends together in pairs
If on release, a large loop is formed, you will __________
FM30.5 Extend understanding of the probability of two events, including events that are:
• mutually exclusive • non-mutually exclusive • dependent • independent. [CN, PS, R, V]
How does this fit with the indicators?
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The Monty Hall Problem• You are shown 3 identical doors. Behind one of them
is a car. The other 2 conceal goats. You are asked to choose, but not open, one of the doors. After doing so, Monty, who knows where the car is, opens one of the two remaining doors. He always opens a door he knows to be incorrect, & randomly chooses which door to open when he has more than one option. After opening an incorrect door, Monty gives you the option of either switching to the other unopened door or sticking with your original choice. You then receive whatever is behind the door you choose. What should you do?
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Student Task
• Draw & explain your solution for whether you should switch or stay.
• Be prepared to convince others of your answer.
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• Students can conduct an experiment using cards. One player is Monty & knows what is behind all three doors.
• Have students collect data always choosing to switch or alternately always choosing to stay. In groups of two, give one student from each group three cards.
• Record how many times you won the car!
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The Sample Space
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• “the monty hall problem” written by Jason Rosenhouse presents a look at the remarkable story of this problem.
• Included in this book are quotes from mathematicians who responded to Marilyn vos Savant, a Q & A columnist for Parade magazine, who answered 2/3 & 1/3 to this problem
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Since you seem to enjoy coming straight to the point, I’ll do the same. In the following question & answer, you blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to ½. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error & in the future being more careful.
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• You blew it, & you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the chances are the same. There is enough mathematical illiteracy in this country, & we don’t need the world’s highest I.Q. propagating more. Shame!
Planning for Inquiry As teachers plan for inquiry, some questions should
continually drive their thinking and decision-making including:
• How can I help my students realize that they have questions and that their questions matter?
• How can I create a classroom environment that supports my students’ inquiries without directing them?
• How can I help my students connect their inquiries to questions and issues of deeper personal and social significance?
• How can I help my students share their learning in interesting, relevant, authentic ways?
(Diane Parker (2007) Planning for Inquiry: It’s Not an Oxymoron! Urbana, IL: NCTE, p. 13.)
LUNCH
Trigonometry
List the key big ideas for trigonometry.
Have a discussion about why they are the keyconcepts.
Where is the Dot?
• http://nrich.maths.org/5615
Developing Conceptual Understanding
Allow students to wrestle with key ideas
Attend to mathematical relationships
An idea that is fully understood is easilyextended
Simple Harmonic Motion
http://www.youtube.com/watch?v=yVkdfJ9PkRQ&feature=player_embedded#!
What Is Inquiry?
“Inquiry is a way of looking at the world, a questioning stance we take when we seek to learn something we don’t yet know.”
(Diane Parker, Planning for Inquiry: It’s Not an Oxymoron! Urbana, IL: NCTE,
2007, p. 1).
• Determine the relationship between foot length and height.
• Determine the Height of an Individual based on foot length.
• Determine height from bone length.
WA30.8 Extend and apply understanding of linear relations including:
• patterns and trends • graphs • tables of values • equations • interpolation and extrapolation • problem solving.
[CN, PS, R, T, V]
• http://www.nytimes.com/interactive/business/buy-rent-calculator.html
Resources
http://fawnnguyen.com/page/2.aspx
http://mrvaudrey.wordpress.com/2012/05/03/the-only-lesson-theyll-remember/
http://emergentmath.wordpress.com/the-great-inquiry-based-math-curriculum-mapping-project/
Resources
• www.nctm.org– http://illuminations.nctm.org/– http://figurethis.org/index.html– http://www.nctm.org/profdev/content.aspx?
id=26594
• http://nrich.maths.org/public/
• http://www.galileo.org/
Contact
Lisa EberharterMathematics Consultantlisa.eberharter@gov.sk.ca787-2072