Transcript Geometry and Trigonometry Vehicle Finance

SAGE 2014
GRADE 12 ESSENTIAL MATH
Shawn Sadler and Matt Nikkel
Sorting Units

Rank the course units in order of “what the
students should know after high school”
Course and Materials Intent
SAGE 2014 – Grade 12 Essential Math
Questions

What is the purpose of Grade 12
Essential Math?
 What
are the strengths of the course?
 What are the weaknesses of the course?

Who is taking this course?
 What
are their skills like?
 What are their needs?
Resources and Materials

Why did I make my own materials from
scratch* for this course?
* Note: materials liberally inspired by other teachers and “borrowed” from
provincial exams.
Challenges
Not enough resources
 Textbook does not cover whole course
 Students struggle with the exam

Good things
Grade 12 Essential Math is actually useful
content!
 Provincial exam is actually pretty good

Goal 1
Prepare students for life
after high school.
Goal 2
Prepare students for the
provincial exam.
Curriculum Documents
SAGE 2014 – Grade 12 Essential Math
Matching
Match exam questions to the
corresponding achievement indicator
 List if the question is an “explain” or
“calculate” question

June, Q10, Calc
Matching

What patterns did you see?
 Explain/Calculate?

What questions are expected?
The Provincial Exam
SAGE 2014 – Grade 12 Essential Math
Units on Exam
Precision Measurement
 Statistics
 Home Finance
 Vehicle Finance
 Geometry and Trigonometry
 Probability

Explain Questions

Many Achievement Indicators in the
curriculum state “Explain ______”
 Roughly
1/3 of the exam is “explain
questions”
Precision Measurement
Explain precision, accuracy or
uncertainty
 Write or use tolerance
More on this in a
 State precision/uncertainty
little bit!
 Real-world tolerance question

Statistics

Mean, median, mode
 (calculate
and explain)
Weighted Mean
 Trimmed Mean
 Percentile Rank

 (calculate
and explain)
Home Finance
One-time moving costs
 Land Transfer Tax
 Ownership and maintenance costs
 Home Insurance
 Property Tax
 Mortgage payments

 (may
include amortization table)
GDSR
 Owning vs. Renting

Vehicle Finance
Leasing vehicle (total cost, residual)
 Base, sticker, total cost, taxes (new and used)
 Repairs, parts and labour
 New vs. Used
 Finance vs. Lease
 Depreciation
 Loan payments, interest paid
 Car Insurance
 Fuel Efficiency

Geometry and Trigonometry

Solve triangle using Sine Law
 With

context and diagram
Solve triangle using Cosine Law (with context)
 With
context and diagram
Properties of triangles or quadrilaterals
 Properties of polygons (𝑛 ≥ 5)
 Sine/Cosine Law question
More on these in
a little bit!
 Polygons in real life question

Probability
Write probability (in different forms)
 Write odds, translate to/from probability
 Expected Value
 Explain probability/odds
 Experimental vs. Theoretical probability

Study Sheets
SAGE 2014 – Grade 12 Essential Math
Study Sheets
“During the test, students may have a
pencil or a pen, an eraser, a ruler, a study
sheet, and a simple or scientific
calculator.”
 Information Bulletin
 In addition to the provided formula sheet
 8.5” x 11” double sided
 Students can put ANYTHING on them

Study Sheets
The process of creating the sheet is more
important than the sheet itself
 Students will need to be taught how to create
an effective study sheet

 Use
study cards throughout the course
 Give a short lesson with tips for an effective
study sheet
 Force them to create their own and don’t allow
photocopied sheets
 Provide exemplars of good and poor sheets
Characteristics of an Effective Study
Sheet
Well Structured and Organized
 Has the required formulas and examples
in the students’ own words
 Doesn’t contain too much information
 Doesn’t have their name on it

“Real World” Questions
SAGE 2014 – Grade 12 Essential Math
Sine/Cosine Law
The Sine (Cosine) Law is often used in construction, commercial,
industrial, or artistic applications.
A) Demonstrate one use of the Sine Law in the real world by
performing the following two steps:
• State a specific example where Sine Law is used.
• Support your example with a written explanation of how Sine Law
is used.
B) Sketch a reasonably neat picture or diagram (not necessarily
to scale) that supports your example in Part A.
Polygons
Polygons are often used in construction, commercial, industrial,
or artistic applications.
A) Demonstrate one use of the various properties of polygons
in the real world by performing the following two steps:
• State a specific example where the various properties of polygons
are used.
• Support your example with a written explanation of how the
various properties of polygons are used.
B) Sketch a reasonably neat picture or diagram (not necessarily
to scale) that supports your example in Part A.
Tolerance
Tolerance is often used in construction, commercial, industrial, or
artistic applications.
Demonstrate one use of tolerance in the real world by performing
the following two steps:
• State a specific example where tolerance is used.
• Support your example with a written explanation of how tolerance is used.
You try!
Sine/Cosine Law Answers
Specific example
 Explanation:

 Why
use? What for?
 Find side length or angle

Diagram
 Must
match example
 Must show that sine/cosine law is needed
Polygons Answers
Specific example
 Explanation

 Why
are the properties of the polygon
needed?

Diagram
 Must
match example
Tolerance
Specific example
 Explanation

 Where
is tolerance used?
 “Range of acceptable values”
Study Sheets
Don’t give students a “canned answer”!
 Students should make their own answer,
and put that on the study sheet!

Real Life
SAGE 2014 – Grade 12 Essential Math
Real Life
Which topics from each unit are important
for real life?
1.
What is the “big idea” for this unit?
2.
Where would they use this in real life?
3.
Why do they need it?

Engagement

How do we get students to realize how
this stuff is important for real life?
How did I structure the course?
SAGE 2014 – Grade 12 Essential Math
Goals
Prepare students for real life
 Prepare students for the exam
 Do.

Major Portfolio Project
Career Life
Home Finance
Vehicle Finance
Wrap-up
Career Life Project
Goal: Find a suitable career
 Parts:
1. Myers-Briggs and Multiple Intelligences
2. Career goal
3. Job for next year and backup plan

Home Finance Project

Goal: find a house that suits the career
they have chosen
 Affordability
and location
Parts:
1. Affordability and needs/wants
2. Find a house
3. Mortgages
4. Moving and ongoing costs

Vehicle Finance Project
Goal: find a vehicle they can afford
 Parts:
1. Affordability and needs/wants
2. Find a new car
3. Find a used car
4. Fuel use and owning costs

Wrapup Project
Goal: combine parts of project to a
“snapshot” of what students’ life might be
like in 5-10 years.
 Parts:
1. Budget
2. Analysis

Other Projects

Probability Project: Create a game of
chance
 Includes
super-awesome-fun carnival!
Other Projects

Trigonometry Project: Build a gazebo!
 Or
porch, to connect from Grade 11 Essential
Math
Unit Order
1.
2.
3.
4.
5.
6.
7.
Career Life
Precision Measurement and Statistics
Home Finance
Probability and Business Finance
Geometry and Trigonometry
Vehicle Finance
Career Life Wrap-up
Resources Structure

Notes:
 Introduce
one new exam topic at a time
 Short, frequent examples

Assignments:
 One
topic at a time, logical progression
 Include questions from old exams

Quizzes:
 Frequent,
short.
 Check for students
Precision Measurement and Statistics
SAGE 2014 – Grade 12 Essential Math
Measuring Activity
Unit Structure

Mutually supporting topics
 Measure

stuff, then do stats about them.
Do!
 No
big projects, lots of smaller activities.
Unit Outline
1.
2.
3.
4.
5.
6.
7.
8.
Measure Lego Do!
Accuracy/precision notes
Measuring the human body Do!
Tolerance notes
Do!
Lego tolerance
Central tendency notes and activity
Trimmed and weighted means
Percentile Rank
Exam Topics
Do!
Resources


You can find these resources online at:
shawnsadler.weebly.com/sage-2014.html
Or talk to me to get these resources on a
USB stick