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”

SAGE 2014 – Grade 12 Essential Math

Course and Materials Intent

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.

SAGE 2014 – Grade 12 Essential Math

Curriculum Documents

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?

SAGE 2014 – Grade 12 Essential Math

The Provincial Exam

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 State precision/uncertainty Real-world tolerance

question

More on this in a little bit!

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 () Sine/Cosine Law question Polygons in real life question

More on these in a little bit!

Probability

Write probability (in different forms)

Write odds, translate to/from probability

Expected Value Explain probability/odds Experimental vs. Theoretical

probability

SAGE 2014 – Grade 12 Essential Math

Study Sheets

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

SAGE 2014 – Grade 12 Essential Math

“Real World” Questions

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!

SAGE 2014 – Grade 12 Essential Math

Real Life

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?

SAGE 2014 – Grade 12 Essential Math

How did I structure the course?

Goals

Prepare students for real life Prepare students for the exam Do.

Major Portfolio Project

Career Life

Home FinanceVehicle FinanceWrap-up

Career Life Project

Goal: Find a suitable career Parts:1. Myers-Briggs and Multiple

Intelligences2. Career goal3. 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/wants2. Find a house3. Mortgages4. Moving and ongoing costs

Vehicle Finance Project

Goal: find a vehicle they can afford

Parts:1. Affordability and needs/wants2. Find a new car3. Find a used car4. 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. Budget2. 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. Career Life2. Precision Measurement and

Statistics3. Home Finance4. Probability and Business

Finance5. Geometry and Trigonometry6. Vehicle Finance7. 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

SAGE 2014 – Grade 12 Essential Math

Precision Measurement and Statistics

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. Measure Lego2. Accuracy/precision notes3. Measuring the human body4. Tolerance notes5. Lego tolerance6. Central tendency notes and activity7. Trimmed and weighted means8. Percentile Rank

Do!

Do!

Do!

Do!

Exam Topics

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