What Math Skills Do Students Need
to Be Successful in the Trades?
TLLP PROJECT
TLLP Project
 The Teacher Learning and Leadership Program (TLLP) is an
annual project-based professional learning opportunity for
experienced classroom teachers.
 The program funds proposals from classroom teachers who
seek a peer leadership role in curriculum, instructional
practice or supporting other teachers.
 Goals of the program:
 create and support opportunities for teacher professional learning
 foster teacher leadership
 facilitate the sharing of exemplary practices with others for the broader
benefit of Ontario's students
 Partnership between Ministry of Education and OTF/FEO
Stage 1 of TLLP
Talk to College Professors to learn about necessary Math
skills for success
 Algonquin College
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Automotive Program, HVAC Program, Carpentry Program, Plumbing
Program, Motive Power Program
 Kemptville College
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Oil and Burner Technician Program, HVAC, Horticulture Program
 St. Lawrence College
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Math teachers who taught the Trade and Apprenticeship Programs
 Some Conversations at this youtube channel
www.youtube.com/channel/UCUaC8oSb-auf6DbZpLMM7Jg
Skills Needed For Success
The following set of skills form a base for success in many Trade and
Apprenticeship Programs:
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Understanding of Decimal, Fraction and Percent
Understanding and Application of Perimeter, Area and Volume
Estimating Skills
Imperial and Metric Measurement
Visual Recognition of Measurement
Mental Math
Angles
Basic Algebra for use in Trade Calculations
Pythagorean’s Theorem and Primary Trig Ratios
Stage 2 of Project
 Develop a template for teachers to use to design
Trade Focused Lessons for grade 10 students in the
Locally Developed Math Pathway
 It was also noted that Reading Comprehension and
Writing Skills are also necessary for success in the
Trade Programs and Apprenticeship Programs
Lesson Template
 Lessons will have 3 parts:
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Part 1: Communication Lesson
Part 2: Knowledge and Skill Development Lesson
Part 3: Hands On Learning Lesson
Example for Automotives
 Part 1: Should Snow Tires be Mandatory in Ontario?
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Students will read and summarize information
 Part 2: Converting between mm and inches
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Students will use mental math to estimate conversions, then use
calculators to convert between these systems
 Part 3: How to Read the Numbers on a Tire and relate
these numbers to tire measurements
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Students will use tires to read the numbers and then measure tires to
consolidate their knowledge
Stage 3 of Project
 We will pilot these lessons to evaluate student
engagement and success of lesson format.
 Share our findings of this project.
College Math Project
A SENECA COLLEGE
LED PROJECT
College Math Project
The College Mathematics Project (CMP) is a
collaborative project involving Colleges of Applied
Arts & Technology and District School Boards set up
to investigate the mathematics achievement of first
year College students in Ontario.
A Seneca College led project, CMP is based at the
York/Seneca Institute for Mathematics, Science and
Technology Education.
Findings of CMP – Seneca College Report
At Risk Students
33% of Ontario college students taking
are at risk
mathematics
of not completing
their programs due to low achievement in that
subject.
Findings of CMP – Seneca College Report
1 in 4 of these first year college students are taking college
preparatory mathematics courses.
BASIC MATH SKILLS TAUGHT IN COLLEGE PREP PROGRAMS:
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Order of Operations
Fractions
Decimals
Percentages
Ratio and Proportion
Algebra
 These basic math concepts and skills are taught in Grades 6 – 8 and
students need to master them then as they are critical for success in
many college programs
Why are Students Lacking these
Basic Math Skills?
A LOOK AT THE HIGH SCHOOL CURRICULUM
High School College Pathway
Ministry Curriculum
CONTENT OF MINISTRY EXPECTATIONS THAT
PREPARE STUDENTS FOR COLLEGE TRADE
AND APPRENTICESHIP PROGRAMS
Foundations of Mathematics
Grade 9, Applied
 Number Sense and Algebra
 Solve problems using proportional reasoning*
 Simplify numerical expressions in one variable,
and solve 1st degree equations *
About 60% * of
course links to
Skills Needed
for Success in
Many Trade and
Apprenticeship
Programs
 Linear Relations
 Relationships between 2 variables
 Characteristics of a linear relations
 Constant rate of change
 Representations of linear relations
 Measurement and Geometry
 Optimal values of measurements *
 Solve problems of 2D and 3D objects *
 Properties of 2D shapes *
Foundations of Mathematics
Grade 10, Applied
 Measurement and Trigonometry
 Similar Triangles *
 Primary Trig Ratios and Pythagorean theorem *
 SA and Volume of 3D figures, imperial and metric
measure *
About 40% * of
course links to
Skills Needed
for Success in
Many Trade and
Apprenticeship
Programs
 Modelling Linear Relations
 Solve Algebraic equations
 Graph and Equation of a line
 Solve Systems of Equations
 Quadratic Relations,
 Algebraic Expressions related to quadratics
 Characteristics of Quadratic Relations
 Interpreting Graphs of Quadratic Relations
Foundations for College
Mathematics, Grade 11
MBF3C
 Mathematical Models
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Quadratic Relations – numeric, graphical, algebraic
Exponential Relations – numeric, graphical, algebraic
Represent Exponential Relations
 Personal Finance
About 25% * of
course links to
Skills Needed
for Success in
Many Trade and
Apprenticeship
Programs
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Simple and Compound Interest, exponential growth
Services available from financial institutions
Owning and Operating a vehicle
 Geometry and Trigonometry
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Represent 2D and 3D objects – design problems *
Sine Law and Cosine Law
 Data Management
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1 variable data
Probability
Foundations for College
Mathematics, Grade 12
MAP4C
 Mathematical Models
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Solving Exponential Equations
Modelling Graphically - linear, quadratic, exponential
Modelling Algebraically - linear, quadratic, exponential
 Personal Finance
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About 25% * of
course links to
Skills Needed
for Success in
Many Trade and
Apprenticeship
Programs
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Understanding Annuities
Renting or Owning Accommodation
Designing Budgets
 Geometry and Trigonometry
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Solving Problems – area and volume *
Investigating Optimal Dimensions *
Solving Problems involving Trigonometry *
 Data Management
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2 variable data
Applying Data Management – media, advertising
Mathematics for College
Technology, Grade 12
MCT4C
 Exponential Functions
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Solving Exponential Equations Graphically
Solving Exponential Equations Algebraically
 Polynomial Functions
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About 15% * of
course links to
Skills Needed
for Success in
Many Trade and
Apprenticeship
Programs
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Investigating Graphs of Polynomial Functions
Connecting Graphs and Equations
Solving Problems
 Trigonometric Functions
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Applying Trigonometric Ratios
Graphs and Equations of Sinusoidal Functions
Solving Problems Involving Sinusoidal Functions
 Applications of Geometry
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Modelling with Vectors
Solve Problems – area and volume *
Circle Properties – arcs, tangents, secants, chords, sectors,
central angles, and inscribed circles
High School Workplace Pathway
Math Curriculum
CONTENT OF EXPECTATIONS THAT PREPARE
STUDENTS FOR THE WORKPLACE
Locally Developed Compulsory Credit Course
Mathematics – Grade 9
MAT1L
Locally Developed Compulsory Credit Courses
Grades 9 and 10
Mathematics
 Developing and Consolidating Money Sense
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2005
 Developing and Consolidating Concepts in
Measurement
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About 90% of
course links to
Skills Needed
for Success in
Many Trade and
Apprenticeship
Programs
Understanding and Using Decimals
Solving Problems Involving Money
Communicating Information about Money
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Understanding and Using the Metric System
Understanding and Using the Imperial System
Understanding and Applying Perimeter, Area and Volume
Communicating Information about Measurement
 Developing Concepts in Proportional Reasoning
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Constructing Understanding of Fractions, Percentages,
Ratios and Rates
Solving Problems
Communicating Information about Proportional
Reasoning
Locally Developed Compulsory Credit Course
Mathematics – Grade 10
MAT2L
Locally Developed Compulsory Credit Courses
Grades 9 and 10
Mathematics
 Extending Money Sense
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Understanding and Using Decimals in Solving Problems
Communicating Information about Money
 Extending Understanding of Measurement
2005
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About 90% of
course links to
Skills Needed
for Success in
Many Trade and
Apprenticeship
Programs
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Estimating and Measuring Using the Metric System
Estimating and Measuring Using the Imperial System
Solving Problems Involving Perimeter, Circumference,
Area and Volume
Communicating Information about Measurement
 Extending Understanding of Proportional
Reasoning
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Applying Fractions, Percentages, Ratios and Rates in
Solving Problems
Communicating Information about Proportional
Reasoning
Mathematics for Work and Everyday Life
Grade 11
MEL3E
 Earning and Purchasing
 Remuneration Methods
 Describing Purchasing Power – payroll deductions
 Purchasing – discounts, sales tax, unit prices, …
All expectations
link to financial
literacy.
 Saving, Investing and Borrowing
 Comparing Financial Services
 Saving and Investing
 Borrowing
 Transportation and Travel
 Owning and Operating a Vehicle
 Travelling by Automobile
 Comparing Modes of Transportation
Mathematics for Work and Everyday Life
Grade 12
MEL4E
 Reasoning with Data
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Interpreting and Displaying Data
Investigating Probability
 Personal Finance
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About 60% of
course links to
Skills Needed
for Success in
Many Trade and
Apprenticeship
Programs
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Renting or Owning Accommodation
Designing Budgets
Filing Income Tax
 Applications of Measurement
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Measuring and Estimating
Applying Measurement and Design – Pythagorean
Theorem, Perimeter, Area, Volume, Scale models
Solving Measurement Problems Using Proportional
Reasoning – ratio, rate, unit rates, equivalent ratios, …
What Can Be Done?
BETTER UNDERSTANDING OF THE
WORKPLACE MATH PATHWAY AND WHERE IT
CAN LEAD
Apprenticeships
 Require a High School Diploma
 Largest Hurdle is often getting a placement
College Programs
 There are many college programs that require only
grade 12 College English
 For many of these programs, Workplace Math would
prepare students better than the College Math based
on the basic math skills suggested in the College
Math Project
What Can Be Done?
MORE COMMUNICATION BETWEEN HIGH
SCHOOL AND COLLEGE MATH TEACHERS
Better Understanding
Knowledge is Powerful
 It would be wonderful to have a Numeracy and
Literacy KEY Skill list for each college program
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High School teachers can differentiate their programming
based on the necessary skill set
 Sample College Course Material
 Let students feel what the college program will be like
What Can Be Done?
TLLP PROJECT 2014 - 2015
Funding through TLLP
 Request Additional Funds to Meet with more College
Professors to continue to build understanding
between the two curriculums