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TLLP PROJECT What Math Skills Do Students Need to Be Successful in the Trades?

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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

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Stage 1 of TLLP Talk to College Professors to learn about necessary Math skills for success Algonquin College Automotive Program, HVAC Program, Carpentry Program, Plumbing Program, Motive Power Program Kemptville College Oil and Burner Technician Program, HVAC, Horticulture Program St. Lawrence College Math teachers who taught the Trade and Apprenticeship Programs Some Conversations at this youtube channel

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Skills Needed For Success The following set of skills form a base for success in many Trade and Apprenticeship Programs: 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

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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

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Lesson Template Lessons will have 3 parts: 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? Students will read and summarize information Part 2: Converting between mm and inches 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 Students will use tires to read the numbers and then measure tires to consolidate their knowledge

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Stage 3 of Project We will pilot these lessons to evaluate student engagement and success of lesson format. Share our findings of this project.

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A SENECA COLLEGE LED PROJECT College Math Project

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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.

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Findings of CMP – Seneca College Report At Risk Students 33% of Ontario college students taking mathematics are at risk of not completing their programs due to low achievement in that subject.

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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: 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

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A LOOK AT THE HIGH SCHOOL CURRICULUM Why are Students Lacking these Basic Math Skills?

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CONTENT OF MINISTRY EXPECTATIONS THAT PREPARE STUDENTS FOR COLLEGE TRADE AND APPRENTICESHIP PROGRAMS High School College Pathway Ministry Curriculum

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About 60% * of course links to Skills Needed for Success in Many 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 1 st degree equations * 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 *

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About 40% * of course links to Skills Needed for Success in Many Trade and Apprenticeship Programs 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 * 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

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About 25% * of course links to Skills Needed for Success in Many Trade and Apprenticeship Programs Foundations for College Mathematics, Grade 11 MBF3C Mathematical Models Quadratic Relations – numeric, graphical, algebraic Exponential Relations – numeric, graphical, algebraic Represent Exponential Relations Personal Finance Simple and Compound Interest, exponential growth Services available from financial institutions Owning and Operating a vehicle Geometry and Trigonometry Represent 2D and 3D objects – design problems * Sine Law and Cosine Law Data Management 1 variable data Probability

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About 25% * of course links to Skills Needed for Success in Many Trade and Apprenticeship Programs Foundations for College Mathematics, Grade 12 MAP4C Mathematical Models Solving Exponential Equations Modelling Graphically - linear, quadratic, exponential Modelling Algebraically - linear, quadratic, exponential Personal Finance Understanding Annuities Renting or Owning Accommodation Designing Budgets Geometry and Trigonometry Solving Problems – area and volume * Investigating Optimal Dimensions * Solving Problems involving Trigonometry * Data Management 2 variable data Applying Data Management – media, advertising

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About 15% * of course links to Skills Needed for Success in Many Trade and Apprenticeship Programs Mathematics for College Technology, Grade 12 MCT4C Exponential Functions Solving Exponential Equations Graphically Solving Exponential Equations Algebraically Polynomial Functions Investigating Graphs of Polynomial Functions Connecting Graphs and Equations Solving Problems Trigonometric Functions Applying Trigonometric Ratios Graphs and Equations of Sinusoidal Functions Solving Problems Involving Sinusoidal Functions Applications of Geometry Modelling with Vectors Solve Problems – area and volume * Circle Properties – arcs, tangents, secants, chords, sectors, central angles, and inscribed circles

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CONTENT OF EXPECTATIONS THAT PREPARE STUDENTS FOR THE WORKPLACE High School Workplace Pathway Math Curriculum

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About 90% of course links to Skills Needed for Success in Many Trade and Apprenticeship Programs Locally Developed Compulsory Credit Course Mathematics – Grade 9 MAT1L Developing and Consolidating Money Sense Understanding and Using Decimals Solving Problems Involving Money Communicating Information about Money Developing and Consolidating Concepts in Measurement 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 Constructing Understanding of Fractions, Percentages, Ratios and Rates Solving Problems Communicating Information about Proportional Reasoning Locally Developed Compulsory Credit Courses Grades 9 and 10 Mathematics 2005

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Locally Developed Compulsory Credit Course Mathematics – Grade 10 MAT2L Extending Money Sense Understanding and Using Decimals in Solving Problems Communicating Information about Money Extending Understanding of Measurement 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 Applying Fractions, Percentages, Ratios and Rates in Solving Problems Communicating Information about Proportional Reasoning Locally Developed Compulsory Credit Courses Grades 9 and 10 Mathematics 2005 About 90% of course links to Skills Needed for Success in Many Trade and Apprenticeship Programs

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All expectations link to financial literacy. 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, … 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

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About 60% of course links to Skills Needed for Success in Many Trade and Apprenticeship Programs Mathematics for Work and Everyday Life Grade 12 MEL4E Reasoning with Data Interpreting and Displaying Data Investigating Probability Personal Finance Renting or Owning Accommodation Designing Budgets Filing Income Tax Applications of Measurement 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, …

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BETTER UNDERSTANDING OF THE WORKPLACE MATH PATHWAY AND WHERE IT CAN LEAD What Can Be Done?

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Apprenticeships Require a High School Diploma Largest Hurdle is often getting a placement

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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

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MORE COMMUNICATION BETWEEN HIGH SCHOOL AND COLLEGE MATH TEACHERS What Can Be Done?

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Better Understanding Knowledge is Powerful It would be wonderful to have a Numeracy and Literacy KEY Skill list for each college program 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

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TLLP PROJECT What Can Be Done?

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Funding through TLLP Request Additional Funds to Meet with more College Professors to continue to build understanding between the two curriculums

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