Grade 10 Academic Math Chapter 1 – Linear Systems Introduction to Linear Systems Day 1 & Finding POI using Graphing Calculators - Day 2

Agenda – Day 1 1. Warm-up 2. Introduction to Linear Systems 3. Warm-up 2 4. Types of Word Problems 5. Homework

Agenda – Day 2 1. Finding POI Real Quiz 2. Using Graphing Calculators to find the POI of Linear Systems 3. Homework

Learning Goal By the end of the lesson… … students will be able to read and interpret a mixture or relative value word problems and create a pair of linear relation equations, resulting in a linear system … students will be able to read and interpret a mixture or relative value word problems and create a pair of linear relation equations, resulting in a linear system

Curriculum Expectations  Solve problems that arise from realistic situations described in words… by choosing an appropriate algebraic… method  Ontario Catholic School Graduate Expectations: The graduate is expected to be… a self-directed life long learner who CGE4f applies effective… problem solving… skills

Mathematical Process Expectations  Connecting – make connections among mathematical concepts and procedures; and relate mathematical ideas to situations or phenomena drawn from other contexts

Warm-up  What are different ways that we can represent a linear relation?  Ex. y = 2x - 4  Pick one way to represent this linear relation and write it down

Warm-up (Cont’d) Is this a: ___Numeric ___Algebraic ___Verbal ___Pictorial/Concrete ___Graphic representation of the relationship? XY

Warm-up (Cont’d) Is this a: ___Numeric ___Algebraic ___Verbal ___Pictorial/Concrete ___Graphic representation of the relationship? y = 2x - 4

Warm-up (Cont’d) Is this a: ___Numeric ___Algebraic ___Verbal ___Pictorial/Concrete ___Graphic representation of the relationship? “Take any number, multiply it by 2 and then subtract 4 from it”

Warm-up (Cont’d) Is this a: ___Numeric ___Algebraic ___Verbal ___Pictorial/Concrete ___Graphic representation of the relationship?

Warm-up (Cont’d) Is this a: ___Numeric ___Algebraic ___Verbal ___Pictorial/Concrete ___Graphic representation of the relationship?

What is a linear system? (Copy) two or more equations (linear) considered together in this course, we will be working with systems that have 2 equations to ‘solve’ a linear system means to find the point of intersection

What is a point of intersection? the point where both lines have the same x and y values the p.o.i is (-2, -1)

What does this p.o.i. mean? Years Owned Value ($) Mrs. B.’s car Mr. B.’s car The number of years Mr. and Mrs. B. own their cars until they are both worth the same.

And this one? Minutes UsedCell Phone Expenses Fido Telus The number of minutes when both plans cost the same amount

3 ways to solve… (Copy) Solving Linear Systems Substitution Elimination Algebraic graphing

Types of Linear Systems (2 lines)(Copy) infinitesamesame 0differentsame 1 different, unless lines intersect on an axis or the origin different # of sol’ns InterceptsSlopeGraphintersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Types of Linear Systems (2 lines) GraphSlopeIntercepts # of sol’ns different different, unless lines intersect on an axis or the origin 1 samedifferent0 samesameinfinite intersecting parallel & distinct coincident

Analyzing Linear Systems (Copy) Include: comparison of slopes and y-intercepts describe graph # of solutions you can determine the number of solutions without graphing rearrange equations to y = mx + b form and compare slopes and y-intercepts you can determine the number of solutions without graphing rearrange equations to y = mx + b form and compare slopes and y-intercepts

Humour Break

Graphing Linear Relations  Graphing linear relations Table of values Table of values Ex. 2x + 3y = 8 and 5x – 2y = 1 Ex. 2x + 3y = 8 and 5x – 2y = 1

Graphing Linear Relations  Graphing linear relations Table of values Table of values Ex. 2x + 3y = 8 and 5x – 2y = 1 Ex. 2x + 3y = 8 and 5x – 2y = 1

Graphing Linear Relations  Graphing linear relations x,y intercepts x,y intercepts Try: 2x + 3y = 8 and 5x – 2y = 1 Try: 2x + 3y = 8 and 5x – 2y = 1

Graphing Linear Relations  Graphing linear relations Slope/intercept Slope/intercept 5x – 2y = 1 5x – 2y = 1 3x – y = 6 3x – y = 6

Day 1 Homework   Page 50, #1, 2 &   Page 60, #6-8

Optional Part II - Warm- Up (Copy)  Select let “x” and let “y” represent statements & write each sentence as an equation with two unknowns: The sum of two numbers is 12 The sum of two numbers is 12 Premium gas costs 15% more than regular gas Premium gas costs 15% more than regular gas You can rent a car for $25 per day, plus $0.15/km You can rent a car for $25 per day, plus $0.15/km The total number of adults and children at the circus was 1254 The total number of adults and children at the circus was 1254 Benoit invested some money at 8% and some at 10%. He earned $235 in interest Benoit invested some money at 8% and some at 10%. He earned $235 in interest

Modelling Types  1.Break-Even Problems  2. Mixture Problems  3. Relative Value Problems  4. Rate Problems

Homework  For homework, identify whether this is a break-even, mixture, relative value or rate word problem  Justify your selection  Select one of the problems assigned to your group and create let x and let y statements as well as the system of linear equations to model the relationship

Homework (Continued… )  Group 1 – p.51 #11, 13, , 20, 21, 23, 26, 33  Group 2 – p.51, #10, 14, 25; p.61, #11, 13, 14, 16  Group 3 – p.71, #11, 13; p.72, #18; p.83, #6, 8, 10, 12; p.84, #19  Group 4 – p.52, #18,19, 24, 28; p.84, #19

Agenda – Day 2 1. Warm-up 2. Types of Word Problems 3. Finding POI with graphing calculators

Finding POI Using Graphing Calculators ..\Day 2 - Finding POI using Graphing Calculators\graph calc letter.docx..\Day 2 - Finding POI using Graphing Calculators\graph calc letter.docx..\Day 2 - Finding POI using Graphing Calculators\graph calc letter.docx  Using questions on handout