grade 10 academic math chapter 1 – linear systems introduction to linear systems day 1 &...

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 GoalBy 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

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?

X Y

-2 -8

-1 -6

0 -4

1 -2

2 0

Warm-up (Cont’d)


y = 2x - 4

Warm-up (Cont’d)


“Take any number, multiply it by 2 and then subtract 4 from it”

Warm-up (Cont’d)


What is a linear system? (Copy)

two or more equations (linear) considered together two or more equations (linear) considered together

in this course, we will be working with systems that have 2 equations 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 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 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

Val

ue

($)

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 Used

Cel

l P

ho

ne

Exp

ense

s

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’nsInterceptsSlopeGraph

intersecting

parallel & distinct

coincident

Types of Linear Systems (2 lines)

Graph Slope Intercepts # of sol’ns

different

different, unlesslines intersect on

an axis or the origin

1

same different 0

same same infinite

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 Ex. 2x + 3y = 8 and 5x – 2y = 1


x,y intercepts Try: 2x + 3y = 8 and 5x – 2y = 1


Slope/intercept 5x – 2y = 1 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 Premium gas costs 15% more than regular gas 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 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, 15- 17, 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

Using questions on handout

grade 10 academic math chapter 1 – linear systems introduction to linear systems day 1 &...

Documents

linear system slide

homework slide

equations linear

linear systems day

types of linear systems

poi of linear systems

linear systems introduction

point of intersection