Grade 10 Academic Math Chapter 1 – Linear Systems Introduction to Linear Systems Day 1 & Finding...
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Transcript of Grade 10 Academic Math Chapter 1 – Linear Systems Introduction to Linear Systems Day 1 & Finding...
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)
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 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
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
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
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
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
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
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
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
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
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
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
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
Graphing Linear Relations Graphing linear relations
Table of values Ex. 2x + 3y = 8 and 5x – 2y = 1
Graphing Linear Relations Graphing linear relations
x,y intercepts Try: 2x + 3y = 8 and 5x – 2y = 1
Graphing Linear Relations Graphing linear relations
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