Life is about change. Introduction Life can seem
chaotic.Sharpen your algebraic skills.Work with patterns of
change.
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There are four components to this course. 1234 Linear Algebra
Rules of Algebra Using Technology Patterns of Change
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Component 1 Patterns in Linear Algebra
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Component 1 Patterns in Linear Algebra Linear Algebra is used
in these fields to show trends and make decisions. 1 Linear Algebra
EconomicsSociologyPolitical Science Medicine Multiple Representatio
ns
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Stage Stage NumberNumber of Counters Used 01 13 25 37 49 511
Independent Dependent IndependentDependent Stage NumberNumber of
Counters Used 01 13 25 37 49 511 1 Linear Algebra
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Stage 1 Linear Algebra IndependentDependent Stage NumberNumber
of Counters Used 01 13 25 37 49 511 = x = y
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Stage IndependentDependent Stage NumberNumber of Counters Used
01 13 25 37 49 511 = x = y (x, y) (0, 1) (x, y) (0, 1) Independent
= xDependent = y Stage Number Number of Counters Used 01 13 25 37
49 511 0 1 1 Linear Algebra
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Stage (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) (x, y)
(0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) IndependentDependent
Stage Number Number of Counters Used 01 13 25 37 49 511 1 Linear
Algebra Did you write the ordered pairs like this?
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Stage (x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) (x, y)
(0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) IndependentDependent
Stage Number Number of Counters Used 01 13 25 37 49 511 1 Linear
Algebra Did you write the ordered pairs like this? (x, y) (0, 1)
(1, 3) (2, 5) (3, 7) (4, 9) (5, 11) (x, y) (0, 1) (1, 3) (2, 5) (3,
7) (4, 9) (5, 11)
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(x, y) (0, 1) (1, 3) (2, 5) (3, 7) (4, 9) (5, 11) (x, y) (0, 1)
(1, 3) (2, 5) (3, 7) (4, 9) (5, 11) 1 Linear Algebra What trend do
you see?
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Independent = xDependent = y Stage NumberNumber of Counters
Used 01 13 25 37 49 511 6 7 13 15 1 Linear Algebra
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Independent = xDependent = y Stage NumberNumber of Counters
Used 01 13 25 37 49 511 6 7 13 15 1 Linear Algebra Independent =
xDependent = y Stage Number Number of Counters Used 01 13 25 37 49
511 613 715 Your Verbal Description Your Verbal Description
Complete the mathematical sentence below. y = ______ Hint Box Y
(number of counters used) = ______ Y (number of counters used) = 1
+ _______ Y (number of counters used) = 1 + the Stage Number times
2 Hint Box Y (number of counters used) = ______ Y (number of
counters used) = 1 + _______ Y (number of counters used) = 1 + the
Stage Number times 2 Check your work Check your work
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Independent = xDependent = y Stage Number Number of Counters
Used 01 13 25 37 49 511 613 715 Complete the mathematical sentence
below. y = ______ Hint Box Y (number of counters used) = ______ Y
(number of counters used) = 1 + _______ Y (number of counters used)
= 1 + the Stage Number times 2 Hint Box Y (number of counters used)
= ______ Y (number of counters used) = 1 + _______ Y (number of
counters used) = 1 + the Stage Number times 2 1 Linear Algebra Your
Verbal Description Your Verbal Description y = 1 + 2x
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Slope Intercept Form The slope will describe the rate of
change. The intercept will describe the data when x = 0. The
equation that describes the work we have done in this component,
written in slope intercept form, is y = 2x + 1. y = 1 + 2x 1 Linear
Algebra
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1 Relationship between the stage number Number of counters in
equation form 1 Linear Algebra A function, like an equation,
describes a relationships between sets of data. A function assigns
each value of the independent variable (x) to only one value of the
dependent variable (y). The function that describes Marias work
would be f(x) = 2x + 1. If the value of x is 3, the function tells
us that f(3) = 2 3 + 1 = 7. Function notation Slope Intercept Form
The slope will describe the rate of change The intercept will
describe the data when x = 0. The equation that describes the work
we have done in this component, written in slope intercept form, is
y = 2x + 1.
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Independent = xDependent = y Stage Number Number of Counters
Used 01 13 25 37 49 511 613 715 1 Linear Algebra 1 Your Verbal
Description Your Verbal Description f(x) = 2x + 1 Geometric Pattern
Table Graph Verbal Descriptio n Algebraic Equation
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Component 1 This concludes Component 1. 1234 Linear Algebra
Rules of Algebra Using Technology Patterns of Change