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TI-83, TI-83TI-83, TI-83++

Technology Technology IntegrationIntegration

DAY 2DAY 2

Matrices,Matrices,Patterns and Relations, Patterns and Relations,

& Probability& Probability

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Remember, Math Should be Remember, Math Should be Fun…Fun…

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Patterns & Patterns & RelationsRelations

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Chapter 2 – Pattern & Chapter 2 – Pattern & RelationsRelationsSection 2.2Section 2.2

First, A Refresher:First, A Refresher: pg. 76, #3 pg. 76, #3- Entering Ordered PairsEntering Ordered Pairs - Adjusting the - Adjusting the

WindowWindow- Graphing a relationship Graphing a relationship - - Finding the Finding the

EquationEquation Students learn to analyze trends in data Students learn to analyze trends in data

from data tables – from data tables – BUTBUT, the TI-83+ can , the TI-83+ can help!help!

(Arithmetic vs. Geometric Progression)(Arithmetic vs. Geometric Progression)

Using the technology, describe the pattern Using the technology, describe the pattern that exists in the data for #6, pg. 76…that exists in the data for #6, pg. 76…

PROVE IT!!!PROVE IT!!! (Think Regression)(Think Regression)

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Page 76, #3:Page 76, #3:

Page 76, #6:Page 76, #6:

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WithoutWithout using technology, let’s complete using technology, let’s complete #13, pg. 78.#13, pg. 78.

Confirm your answers Confirm your answers withwith the technology. the technology.Section 2.2 – Linear & Non-Linear RelationshipsSection 2.2 – Linear & Non-Linear Relationships Key relationships: Key relationships: (1)(1) LinearLinear (2) Quadratic (2) Quadratic (3) (3)

ExponentialExponential

Complete Complete #3, pg. 85#3, pg. 85 – Determine the – Determine the equations for each – Check with Technology equations for each – Check with Technology

#4, pg. 85#4, pg. 85

The TI-83+ can reinforce recognition of The TI-83+ can reinforce recognition of ‘repeated addition and/or multiplication’ in data ‘repeated addition and/or multiplication’ in data

tablestables

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#13, pg.78:#13, pg.78:

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Using Technology to Using Technology to Compare RelationshipsCompare Relationships

Section 2.3 – Slope & Line PropertiesSection 2.3 – Slope & Line PropertiesWork through the Student Activity: Work through the Student Activity: Student Activity, Student Activity,

pg. 110pg. 110. .

– – Properties of Slope and the Y-InterceptProperties of Slope and the Y-Intercept

Have the students Match the Graphs with the Have the students Match the Graphs with the Equations!Equations!

In partners, complete #16, pg. 87In partners, complete #16, pg. 87

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- #16, pg. 87#16, pg. 87

- Analyzing Slope & Interpreting Graphs:Analyzing Slope & Interpreting Graphs:

““Walk The Graph Activity: CBR Walk The Graph Activity: CBR and TI-83+and TI-83+

Comparable to #8, 9, 11, pg. 99, 100Comparable to #8, 9, 11, pg. 99, 100If Time: Complete Together, #14, 15, pg. 101If Time: Complete Together, #14, 15, pg. 101

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Graphing Functions &Finding Graphing Functions &Finding SlopeSlope

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Graphing Linear FunctionsGraphing Linear Functions

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Section 2.4 – The Equation Section 2.4 – The Equation of a Lineof a Line

Re-confirming graphing functions Re-confirming graphing functions methods, try: pg. 106, #8 using only methods, try: pg. 106, #8 using only technologytechnology

Let’s use the technology to complete:Let’s use the technology to complete:

#11, pg. 107#11, pg. 107

Try: Try: “Temperature Vs. Time”“Temperature Vs. Time” Problem Problem Complete #17, pg. 109Complete #17, pg. 109

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Equations & Equations & InequalitiesInequalities

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Chapter 3: Equations & Chapter 3: Equations & InequalitiesInequalities

Section 3.1 – Solving Single Variable EquationsSection 3.1 – Solving Single Variable Equations DTM, pg. 132 - How can we solve the equation:DTM, pg. 132 - How can we solve the equation:

• Remember, this can also be considered as an Remember, this can also be considered as an equality statement between two equations!equality statement between two equations!

• What are we being asked? What might it look What are we being asked? What might it look like?like?

• Asking students to state the two equations in Asking students to state the two equations in Form is extremely powerful!Form is extremely powerful!Graph both equations!Graph both equations!

7335 xx

Solving EquationsSolving Equations Solving the unknown that makes the statement Solving the unknown that makes the statement

truetrue At what value of ‘x’, do the equations meet, At what value of ‘x’, do the equations meet,

cross, cross, intersectintersect?? Need to find the Need to find the intersection intersection of 1of 1stst and 2 and 2ndnd

functionfunction Try: Try:

What are the two equations? Where do they What are the two equations? Where do they meet?meet?

(2, 8)(2, 8) x = 2x = 2

What if we rearranged this equation? What if we rearranged this equation?

823 x

8

23

y

xy

6

3

y

xy

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Your Turn: Your Turn:

Enter both equations in Enter both equations in screenscreen

11stst Curve/2 Curve/2ndnd Curve Curve

(4, 8) – The x-value that makes this (4, 8) – The x-value that makes this equality equality statement true is 4. statement true is 4.

- 8, is the y-value of both equations when x - 8, is the y-value of both equations when x =4.=4.

xx 320)164(4

1

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You Try:You Try:

Pg. 142, #11 (d), (e), & (f)Pg. 142, #11 (d), (e), & (f) Now let’s explore deeper…Now let’s explore deeper…

- Together, let’s attempt #16, pg. 142.- Together, let’s attempt #16, pg. 142.

- #16 (d) – Our introduction to - #16 (d) – Our introduction to Inequalities!Inequalities!

- 2 intersection points- 2 intersection points

- Feasible Regions?- Feasible Regions? Your Turn: Chapter Problem – pg. 143, Your Turn: Chapter Problem – pg. 143,

#19#19

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InequalitiesInequalities Let’s explore pg. 156, #6Let’s explore pg. 156, #6 (a) (a) Ask ourselves where the function Ask ourselves where the function

is less than (below) or equal to the function:is less than (below) or equal to the function:

Graph both functions and discuss/observe their Graph both functions and discuss/observe their graphs.graphs.

Would you agree that where Would you agree that where

Is true when we consider all x-values greater Is true when we consider all x-values greater than, and equal to the intersection point of the than, and equal to the intersection point of the two functions?two functions?

28572 xx72 xy

285 xy

28572 xx

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Find the Intersection Point.Find the Intersection Point. (-7, -7) – the inequality statement is (-7, -7) – the inequality statement is

true when true when

Now try: #6, (c), (e), & (f)Now try: #6, (c), (e), & (f) Try: #16, pg. 157Try: #16, pg. 157

7x

Inequality ApplicationsInequality ApplicationsTI-83+/TI-84 +TI-83+/TI-84 +

Graph the following set of Graph the following set of inequalities:inequalities:

Region of FeasibilityRegion of Feasibility – – Shaded region of Shaded region of the graph where all coordinates within the graph where all coordinates within the region satisfy the inequalities.the region satisfy the inequalities. (mind (mind your solid and dotted lines!)your solid and dotted lines!)

Graph the following: Graph the following:

82 xy 64 xy

104

104

104

104

3

4

xy

xy

xy

xy

y

y

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InequalitiesInequalities

xy

yx

xy

x

4

42

1352

3

42

043

0632

y

yx

yx

yx

xy

yx

yx

xx

3

0252

10283

43

1264

xy

xy

yx

xy

xy

23

46

43

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MATRICESMATRICES

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Matrices – (Guide pg.28)Matrices – (Guide pg.28)Gr. 9 Text: pg. 52-59Gr. 9 Text: pg. 52-59

Rectangular array of #’s in rows and columns, Rectangular array of #’s in rows and columns, surrounded by square bracketssurrounded by square brackets

▪ ▪ (r, c)(r, c)

▪ ▪ 2 rows, 2 columns2 rows, 2 columns

▪ ▪ Dimensions Dimensions (Order):(Order): 2 x 2 2 x 2

▪ ▪ Each entry is an Each entry is an ElementElement

▪ ▪ Element (2, 1) in the matrix is ‘3’Element (2, 1) in the matrix is ‘3’

Let’s examine pg. 56-57, ‘Check Your Let’s examine pg. 56-57, ‘Check Your Understanding’Understanding’

#1 for quick review.#1 for quick review.

73

41

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Adding & Subtracting Adding & Subtracting MatricesMatrices

In order to add or subtract matrices, In order to add or subtract matrices, they must be of the same ‘they must be of the same ‘OrderOrder.’.’

If so, you will add or subtract If so, you will add or subtract corresponding elements in each corresponding elements in each matrix.matrix.

To access the Matrix Menu:To access the Matrix Menu:

- -

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Matrix Menu ExplanationMatrix Menu Explanation

NAMESNAMES

» Defines matrices by letter; move matrices » Defines matrices by letter; move matrices from this list to from this list to HOME SCREENHOME SCREEN for matrix for matrix operationsoperations

MATHMATH

» No substantial applications for gr. 9» No substantial applications for gr. 9

EDITEDIT

» To create a Matrix with defined order, do so » To create a Matrix with defined order, do so from this option.from this option.

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Examining the TextExamining the Text Pg. 56, #1b – Pg. 56, #1b – Entering a MatrixEntering a Matrix

ENTER

Define the Order: Row x Column (2 x 4) 2 2 44 Enter Elements across each row Enter Elements across each row (1, (1, enter,enter, 56, 56, enterenter…)…) Complete Complete

Matrix [A]Matrix [A]

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Deleting a MatrixDeleting a Matrix [+]

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Adding & Subtracting Adding & Subtracting MatricesMatrices

Together, let’s try #3(a) pg. 57Together, let’s try #3(a) pg. 57

- access Home Screen- access Home Screen

32

32

15

44+

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To Add Matrix [A] & [B]To Add Matrix [A] & [B]……

Now you try: #4, pg. 56 (Communicating Key Ideas)

Finish: #3(b), #4(a), (b), pg. 57

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Multiplying a Matrix by a Multiplying a Matrix by a ScalarScalar

Scalar – a numerical quantityScalar – a numerical quantity Multiply each element in a matrix by Multiply each element in a matrix by

the scalarthe scalar i.e.: i.e.:

Create the Matrix, Create the Matrix, etc. etc. , [names], 1:[A] [enter] x 3 [enter], [names], 1:[A] [enter] x 3 [enter]

94

205

105

3

94

205

105

3

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Try Some using TI-83+Try Some using TI-83+

#3 (c), (d), pg. 57#3 (c), (d), pg. 57 #4 (c), pg. 57#4 (c), pg. 57 #5, pg. 57#5, pg. 57 ““Matrix Theory Application”Matrix Theory Application” Problem Problem ““Assessment Question”Assessment Question” Worksheet Worksheet #19, pg. 62 Review#19, pg. 62 Review

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ProbabilityProbability

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Experimental / Theoretical Experimental / Theoretical ProbabilityProbability

Section 4.1, pg. 178Section 4.1, pg. 178 DTM – DTM – A Fishy Probability ProblemA Fishy Probability Problem Creating a Fish Community – Creating a Fish Community –

different fish; 10 in total; different fish; 10 in total; 10 random selection trials10 random selection trials Pick Marbles APP.Pick Marbles APP. Trial Set – 10Trial Set – 10 Types – 4Types – 4 Graph - FreqGraph - Freq 10 trials, 50 trials, 100 trials, 200 10 trials, 50 trials, 100 trials, 200

trials…trials…

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More on Probability…More on Probability…

Pick Marbles – pg. 186, #13Pick Marbles – pg. 186, #13 Toss CoinsToss Coins Roll Dice – pg. 184, #6Roll Dice – pg. 184, #6 Spin Spinner – Spin Spinner – pg. 184, #9, Sect. 4.4, pg. 184, #9, Sect. 4.4,

pg. 202-203pg. 202-203 Draw cardsDraw cards Random NumbersRandom Numbers

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THE ENDTHE END Q & AQ & A Possibilities for further extension on TI-Possibilities for further extension on TI-

83+83+ Suggestions for future PD sessionsSuggestions for future PD sessions Wrap-up; Sub Claim FormsWrap-up; Sub Claim Forms

Contact InformationContact Information::Sohael AbidiSohael Abidi

Leader, MathematicsLeader, MathematicsHalifax Regional School BoardHalifax Regional School Board

Ph: 464-2000 ext. 4456Ph: 464-2000 ext. 4456sabidi@hrsb.ns.casabidi@hrsb.ns.ca