# HRSB, 2009 TI-83, TI-83 + Technology Integration DAY 2 Matrices, Patterns and Relations, & Probability.

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HRSB, 2009 TI-83, TI-83 + Technology Integration DAY 2 Matrices, Patterns and Relations, & Probability

HRSB, 2009 Remember, Math Should be Fun…

HRSB, 2009 Patterns & Relations

HRSB, 2009 Chapter 2 – Pattern & Relations Section 2.2 First, A Refresher: pg. 76, #3 - Entering Ordered Pairs- Adjusting the Window - Graphing a relationship - Finding the Equation Students learn to analyze trends in data from data tables – BUT, the TI-83+ can help! Students learn to analyze trends in data from data tables – BUT, the TI-83+ can help! (Arithmetic vs. Geometric Progression) Using the technology, describe the pattern that exists in the data for #6, pg. 76… Using the technology, describe the pattern that exists in the data for #6, pg. 76… PROVE IT!!! (Think Regression)

HRSB, 2009 Page 76, #3: Page 76, #3: Page 76, #6: Page 76, #6:

HRSB, 2009 Without using technology, let’s complete #13, pg. 78. Without using technology, let’s complete #13, pg. 78. Confirm your answers with the technology. Confirm your answers with the technology. Section 2.2 – Linear & Non-Linear Relationships Key relationships: Key relationships: (1) Linear(2) Quadratic (3) Exponential Complete #3, pg. 85 – Determine the equations for each – Check with Technology Complete #3, pg. 85 – Determine the equations for each – Check with Technology #4, pg. 85 #4, pg. 85 The TI-83+ can reinforce recognition of ‘repeated addition and/or multiplication’ in data tables

HRSB, 2009 #13, pg.78: #13, pg.78:

HRSB, 2009 Using Technology to Compare Relationships Section 2.3 – Slope & Line Properties Section 2.3 – Slope & Line Properties Work through the Student Activity: Student Activity, pg. 110. – Properties of Slope and the Y-Intercept Have the students Match the Graphs with the Equations! In partners, complete #16, pg. 87

HRSB, 2009 - #16, pg. 87 - Analyzing Slope & Interpreting Graphs: “ Walk The Graph Activity: CBR and TI-83+ Comparable to #8, 9, 11, pg. 99, 100 If Time: Complete Together, #14, 15, pg. 101

HRSB, 2009 Graphing Functions &Finding Slope

HRSB, 2009 Graphing Linear Functions

HRSB, 2009 Section 2.4 – The Equation of a Line Re-confirming graphing functions methods, try: pg. 106, #8 using only technology Re-confirming graphing functions methods, try: pg. 106, #8 using only technology Let’s use the technology to complete: Let’s use the technology to complete: #11, pg. 107 #11, pg. 107 Try: “Temperature Vs. Time” Problem Try: “Temperature Vs. Time” Problem Complete #17, pg. 109 Complete #17, pg. 109

HRSB, 2009 Equations & Inequalities

HRSB, 2009 Chapter 3: Equations & Inequalities Section 3.1 – Solving Single Variable Equations Section 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 equality statement between two equations! Remember, this can also be considered as an equality statement between two equations! What are we being asked? What might it look like? What are we being asked? What might it look like? Asking students to state the two equations in o Asking students to state the two equations in o Form is extremely powerful! Graph both equations!

Solving Equations Solving the unknown that makes the statement true Solving the unknown that makes the statement true At what value of ‘x’, do the equations meet, cross, intersect? At what value of ‘x’, do the equations meet, cross, intersect? Need to find the intersection of 1 st and 2 nd function Need to find the intersection of 1 st and 2 nd function Try: Try: What are the two equations? Where do they meet? What are the two equations? Where do they meet? (2, 8)x = 2 What if we rearranged this equation?

HRSB, 2009 Your Turn: Your Turn: Enter both equations in o screen Enter both equations in o screen y r 1 st Curve/2 nd Curve (4, 8) – The x-value that makes this equality statement true is 4. - 8, is the y-value of both equations when x =4.

HRSB, 2009 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. - #16 (d) – Our introduction to Inequalities! - 2 intersection points - Feasible Regions? Your Turn: Chapter Problem – pg. 143, #19 Your Turn: Chapter Problem – pg. 143, #19

HRSB, 2009Inequalities Let’s explore pg. 156, #6 Let’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: Graph both functions and discuss/observe their graphs. Would you agree that where Is true when we consider all x-values greater than, and equal to the intersection point of the two functions?

HRSB, 2009 Find the Intersection Point. Find the Intersection Point. (-7, -7) – the inequality statement is true when (-7, -7) – the inequality statement is true when Now try: #6, (c), (e), & (f) Now try: #6, (c), (e), & (f) Try: #16, pg. 157 Try: #16, pg. 157

Inequality Applications TI-83+/TI-84 + Graph the following set of inequalities: Graph the following set of inequalities: Region of Feasibility – Shaded region of the graph where all coordinates within the region satisfy the inequalities. (mind your solid and dotted lines!) Graph the following:

HRSB, 2009 Inequalities

MATRICES

Matrices – (Guide pg.28) Gr. 9 Text: pg. 52-59 Rectangular array of #’s in rows and columns, surrounded by square brackets Rectangular array of #’s in rows and columns, surrounded by square brackets ▪ (r, c) ▪ 2 rows, 2 columns ▪ Dimensions (Order): 2 x 2 ▪ Each entry is an Element ▪ Element (2, 1) in the matrix is ‘3’ Let’s examine pg. 56-57, ‘Check Your Understanding’ Let’s examine pg. 56-57, ‘Check Your Understanding’ #1 for quick review.

HRSB, 2009 Adding & Subtracting Matrices In order to add or subtract matrices, they must be of the same ‘Order.’ In order to add or subtract matrices, they must be of the same ‘Order.’ If so, you will add or subtract corresponding elements in each matrix. If so, you will add or subtract corresponding elements in each matrix. To access the Matrix Menu: To access the Matrix Menu: - - y 

HRSB, 2009 Matrix Menu Explanation NAMES » Defines matrices by letter; move matrices from this list to HOME SCREEN for matrix operations MATH » No substantial applications for gr. 9 EDIT » To create a Matrix with defined order, do so from this option.

HRSB, 2009 Examining the Text Pg. 56, #1b – Entering a Matrix Pg. 56, #1b – Entering a Matrix y  1 1 y  1 1 ENTER Define the Order: Row x Column (2 x 4) 2 1 4 1 2 1 4 1 Enter Elements across each row Enter Elements across each row (1, enter, 56, enter…) Complete Matrix [A] (1, enter, 56, enter…) Complete Matrix [A]

HRSB, 2009 Deleting a Matrix y [+]

HRSB, 2009 Adding & Subtracting Matrices Together, let’s try #3(a) pg. 57 Together, let’s try #3(a) pg. 57 Y y 5 - access Home Screen Y y 5 - access Home Screen +

HRSB, 2009 To Add Matrix [A] & [B]… Y Now you try: #4, pg. 56 (Communicating Key Ideas) Finish: #3(b), #4(a), (b), pg. 57

HRSB, 2009 Multiplying a Matrix by a Scalar Scalar – a numerical quantity Scalar – a numerical quantity Multiply each element in a matrix by the scalar Multiply each element in a matrix by the scalar i.e.: i.e.: Create the Matrix, y  etc. y 5 Create the Matrix, y  etc. y 5 y , [names], 1:[A] [enter] x 3 [enter] y , [names], 1:[A] [enter] x 3 [enter]

HRSB, 2009 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” Problem “Matrix Theory Application” Problem “Assessment Question” Worksheet “Assessment Question” Worksheet #19, pg. 62 Review #19, pg. 62 Review

HRSB, 2009 Probability

Experimental / Theoretical Probability Section 4.1, pg. 178 Section 4.1, pg. 178 DTM – A Fishy Probability Problem DTM – A Fishy Probability Problem Creating a Fish Community – different fish; 10 in total; Creating a Fish Community – different fish; 10 in total; 10 random selection trials 10 random selection trials Pick Marbles APP. Pick Marbles APP. Trial Set – 10Types – 4 Trial Set – 10Types – 4 Graph - Freq Graph - Freq 10 trials, 50 trials, 100 trials, 200 trials… 10 trials, 50 trials, 100 trials, 200 trials…

HRSB, 2009 More on Probability… Pick Marbles – pg. 186, #13 Pick Marbles – pg. 186, #13 Toss Coins Toss Coins Roll Dice – pg. 184, #6 Roll Dice – pg. 184, #6 Spin Spinner – pg. 184, #9, Sect. 4.4, pg. 202-203 Spin Spinner – pg. 184, #9, Sect. 4.4, pg. 202-203 Draw cards Draw cards Random Numbers Random Numbers

HRSB, 2009 THE END Q & A Q & A Possibilities for further extension on TI-83+ Possibilities for further extension on TI-83+ Suggestions for future PD sessions Suggestions for future PD sessions Wrap-up; Sub Claim Forms Wrap-up; Sub Claim Forms Contact Information: Sohael Abidi Leader, Mathematics Halifax Regional School Board Ph: 464-2000 ext. 4456 sabidi@hrsb.ns.ca

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