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TI-83, TI-83 + Technology Integration

TI-83, TI-83 + Technology Integration. DAY 2 Matrices, Patterns and Relations, & Probability. Remember, Math Should be Fun…. Patterns & Relations. Chapter 2 – Pattern & Relations Section 2.2. First, A Refresher: pg. 76, #3 Entering Ordered Pairs - Adjusting the Window

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TI-83, TI-83 + Technology Integration

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

  2. Remember, Math Should be Fun… HRSB, 2009

  3. Patterns & Relations HRSB, 2009

  4. Chapter 2 – Pattern & RelationsSection 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! (Arithmetic vs. Geometric Progression) • Using the technology, describe the pattern that exists in the data for #6, pg. 76… PROVE IT!!!(Think Regression) HRSB, 2009

  5. Page 76, #3: • Page 76, #6: HRSB, 2009

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

  7. #13, pg.78: HRSB, 2009

  8. Using Technology to Compare Relationships • 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

  9. #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

  10. Graphing Functions &Finding Slope HRSB, 2009

  11. Graphing Linear Functions HRSB, 2009

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

  13. Equations & Inequalities HRSB, 2009

  14. Chapter 3: Equations & Inequalities • Section 3.1 – Solving Single Variable Equations • DTM, pg. 132 - How can we solve the equation: • Remember, this can also be considered as an equality statement between two equations! • What are we being asked? What might it look like? • Asking students to state the two equations in o Form is extremely powerful! Graph both equations! HRSB, 2009

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

  16. Your Turn: • Enter both equations in o screen y r 1st Curve/2nd 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

  17. You Try: • Pg. 142, #11 (d), (e), & (f) • 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 HRSB, 2009

  18. Inequalities • Let’s explore pg. 156, #6 • (a) • 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

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

  20. Inequality ApplicationsTI-83+/TI-84 + • 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:

  21. Inequalities HRSB, 2009

  22. MATRICES HRSB, 2009

  23. Matrices – (Guide pg.28)Gr. 9 Text: pg. 52-59 • 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’ #1 for quick review. HRSB, 2009

  24. Adding & Subtracting Matrices • 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. • To access the Matrix Menu: - y — HRSB, 2009

  25. 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

  26. Examining the Text • Pg. 56, #1b – Entering a Matrix • y — 1 1ENTER • Define the Order: Row x Column (2 x 4) • 2 1 41 • Enter Elements across each row • (1, enter, 56, enter…) Complete Matrix [A] HRSB, 2009

  27. Deleting a Matrix • y [+] HRSB, 2009

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

  29. 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

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

  31. Try Some using TI-83+ • #3 (c), (d), pg. 57 • #4 (c), pg. 57 • #5, pg. 57 • “Matrix Theory Application” Problem • “Assessment Question” Worksheet • #19, pg. 62 Review HRSB, 2009

  32. Probability HRSB, 2009

  33. Experimental / Theoretical Probability • Section 4.1, pg. 178 • DTM – A Fishy Probability Problem • Creating a Fish Community – different fish; 10 in total; • 10 random selection trials • Pick Marbles APP. • Trial Set – 10 Types – 4 • Graph - Freq • 10 trials, 50 trials, 100 trials, 200 trials… HRSB, 2009

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

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

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