MPM 2 D Hand Back Take Up Day
MPM 2 D Hand Back & Take Up Day November 17 th, 2010
Analytic Geometry Test Average Median KU 75. 5% App 68. 1% Comm 75. 8% KU 85. 9% App 68% Comm 78%
KU – 11 marks 1. A rhombus is a parallelogram – TRUE 2. A rectangle is a square – FALSE 3. A perpendicular slope to 2/10 is -5 – TRUE 4. Two points on the circle x 2 + y 2 = 16 (4, 0) (-4, 0) (0, 4) (0, -4) easiest
KU – 11 marks (continued) 5. Distance between (2, 5) and (-6, 2) 6. Determine the midpoint of A(-3, -3) and B(1, 5)
KU – 11 marks (continued) a) FG is called a(n) perpendicular bisector, chord b) BD is called a(n) median c) AH is called a(n) altitude d) LMN is a(n) right-angled scalene triangle e) Point D is a(n) midpoint
Part B - Application 8. Classify Quadrilateral ABCD. Justify. Opposite pairs of sides are equal. (One pair 8, one pair 5). Negative reciprocal slopes (1/3 and -3), this means 90° angles. Therefore, this quadrilateral is a rectangle.
Part B – Application (continued) 9. Determine the equation of the altitude from Vertex A. A(-3, 4) B(5, 6) C(0, -4) Slope of BC:
Part B – Application (continued) 10. Write the equation for a circle centered at (0, 0) and passes through (-5, 2).
Part B – Application (continued) 11. a) difference between the areas of circles: x 2 + y 2 = 125 and x 2 + y 2 = 200 b) Where is the point (2, 13)? (inside both, outside both, between). Justify. This circle has a radius of sqrt(173). This is larger than the sqrt(125) but less than the sqrt(200) and therefore lies between the two circles.
Part B – Application (continued) 12. A plan is being constructed to connect houses in a new neighbourhood to a water main. A house located at (2, 9) is to be connected to a water main that runs along the line y = (2/3)x – 1. What is the minimum length of plastic pipe needed to connect the house to the water main? Assume all units are in meters.
Question 12 - Solution Slope of Watermain = 2 / 3 Find POI from house to water main: Perpendicular slope = -3 / 2 Equation from house to water main: Calculate distance: House to water main: Therefore the minimum pipe length is approximately 7. 2 m long.
Part B – Application (continued) 13. Curling Game. Rings have radius of 6 ft. Rock is placed center at (5, 4) Rocks radius is 4. 7”. Will it score? Distance to center of rock: 6 ft * 12 = 72 inches The center of the rock is outside of the rings, so the radius of the rock comes into play. Distance to center of rock – radius of rock: 76. 8 inches – 4. 7 inches = 72. 1 inches 6. 4 * 12 = 76. 8 inches Therefore, there is 0. 1 inches between the rings and the edge of the rock. The rock will not score.
Part B – Application (continued) 14. Show that the slope of JK is parallel to AC. Get K (midpoint of AB): Get J (midpoint of BC):
Question #14 - continued Find slope of AC: Find slope of JK
Linear Systems – Level 4
Step #1 – Determine equations for each band. • Let C represent the total cost of the band, • Let h represent the number of hours the band would play. • Linear Systems C = 65 h + 400 • Coefficients C = 80 h + 250 • Prime Factors C = 150 h
Step #2 – Table of Values Hours Linear Systems (Cost in $) Coefficients (Cost in $) Prime Factors (Cost in $) 0 400 250 0 1 465 330 150 2 530 410 300 3 595 490 450 4 660 570 600 5 725 650 750 6 790 730 900 7 855 810 1050 8 920 890 1200 9 985 970 1350 10 1050 1500 11 1115 1180 1650 12 1180 1210 1800
Step #3 Graph
Step #4 – Find POI C = 150 h C = 80 h + 250 Exactly where Coefficients and Linear Systems meet!! 150 h = 80 h + 250 70 h = 250 / 70 **hours is approx 3. 5714 C = 150 h C = 150(250 / 70) C = 3750 / 7 **Cost is approx 535. 7142
Step #5 - TI Could confirm calculations using TI Calculator!!
Step #6 - Conclusion • The problem does not specify how long the dance-a-thon will be. . . so I am making a general conclusion for multiple lengths. • If the dance-a-thon is less than 3. 5 hours in length (although this wouldn’t be a dance-a-thon in my opinion) SRB should decide to hire the Prime Factors as their band. They would be the cheapest for this length of dance. • If the dance-a-thon is somewhere between 3. 5 hours and 10 hours in length (now this is more like the length of a dance-a-thon) SRB should decide to hire the Coefficients as their band. They are the cheapest for this length of dance. • If SRB is truly doing a dance-a-thon and going over 10 hours in length, they should hire the Linear Systems. They are the cheapest for this length of dance.
Analytic Geometry Performance Assessment Comments
Application vs Thinking (evaluation categories) • Application – – What everyone did! (You showed me what you knew!! ) Applies knowledge & skills in familiar contexts Transfers knowledge & skills into new contexts Making connections between contexts • Concepts, representations, prior knowledge, real world, etc. • Thinking From: Curriculum Achievement Chart – What you need to work on! – Use of planning skills • Formulating and interpreting the problem, making conjectures, making a plan for solving the problem – Use of process skills • Carrying out a plan, looking back at solution (evaluating reasonableness, making arguments, reasoning, justifying, proving, reflecting) – Use of critical / creative thinking processes • Problem solving, inquiry
What are we looking for … • Overall expectations … vs Specific expectations – Specific – solve using subsitution and elimination – Overall – solve problems involving intersection of straight lines • Thinking … vs Application • Creativity • Planning
Next Steps … • Less calculations … what could have been: – Use grid to calculate slopes instead of slope formula every single time – Show one/two calculation(s) of distance, and estimate others for use in other problems – use technology (TI) to quickly calculate
Next Steps … • Look at possible indicators on rubric: – Representing • Models – Diagrams – Accurate Calculations – Reasoning & Reflecting • Reasoning – Drawing Conclusions – Estimating – Assuming – Evaluating Results – Making Judgements – Planning – Reasonableness of … Efficiency – Generalizing – Alternative Approaches – Communicating • Labelled Pictures – Graphs – Symbols – Notation Conventions – Explains & Justifies
Effectiveness – Look Fors • Rubric – got this at PD Session • Look at Level 3 … (meeting expectations) • Multiple Strands – For now means overall expectations – For summative means – Analytic Geometry, Quadratics, Trigonometry
Reflecting • Next time … will give at start (reflect as you go!) • For summative 50/50 for time – Task and Reflecting • Don’t want a regurgitation of what you said in the task … Thinking … – What if … – How could you have done it differently … – Is there another way to think about the image … • Most … If I had more time I would have calculated, calculated … what about summative? ! • Does not specify grade 10 in reflection? ! • Sample!
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