Schools That Lead the Way

SCHOOLS THAT LEAD THE WAYKentucky Association of School Councils Conference September 22, 2009 Williamstown Jr/Sr High SchoolContact Us Ann Rourk - [email protected] Deana Cummins - [email protected] Misty Buchanan – [email protected]Graphic Organizers – www.sw-georgia.resa.k12.ga.us/mathk12.htmlPage 1 Open-Response QuestionThe Values of Integers In the table below, p, t, v, and z each represent a different integer. If v  0, find each of the following values. Explain your reasoning using the real number properties. v  0 v  p = v t + p = p v + 5 = t8  z = p a) What is the numerical value of p? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. b) What is the numerical value of t? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. c) What is the numerical value of v? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. d) What is the numerical value of z? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. Scoring GuideSCORE DESCRIPTION4 Student scores 4 points.3 Student scores 3 – 3.5 points.2 Student scores 2 – 2.5 points.1 Student scores 0.5 – 1.5 points.0 Student’s response is totally incorrect or irrelevant.Blank No student response. Score PointsPart a: score 1 point correct numerical value and reasoning explained using the correct property of real numbers OR score 0.5 point correct numerical value and reasoning explained using the incorrect property of real numbers OR correct numerical value and no reasoning is used to explain the value Part b: score 1 point correct numerical value and reasoning explained using the correct property of real numbers OR score 0.5 point correct numerical value and reasoning explained using the incorrect property of real numbers OR correct numerical value and no reasoning is used to explain the value Part c: score 1 point correct numerical value and reasoning explained using the correct property of real numbers OR score 0.5 point correct numerical value and reasoning explained using the incorrect property of real numbers OR correct numerical value and no reasoning is used to explain the value Part d: score 1 point correct numerical value and reasoning explained using the correct property of real numbers OR score 0.5 point correct numerical value and reasoning explained using the incorrect property of real numbers OR correct numerical value and no reasoning is used to explain the value Open-Response QuestionThe Values of Integers In the table below, p, t, v, and z each represent a different integer. If v  0, find each of the following values. Explain your reasoning using the real number properties. v  0 v  p = v t + p = p v + 5 = t8  z = p a) What is the numerical value of p? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. b) What is the numerical value of t? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. c) What is the numerical value of v? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. d) What is the numerical value of z? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. Program of Studies: MA-HS-NPO-S-PNO1 “Students will identify and apply real number properties.”Program of Studies: MA-HS-NPO-S-PNO4 “Students will justify the solution steps in simplifying expressions or solving an equation.”Core Content Code: 1.5.1 “Students will identify real number properties (commutative properties of addition and multiplication, associative properties of addition and multiplication, distributive property of multiplication over addition and subtraction, identity properties of addition and multiplication and inverse properties of addition and multiplication) when used to justify a given step in simplifying an expression or solving an equation.” Open-Response QuestionCorrect AnswersThe Values of Integers In the table below, p, t, v, and z each represent a different integer. If v  0, find each of the following values. Explain your reasoning using the real number properties. v  0 v  p = v t + p = p v + 5 = t8  z = p a) What is the numerical value of p? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. p = 1 v · 1 = v due to the identity of multiplication, a · 1 = a, any number multiplied by 1 equals that number b) What is the numerical value of t? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. t = 0 0 + p = p due to the additive identity property, a + 0 = a, any number added to 0 equals that number c) What is the numerical value of v? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. v = 5 Since you know t = 0, the equation v + 5 = 0 can be used to solve for v. If v + 5 = 0, then v must equal  5 to have the equation equal 0, due to the additive inverse property. The sum of any number and its opposite is zero. d) What is the numerical value of z? Write the equation or equations you used to find its numerical value and explain your reasoning using the real number properties. z = Since you know p = 1, the equation 8  z = 1 can be used to solve for z. If 8  z = 1, then z must equal to have the equation equal 1, due to the multiplicative inverse property. Any number multiplied by its inverse equals 1.Open-Response QuestionInternet Service ProviderMegan wants to change her Internet Service Provider. She is considering three different plans: Plan 1 charges a $15 monthly fee, plus $0.08 per minute of use.Plan 2 charges a $5 monthly fee, plus $0.11 per minute of use.Plan 3 charges a flat monthly fee of $49.95. a) For each plan, write an algebraic equation that represents the monthly cost, C, for m minutes per month. b) Graph each of the three equations on the same coordinate axes (with correct labels and scales). Label each line. c) Megan expects to use 500 minutes per month. In which plan do you think Megan should enroll? Explain your reasoning.Scoring GuideSCORE DESCRIPTION4 Student scores 4 points. 3 Student scores 3 – 3.5 points.2 Student scores 2 – 2.5 points.1 Student scores 0.5 – 1.5 points.0 Student’s response is totally incorrect or irrelevant.Blank No student response. Score PointsPart a: score 1.5 points .5 points each for correct equation given for each planPart b: score 1.5 point .5 points each for correct graph of each planOR score 1 point graph itself is not labeled, or scale is incorrect, however, all three equations are graphed correctlyPart c: score 1 point correct answer with reasoning explainedOR score 0.5 point correct answer with no explanation providedOpen-Response QuestionInternet Service ProviderMegan wants to change her Internet Service Provider. She is considering three different plans:Plan 1 charges a $15 monthly fee, plus $0.08 per minute of use. Plan 2 charges a $5 monthly fee, plus $0.11 per minute of use.Plan 3 charges a flat monthly fee of $49.95. a) For each plan, write an algebraic equation that represents the monthly cost, C, for m minutes per month. b) Graph each of the three equations on the same coordinate axes (with correct labels and scales). Label each line. c) Megan expects to use 500 minutes per month. In which plan do you think Megan should enroll? Explain your reasoning.Core Content Code: 5.3.3 “Students will model, solve and graph first degree, two-variable equations and inequalities in real-world and mathematical problems.”Program of Studies: MA-HS-AT-S-EI17 “Students will write and solve linear sentences, describing real-world situations by using and relating formulas, tables, graphs and equations.”Open-Response Question Correct AnswersInternet Service ProviderMegan wants to change her Internet Service Provider. She is considering three different plans:Plan 1 charges a $15 monthly fee, plus $0.08 per minute of use. Plan 2 charges a $5 monthly fee, plus $0.11 per minute of use. Plan 3 charges a flat monthly fee of $49.95. a) For each plan, write an algebraic equation that represents the monthly cost, C, for m minutes per month.Plan 1: C = 15 + 0.08m Plan 2: C = 5 + 0.11m Plan 3: C = 49.95 b) Graph each of the three equations on the same coordinate axes (with correct labels and scales). Label each line.Internet Service Provider Plans 70 65 60 55 50 45 t 40 s 35 o Plan 1C 30 25 Plan 2 20 Plan 3 15 10 5 0 0 50 100 150 200 250 300 350 400 450 500 550Minutes c) Megan expects to use 500 minutes per month. In which plan do you think Megan should enroll? Explain your reasoning.Megan should enroll in Plan 3. The graph in part b shows that at 500 minutes, she would be paying $49.95 for plan 3, about $60 for Plan 2, and about $55 for Plan1. Therefore, plan 3 is the most economical plan.Open-Response QuestionQuadrilateralConsider the following points: A(-2,1) , B( 2, - 2) , C( 8,7) , D ( 4,10) a) Graph the quadrilateral ABCD. b) Find the slope of each side of the quadrilateral. c) Find the perimeter of quadrilateral ABCD. d) What is the most precise name for the quadrilateral ABCD? Justify your choice.Scoring GuideSCORE DESCRIPTION4 Student scores 4 points.3 Student scores 3 – 3.5 points.2 Student scores 2 – 2.5 points. 1 Student scores 0.5 – 1.5 points.0 Student’s response is totally incorrect or irrelevant.Blank No student response.Score PointsPart a: score 1 point correct graphing of all 4 ordered pairsPart b: score 1 point correct slope of all 4 sidesPart c: score 1 point correct lengths of all 4 sides and correct perimeterOR score 0.5 point correct lengths of all 4 sides without perimeterPart d: score 1 point correct naming of quadrilateral with correct justificationOR score 0.5 point only correct naming of quadrilateral Open-Response QuestionQuadrilateralConsider the following points: A(-2,1) , B( 2, - 2) , C( 8,7) , D ( 4,10) a) Graph the quadrilateral ABCD. b) Find the slope of each side of the quadrilateral. c) Find the perimeter of quadrilateral ABCD. d) What is the most precise name for the quadrilateral ABCD? Justify your choice.Program of Studies: MA-HS-G-S-CG1 “Students will use the coordinates of two points on a line to determine its slope and use slope to express the parallelism and perpendicularity of lines.”Program of Studies: MA-HS-G-S-CG3 “Students will find the distance between two points using their coordinates and the Pythagorean theorem or the distance formula.”Program of Studies: MA-HS-G-S-CG6 “Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, spherical systems) to analyze geometric situations.”Core Content Code: MA-HS-3.3.1 “Students will apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., parallel and perpendicular lines, the distance between two points, the slope of a segment).” Open-Response QuestionCorrect AnswersQuadrilateral Consider the following points: A(-2,1) , B( 2, - 2) , C( 8,7) , D ( 4,10) a) Graph the quadrilateral ABCD. b) Find the slope of each side of the quadrilateral. -3 3 -3 3 mAB = ; mBC = ; mCD = ; mAD = 4 2 4 2 c) Find the perimeter of quadrilateral ABCD. AB = 5 ; BC = 117 ; CD = 5 ; AD = 117P =2(5) + 2( 117) = 10 + 2 117 = 31.63 d) What is the most precise name for the quadrilateral ABCD? Justify your choice. The most precise name for quadrilateral ABCD is PARALLELOGRAM. Both pair of opposite sides are parallel, but slopes are not opposite reciprocals, so the angles are NOT right angles. Therefore, the quadrilateral can’t be rectangle. In addition, the lengths of the four sides are not congruent, so it is not a rhombus. Writing an Equation for an Arithmetic Sequence a1 = first term d= common difference th n = n term of the sequence an = a1 + (n – 1)d an = a1 + (n – 1)d Formula for the nth term of an Arithmetic Sequence Follow the steps below to write an equation to represent the arithmetic sequence described. Loans: The following arithmetic sequence represents the amount of money that Ed owes his brother each week after he borrows the same amount: 2, -2, -6, -10, … a) Write an equation for the nth term of the sequence. Determine the common difference th Substitute into the n term formula. a1 = ______d = ______an = a1 + (n – 1)d Simplify the equation for the nth term. b) Use the equation to find how much Ed owes his brother after 25 weeks. Replace n with 25 in your equation for the nth term. Simplify. Graphic Organizer by Ann Rourk Williamstown Jr/Sr High School MULTIPLYING POLYNOMIALS Product of First Product of Product of Product of Last + + + Terms Outer Terms Inner Terms Terms= + + +(b + 8)(b + 2) = + + += + += + + +(x + 9)(x – 4) = + + += + = + + +(4x + 7)(3x – 8) = + + +=  = + + +(3y + 6)(y – 2) = + + += Try the following on your own:1) (x + 2)(x + 3) 2) (p – 4)(p + 2)3) (3x + 1)(4x + 3) 4) (a – 3b)(2a 5b) How do I find EXAMPLE the inverse of f(x) = 3x2 - 8 a function?Switch to the y = notation from the f(x) =.Exchange x and y in the problem and solve for y.Rewrite as f-1(x) = .Graphic Organizer by Dale Graham and Linda Meyer Thomas County Central High School; Thomasville GAB opposite leg What are the sin A  hypotenuse three basic trigonometry sin A = _____ functions? sin B = _____ adjacent leg cos A  hypotenuse c cos A = _____ a cos B = _____ opposite leg tan A  adjacent leg tan A = _____ tan B = _____ A b C Chief SohCahToa Graphic Organizer by Dale Graham and Linda Meyer Thomas County Central High School Thomasville, Ga.

Schools That Lead the Way

Details

Download

Copyright

We respect the copyrights and intellectual property rights of all users. All uploaded documents are either original works of the uploader or authorized works of the rightful owners.

Support