Deer Valley Unified School District



S5.C1.PO1- Select an algorithm that explains a particular mathematical process; determine the purpose of a simple mathematical algorithm.Teresa wanted to know how to find the altitude of a triangle if the base and area were given in a problem. Which of the following equations would help her solve her problem?P=2l+2wh=2ABh=12ABI=PrtS5.C1.PO2- Analyze algorithms for validity and equivalence recognizing the purpose of the algorithm.Jackson is solving this multi-step equation:-2x-3+4x=5-x+7-8 Which one of the following would be a correct first step in solving this equation?–2x-3+4x=5x+7-8–2x-6+4x=5x+35-8–2x+6+4x=-5x+35-82x+6+4x=5x-35-8S5.C2.PO1- Analyze a problem situation, determine the question(s) to be answered, organize given information, determine how to represent the problem, and identify implicit and explicit assumptions that have been made.A light year is approximately 5,880,000,000,000 miles. The speed of light is about 1.86 x 105 miles/second. How many miles is it from Earth to the star Vega, if Vega is 23 light years away? (Answer in scientific notation.)1.35 x 1014135.24 x 101213.524 x 10121.35 x 1010S5.C2.PO2- Solve problems by formulating one or more strategies, applying the strategies, verifying the solution(s), and communicating the reasoning used to obtain the solution(s).9?1200 ydxA small plane takes off from Stellar Airpark and climbs at a 9? angle with the ground. Without actually finding the distance that it climbs, find the equation that you would use to solve this problem.sin 9°=1200xsin 9°=x1200cos 9°=x1200cos 9°= 1200xS5.C2.PO3- Evaluate a solution for reasonableness and interpret the meaning of the solution in the context of the original problem.Marcus was helping his father build a house and wanted to check to see if the room had right angles, so he used the Pythagorean theorem to check that the diagonal of the room would be the correct length of the hypotenuse of the right triangle formed with the length and the width. (See the picture below.)9 ft11 ftSince Marcus didn’t have a calculator, which method and answer would be most reasonable in house building?92+112=c2;c= 202 ft92+ 112= c2;c= 40 ft92+ 112=c2;c ≈14.2 ft92+ 112=c2 ;c ≈6.3 ftS5. C2. PO4- Generalize a solution strategy for a single problem to a class of related problems; explain the role of generalizations in inductive and deductive reasoning.What is the first step in solving the following equation?x2+3x-18=xTake the square root of both sides.Square both sides.Factor the quadratic equation on the left side.Set the whole equation equal to zero.S5.C2.PO5- Summarize and communicate mathematical ideas using formal and informal reasoning.If a tangent line and a secant line intersect outside a circle then the length of the tangent segment squared equals the product of the whole secant segment and the external secant segment. Use the picture below to determine which equation demonstrates this property.xyz x=y ?zx2=yy+zx2=y?zx= y2?zS5.C2.PO6- Synthesize mathematical information from multiple sources to draw a conclusion, make inferences based on mathematical information, evaluate the conclusions of others, analyze a mathematical argument, and recognize flaws or gaps in reasoning.Which formula could not be used to generate the sequence that begins 9, 16, 25, 36, …?an=n+8an =n+22an= n2+ 4n+4an=an-1+2n+1 given a1=9S5.C2.PO7- Find structural similarities within different algebraic expressions and geometric figures.The area of a rectangle is given by the quadratic expression 2x2-11x-40. If the length of the rectangle is 2x+5, which expression would be the correct width?2x-82x+8x+8x-8S5.C2.PO8- Use inductive reasoning to make conjectures, use deductive reasoning to analyze and prove a valid conjecture, and develop a counterexample to refute an invalid conjecture.Katie claimed that the value of the area of a circle (A=πr2) is never equal to the value of its circumference(C=2πr). Which of these values for radius is a counterexample that shows that Katie’s conjecture is NOT true?r= 5 cmr= 3 cmr= 2 cmr= 1 cmS5.C2.PO9- State the inverse, converse, and contrapositive of a given statement and state the relationship between the truth value of these statements and the original statement.If a parallelogram is a rectangle, then it has congruent diagonals. Which of the following choices is correct based on the given statement?If a parallelogram is not a rectangle, then it does not have congruent diagonals. This is the converse of the given statement and it is true.If a parallelogram is not a rectangle, then it does not have congruent diagonals. This is the converse of the given statement and it is false.If a parallelogram is not a rectangle, then it does not have congruent diagonals. This is the inverse of the given statement and it is true.If a parallelogram is not a rectangle, then it does not have congruent diagonals. This is the inverse of the given statement and it is false.S5.C2.PO10- List related if…then statements in logical order.Put the following conditional statements in logical order.If a number is an integer then it is rational.If a number is a natural (counting) number, then it is a whole number.If a number is a whole number, then it is an integer.If a number is a rational number, then it is a real number.2, 3, 1, 41, 2, 3, 43, 1, 4, 24, 3, 2, 1S5.C2.PO11- Draw a simple valid conclusion from a given if…then statement and a minor premise.Given the following statement and information, choose a valid conclusion.If the measure of an angle is less than 90?, then it is acute.<ABC is 83?<ABC is pretty large.<ABC is obtuse.<ABC is a complimentary angle.<ABC is acute.S5.C2.PO12- Construct a simple formal deductive proof.Study the proof of the parallel lines below, and then give the correct answer for the missing reason in the proof.Given: <1 is supplementary to <41234mnStatementsReasons1. <1 is supplementary to <4.2. <3 and <4 form a linear pair.3. <3 is supplementary to <4.4. <1 ? <35. m // n1. Given2. If two angles form a straight line, they are a linear pair.3. If angles form a linear pair, then they are supplementary.4. If two angles are supplements of the same angle, then they are congruent.5. ______________________________________________Prove: m // nIf corresponding angles are congruent, then the lines are parallel.If alternate interior angles are congruent, then the lines are parallel.If angles are supplementary, then the lines are parallel.If alternate angles are congruent, then the lines are parallel.S5.C2.PO13- Identify and explain the roles played by definitions, postulates, propositions, and theorems in the logical structure of mathematics, including Euclidean geometry.Which statement is not true about postulates, theorems, and definitions?A good definition is reversible, which means it can be written as a true biconditional.A postulate is something that is assumed to be true without proof.A theorem is a statement that can be proven.Postulates, theorems, and definitions cannot be used as reasons in proofs.Answers for Strand 5:S5.C1.PO1- bS5.C1.PO2- cS5.C2.PO1- aS5.C2.PO2- dS5.C2.PO3- cS5.C2.PO4- bS5.C2.PO5- bS5.C2.PO6- aS5.C2.PO7- dS5.C2.PO8- cS5.C2.PO9- cS5.C2.PO10- aS5.C2.PO11- dS5.C2.PO12- aS5.C2.PO13- d ................
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