MR21 Curriculum Map and Homework Sheet



MR21 Curriculum Map and Homework Sheet

|Lesson |Performance |Topic |Read |Homework |Writing |

| |Indicator | | | | |

|1 |A2.N3 |How do we perform operations with| |Handout |How is the procedure for |

| | |polynomial expressions containing| | |multiplying a pair of binomials|

| | |rational coefficients? | | |(FOIL) similar to using the |

| | | | | |distributive law twice? |

|2 |A2.N3 |How do we divide polynomials? | |Handout |How is the division of a |

| | | | | |polynomial by a binomial like |

| | | | | |the process of long division of|

| | | | | |two numbers? |

|3 |Review |How do we solve first degree | |Handout |Compare the axioms that allow |

| | |equations and inequalities? | | |us to solve an equation to |

| | | | | |those that govern the solution |

| | | | | |of an inequality. |

|4 | |How do we solve and graph | |Handout |Often the result of a |

| | |compound linear inequalities | | |disjunction is a set that has |

| | |involving the conjunction and | | |more elements than the set of a|

| | |disjunction? | | |conjunction. How is it possible|

| | | | | |for an |

| | | | | |“and” situation result in fewer|

| | | | | |elements than and “or” |

| | | | | |situation? |

|5 |A2.A46 |How do we graph absolute value | |Handout |What is the relationship of the|

| | |relations and functions? | | |coefficient a in |

| | | | | |y =[pic]? |

|6 |A2.A1 |How do we solve linear equations | |Handout |What are the common mistakes |

| | |in one variable involving | | |made when solving linear |

| | |absolute values? | | |equations involving absolute |

| | | | | |values? |

|7 |A2.A1 |How do we solve linear absolute | |Handout |When will the graph of the |

| | |value inequalities involving one | | |solution set to an absolute |

| | |variable? | | |value inequality be made up of |

| | | | | |two disjointed sets/continuous |

| | | | | |interval? |

|8 |A2.A7 |How do we factor polynomials? | |Handout |Why is factoring a polynomial |

| | | | | |like a question from the quiz |

| | | | | |show Jeopardy? |

|9 |A2.A7 |How do we factor the difference | |Handout |How is factoring a polynomial |

| | |of two perfect squares and factor| | |completely like reducing a |

| | |polynomials completely? | | |fraction to lowest terms? |

|10 | |How do we solve quadratic | |Handout |What conclusion can be drawn |

| | |equations by factoring? | | |when the product of two factors|

| | | | | |is zero? |

|MR12 Homework Sheet |

|Lesson |Performance |Topic |Read |Homework |Writing |

| |Indicator | | | | |

|11 | |How do we graph the parabola y = |pp.262-263 |Handout |What are the steps for graphing|

| | |ax2 + bx +c? | | |a parabola? |

|12.1 |A2.A4 |How do we solve and graph a |pp.30-34 |p. 35 #7,8,11,14,16 |How can the graphing calculator|

| | |quadratic inequality | |p. 37 #3,5, 7 |be used to verify the solution |

| | |algebraically? | | |set of its related quadratic |

| | | | | |inequality? |

|12.2 |A2.A4 |How do we solve and graph a |pp.233-235 |p.237 # 38, 39, 40, 41,42 | |

| | |quadratic inequality | |p. 37 #9, 11, 12 | |

| | |algebraically? | | | |

|13 |A2.A4 |How can we use the graph of a |pp.233-235 |p.238 #44, 45, 47, 50 |How do we determine what |

| | |parabola to solve quadratic | |p.37 # 6,8, 10 |x-values to use in |

| | |inequalities in two variables? | | |order to create a complete |

| | | | | |graph of the parabola? |

|14 |A2.A4 |How do we solve more complex | |Handout |What are some common mistakes |

| | |quadratic inequalities? | | |made when solving quadratic |

| | | | | |inequalities? |

|15 |A2.A13 A2.N2 |How do we simplify radicals? |pp. 88-93 |pp.93-94 #7,8,15,19,45 |Describe how you would |

| | | | |p.37 # 13,14 |recognize an irrational number?|

|16 |A2.A14 |How do we add and subtract |pp.94-96 |p.97 #4,7, 10, 16, 22,23, 38 |Why is x6 a perfect square |

| |A2.N2 |radicals? | |p.37 #15 |monomial and |

| |A2.N4 | | | |x 9 not a perfect square |

| | | | | |monomial? |

|17 |A2.A14 | How do we multiply and divide |pp.98-100 |p.101 #4, 8,13, 22,32 |Compare operations with |

| |A2.N2 |radicals? |pp.102-103 |p.103 #5,8,11,18 |radicals to operations with |

| |A2.N4 | | |p.37 # 16 |monomials. In what ways are |

| |A2.N5 | | | |they the same or different? |

|18.1 |A2.A15 |How do we rationalize a fraction |pp.104-107 |p.108 |Why is it the convention to |

| |A2.N5 |with a radical denominator | |#11,12, 14,19,21 |rationalize denominators? |

| | |(monomial or binomial)? | |p. 37 #17,18 | |

|18.2 |A2.A15 |How do we rationalize a fraction | |pp.108 #20, 22, 23, 25,32 | |

| |A2.N5 |with a radical denominator | |p.37 # 19 | |

| | |(monomial or binomial)? | | | |

|19 |A2.A24 |How do we complete the square? |pp.187-191 |p.192 #15,18,21,22 |Why do we refer to numbers |

| | | | |p. 37 #21,22 |like: 16, 25 and 100 as perfect|

| | | | | |“square” numbers? Explain |

| | | | | |whether or not your answer to |

| | | | | |this first question also |

| | | | | |applies to perfect square |

| | | | | |trinomials. Give an example of |

| | | | | |a perfect square trinomial. |

|20 |A2.A24 |How do we apply the quadratic |pp.193-195 |p.196 # #3, 4,11 |How is the quadratic formula |

| |A2.A25 |formula to solve quadratic | |p. 37 # 23, 25 |related to the process of |

| | |equations with rational roots? | | |completing the square? |

|21 |A2.A25 |How do we apply the quadratic |pp.193-195 |p.196 #5, 6, 12,13 |How can the graphing calculator|

| | |formula to solve quadratic | |p. 37 #26, 27 |be used to verify the solution |

| | |equations with irrational roots? | | |set of the related quadratic |

| | | | | |function? |

|22 | |How do we apply the quadratic |pp.193-195 |pp.196-197 #19, 20,21,26 |In what real world situation |

| | |formula to solve verbal problems?| |p.37 #28, 29 |would both roots be a valid |

| | | | | |answer? |

|23 |A2.N6 |What are properties of complex |pp. 203-207 |p.208 # 4,7, 8, 19, |Describe how you would |

| |A2.N7 |numbers? | |20,35,36,43 |recognize a complex number. |

| | | | |p. 37 #30 | |

|24 |A2.N8 |How do we add and subtract |pp.209-215 |p.215-216 #3,6,7, 16,17 |Complex numbers are a new group|

| |A2.N9 |complex numbers? | |p. 37 # 31, 32 |of numbers yet they behave like|

| | | | | |variables or radicals under |

| | | | | |binary operations. Describe |

| | | | | |these similarities. |

|25 | |How do we multiply complex |pp.209- 215 |pp.216 # 18, 19, 26, 29, 34 |How are conjugate pairs related|

| | |numbers? | |p. 37 #33,34 |to the conjugate pairs we found|

| | | | | |we |

| | | | | |rationalizing the denominator |

| | | | | |of a fraction with an |

| | | | | |irrational binomial |

| | | | | |denominator? |

|26 |A2.N8 |How do we divide complex numbers?|pp.209-215 |p.216 #38, 40, 46,47,50, |How do conjugate pairs help to |

| |A2.N9 | | |53,56 |simplify fractions with complex|

| | | | |p. 37 #35 |denominators? |

|27 |A2.A2 |How do we find complex roots of a|pp.217-218 |p.219 #3,4,8,13, 14 |Explain why some quadratic |

| | |quadratic equation using the | |p. 37 #36,37 |equations have imaginary or |

| | |quadratic formula? | | |complex roots. |

|28 |A2.A2 |How do we use the discriminant to|pp.198-201 |p.202 |Justify the use of the |

| | |determine the nature of the roots| |15, 17,19, 20,25 |discriminant as the quickest |

| | |of a quadratic equation? | |p.37 #38,39 |way to determine the nature of |

| | | | | |the roots of a quadratic |

| | | | | |equation. |

|29 |A2.A20 |How do we find the sum and |pp.219-222 |p.223 #4,7,10,13,19,25 |We are often asked to find the |

| |A2.A21 |product of the roots of a | |p. 38 #42 |equation given its roots. How |

| | |quadratic equation? | | |does the relationship between |

| | | | | |the sum and product of the |

| | | | | |roots make it easier |

| | | | | |to find the equation when the |

| | | | | |roots are complex? |

|30 | |How do we solve quadratic-linear |pp.229-233 |pp.236-237 #4,9,11, 13, 17 |Describe the significance of |

| | |systems of equations using the | |p. 38 #43 |choosing the correct graphing |

| | |graphing calculator? | | |window for a system of |

| | | | | |equations whose solution you |

| | | | | |are |

| | | | | |seeking. Give an example in |

| | | | | |which the window parameters are|

| | | | | |critical. |

|31 |A2.A3 |How do we solve quadratic-linear |pp.229- 233 |pp.236-237 # 18, 19,20, 24, |A quadratic-linear system can |

| | |systems of equations | |34 |have one, two or no solutions. |

| | |algebraically? | |p.38 #44 |By referring to the graphs of a|

| | | | | |quadratic-linear system, |

| | | | | |explain how this is possible. |

|32 |A2.A16 |How do we reduce rational |pp.44-47 |p.48 #12,13, 16, 22,24, 25, |Under what circumstances is the|

| | |expressions? | |26 |expression |

| | | | |p. 117 #2 |[pic]not equal to 1? Explain |

| | | | | |what impact this might have on |

| | | | | |the reduction of a rational |

| | | | | |expression. |

|33 |A2.A16 |How do we multiply and divide |pp. 48-51 |p.52 |If the expression [pic] |

| | |rational expressions? | |#3,5,7, 10,13, 17, 19, 22 |is equal to one, explain why |

| | | | |p. 117 #3 |the expression |

| | | | | |[pic] is not equal to one. What|

| | | | | |is the value of this expression|

| | | | | |and how can this be used to |

| | | | | |reduce a rational expression? |

|34 |A2.A16 |How do we add and subtract |pp.53-56 |p.56 #3,4,6,9,10 |How are adding or subtracting |

| | |rational expressions with like | |p.117 #4,5 |rational expressions with like |

| | |denominators or unlike monomial | | |denominators similar to |

| | |denominators? | | |combining like terms? |

|35 |A2.A16 |How do we add and subtract |pp.53-56 |p.56 #15,16,17,18,19 |Why is it inaccurate to simply |

| | |rational expressions with unlike | |p.117 #6,7 |add the numerators of two |

| | |polynomial denominators? | | |fractions with unlike |

| | | | | |denominators? |

|36 |A2.A17 |How do we reduce complex |pp.61-63 |p.64 #6,7,9, 13,14, 17, 19 |How can the multiplicative |

| | |fractions? | |p.117 # 8, 10 |property of one be used to |

| | | | | |simplify a complex fraction? |

|Lesson |Performance |Topic |Read |Homework |Writing |

| |Indicator | | | | |

|37 |A2.A23 |How do we solve rational |pp.64-69 |p.69 # 4,13,18,19, 20 |Compare and contrast the |

| | |equations? | | |process of combining algebraic |

| | | | | |fractions with solving |

| | | | | |fractional equations. |

|38 |A2.A4 |How do we solve rational |pp.70-73 |p.73 #3,4,8,11,13 |How is the multiplication of |

| |A2.A23 |inequalities? | | |both sides of an inequality |

| | | | | |different from multiplication |

| | | | | |of both sides of an equation? |

|39 |A2.A8 |How do we evaluate expressions |pp.289-291 |p. 292 #16,36,45, 49 |Explain the difference between |

| |A2.A9 |involving negative and rational |pp.293-296 |p. 296- 297 # 9, 14, 18,40,48|the meaning of |

| |A2.A10 |exponents? | | |x1/3 and x−3 . Give an example|

| |A2.A11 | | | |that supports your explanation.|

| |A2.N1 | | | | |

|40 |A2.A22 |How do we find the solution set |pp.108-112 |pp. 112-113 #6,9,10, 16,19, |Sometimes the solution to a |

| | |for radical equations? | |22, 30 |radical equation produces an |

| | | | | |extraneous root. Describe what |

| | | | | |an extraneous root is and tell |

| | | | | |what it is about the process of|

| | | | | |solving radical equations that |

| | | | | |causes the extraneous root to |

| | | | | |occur. |

|41 | |How do we find the solution set |pp.304-305 |p.305 #3,7,8, 12,13,19,20 |How does the process used to |

| | |of an equation with fractional | | |solve an equation with |

| | |exponents? | | |fractional exponents produce |

| | | | | |extraneous roots? How do we |

| | | | | |guard |

| | | | | |against claiming that we have a|

| | | | | |root when it really is an |

| | | | | |extraneous root? |

|42 |A2.A37 |What are relations? | |p. 236-238 # 1,3, 5,6,9,12, |The words input and output are |

| |A2.A39 | | |18 p.94 #10 |often used to describe the |

| |A2.A51 | | | |domain and range of a relation.|

| |A2.A52 | | | |Explain why these words make |

| | | | | |sense and justify why a |

| | | | | |relation is sometimes compare |

| | | | | |to a “machine.” |

|43 |A2.A37 |What are functions? | |pp.245-247 #1,3,10, |Explain the following analogy: |

| |A2.A38 | | |12,14,17,23, 28 p.94 #11 |poodle is to dog as function is|

| |A2.A39 | | | |to relation |

| |A2.A51 | | | | |

| |A2.A43 | | | | |

| |A2.A52 | | | | |

|44 |A2.A39 |How do we use function notation? | |pp.249-250 # 1,4,7, |If function notation is just |

| |A2.A40 | | |13a,14a,15,23,25 p.94 #12 |another way to write “y,” what |

| |A2.A41 | | | |is the reason for inventing |

| |A2.A43 | | | |this notation? |

|45 |A2.A42 |What is composition of functions?| |pp.286-287 # 1,2,5,6,9,10, |Addition is a binary operation.|

| | | | |17, 28 p.94 #13 |Many textbooks refer to |

| | | | | |composition as a binary |

| | | | | |operation. Explain this |

| | | | | |thinking. |

|46 |A2.A44 |How do we find the inverse of a | |pp.292-293 #1,4,8,17,20,23,24|Each function has a domain and |

| |A2.A45 |given relation? | |p.94 #14 |a range. When the inverse of a |

| | | | | |function is found, the domain |

| | | | | |and range are reversed. What |

| | | | | |transformation of the plane is |

| | | | | |created when the x and the y |

| | | | | |values are reversed? What does |

| | | | | |this mean about the |

| | | | | |graphical relationship between |

| | | | | |a function and its inverse? |

|47 |A2.A6 |What is an exponential function? | |pp.479-480 #3,4,5,14 |Compare π to e. |

| |A2.A12 | | |p.203 #55a | |

| |A2.A53 | | | | |

|48 |A2.A12 |What is the inverse of the | |p.490 # 1,10,11 |When we form the inverse of a |

| |A2.A54 |exponential function? | |p.203 #56a |function we interchange the x |

| | | | | |and y. Form the inverse of y=ax|

| | | | | |and describe the difficulty in |

| | | | | |solving for y in this example. |

| | | | | |How do we resolve this |

| | | | | |difficulty? |

|49 |A2.A12 |How do we find the | |p.494 #1,5,13,19, 25, 34, |The technique of logarithms was|

| |A2.A18 |log b a? | |35,37 |invented before the invention |

| |A2.A19 | | |p.203 #58 |of the hand-held calculator. |

| |A2.A28 | | | |What advantage did logarithms |

| | | | | |provide to a world without |

| | | | | |calculators? |

|50 |A2.A19 |How do we use logarithms to find | |p.501 #1,4,7,16,19,22, 25,31 |Explain why logarithms can be |

| | |values of products and quotients?| |p.203 #59 |helpful in finding products and|

| | | | | |quotients but are not helpful |

| | | | | |in finding sums and |

| | | | | |differences. |

|51 |A2.A19 |How do we use logarithms for | |pp.518-520 #2,5,6,15,3235,38 |If logarithms were useful in a |

| | |raising a number to a power or | | |time without calculators, why |

| | |finding roots of numbers? | | |then do we still need to study |

| | | | | |logarithms? |

|52 |A2.A6 |How do we solve exponential | |P530 #1,4,7,10 |Explain how the graph of an |

| |A2.A27 |equations? | |p.203 #60 |exponential function can be |

| | | | | |used to solve specific |

| | | | | |exponential equations. |

|53 |A2.A6 |How do we solve exponential and | |Handout |Describe three ways that 2x=8 |

| |A2.A27 |logarithmic equations? | | |can be solved. |

|54 |A2.A.27 |How do we solve verbal problems | |p.480 #16,17,18 |Jacob has 18 kg of radium. If |

| | |involving exponential growth or | |p.203 #61 |the half-life of radium is 13 |

| | |decay? | | |years, how many years will it |

| | | | | |take until the radium is all |

| | | | | |“gone”? |

|55 | |What are the transformations | |p.207 #3,4 p.211 |Give an example of a |

| | |involving reflections? | |#1,2,3,4,8,12 p.218 #2 |transformation in nature. |

| | | | |p.203 #62 | |

|56 |A2.A46 |What are geometric translations, | |p.225 #4,9 pp.228-229 |Explain how is it possible to |

| | |dilations and rotations? | |#1,5,10,13,15,23 |have a negative constant of |

| | | | |p.203 #63 |dilation? |

|57 |A2.A46 |How do we perform transformations| |Handout |Transformations are mappings |

| | |of the plane on relations and | | |that assign each point on the |

| | |functions? | | |plane onto its image according |

| | | | | |to a rule. Compare each of the |

| | | | | |transformation rules discussed |

| | | | | |in class today. Describe how |

| | | | | |the function and its image are |

| | | | | |the same and how they are |

| | | | | |different. |

|58 |A2.A47 |How do we graph and write the | |Handout |For circles with center at (h, |

| |A2.A49 |equation of a circle? | | |k), explain how the equation |

| |A2.A48 | | | |reflects the fact that the |

| | | | | |circle has been translated from|

| | | | | |the origin. |

|59 |A2.A5 |What is direct and inverse | |pp.281 #1,2,3,6 |Describe a real-life |

| | |variation? | |p.230 #21,23,25 |circumstance that illustrates |

| | | | | |the concept of direct |

| | | | | |variation. Amend your idea to |

| | | | | |illustrate the concept of |

| | | | | |inverse variation. |

|60 |A2.A26 |How do we find the roots of | |Handout |Describe why the exponents of |

| |A2.A50 |polynomial equations of higher | | |each variable term in an |

| | |degree by factoring and by | | |polynomial expression in |

| | |applying the quadratic formula? | | |quadratic form can be written |

| | | | | |in the form of 2n, n and 0 |

| | | | | |where n is an integer. |

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