Liberal High School Lesson Plans

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1 Monday, 5/8/2017 Liberal High School Lesson Plans er:david A. Hoffman Class:Algebra III 5/8/2017 To 5/12/2017 Students will perform math operationsto solve rational expressions and find the domain. How do you find the solution set of a rational expression? rational expression, quotient, polynomial, domain, undefined, numerator, denominator, equivalent, least common multiple, least common denominator, complex rational expression Perform math operations on rational expressions after finding least common denominator, factor, and cancel like terms. ARK Ask Question Choose an item. Choose an item. Notes for ARK:Review ratio, numerator, denominator, and domain of a rational expression Modeling Explaining a Collaboration Notes for TIP/SAP:Cornell notes, Think Aloud, and guided practice over linear and quadratic equations with examples then student collaboration on R5 homework problems, pp , 2-36 every other even and ISS Word Summary Choose an item. Choose an item. Students will explain how to find the domain and solve rational expressions. Tuesday, 5/9/2017 Word Wall Review/Interaction Choose an item. Choose an item. Notes for : Students will perform math operationsto solve rational expressions and find the domain. How do you find the solution set of a rational expression? rational expression, quotient, polynomial, domain, undefined, numerator, denominator, equivalent, least common multiple, least common denominator, complex rational expression Perform math operations on rational expressions after finding least common denominator, factor, and cancel like terms. ARK Inquiry Choose an item. Choose an item. Notes for ARK:Bell work to solve a complex rational expression Questioning Summarizing Collaboration Notes for TIP/SAP:Think Aloud, and guided practice over linear and quadratic equations with examples then student collaboration on R5 homework problems, pp , 2-36 every other even and ISS 6 8 A-B Partner Choose an item. Choose an item. Wednesday, 5/10/2017 Concept Mapping Choose an item. Choose an item. Notes for : Students will simplify radical expressions, rationalize denominators or numerators, convert between exponential and radical notation, and simplify expressions with rational exponents. How do you simplify radical expressions, rationalize them, and simplify expressions with rational exponents? square root, cube root, nth root, index, radical, radicand, principal root, right triangle, legs, hypotenuse, rationalize denominator or numerator, conjugate, rational exponent Use rules for radical expressions and rational exponents.

2 ARK Inquiry Choose an item. Choose an item. Notes for ARK:Bell work with examples of radicals and rational exponents Modeling Explaining a Collaboration Notes for TIP/SAP:Cornell notes with Think Aloud and guided practice on R6 and then student collaboration over R7 homework problems, pp , 2-60 evens, evens, and even ISS 6 8 Graphic Organizer Choose an item. Choose an item. Thursday, 5/11/2017 Word Wall Review/Interaction Choose an item. Choose an item. Notes for : Students will simplify radical expressions, rationalize denominators or numerators, convert between exponential and radical notation, and simplify expressions with rational exponents. How do you simplify radical expressions, rationalize them, and simplify expressions with rational exponents? square root, cube root, nth root, index, radical, radicand, principal root, right triangle, legs, hypotenuse, rationalize denominator or numerator, conjugate, rational exponent Use rules for radical expressions and rational exponents ARK Ask Question Choose an item. Choose an item. Notes for ARK:Bell work with examples of radicals and rational exponents Clarifying Summarizing Collaboration Notes for TIP/SAP:Cornell notes with Think Aloud and guided practice on R6 and then student collaboration over R7 homework problems, pp , 2-60 evens, evens, and even ISS 6 8 A-B Partner Choose an item. Choose an item. Word Wall Review/Interaction Choose an item. Choose an item. Notes for : Friday, 5/12/2017 Distinguish and classify various numbers in the real number system. use interval notation to write a set of numbers, identify properties of real numbers, and find absolute value of a real number, simplify expressions with integer exponents, solve problems using scientific notation, and use rules for order of operations, identify the terms, coefficients, and degree of a polynomial as well as add, subtract, and multiply polynomials; Students will find the domain of a rational function and simplify rational expressions and rational functions in simplest form, perform operations like multiplication, division, addition, and subtraction on rational expressions, simplify complex fractions, and solve fractional equations (equation containing a fraction) and solve life application rate of work problems and uniform motion problems., simplify expressions with rational exponents, write exponential expressions as radical expressions and radical expressions as exponential expressions, and simplify radical expressions that are roots of perfect powers, simplify radical expressions, approximate irrational numbers if the number is not a perfect power, add and subtract radicals, multiply, and divide radical expressions, find the domain of a radical function and graph a radical function, solve equations containing one or more radical expressions and solve application problems with the Pythagorean Theorem, simplify complex numbers and imaginary numbers, add and subtract as well as multiply and divide complex numbersdistinguish and classify various numbers in the real number system. use interval notation to write a set of numbers, Students will solve quadratic equations by factoring, write a quadratic equation given its solutions, and solve quadratic equations by taking square roots, solve quadratic equations by completing the square and by using the quadratic formula, and solve radical and rational equations that have quadratic work embedded, solve quadratic application problems, solve and graph a quadratic inequality in one variable as well as solve and graph polynomial and rational inequalities, and graph a quadratic function after finding the vertex and axis of symmetry as well as find the x- intercepts and zeros of a parabola, graph functions by using vertical and horizontal translations or shifts on a coordinate plane, perform algebraic operations on f(x) and g(x) functions with x as an element of the domain of each function and find the composition of two functions, determine whether a function is one-to-one (1-1), apply the horizontal line test, find the inverse of a function, and use the composition of inverse functions property, identify properties of real numbers, and find absolute value of a real number, simplify expressions with integer exponents, solve problems using scientific notation, and use rules for order of operations, identify the terms, coefficients, and degree of a polynomial as well as add, subtract, and multiply polynomials, compare and contrast linear and quadratic equations as well as solve equations with multiple steps using algebraic principles, perform

3 math operationsto solve rational expressions and find the domain, and simplify as well as solve radical expressions, rationalize the denominator, use conjugates, and simplify rational exponents. Can you simplify a rational expression and find the domain? Can you multiply, divide, add and subtract rational expressions? Can you simplify a fraction whose numerator or denominator contains one or more fractions? Can you solve equations that contain a fraction and work application problems? How do you simplify rational exponents, convert rational exponents to radicals, and vice versa, and simplify radical expressions as roots of perfect powers? How do you simplify radical expressions with no perfect power as well as perform math operations on radicals such as addition, subtraction, multiplication, and division? Can you find the domain of a radical function with real numbers and graph the function? How do you solve radical equations with the Property of Powers as well as application problems for right triangles? How do we simplify and perform math operations on complex numbers? How do you solve, write equations, and solve quadratic equations by taking square roots? How does a quadratic equation differ from a linear equation? How do you solve quadratic equations by completing the square and the quadratic formula? Can you solve a rational equation that will require you to use the quadratic formula?can you set up a quadratic equation and solve it in order to answer an application type question? How do you solve and graph nonlinear inequalities? How are quadratic functions and parabolas related and how do you find the coordinates on a graph? How can you translate a figure or move a figure on the coordinate plane without changing its shape or turning it? What are the effects on the x-coordinates and y-coordinates of the figure in a vertical translation? Horizontal translation? How can you perform various algebraic operations on two functions as well as use composition on two different functions? How can you know if a function is 1-1 and find the inverse of a function as well as composition of inverse functions? Review real number system, interval notation, math properties, absolute value, review exponents, scientific notation, and order of operations; Review of polynomials and how to perform various math operations on them; solve linear and quadratic equations; find the solution set of a rational expression and radical expressions. Numerator, denominator, polynomial, rational expression, function, rational function, evaluate a function, domain, simplest form of a rational expression, Greatest Common Factor, product, reciprocal, factor, LCM, common denominator, complex fraction, rational equation, fractional equation, denominator, LCM, variable expression, undefined solution, rate of work, complete task, uniform motion, rate of speed, rational number, exponent, rational exponent, nth root, radical, index, radicand, exponential expression, radical expression, principal square root, fourth root, fifth root, perfect fourth power, perfect fifth power, square root, perfect square, perfect cube, cube root, radical expression, perfect power (perfect square, cube, fourth root, fifth root, etc.), irrational number, Product Property of Radicals, like terms, Distributive Property, radicands, index or indices, conjugates, Quotient Property of Radicals, simplest form, rationalizing the denominator, radical function, fractional exponent, variable underneath a radical, set of real numbers, domain, interval notation, set-builder notation, index of a radical expression, ordered pairs, graph, radical, radicand, radical equation, Property of Powers, constant, right triangle, hypotenuse, legs, imaginary number, complex number, real part, imaginary part of complex number, quadratic equation, standard form, Principle of Zero Products, second-degree equation, double root, solutions, square roots, radicals, square of a binomial, complex numbers, imaginary numbers, perfect-square trinomial, square of a binomial, coefficient, constant term, completing the square, exact solutions, quadratic formula, discriminant, real and complex solutions, equation expressed in quadratic form, extraneous solution, radical equation, fractional equation, Least Common Multiple (LCM), denominator, variable, integer, uniform motion, geometry problem, quantity, less than, greater than, standard form, intersection, union, solution set, quadratic inequality in one variable, linear factors, zero product property, quadratic function, parabola, input, output, input/output table, vertex, axis of symmetry, x-intercept, zero, solutions, tangent, complex zeros, discriminant, natural numbers, whole numbers, integers, rational numbers, irrational numbers, Translation of a graph, vertical translation, function, constant, vertical shift, horizontal translation, horizontal shift, sum, difference, product, quotient, domain, operations, functions, evaluate, undefined, algebraic expression, composition of functions, output, input, composite, notation, one-to-one function (1-1), horizontal line test, function, ordered pairs, intersect, inverse of a function, coordinates, domain, range, Translation of a graph, vertical translation, function, constant, vertical shift, horizontal translation, horizontal shift, sum, difference, product, quotient, domain, operations, functions, evaluate, undefined, algebraic expression, composition of functions, output, input, composite, notation, one-to-one function (1-1), horizontal line test, function, ordered pairs, intersect, inverse of a function, coordinates, domain, range, real numbers, number line, less than, greater than, element, subset, interval notation, open interval, endpoints, closed interval, closed interval, infinity, negative infinity, commutative, associative, additive identity, additive inverse, multiplicative identity, multiplicative inverse, distributive, absolute value, distance, integer, base, exponent, negative exponent, zero exponent, scientific notation, light-year, grouping symbols, polynomial in one variable, coefficient, terms, leading coefficient, constant term degree, descending order, polynomial in several variables, degree of a term, degree of a polynomial, monomial, binomial, trinomial, like terms, FOIL method, special products of binomials, linear equation, variable, constant, coefficient, quadratic equation, addition principle, subtraction principle, multiplication principle, division principle, principle of zero products, principle of square roots, equivalent, no solution, index, radicand, radical, principal root, rationalize, conjugate, rational exponent Common factors are excluded or removed in rational expressions or functions and prevent division by zero in rational functions because it would be undefined; Factor rational expressions to find common factors to simplify, product of a rational number and its reciprocal equals 1, find common denominator or LCM when adding or subtracting rational expressions and simplify with resulting sum or difference; Choose between one of two

4 methods of solving complex fractions -- use LCM or rewrite numerator and denominator of the complex fraction as a single fraction and then divide numerator by denominator; Use Least Common Multiple of denominators of a fractional equation and apply formulas to solve rate of work and rate of speed problems; use rules of exponents for rational exponents and rules of radicals for radical expressions; Use properties of rules to reduce radicals without perfect powers, combine like terms, use conjugates, and rationalize the denominators with radicals; evaluate a radical function with values after choosing values in the domain and graph ordered pairs by hand and with a graphing calculator then state the domain in interval as well as set-builder notation; check solutions when solving radical equations especially when raising both sides of an equation to an even power; use Pythagorean Theorem to solve right triangles; and square root of a negative number becomes an imaginary number with symbol i; identify real part and imaginary part of a complex number; when multiplying square roots of negative numbers, rewrite radical expressions with i;; combine like terms and use product property; use conjugate when dividing complex numbers; Factor and use the Principle of Zero Products to solve quadratic equations and use Principle of Square Roots to realize some roots are positive and some are negative; follow specific steps for solving a quadratic equation by either the completing the square method or the quadratic formula method. The exact solutions will either be real number solutions or complex number solutions with an imaginary number i, and substitute or replace term that is 1/2 degree by u to see if it is quadratic in form, write in standard form, check solutions to see if one is extraneous, square sides for radical expressions, solve by factoring and check solutions. Use strategies for solving an application problem such as determine the type of problem, choose a variable to represent unknown quantities, write numerical or variable expressions for all remaining quantities, record in a table, determine how quantities are related, and check solutions because a negative number is not a solution; use graphical method, number line, and factoring laws as well as factor by grouping and other steps; find coordinates of a quadratic function in order to graph a parabola by using vertex and evaluating various values of x in a table to find ordered pairs to determine shape of the graph; Describe translation of a graph of f(x) function to g(x) function with a constant(s) as up or down for vertical shift and left or right for a horizontal shift when replacing a variable by another quantity; perform operations such as addition, subtraction, multiplication, and division on two different functions as well as combine functions by using the output of one function as the input for a second function; reinforce concept that in a 1-1 function no two ordered pairs have the same second coordinate; to find the inverse of a function, interchange x and y then solve for y; if two functions are inverses of each other, then their graphs are mirror images with respect to the graph of the line y = x, and use composition of inverse functions property; use Venn diagram to classify sets of real numbers, compare and contrast types of interval notation for sets of numbers, identify math properties, and explain absolute value as distance from zero on a number line; Follow rules of exponents and rules for order of operations; identify number of terms, like terms, degree of a term, perform math operations on polynomials, and use special methods and patterms such as FOIL and special products; use inverse operations and algebraic principles to simplify and solve equations ARK Inquiry Choose an item. Choose an item. Notes for ARK:Questions on radicals, rationalize the denominator, and rational exponents Inquiry Clarifying Collaboration Notes for TIP/SAP:Comprehensive final exam review sheet ISS 6 8 Exit Slip Choose an item. Choose an item. Notes for : Monday, 5/8/2017 Liberal High School Lesson Plans er:david A. Hoffman Class:Geometry 5/8/2017 To 5/12/2017 Students will calculate measures of angles formed by lines intersecting on or inside a circle and find measures of angles formed by lines intersecting outside the circle G.C.4 -- construct a tangent line from a point outside a given circle to the circle. secant, interior angles, intercepted arcs, exterior angles, inscribed angle, tangent, absolute value If vertex of an angle is on the circle, then the angle measure is one half the measure of the intercepted arc. If the

5 vertex is inside the circle, then the angle measure is one half the measure of the sum of the intercepted arc. If the vertex of an angle is outside the circle, then the angle measure is one half the measure of the difference of the intercepted arcs. ARK Ensure Students Understand Lesson Objective Graphic Organizer Choose an item. Notes for ARK:Bell work with diagrams to compare and contrast the vertex of an angle and how segments differ if they are chords, tangents, or secants and any combination of those segments. Writing Clarifying Collaboration Notes for TIP/SAP:Think Aloud on 10.7 Cornell notes study guide and guided practice; Student collaboration on 10.7 practice skills worksheet ISS 6 8 Graphic Organizer Idea Wave Outcome Sentences Students will complete the statement "I discovered or learned that... " Tuesday, 5/9/2017 Notes for : Students will calculate measures of angles formed by lines intersecting on or inside a circle as well as measures of angles formed by lines intersecting outside the circle. G.C.4 -- construct a tangent line from a point outside a given circle to the circle secant, chord, intercepted arcs, interior, sum, vertical angle, tangent, point of tangency, exterior, differenc e When two secants or a secant and a tangent intersect on the circle, the angle measure if one half the measure of the intercepted arc. When two secants intersect inside the circle, the angle measure and its vertical angle is one half the measure of the sum of the intercepted arcs. When two secants, or a secant and a tangent, or two tangents intersect outside the circle, the angle measure is one half the measure of the difference of the intercepted arcs. ARK Ensure Students Understand Lesson Objective Graphic Organizer Choose an item. Notes for ARK:Bell work to portray diagrams of the three different concepts dealing with secants and tangents on, inside, or outside a circle with corresponding intercepted arcs and angle relationships. Writing Explaining a Collaboration Notes for TIP/SAP:Think Aloud on 10.6 Cornell notes study guide and guided practice; Student collaboration on 10.6 practice skills worksheet ISS 6 8 Graphic Organizer 20 Word Summary Choose an item. Wednesday, 5/10/2017 Notes for : Students will write the equation of a circle and graph a circle on the coordinate plane. G.GPE.1 -- Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G.GPE.6 -- Find the point on a directed line segment between two given points that partitions the segment in a given ratio. compound locus, equidistant, center, radius Use distance formula and Pythagorean Theorem to develop an equation for a circle depending upon whether the point is on the circle or at the center. The standard form of the equation of a circle with center at (h, k) and radius r is also called the center-radius form. A technique called completing the square is used for quadratic expressions and then write the equation in standard form to identify the h, k, and r. The Quadratic Formula can also be used besides factoring and completing the square and taking square roots to solve quadratic equations. ARK Inquiry Choose an item. Choose an item. Notes for ARK:Bell work to review distance formula and Pythagorean Theorem to introduce standard form of the equation of a circle.

6 Explaining a Clarifying Collaboration Notes for TIP/SAP:Think Aloud on 10.8 Cornell notes study guide and guided practice; Student collaboration on 10.8 practice skills worksheet ISS 6 8 A-B Partner Idea Wave Choose an item. Thursday, 5/11/2017 Notes for : Students will write the equation of a circle and graph a circle on the coordinate plane. G.GPE.1 -- Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G.GPE.6 -- Find the point on a directed line segment between two given points that partitions the segment in a given ratio. compound locus, equidistant, center, radius Use distance formula and Pythagorean Theorem to develop an equation for a circle depending upon whether the point is on the circle or at the center. The standard form of the equation of a circle with center at (h, k) and radius r is also called the center-radius form. A technique called completing the square is used for quadratic expressions and then write the equation in standard form to identify the h, k, and r. The Quadratic Formula can also be used besides factoring and completing the square and taking square roots to solve quadratic equations. ARK Graphic Organizer Ask Question Choose an item. Notes for ARK:Bell work to review standard equation of a circle with center point at the origin as well as not on the origin Questioning Summarizing Collaboration Notes for TIP/SAP:Think Aloud and guided practice over 10.8 practice worksheet and graphing of circles with a compass on graph paper ISS 6 8 Exit Slip Choose an item. Choose an item. List, Group, Label Concept Mapping Choose an item. Notes for : Friday, 5/12/2017 Students will be able to identify and use parts of circles and solve problems involving the circumference of a circle, use angle measures to find central angles, arc measures of a circle or of congruent circles such as major arcs, minor arcs, and semicircles and find arc lengths, use relationships of corresponding congruent arcs and chords and diameters in a circle or in congruent circles, and find measures of inscribed angles, intercepted arcs as well as measures of angles of inscribed polygons, use properties of tangents and solve problems involving circumscribed polygons, calculate measures of angles formed by lines intersecting on or inside a circle and find measures of angles formed by lines intersecting outside the circle, calculate measures of angles formed by lines intersecting on or inside a circle as well as measures of angles formed by lines intersecting outside the circle, and write the equation of a circle and graph a circle on the coordinate plane. G.CO.1 -- Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.C.1 -- Prove that all circles are similar. G.C.2 -- Identify and describe relationships among inscribed angles, radii, and chords. G.C.5 -- Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Big Idea #14 -- SHAPES & SOLIDS: Two- and three-dimensional objects with or without curved surfaces can be described, classified, and analyzed by their attributes. Big Idea #17 -- MEASUREMENT: Some attributes of objects are measurable and can be quantified using unit amounts. EQ: How do we differentiate the various measurable units of objects and visually represent them in circles? G.MG.3 -- Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios) G.C Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

7 G.CO make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.C.4 -- construct a tangent line from a point outside a given circle to the circle. G.GPE.1 -- Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G.GPE.6 -- Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Circle, center, equidistant, segment, radius, chord, diameter, coplanar, concentric circles, circumference, pi, inscribed, circumscribed, intersection, circumcircle, area, arcs, chords, secant lines, tangent lines, central and inscribed angles, sectors, central angle, minor arc, major arc, semicircle, congruent circles, congruent arcs, degree, perpendicular, bisector, congruent, equidistant, vertex, inscribed angle, intercepted arc, congruent arcs, inscribed polygons, opposite angles, quadrilateral, supplementary, tangent, point of tangency, common tangent, exterior point, congruent tangents, circumscribed polygons, secant, interior angles, intercepted arcs, exterior angles, inscribed angle, tangent, absolute value, secant, chord, intercepted arcs, interior, sum, vertical angle, tangent, point of tangency, exterior, differenc e, compound locus, equidistant, center, radius Label parts of a circle and find circumference with formula by using either radius or diameter, compare central angle with arcs, figure measure of an arc in relation to a circle, and compare circles, figure length of arcs and chords with specific theorems, utilize inscribed angle theorem and inscribed polygons with congruent arcs and congruent angles to show special properties; Draw common tangents to circles if possible and use theorems regarding a tangent line to a circle only if it is perpendicular to a radius at the point of tangency, and use tangents to find missing external lengths and measures in circumscribed polygons; If vertex of an angle is on the circle, then the angle measure is one half the measure of the intercepted arc. If the vertex is inside the circle, then the angle measure is one half the measure of the sum of the intercepted arc. If the vertex of an angle is outside the circle, then the angle measure is one half the measure of the difference of the intercepted arcs, When two secants or a secant and a tangent intersect on the circle, the angle measure if one half the measure of the intercepted arc. When two secants intersect inside the circle, the angle measure and its vertical angle is one half the measure of the sum of the intercepted arcs. When two secants, or a secant and a tangent, or two tangents intersect outside the circle, the angle measure is one half the measure of the difference of the intercepted arcs. Use distance formula and Pythagorean Theorem to develop an equation for a circle depending upon whether the point is on the circle or at the center. The standard form of the equation of a circle with center at (h, k) and radius r is also called the center-radius form. A technique called completing the square is used for quadratic expressions and then write the equation in standard form to identify the h, k, and r. The Quadratic Formula can also be used besides factoring and completing the square and taking square roots to solve quadratic equations. ARK Graphic Organizer Reading Choose an item. Notes for ARK: Questioning Clarifying Collaboration Notes for TIP/SAP:Chapter 10 practice test ISS 6 8 Idea Wave A-B Partner Choose an item. Notes for :