MVP IM 2 *Updated Version*

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1 MVP IM 2 *Updated Version* MVP IM 2 *Updated Version* Module 1: Quadratic Functions Module 2: Structures of Expressions Module 3 Quadratic Functions Module 4: More Functions, More Features Module 5: Geometric Figures Module 6: Similarity and Right Triangle Trigonometry Module 7: Circle from a Geometric Perspective Module 8: Circles and Other Conics Modules 9: Probability

2 Module 1: Quadratic Functions Task # Title Topic Old Version Ready-Set-Go 1.1 Something to talk about - Develop An introduction to quadratic functions, designed to elicit representations and surface a new type of pattern and change 1.1 R: Distributive Property S: Recognizing linear exponential and quadratic functions G: Rates of change from multiple representations 1.2 I Rule - Solidi ication of quadratic functions begins as quadratic patterns are examined in multiple representations and contrasted with linear relationships 1.2 R: Distributive Property S : Comparing Area and perimeter G : Greatest Common Factor 1.3 Scott s Macho March - Focus speci ically on the nature of change between values in a quadratic being linear 1.3 R : Multiplying two binomials S : Distinguishing between linear and quadratic patterns G: Interpreting recursive equations to write a sequence 1.4 Rabbit Run - Focus on maximum/minimum point as well as domain and range for quadratics 1.4 R : Applying slope formula S: Investigating perimeters and areas G: Comparing linear and exponential rates of change Pg. 1

3 1.5 Tortoise and Hare - Comparing quadratic and exponential functions to clarify and distinguish between each type of growth as well as how that growth appears in each of their representations 1.6 R :Recognizing Functions S :Comparing rates of change in linear, quadratic, and exponential functions G :Identify domain and range from a graph 1.6 How does it Grow - Incorporating quadratics with the understandings of linear and exponential functions 1.7 R : Transforming lines S: Distinguish between linear, exponential and quadratic functions G: Matching function representations Pg. 2

4 Module 2: Structures of Expressions Task # Title Topic Old Version Ready-Set-Go 2.1 Transformers: Shifty y s A Develop 2.2 Transformers: More Than Meets the y s A 2.3 Building the Perfect Square A Develop 2.4 A Square Deal A 2.5 Be There or Be Square A Connecting transformations to quadratic functions and parabolas Working with vertex form of a quadratic, connecting the components to transformations Visual and algebraic approaches to completing the square Visual and algebraic approaches to completing the square Visual and algebraic approaches to completing the square R: Finding Key features in the graph of quadratic expression S: Transformations on quadratics G: Finding Square roots R: Standard form of quadratic equations S: Graphing a standard. Writing the equation of a transformed parabola in vertex form G: Features of Parabolas R : Graphing lines using the intercepts S: Completing the squares by paying attention to the parts G: Features of horizontal and vertical lines R: Find y-intercepts in parabolas S: Completing the square when a>1 G: Evaluating functions R : Recognizing Quadratic Equations S: Changing from standard form of quadratic to vertex form G : Writing Recursive equations for quadratic functions Pg. 3

5 2.6 Factor Fixin A Connecting the factored and expanded forms of a quadratic R : Creating Binomial Quadratics S: Factoring Trinomials G: Taking the square root of perfect squares 2.7 The x Factor A Connecting the factored and expanded or standard forms of a quadratic R : Exploring the density of the number line S: Factoring Quadratics G: Graphing Parabolas 2.8H The Wow Factor A Connecting the factored and expanded forms of a quadratic when a-value is not equal to one *NEW* R : Comparing arithmetic and geometric sequences S: Writing an area model as a quadratic expression. Factoring quadratic expressions when a>1 G: Finding the equation of the line of symmetry of a parabola 2.9 Lining Up Quadratics A Focus on the vertex and intercepts for quadratics R : Multiplying Binomials using Two-Way tables S: Factored Form of a Quadratic Function G: Vertex Form of a Quadratic Equation 2.10 I ve Got a Fill-in A Building luency in rewriting and connecting different forms of a quadratic R : Quadratic written in multiple forms S : Finding multiple representations of a quadratic G: Factoring Quadratics Pg. 4

6 Module 3 Quadratic Functions Task # Title Topic Ready-Set-Go 3.1 Experimenting with Exponents - Develop 3.2 Half Interested More Interesting Radical Ideas Throwing an Interception - Develop 3.6 Curbside Rivalry - Examining the values of continuous exponential functions between integers Connecting radical and rules of exponents to create meaning for rational exponents Verifying that properties of exponents hold true for rational exponents Becoming fluent converting between exponential and radical forms of expressions Developing the Quadratics formula as a way for finding x-intercepts and roots of quadratic functions Examining how different forms of a quadratic expression can facilitate the solving of quadratic equations. R Comparing additive and Multiplicative patterns S: Evaluate Expression with Rational Exponents G: Simplifying Exponents R: Simplifying Radicals S: Finding arithmetic and geometric means G: Simplifying Exponents R: Meaning of Exponents S: Finding equivalent expressions and functions G: Using rules of exponents R: Standard form Factored Quadratic form S: Radical notation and radical exponents G: x-intercepts for linear, exponential and Quadratics functions R: Converting measurement of area and perimeter S: Transformations and parabolas, symmetry and parabolas G: Function Notation and Evaluating Functions R: Finding x-intercepts for linear equations S: Solving Quadratics and connecting Quadratics with Area G: Factoring Expressions Pg. 5

7 3.7 Perfecting my Quads To be Determined - Develop 3.9 My Irrational and Imaginary Friends inumbers Quadratic Quandaries - Develop 3.12H Complex Computations H All Systems Go! - Building fluency with solving quadratic equations Surfacing the need for complex numbers as solutions for some quadratic equations Extending the real dna complex number systems Examining the arithmetic of real and complex numbers Solving Quadratic Inequalities Representing the arithmetic of complex numbers on the complex plane. Solving system of equations using inverse Matrices R: Symmetry and Distance S: Solving Quadratics Efficiently G: Solving Quadratics and finding essential features. Solving systems of equations R: Simplifying radicals S: Determine nature of Quadratic root G: Solving quadratics by factoring and quadratic formula R: Classifying numbers S: Simplifying radicals and imaginary numbers G: Solving Quadratic Equations R: Attributes of quadratics and other functions S: Operations on different number sets G: Solving quadratics. Simplifying radicals R: Factoring Polynomials S: Solving quadratic Inequalities G: Vertex form for Quadratics R: Solving systems of linear equations S: Operations with imaginary numbers G: Solving Quadratics R: Rational exponents and solving Quadratics S: Solving 3x3 systems with Matrices G: Solving Quadratics Pg. 6

8 Module 4: More Functions, More Features Task # Title Topic Ready-Set-Go 4.1 Some of This, Some of That -Develop 4.2 Bike Lovers More Functions with Features Reflections of a Bike Lover - practice 4.5 What s your Pace? - Develop 4.6 Bernie s Bikes More Features, More Functions - Use prior knowledge of functions to develop understanding of piecewise functions Solidification of graphing and writing equations for piecewise functions Incorporating absolute value as piecewise-defined functions Fluency with domain, range, absolute value and piecewise-defined functions Comparing input and output values to develop understanding of inverse functions ing inverse functions using multiple representations Using prior knowledge to identify features of a function as well as to create functions when given features R: Reading function values in a piece-wise graph S: Writing piece-wise defined functions G:Using point-slope formula to write the equation of lines R: Solving absolute value equations S: Reading the domain and range from a graph G: Transformations on quadratic functions R: Finding x-intercepts for a quadratic function S: Absolute value equations G: Interpreting absolute value R: Reflecting images S: Absolute value and non-linear functions G: Simplifying radical expressions R: Square roots S: Inverse functions G: Multiplying Square roots R: Identifying features of functions S: Square root functions G: Solving literal equations for a variable R: Geometric symbols S: Features of functions G: Inverse Functions Pg. 7

9 Module 5: Geometric Figures Task # Title Topic Ready-Set-Go Videos 5.1 How Do You Know That? - Develop 5.2 Do you See What I See? - Develop 5.3 It s All in Your Head- 5.4 Parallelism Preserved - Develop 5.5 Conjectures and Proof Parallelogram Conjectures and Proof - An introduction to proof illustrated by the triangle interior angle sum theorem Reasoning from a diagram to develop proof like arguments about lines and angles, triangles and parallelograms Organizing proofs about lines, angles and triangles using flow diagrams and two column proof formats Examining parallelism from a transformational perspective Generating conjectures from a diagram and writing formal proofs to prove the conjectures about lines, angles and triangles Proving conjectures about parallelograms R: Geometric Figures S: Linear Pairs G: Algebra of linear pairs R: Symbols in geometry S: Construct midpoint, perpendicular bisectors, and angle bisector. G: Translations, reflections, and rotations R: Congruence statements and sketches S: Organizing proofs G: Transformations R: Special Quadrilaterals S: Transformation preservations G: Identify congruence patterns in triangles R Properties of quadrilaterals S: Parallel lines with transversals, vertical angles, and exterior angles of a triangle G: Complementary and supplementary angles R: Sketching quadrilaterals based on specific features S: Properties of parallelograms G: Using mathematical symbols Pg. 8

10 5.7 Guess My Parallelogram Denters of a Triangle - Identifying parallelograms from information about the diagonals Reading and writing proofs about the concurrency of medians, angle bisectors and perpendicular bisectors of the sides of a triangle R: Constructing perpendicular bisectors and angle bisectors S: Testing for parallelograms G: Features of triangles and quadrilaterals R:Test prep S: Writing proofs G: The algebra of parallelograms Pg. 9

11 Module 6: Similarity and Right Triangle Trigonometry Task # Title Topic Ready-Set-Go Videos 6.1 Photocopy Faux Pas- Develop 6.2 Triangle Dilations Similar Triangles and Other Figures Cut by a transversal Measured Reasoning - Describing the essential of a dilation Examining proportionality relationships in triangles that are known to be similar to each other based on dilations Comparing definitions of similarity based on dilations and relationships between corresponding sides and angles Examining proportional relationships of segments when two transversals intersect sets of parallel lines Applying theorems about lines, angles, and proportional relationships when parallel lines are crossed by multiple transversals R Scale factors for similar shapes S Dilations in real world contexts G Rates of change of linear, exponential and quadratic R angle relationships S Creating dilations and examining their parts G Classify the transformation and define it. R Solving proportions S Proving similarity G Ratios in dilated polygons R Pythagorean Theorem and Ratios for similar triangles S Proportionality of transversals across parallel lines G Similarity in slope triangles R Pythagorean theorem and ratios of similar triangles S Using parallel lines and angle relationships to find missing values G Solve equations including those including proportions Pg. 10

12 6.6 Yard Work in Segments Pythagora by Proportions Are Relationships Predictable - Develop 6.9 Relationships with Meaning Finding the Value of a Relationship Solving Right Triangles Using Trigonometric Relationships - Applying understanding of similar and congruent triangles to find midpoint or any point on a line segment that partitions the segment in a given ratio Using similar triangles to prove the Pythagorean theorem and theorems about geometric means in right triangles Developing and understanding of right triangle trigonometric relationships based on similar triangles Finding relationships between sine and cosine ratios for right triangles, including the Pythagorean identity Solving for unknown values in right triangles using trigonometric ratios setting up and solving right triangles to model real world contexts. R Averages and center S Midpoints of segments and proportionality of sides in embedded similar triangles G Proportionality with parallel lines R Determining similarity and congruence in triangles S Similarity in right triangles G Using Similarity and parallel lines to solving problems R Properties of Right Triangles S Creating Trigonometric Ratios for Right Triangles G Factoring Quadratics R Solving equations and proportions S trigonometric Ratios and Connections between them G Slope as a ratio R Modeling contexts with visuals S Solving triangles using Trigonometric Ratios G Trigonometric Ratios R Similar triangles and proportional relationships with parallels S Solving trigonometric ratios and pythagorean theorem G Applying trigonometric ratios and identities to solve problems Pg. 11

13 Module 7: Circle from a Geometric Perspective Task # Title Topic Ready-Set-Go Vidoes 7.1 Centered - Develop Searching for center of rotation using perpendicular bisectors as a tool. R Scale factors and center of dilations S Finding the center of rotation G Finding the circumference and area for circles. 7.2 Circle Dilations Cyclic Polygons Planning the Gazebo - Develop Proving circles are similar. Examining relationships between central angles, inscribed angles, circumscribed angles and their arcs. Developing formulas for perimeter and area of regular polygons. R Finding missing angles, rotational symmetry, and regular polygons S Dilations, proportionality between similar figures. G Finding lines of reflection, finding the center of a circle. R Symmetry, Trigonometric Ratios S Angles and how they connect with arcs. G Finding length of arcs R Radius and Area of Circumference S Finding area and perimeter of regular polygons G Find area of a sector of a circle 7.5 From Polygons to Circles - Justifying formula for circumference and area of circles using intuitive limit arguments. R Angles and Arcs of circles, ratios with similar shapes S Connecting polygons with circles G Finding arc length as a distance 7.6 Circular Reasoning - Practicing circle relationships R Measurement conversion and scaling Pg. 12

14 7.7 Pied - Develop Using Proportional reasoning to calculate arc length and area of sectors S Arc Length, arc measure, central and inscribed angles G Area and Distance for composed figures R Circumference and ratios S Fluency with area and circumference and sectors of circles G Finding area and decomposing area 7.8 Madison s Round Garden - and Develop 7.9 Rays and Radians - and 7.10 Sand Castles H Cavalieri to the Rescue - Using the ratio of arc length of radius to develop radians as a way of measuring angles. Converting between degree measures and radian measure of an angle. Working with volume and scaling to see relationships. Working with Cavalieri s principle R Finding volume and surface area S Radians G Same angles with different size sectors and arcs, accompanying ratios R Angles, arcs and areas S Converting between radians and degrees G Finding centers of rotation R Finding the center of a circle S Finding surface area and volume G Radian and degree conversions; sectors of circles. R Using the distance formula S Applying Cavalieri s theorem G Congruent and similar solids Pg. 13

15 Module 8: Circles and Other Conics Task # Title Topic Ready-Set-Go Vidoes 8.1 Circling Triangles -Develop 8.2 Getting Centered Circle Challenge Directing our Focus - Develop 8.5 Functioning with Parabolas Turn it Around - Deriving the equation of a circle using the pythagorean Theorem Completing the square to find the center and radius of a circle given by an equation Writing the equation of a circle given various information Derive the equation of a parabola given a focus and directrix Connecting the equations of a parabolas to prior work with quadratic functions Writing the equation of a parabola with a vertical directrix, and constructing an argument that all parabolas are similar R: Special products and factors. S: Writing the equations of circles. G: Verifying pythagorean triples. R Making perfect square trinomials S Writing equations of circles with center (h,k) and radius r. G Verifying if a point is a solution. R Finding the distance between 2 points. S Writing equations of a circle. G Finding the middle term in perfect square trinomials. R Graphing quadratics S Sketching parabolas from a conic definition G Writing the center and radius of a circle. R Standard form of a quadratic S The equation of a parabola based on the geometric definition G The maximum or minimum value of the quadratic. R Review of circles. S Writing equations of horizontal parabolas. G: Identifying key features of a quadratic Pg. 14

16 8.7H Operating on a Shoestring - 8.8H What happens if? - Build understanding of the definition of a parabola as the set of all points equidistant from a given point and a line To develop the definition of a hyperbola as the set of all points in the plan such that the difference between the distances from the point to each of the two foci is constant. written in vertex form. R Solving radical equations S Graphing Ellipses G Point-Slope form of a line. R Identifying foic sections by their equations. S Graphing hyperbolas G Writing the equations of conic sections in standard form. Pg. 15

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18 Modules 9: Probability Task # Title Topic Ready-Set-Go Vidoes 9.1 TB or not TB - Develop 9.2 Chocolate Vs Vanilla - Estimating conditional probabilities and interpreting the meaning of a set of data Examining conditional probability using multiple representations. R Venn diagrams, cated and read. S Interpret tree diagram, making observations of probability G Basic probability R Analzying data in a Venn Diagram S Writing conditional statements from two-way tables G Fractions, percents and operations. 9.3 Fried Freddy s - Using sample to estimate probabilities R Independent and dependent events. S Additional rule, interpreting a Venn Diagram. G Equivalent ratios and proportions. 9.4 Visualizing with Venn - Creating Venn diagrams using data while examining the addition rule for probability R Products of probabilities, multiplying and dividing fractions. S addition rule for probability G Writing conditional statements from two-way tables Pg. 17

19 9.5 Freddy Revisited Striving for Independence - Examining independence of events using two-way tables Using data in various representations to determine independence. R Quadratic function review S Independence G Probabilities from two-way tables R End of year review S Representing independent events in Venn Diagrams G Conditional probability and independence Pg. 18