School Year at-a-glance
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1 MVP IM 2 Honors School Year at-a-glance Quarter 1 Aug. 6 - Oct. 5 Quarter 3 Jan. 7 - Mar. 15 Module 5 Geometric Figures 20 Days Module 2 Structure Of Expressions Connecting Quadratics In Various Forms 15 Days Module 6 Similarity & Right Triangle Trigonometry 24 Days Module 3 Solving Quadratic And Other Equations 25 Days Quarter 2 Oct.8 - Dec. 14 Quarter 4 Mar May 24 Module 9 Probability 15 Days Module 4 More Functions, More Features 15 Days Module 1 Quadratic Functions 12 Days Module 7 Circles: A Geometric Perspective 19 Days Module 2 Structure Of Expressions H,K Shifts, Vertex Form, And Completing The Square 12 Days Module 8 Circles And Other Conics As time allows Review & Finals 5 Days Review & Finals 5 Days
2 In this Document Student support page: Graphing Calculators Tasks denoted with require the use of graphing technology Desmos Geogebra R-S-G Ready- Get ready for upcoming lessons Set - Reinforce what was learned in current Task Go - Practice previously-learned skills
3 Module 5: Geometric Figures (20 Days) 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 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 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 5.5 Claims and Conjectures Justification and Proof - Practice 5.7 Parallelogram Conjectures and Proof Guess My Parallelogram - Practice 5.9 Centers of a Triangle - Practice Generating conjectures from a diagram about lines, angles, and triangles. Write formal proofs to prove conjectures about lines, angles and triangles. Proving conjectures about parallelograms 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 Properties of quadrilaterals S: Parallel lines with transversals, vertical angles, and exterior angles of a triangle G: Complementary and supplementary angles R Recalling features of rigid-motion transformations S Solving for missing angles G Connecting a piecewise defined equation with the corresponding absolute value equation. R: Sketching quadrilaterals based on specific features S: Properties of parallelograms G: Using mathematical symbols 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
4 Module 6: Similarity and Right Triangle Trigonometry (24 days) 6.1 Photocopy Faux Pas- Develop (1 day) 6.2 Triangle Dilations Similar Triangles and Other Figures - (3 days) 6.4 Cut by a transversal Measured Reasoning - Practice (1 day) 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 One day for extra practice on using theorems about parallel lines crossed by multiple transversals Quiz Yard Work in Segments - (2 days) 6.7 Pythagora by Proportions - Practice 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 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
5 6.8 Are Relationships Predictable - Develop Developing and understanding of right triangle trigonometric relationships based on similar triangles R Properties of Right Triangles S Creating Trigonometric Ratios for Right Triangles G Factoring Quadratics One day for extra practice on special right triangles 6.9 Relationships with Meaning - (2 days) One day for extra practice on sine and cosine ratios for right triangles 6.10 Finding the Value of a Relationship - One day fo r extra practice on solving for unknowns in right triangles 6.11 Solving Right Triangles Using Trigonometric Relationships - Practice Finding relationships between sine and cosine ratios for right triangles, including the Pythagorean identity Solving for unknown values in right triangles using trigonometric ratios Practice setting up and solving right triangles to model real world contexts. 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
6 Modules 9: Probability (15 days) 9.1 TB or not TB - Develop 9.2 Chocolate Vs Vanilla Fried Freddy s Visualizing with Venn Freddy Revisited - (1 day) 9.6 Striving for Independence - Practice Estimating conditional probabilities and interpreting the meaning of a set of data Examining conditional probability using multiple representations. Using sample to estimate probabilities Creating Venn diagrams using data while examining the addition rule for probability Examining independence of events using two-way tables Using data in various representations to determine independence. 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. R Independent and dependent events. S Additional rule, interpreting a Venn Diagram. G Equivalent ratios and proportions. R Products of probabilities, multiplying and dividing fractions. S addition rule for probability G Writing conditional statements from two-way tables 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
7 Module 1: Quadratic Functions (12 Days) 1.1 Something to talk about - Develop (1 day) 1.2 I Rule Scott s Macho March Rabbit Run - (1 day) 1.5 Tortoise and Hare How does it Grow - Practice An introduction to quadratic functions, designed to elicit representations and surface a new type of pattern and change Solidification of quadratic functions begins as quadratic patterns are examined in multiple representations and contrasted with linear relationships Focus specifically on the nature of change between values in a quadratic being linear Focus on maximum/minimum point as well as domain and range for quadratics 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 Incorporating quadratics with the understandings of linear and exponential functions R: Distributive Property S: Recognizing linear exponential and quadratic functions G: Rates of change from multiple representations R: Distributive Property S: Comparing Area and perimeter G: Greatest Common Factor R: Multiplying two binomials S: Distinguishing between linear and quadratic patterns G: Interpreting recursive equations to write a sequence R: Applying slope formula S: Investigating perimeters and areas G: Comparing linear and exponential rates of change R:Recognizing Functions S:Comparing rates of change in linear, quadratic, and exponential functions G:Identify domain and range from a graph R: Transforming lines S: Distinguish between linear, exponential and quadratic functions G: Matching function representations
8 Module 2: Structures of Expressions Break down of Module A Days (Semester 1) B Days (Semester 2) 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 (3 days) 2.4 A Square Deal A (3 days) 2.5 Be There or Be Square A Practice 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 End Semester 1
9 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 (3 days) 2.9 Lining Up Quadratics A Connecting the factored and expanded forms of a quadratic when a-value is not equal to one Focus on the vertex and intercepts for quadratics 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 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 Practice (1 day) Building fluency 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
10 Module 3 Quadratic Functions (25 Days) 3.1 The In- Betweeners Develop Examining the values of continuous exponential functions between integers R Comparing additive and Multiplicative patterns S: Evaluate Expression with Rational Exponents G: Simplifying Exponents 3.2 Half Interested More Interesting - (1 day) 3.4 Radical Ideas - Practice (3 days) 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 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 Quiz Throwing an Interception - Develop (3 days) Developing the Quadratics formula as a way for finding x-intercepts and roots of quadratic functions R: Converting measurement of area and perimeter S: Transformations and parabolas, symmetry and parabolas G: Function Notation and Evaluating Functions 3.6 Curbside Rivalry - Examining how different forms of a quadratic expression R: Finding x-intercepts for linear equations
11 (3 days) 3.7 Perfecting my Quads - ( 2 days) + 1 Day Review Quiz To be Determined - Develop can facilitate the solving of quadratic equations. Building fluency with solving quadratic equations Surfacing the need for complex numbers as solutions for some quadratic equations S: Solving Quadratics and connecting Quadratics with Area G: Factoring Expressions 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 3.9 My Irrational and Imaginary Friends inumbers -Practice (1 day) 3.11 Quadratic Quandaries - Develop 3.12H Complex Computations H All Systems Go! - 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: 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
12 Module 4: More Functions, More Features (15 Days) 4.1 Some of This, Some of That -Develop (1 day) 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 - 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 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
13 G: Solving literal equations for a variable 4.7 More Features, More Functions - Practice Using prior knowledge to identify features of a function as well as to create functions when given features R: Geometric symbols S: Features of functions G: Inverse Functions Module 7: Circle from a Geometric Perspective (19 days) 7.1 Centered - Develop (1 day) 7.2 Circle Dilations - (1 day) 7.3 Cyclic Polygons - Searching for center of rotation using perpendicular bisectors as a tool. Proving circles are similar. Examining relationships between central angles, inscribed angles, circumscribed angles and their arcs. R Scale factors and center of dilations S Finding the center of rotation G Finding the circumference and area for circles. 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 7.4 Planning the Gazebo - Develop Developing formulas for perimeter and area of regular polygons. 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 - (2 days) 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
14 7.6 Circular Reasoning - Practice ( 1 day) 7.7 Pied - Develop ( 2 days) 7.8 Madison s Round Garden - Practice and Develop ( 2 days) 7.9 Rays and Radians - and Practice ( days) 7.10 Sand Castles - Practice 7.11 Footprints in the Snad. 7.12H Cavalieri to the Rescue - Practicing circle relationships Using Proportional reasoning to calculate arc length and area of sectors 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 Measurement conversion and scaling 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 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
15 Module 8: Circles and Other Conics (as time allows) 8.1 Circling Triangles -Develop 8.2 Getting Centered Circle Challenge - Practice 8.4 Directing our Focus - Develop 8.5 Functioning with Parabolas - 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 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.
16 8.6 Turn it Around - 8.7H Operating on a Shoestring - 8.8H What happens if? - Writing the equation of a parabola with a vertical directrix, and constructing an argument that all parabolas are similar 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. R Review of circles. S Writing equations of horizontal parabolas. G: Identifying key features of a quadratic 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.
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