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Common Core Geometry FIRST SEMESTER Proving Lines and Angles Theorems (GEO #9) – 10 days Language of Geometry and Algebraic Intro conditional statements project properties first day of school – Due following week! Midpoint, Segment bisector, Segment Addition Review Angle Vocabulary and Types of Angles/Angle Addition Quiz + Angles created by parallel lines Angles and properties created by parallel lines and perpendicular lines Conditional Statements and Proofs intro (vertical angles, segment/angle addition) Proofs – Proving if 2 || lines…, then alt. int. and corresp angles are congruent Proofs – Proving segment joined by midpoints of triangle is parallel to base Proofs – Proving points on a perpendicular bisector of line are equidistant to endpoints Test Intro parallel lines city project Due day of test 1 day Conditional Statements Advertisement mini project 1 day 1 day 1 day 1 day Parallel Lines City Project 1 day 1 day 1 day 1 day 1 day Proving Triangle and Parallelogram Theorems (GEO #10 – 11, GMD #6, GPE #4, GSRT #5) – 12 days Observations on triangles Experiment: Triangle inequality theorem, angles 2 days opposite longer sides are longer and apply to the world Proofs – Interior angle sum = 180, Polygon 1 day interior and exterior angle sum Finding angles in triangles and Proofs – base angles of isosceles triangle are congruent Congruent Triangles (SSS, SAS, ASA) Review CPCTC Quiz + Distance formula Proofs –||gram – Day 1 Proofs–||gram – Day 2 Prove it’s a parallelogram Coordinate Geometry Test Review Equilateral and Isosceles Triangle proofs 1 day 1 day radical review Opposite sides are congruent, opposite angles are congruent + practice Diagonals bisect, Rectangles/Squares have congruent diagonals + practice 1 day 1 day 1 day 1 day 1 day 1 day Algebraic Expressions (N&Q RN #1 – 3, N&Q CN #1 – 2, A SSE #1-3a, A APR #1) – 9 - 10 days Review of exponent properties and 2 days extend to rational exponents Write radical as rational exponent and vice versa + Mixed review + square root list (72 = 49) Application of exponent properties: Intro to i, operations with i Quiz + Factoring Pre-assessment Operations with Monomials, Explain that operations are closed (like integers) over +/* Perfect square trinomials and completing the square (just the trinomial) Review Factoring trinomials, Greatest common factor, difference of squares Test Function Introduction 5 days Review of function basics FIF 4, 5, 6, 7, 8b, 9, FBF 1, FLE 3, AREI 7 Function graphs Day 1 Observations FIF 4, 5, 6, 7, 8b, 9, FBF 1, FLE 3, AREI 7 Function graphs Day 2 FIF 4, 5, 6, 7, 8b, 9, FBF 1, FLE 3, AREI 7 Review of function basics FIF 4, 5, 6, 7, 8b, 9, FBF 1, FLE 3, AREI 7 Quiz + Mock Final Review 1 day 1 day 1 day 1 day 1 day (1-2 days depending on Pre-assessment) Include Rewriting 𝑥 4 − 𝑦4 = (𝑥 2)2 − (𝑦2 )2. 1 day 1 day Domain, range, generating coordinates from function (organizing in table/graph), write a function given a table Identifying Max/Min, intercepts (simple examples: Linear, abs. value, quadratic) all graphed by hand describe similarities and differences + Mini Factoring review Have students graph linear, quadratic, square root, cube root, piece-wise, exponential and abs. value using technology. Describe similarities and difference + Mini Factoring review Domain, range, generating coordinates from function (organizing in table/graph), write a function given a table Quiz topic: Can compare two functions when represented in a different way (Ex: given a graph of one quadratic function and an absolute value equation for another. 1 day Project – Function analysis packet 1 day 1 day 1 day 1 day Final Exam Review - 4 days Review Day 1 Review Day 2 Review Day 3 Final Exam (Taken last week of December) Performance Task (out of 20) Multiple Choice Section (out of 30) 1 day 1 day 1 day 1 day - Outline with analysis of results - Two mock finals (8 MC questions and 1 performance task) Students who perform below 70% must retake the final exam during finals week in January. SECOND SEMESTER (Begins first day of January return) Functions and Quadratics 8 days Derive equation of parabola given a focus and directrix G GPE 2 FIF 4, 5, 6, 7, 8b, 9, FBF 1, FLE 3, AREI 7 Fundamental Theorem of Algebra NCN 9 and Focus on Roots: Quadratic Functions by factoring and zero product property ASSE 3a, AREI 4ab Focus on Roots/MaxMin: Quadratic Functions by square root and completing the square ASSE 3b Review + Quiz Focus on Roots: Quadratic Functions by quadratic formula AREI 4ab Application of quadratic functions Review + Project Day Test + Project Due Similarity 6 days Side Splitting Theorem GSRT 4, G GPE 6 1 day For real and imaginary solutions 𝑥 2 − 4 = (𝑥 + 2)(𝑥 − 2) = 2, -2 𝑥 2 + 4 = (𝑥 + 2𝑖)(𝑥 − 2𝑖)= 2i, -2i 1 day Use completing square to reveal max/min of quadratic function 1 day Intro project Be able to derive the quadratic formula 1 day 1 day Motion of an object under force of gravity 1 day 1 day 1 day + review of proportions + Find point on line segment between two given points that partitions the segment given a ratio Review/Intro to dilations Use dilations of triangles 1 day Definition of Similar + Mini Quiz GSRT 2, 5 Similar Polygons 1 day Similar Triangle Proofs GSRT 3, 4 +Prove AA by using Dilations +Proof of side splitting theorem +Proof of Pythagorean theorem 1 day What is a scale factor? GSRT 1ab Similar Triangles and Polygon Review GSRT 5 Test 1 day Project – Children’s story book maybe? Properties preserved (invariant) under a dilation: 1. angle measures (remain the same) 2. parallelism (parallel lines remain parallel) 3. colinearity (points stay on the same lines) 4. midpoint (midpoints remain the same in each figure) 5. orientation (lettering order remains the same) --------------------------------------------------------------6. distance is NOT preserved (NOT an isometry) 1 day 1 day Similarity in Right Triangles 8 days (Warm – up each day about Pythagorean Theorem) Pythagorean Theorem Review + In 1 day depth discovery/observations of 30,60,90 and 45, 45, 90 triangles. Why are they “special”? GRST 8.1 “Generating” a trig table including (but Discovery of similar right triangle 1 day not limited to) 30, 45, 60, and 90 ratios GRST 6 Using your Trig functions to find side 1 day lengths of a triangle GRST 8 Using your Trig functions to find 1 day angles of a triangle GRST 8 Quiz + Angles of elevation and 1 day depression GRST 8 Assign TRIG Ladder Company Project Use “friendly-ish” numbers. No Calculators!!! Pythagorean Identity Proofs and observations of Sine and Cosine of Complementary Angles GRST 7 FTF 8 Review + Project Day Test Circles 6 days Circle Vocabulary and Proof of and Finding circumference and area of circles G C 2, G GMD 1 Equation of circle G GPE 1 Mini Quiz + Angles in circles: Inscribed, central, and circumscribed + Construction G C 2, 3 Tangent lines + Construction 1 day 1 day 1 day *Key vocab: Diameter, radius, circumference, inscribed angle, central angle, circumscribed angle, chord, tangent line, arc 1 day *Derive through Pythagorean theorem, complete square to find center/radius *Construct – inscribed and circumscribed circles of a triangle *Prove properties of angles for a quadrilateral inscribed in a circle *Construct – a tangent line from a point outside a given circle to the circle Properties of tangent lines and chords, use Pythagorean theorem to find various segment lengths. 1 day Review Test Area and Volume and Similarity 6 days Prove that all circles are similar, Arc length and area of sector G C 1, 5 Volume discovery: Cylinder, Pyramid, Cone, Rectangular Prism G GMD 1, 2 Mini-Quiz + Introduce Project + Project Time *Similarity Project about comparing scale values of k, 𝑘 2 , 𝑘 3 G GMD 5 Review topics: Similarity/Right Triangles + Project Time Review topics: Volume Practice + Project Time Test Stats and Probability 6 days Intro to Stats concepts and short project intro Compound Events Project Day Project Day TRIG Ladder project due I strongly urge you to use MVP materials under Math II (Circles from Geometric perspective & Circles) 1 day 1 day 1 day 1 day Derive using similarity the fact that arc length of an arc is proportional to radius, Define radian measure as a constant of proportionality, derive formula of area of sector Use dissection arguments, Cavalieri’s principle, informal limit arguments for discovery/proof 1 day 1 day 1 day Cereal Project + Snowman Project 1 day 1 day 1 day Project Due Aim to hit S CP 1, 2, 3 with examples and practice 1 day S CP 6, 7, 8 Use permutations and combinations to compute probabilities of compound events and solve problems In pairs have students devise an experiment that they can collect data on (Example S CP 4). Then students estimate probability of random sampling. Presentation includes students recognizing and explaining concepts of conditional probability and independence in their own words (S CP 5). They 1-2 days 1 day 1 day Presentations + Quiz have to use their estimated probability to make a decision/conclusion and analyze a decision/strategy based on those results (S MD 6, 7). Presentation + Quiz = Test Score! (No Test for this chapter) 1 day If started Right triangles week after finals week you will end May 12th – 16th (using max amount of days per chapter) I recommend doing 2 weeks of final exam review and administering a final exam first week of June. Analyze results with students to identify weaknesses and strengths and students with below 70% must retake final exam during finals week. Students who perform above will begin learning material for Math III (mostly independently or with video stations), while the other group does intensive review with teacher. Finals week students either take final exam (last chance) or short Math III quiz/test (open notes if you like). May 19 – 23 Review May 26 – 30 Review June 1 – 6 Final and Analysis June 9 – 13 Review/Math III June 16 – 20 Review/Math III June 23 – 26 Final/Math III assessment