Instructional Unit CPM Geometry Unit Content Objective Performance Indicator Performance Task State Standards Code:

Transcription

1 306 Instructional Unit Area 1. Areas of Squares and The students will be -Find the amount of carpet E Rectangles able to determine the needed to cover various plane 2. Areas of Parallelograms and areas of squares, figures. Triangles rectangles, 3. Areas of Trapezoids parallelograms, 4. Areas of Regular Polygons rhombuses, triangles, 5. Circumference of a Circle and trapezoids, regular Arc Length polygons, circles, and 6. Areas of Circles, Sectors, and other plane figures that Shaded Parts of a Circle are combinations of 7. Comparison of Areas of Similar these. Figures 1. Areas of Squares and The students will be -Find the area of a larger figure E Rectangles able to compare the by using a small model. 2. Areas of Parallelograms and areas of similar -Compare the areas of similar Triangles figures. figures. 3. Areas of Trapezoids 4. Areas of Regular Polygons 5. Circumference of a Circle and Arc Length 6. Areas of Circles, Sectors, and Shaded Parts of a Circle 7. Comparison of Areas of Similar Figures

2 Area 1. Areas of Squares and The students will be -Explain how a change to the A Rectangles able to determine how length of the side of a polygon 2. Areas of Parallelograms and the area of a polygon will affect the area. Triangles changes when a 3. Areas of Trapezoids dimension of the 4. Areas of Regular Polygons polygon is increased or 5. Circumference of a Circle and decreased. Arc Length 6. Areas of Circles, Sectors, and Shaded Parts of a Circle 7. Comparison of Areas of Similar Figures 1. Areas of Squares and The students will be -Explain the steps needed to F Rectangles able to recognize the find the area of any shaded 2. Areas of Parallelograms and arc lengths and region of a circle. Triangles shaded regions of a 3. Areas of Trapezoids circle. 4. Areas of Regular Polygons 5. Circumference of a Circle and Arc Length 6. Areas of Circles, Sectors, and Shaded Parts of a Circle 7. Comparison of Areas of Similar Figures

3 Circles 1. Circles, Inscribed and The students will be -Solve problems, some that F Circumscribed Circles able to use the involve real life applications 2. Properties of Tangents to a properties of angles, (e.g., tangents related to an Circle arcs, chords, tangents, eclipse). 3. Arcs, Chords, and Central and secants to solve Angles problems involving 4. Inscribed Angles and Inscribed circles. Polygons 5. Tangents, Secants, and the Angles that They Form 1. Circles, Inscribed and The students will be -Explain the relationships of a E Circumscribed Circles able to solve problems circle and the sides of an 2. Properties of Tangents to a involving inscribed and inscribed polygon or a Circle circumscribed circumscribed polygon. -Solve 3. Arcs, Chords, and Central polygons. the problem. Angles 4. Inscribed Angles and Inscribed Polygons 5. Tangents, Secants, and the Angles that They Form

4 Congruent Triangles 1. Correspondence and The students will be -Construct and discover where A Congruence able to construct and the medians, altitudes, angle 2. Proving Triangles Congruent compare medians, bisectors, and perpendicular 3. Using Congruent Triangles altitudes, angle bisectors meet. 4. Medians, Altitudes, and bisectors, and Bisectors perpendicular 5. Proving Right Triangles bisectors of the sides Congruent of a triangle. 1. Correspondence and The students will be -Explain why two triangles are B Congruence able to distinguish congruent by means of the HL 2. Proving Triangles Congruent when two right Theorem. 3. Using Congruent Triangles triangles are 4. Medians, Altitudes, and congruent. Bisectors 5. Proving Right Triangles Congruent 1. Correspondence and The students will be -Determine the measures of the D Congruence able to express if two parts of congruent triangles. 2. Proving Triangles Congruent triangles or two 3. Using Congruent Triangles polygons are 4. Medians, Altitudes, and congruent and will be Bisectors able to identify the 5. Proving Right Triangles corresponding parts in Congruent congruent triangles to solve problems.

5 Congruent Triangles 1. Correspondence and The students will be -Write a formal proof showing B Congruence able to prove two that two triangles are 2. Proving Triangles Congruent triangles are congruent congruent. 3. Using Congruent Triangles by constructing a 4. Medians, Altitudes, and formal deductive proof. Bisectors 5. Proving Right Triangles Congruent

6 Inequalities in Triangles 1. Isosceles Triangle Theorem The students will be -State the range of the length A 2. Properties of Inequalities able to apply the of the third side when given the 3. Writing Indirect Proofs inequality properties of lengths of two sides of a 4. Indirect Proof and Inequalities the sides and angles triangle. 5. Inequalities in One Triangle for one triangle and for 6. Inequalities in Two Triangles two triangles. 1. Isosceles Triangle Theorem The students will be -Justify the steps leading to the B 2. Properties of Inequalities able to apply the solutions of problems 3. Writing Indirect Proofs theorems concerning containing isosceles triangles. 4. Indirect Proof and Inequalities isosceles triangles in 5. Inequalities in One Triangle problem solving. 6. Inequalities in Two Triangles 1. Isosceles Triangle Theorem The students will be -Analyze parts of indirect A 2. Properties of Inequalities able to validate proofs that other students have 3. Writing Indirect Proofs conjectures by written. 4. Indirect Proof and Inequalities creating indirect 5. Inequalities in One Triangle proofs. 6. Inequalities in Two Triangles

7 Parallelism 1. Lines, Planes, and Transversals The students will be -Determine (when possible) the E able to utilize their measures of various angles 2. Properties of Parallel Lines knowledge of parallel when parallel lines are present. 3. Proving Lines Parallel lines for problem 4. Using Parallel Lines to Prove solving. Properties About the Angles of a Triangle 5. Polygons 6. Angles of a Polygon 1. Lines, Planes, and Transversals The students will be -Develop and use formulas in C able to use inductive finding interior and exterior 2. Properties of Parallel Lines reasoning to determine angles of regular convex 3. Proving Lines Parallel the sum of the interior polygons. 4. Using Parallel Lines to Prove angles, the sum of the Properties About the Angles of a exterior angles, and Triangle the relationships 5. Polygons between the interior 6. Angles of a Polygon and the exterior angles of any convex polygon.

8 Parallelism 1. Lines, Planes, and Transversals The students will be -Solve problems involving the I able to use the interior or exterior angles of a 2. Properties of Parallel Lines properties of parallel triangle. 3. Proving Lines Parallel lines to determine the 4. Using Parallel Lines to Prove relationships of the Properties About the Angles of a interior angles and the Triangle exterior angles of a 5. Polygons triangle. 6. Angles of a Polygon 1. Lines, Planes, and Transversals The students will be -Explain the properties of C able to determine the parallel lines when information 2. Properties of Parallel Lines properties of parallel is given about the 3. Proving Lines Parallel lines. corresponding angles, alternate 4. Using Parallel Lines to Prove interior angles, or same side Properties About the Angles of a interior angles. Triangle 5. Polygons 6. Angles of a Polygon

9 Quadrilaterals 1. The Parallelogram, a Special The students will be -Write and analyze proofs of C Quadrilateral able to prove the the properties of various 2. Finding Quadrilaterals that Are properties of quadrilaterals. Parallelograms quadrilaterals involving 3. Parallel Lines Containing opposite sides and Midpoints of the Sides of a Triangle angles, consecutive sides and angles, and 4. Rectangles, Rhombuses, and diagonals by using Squares deductive proofs. 5. Trapezoids 1. The Parallelogram, a Special The students will be -Write and justify solutions to D Quadrilateral able to compare, problems involving 2. Finding Quadrilaterals that Are contrast and apply the quadrilaterals. Parallelograms various properties of 3. Parallel Lines Containing parallelograms, Midpoints of the Sides of a Triangle rhombuses, squares, rectangles, trapezoids, 4. Rectangles, Rhombuses, and and kites in solving Squares problems. 5. Trapezoids

10 Quadrilaterals 1. The Parallelogram, a Special The students will be -Explain conclusions about the D Quadrilateral able to determine the sides and angles of a 2. Finding Quadrilaterals that Are properties of parallelogram. Parallelograms parallelograms 3. Parallel Lines Containing involving opposite Midpoints of the Sides of a Triangle sides and angles, consecutive sides and 4. Rectangles, Rhombuses, and angles, and diagonals. Squares 5. Trapezoids

11 Right Triangles 1. Right Triangle Similarity The students will be -Draw models involving right B 2. Pythagorean Theorem able to identify, create, triangles. 3. Converse of the Pythagorean and solve practical -Write equations using the Theorem problems involving right Pythagorean Theorem. 4. Special Right Triangles triangles and the ( and ) Pythagorean Theorem. 1. Right Triangle Similarity The students will be -Utilize the appropriate theorem A 2. Pythagorean Theorem able to solve problems to find the lengths of the sides 3. Converse of the Pythagorean involving and of a right triangle. Theorem triangles. 4. Special Right Triangles ( and )

12 Similarity 1. Ratio and Proportion The students will be -Show several equivalent I 2. Properties of Proportions able to use equivalent proportions that could be used 3. Proving Triangles Similar forms of proportions to solve a problem. 4. Applications of Similar for interpreting and Triangles solving a variety of 5. Proportional Segments geometric problems. 1. Ratio and Proportion The students will be -Justify why two triangles are B 2. Properties of Proportions able to express that similar. 3. Proving Triangles Similar two triangles or two 4. Applications of Similar polygons are similar. Triangles 5. Proportional Segments 1. Ratio and Proportion The students will be -Use proportions to compare I 2. Properties of Proportions able to model situations scale diagrams with real 3. Proving Triangles Similar geometrically to objects. 4. Applications of Similar formulate and solve Triangles problems. 5. Proportional Segments

13 The Language of Geometry 1. Points, Lines, and Planes The students will be -Portray the correct geometric B 2. Segments and Rays able to express basic terminology in explaining 3. Angles and Angle Bisectors geometric terminology problems and their solutions. 4. Angle Pairs: Complementary, in written and oral Supplementary, Vertical, and communication. Linear 5. Perpendicular Lines 6. Analyzing a Figure 1. Points, Lines, and Planes The students will be -Identify the angles or angle B 2. Segments and Rays able to measure, pairs when an angle is given or 3. Angles and Angle Bisectors identify, and classify measured. 4. Angle Pairs: Complementary, various types of -Classify the angles or angle Supplementary, Vertical, and angles and angle pairs when an angle is given or Linear pairs. measured. 5. Perpendicular Lines 6. Analyzing a Figure 1. Points, Lines, and Planes The students will be -Use algebraic equations to A 2. Segments and Rays able to apply theorems solve problems involving 3. Angles and Angle Bisectors concerning perpendicular lines, 4. Angle Pairs: Complementary, perpendicular lines, supplementary angles, and Supplementary, Vertical, and supplementary angle, complementary angles. Linear and complementary 5. Perpendicular Lines angles. 6. Analyzing a Figure

14 The Language of Geometry 1. Points, Lines, and Planes The students will be -Identify the relationships and D 2. Segments and Rays able to analyze a measurements of the angles 3. Angles and Angle Bisectors geometric diagram and segments in a diagram that 4. Angle Pairs: Complementary, and make was never seen before. Supplementary, Vertical, and conclusions about -Explain the relationships and Linear the various geometric measurements of the angles 5. Perpendicular Lines figures in the diagram. and segments in a diagram that 6. Analyzing a Figure they have not seen in the past.

15 The Logic of Geometry 1. Conditional Statements The students will be -Write conditional, converse, B 2. Converses, Inverses and able to write and inverse, contrapositive, and Contrapositives analyze conditional, biconditional statements. 3. Properties from Algebra converse, inverse, -Determine the truth value of 4. Logical Reasoning and Writing contrapositive, and these statements. Proofs biconditional 5. Inductive Reasoning statements and 6. Indirect Proofs determine their validity. 1. Conditional Statements The students will be -Explain a solution to a problem 2. Converses, Inverses and able to recognize and by justifying each step. Contrapositives use algebraic 3. Properties from Algebra properties as reasons 4. Logical Reasoning and Writing to justify steps in Proofs geometric problems. 5. Inductive Reasoning 6. Indirect Proofs 1. Conditional Statements The students will be -Develop proofs about A 2. Converses, Inverses and able to develop simple complementary, supplementary, Contrapositives formal proofs to or vertical angles. 3. Properties from Algebra support their 4. Logical Reasoning and Writing conclusions. Proofs 5. Inductive Reasoning 6. Indirect Proofs