Content Skills Assessments Lessons

Transcription

1 Teacher: CORE GEOMETRY Year: Course: GEOMETRY Month: All Months S e p t e m b e r Basic Terminology draw and measure two and threedimensional investigate and analyze two and threedimensional Am I able to use technology to investigate and explore properties? make and test conjectures? logically writing as well as orally? Content Skills Assessments Lessons Points, Lines, Planes, Space, Segments, Rays, Opposite Rays, Collinear Points, Coplanar Points Congruent Segments, Midpoint of a segment Types of angles by measurement Adjacent Angles, Congruent Angles, Angle Bisectors Complementary Angles, Supplementary Angles, Vertical Angles Types of Lines â Parallel, skew, perpendicular If-then statements and converses Read and write the correct symbolism. Draw appropriate diagrams for stated conditions of points, lines, planes, segments, rays, collinear points, and coplanar points. Interpret given information on a diagram. Make proper conclusions from a diagram. Apply the concepts of complementary, supplementary, and vertical angles. Use Algebra to solve problems. Determine the hypothesis and conclusion in an if-then statement. State the converse of an Homework 9/1/2012 Quizzes 9/1/2012 Tests 9/1/2012 Geometers' Sketchpad Labs 9/1/2012 Learning Benchmarks Students will know and be able to define and identify basic terminology. Standards M G.01- Geometry ~ Identify figures using sides, angles, and diagonals. Identify the figures' type(s) of symmetry. M G.02- Geometry ~ Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments.

2 O c t o b e r Parallel Lines draw and measure two and threedimensional Am I able to use technology to investigate and explore properties? make and test conjectures? logically writing as well as orally? if-then statement. Content Skills Assessments Lessons Properties of Parallel Lines â corresponding angles, alternate interior, sameside interior With the given information determine if lines are parallel. Identify pairs of angles (corresponding angles, alternate interior, sameside interior) formed by two lines cut by a transversal. Apply the angles formed by parallel lines and a transversal. Use information about angles to conclude whether or not lines are parallel. Homework 10/1/2012 Quizzes 10/1/2012 Tests 10/1/2012 Geometers' Sketchpad Labs 10/1/2012 Learning Benchmarks Students will know and be able to apply parallel lines. Standards M G.02- Geometry ~ Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments. M G.03- Geometry ~ Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and

3 Properties of Triangles investigate and analyze two and threedimensional Am I able to use technology to investigate and explore properties? make and test conjectures? logically writing as well as orally? Content Skills Assessments Lessons Types of Triangles (Scalene, Isosceles, Equilateral, Acute, Right, Obtuse, Equiangular) Sum of the angles of a triangle is 180 degrees. Properties of isosceles triangles. Triangle inequality. Distinguish between various types of triangles. Apply the concept of the sum of the angles of a triangle is 180 degrees. Apply the isosceles triangles. Apply the concepts of triangle inequalities within a triangle. Homework 10/1/2012 Quizzes 10/1/2012 Tests 10/1/2012 Geometers' Sketchpad Labs 10/1/2012 Learning Benchmarks Students will know and be able to identify and apply various types of triangles. Standards major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle. M G.01- Geometry ~ Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry. M G.02- Geometry ~ Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments. M G.05- Geometry ~ Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem. M G.06- Geometry ~ Use the special triangles (e.g., isosceles, equilateral,

4 N o v e m b e r Congruent Triangles draw and measure two and threedimensional reason by a variety of methods? (i.e., 2 column proof, paragraph proof, indirect proof, inductively) logically writing as well as orally? Content Skills Assessments Lessons Methods of proving that triangles are congruent (SSS, SAS, ASA, AAS, HL). Corresponding parts of congruent triangles are congruent. Proofs involving isosceles triangles and triangles that are overlapping. Demonstrate that two triangles are congruent by SS, SAS, ASA, AAS, and HL. Identify congruent parts of congruent figures. Write a proof (2 column, paragraph, flow chart, or,...) for proving two triangles are congruent and/or corresponding parts of congruent triangles are congruent. Apply congruent triangle methods to triangles that are isosceles. Apply congruent triangle methods to triangles that Homework 11/1/2012 Quizzes 11/1/2012 Tests 11/1/2012 Geometers' Sketchpad Labs 11/1/2012 Learning Benchmarks Students will know and be able to use various techniques to prove triangles are congruent. 30Â â 60Â â 90Â, 45Â â 45Â â 90Â ) to solve problems. Standards M G.04- Geometry ~ Apply congruence and similarity correspondences (e.g., DXYZ) and the figures to find missing parts of figures, and provide logical justification. M G.06- Geometry ~ Use the special triangles (e.g., isosceles, equilateral, 30Â â 60Â â 90Â, 45Â â 45Â â 90Â ) to solve problems.

5 Polygons (Nov - Dec) are overlapping. D e c e m b e r draw and measure two and threedimensional investigate and analyze two and threedimensional logically writing as well as orally? Content Skills Assessments Lessons Types of Polygons Sum of the interior angles and exterior angles. Properties of Parallelograms draw and measure two and threedimensional investigate and analyze two and Distinguish between various types of polygons. Find the measures of interior and exterior angles of convex polygons. Homework 11/1/2012 Quizzes 11/1/2012 Tests 11/1/2012 Geometers' Sketchpad Labs 11/1/2012 Content Skills Assessments Lessons Types of quadrilaterals. Properties of Parallelograms Properties of special parallelograms (rectangle, rhombus, square). Properties of Distinguish between various types of quadrilaterals. Apply the parallelograms. Apply the special Homework 12/1/2012 Quizzes 12/1/2012 Tests 12/1/2012 Geometers' Sketchpad Labs 12/1/2012 Learning Benchmarks Learning Benchmarks Students will know and be able to identify, analyze, and apply angle different types of polygons. Students will know and be able to apply quadrilaterals. Standards Standards M G.01- Geometry ~ Identify figures using sides, angles, and diagonals. Identify the figures' type(s) of symmetry. M G.05- Geometry ~ Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem. M G.01- Geometry ~ Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of symmetry. M G.02- Geometry ~ Draw congruent and similar figures using a

6 threedimensional and Isosceles Trapezoids Trapezoids. reason by a variety of methods? (i.e., 2 column proof, paragraph proof, indirect proof, inductively) Am I able to use technology to investigate and explore properties? make and test conjectures? logically writing as well as orally? parallelograms (rectangle, rhombus, and square). Apply the trapezoids and isosceles trapezoids. compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments. M G.06- Geometry ~ Use the special triangles (e.g., isosceles, equilateral, 30Â â 60Â â 90Â, 45Â â 45Â â 90Â ) to solve problems. J a n u a r y Review for Semester I Exam draw and measure two and threedimensional Content Skills Assessments Lessons Learning Benchmarks Standards M G.01- Geometry ~ Identify figures using properties of sides, angles, and diagonals. Identify the figures' type(s) of

7 investigate and analyze two and threedimensional reason by a variety of methods? (i.e., 2 column proof, paragraph proof, indirect proof, inductively) work in the coordinate plane and apply appropriate formulas to find solutions? Do I use the most effective tool to determine and calculate measurements? logically writing as well as orally? symmetry. M G.02- Geometry ~ Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments. M G.03- Geometry ~ Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle. M G.04- Geometry ~ Apply congruence and similarity correspondences (e.g., DXYZ) and the figures to find missing parts of figures, and provide logical justification. M G.05- Geometry ~ Solve simple triangle problems using the triangle angle sum

8 F e b r u a r y M a r c h Similarity and Proportionality (Jan - Feb) Content Skills Assessments Lessons draw Ratio/Proportion and measure two and threedimensional Polygons Similar Similar reason Triangles (AA) by a variety of Proportional methods? (i.e., Lengths 2 column proof, paragraph proof, indirect proof, inductively) logically writing as well as orally? Right Triangles and Area (Feb - Mar) Simplify ratios (including use of appropriate units) Solve problems using ratios and proportions. Apply the similar polygons. Use AA to demonstrate that triangles are similar. Apply Triangle Proportionality and Proportion of an Angle- Bisector of a Triangle. Homework 2/1/2013 Quizzes 2/1/2013 Tests 2/1/2013 Geometers' Sketchpad Labs 2/1/2013 Learning Benchmarks Students will know and be able to identify and apply similar figures. Content Skills Assessments Lessons Learning Benchmarks Standards property and/or the Pythagorean theorem. M G.06- Geometry ~ Use the special triangles (e.g., isosceles, equilateral, 30Â â 60Â â 90Â, 45Â â 45Â â 90Â ) to solve problems. Standards M G.04- Geometry ~ Apply congruence and similarity correspondences (e.g., DXYZ) and the figures to find missing parts of figures, and provide logical justification. draw and Perfect Squares, Simplify Homework Students M G.05-

9 measure two and threedimensional Do I use the most effective tool to determine and calculate measurements? logically writing as well as orally? square roots, and basic equations that require square root in solution Pythagorean Theorem , Area of Rectangles/Squares Area of Parallelogram Area of Triangles and Trapezoids expressions with square roots. Solve basic equations that require a square root in the solution. Apply the Pythagorean Theorem. Determine lengths of the sides of and triangles. Use the formulas to find the areas of rectangles, parallelograms, triangles, and trapezoids. 3/1/2013 Quizzes 3/1/2013 Tests 3/1/2013 Geometers' Sketchpad Labs 3/1/2013 will know and be able to apply the Pythagorean Theorem and properties of Special Right Triangles. Students will know and be able to calculate the area of various figures. Geometry ~ Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem. M G.06- Geometry ~ Use the special triangles (e.g., isosceles, equilateral, 30Â â 60Â â 90Â, 45Â â 45Â â 90Â ) to solve problems. M M.01- Measurement ~ Calculate perimeter, circumference, and area of common figures such as parallelograms, trapezoids, circles, and triangles. M M.03- Measurement ~ Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume. M M.04- Measurement ~ Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements. M N.01-Number Sense and Operations ~ Identify and use the

10 A p r i l Circles draw and measure two and threedimensional Content Skills Assessments Lessons Circle Terminology Properties of tangents, chords, and inscribed Define and identify the terminology related to circles. Homework 4/26/2013 Quizzes 4/26/2013 Tests 4/26/2013 Learning Benchmarks Students will know and be able to apply circles. operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nthroots of positive real numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number. M N.03-Number Sense and Operations ~ Find the approximate value for solutions to problems involving square roots and cube roots without the use of a calculator, e.g., à 32-1 » 2.8. M N.04-Number Sense and Operations ~ Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers. Standards M G.02- Geometry ~ Draw congruent and similar figures using a compass, straightedge, protractor, and other

11 investigate and analyze two and threedimensional Am I able to use technology to investigate and explore properties? make and test conjectures? logically writing as well as orally? angles Circumference and Area of a Circle Length of an arc, Area of a sector, Area of shaded regions Apply tangents, chords, central angles, and inscribed angles. Calculate the area and circumference of circles as well as the lengths of an arc, area of a sector, and area of shaded regions. Geometers' Sketchpad Labs 4/26/2013 Students will know and be able to calculate the area of various figures. tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments. M G.03- Geometry ~ Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle. M G.06- Geometry ~ Use the special triangles (e.g., isosceles, equilateral, 30Â â 60Â â 90Â, 45Â â 45Â â 90Â ) to solve problems. M G.10- Geometry ~ Demonstrate the ability to visualize solid objects and recognize their projections and cross sections. M M.01- Measurement ~ Calculate perimeter, circumference, and area of common figures such as parallelograms, trapezoids, circles, and

12 Volume and Surface Area (Apr - May) draw and measure two and threedimensional investigate and analyze two and threedimensional Do I use the most effective tool to determine and calculate measurements? Content Skills Assessments Lessons Volume and Surface Area of Right Prisms, Right Square Pyramids, Right Cylinders, Right Cones, Spheres Use formulas to find the volume and surface area of right prisms, right square pyramids, right cylinders, right cones, and spheres. Homework 4/26/2013 Quizzes 4/26/2013 Tests 4/26/2013 Learning Benchmarks Standards Students will know and be able to calculate the volume and surface area of various solids. triangles. M M.03- Measurement ~ Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume. M M.04- Measurement ~ Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements. M G.05- Geometry ~ Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean theorem. M G.06- Geometry ~ Use the special triangles (e.g., isosceles, equilateral, 30Â â 60Â â 90Â, 45Â â 45Â â 90Â ) to solve problems. M G.10- Geometry ~ Demonstrate the ability to visualize solid objects and recognize

13 M a y logically writing as well as orally? MCAS Preparation Content Skills Assessments Lessons Learning Standards their projections and cross sections. M M.01- Measurement ~ Calculate perimeter, circumference, and area of common figures such as parallelograms, trapezoids, circles, and triangles. M M.02- Measurement ~ Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area. M M.03- Measurement ~ Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume. M M.04- Measurement ~ Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements.

14 MCAS Preparation Benchmarks M D.01-Data Analysis, Statistics, and Probability ~ Select, create, and interpret an appropriate graphical representation (e.g., scatter-plot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to information about the data. Use these notions to compare different sets of data. M D.02-Data Analysis, Statistics, and Probability ~ Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate. M D.03-ta Analysis, Statistics, and Probability ~ Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data. M G.01- Geometry ~ Identify figures using properties of sides, angles, and diagonals. Identify the

15 figures' type(s) of symmetry. M G.02- Geometry ~ Draw congruent and similar figures using a compass, straightedge, protractor, and other tools such as computer software. Make conjectures about methods of construction. Justify the conjectures by logical arguments. M G.03- Geometry ~ Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle. M G.04- Geometry ~ Apply congruence and similarity correspondences (e.g., DXYZ) and the figures to find missing parts of figures, and provide logical justification. M G.05- Geometry ~ Solve simple triangle problems using the

16 triangle angle sum property and/or the Pythagorean theorem. M G.06- Geometry ~ Use the special triangles (e.g., isosceles, equilateral, 30Â â 60Â â 90Â, 45Â â 45Â â 90Â ) to solve problems. M G.07- Geometry ~ Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments, and distances between two points, and apply the results to the solutions of problems. M G.08- Geometry ~ Find linear equations that represent lines either perpendicular or parallel to a given line and through a point, e.g., by using the â œpoint-slopeâ form of the equation. M G.09- Geometry ~ Draw the results, and interpret transformations on figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems. M G.10-

17 Geometry ~ Demonstrate the ability to visualize solid objects and recognize their projections and cross sections. M G.11- Geometry ~ Use vertex-edge graphs to model and solve problems. M M.01- Measurement ~ Calculate perimeter, circumference, and area of common figures such as parallelograms, trapezoids, circles, and triangles. M M.02- Measurement ~ Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area. M M.03- Measurement ~ Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume. M M.04- Measurement ~ Describe the effects of approximate error in

18 measurement and rounding on measurements and on computed values from measurements. M N.01-Number Sense and Operations ~ Identify and use the operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nthroots of positive real numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number. M N.02-Number Sense and Operations ~ Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(24â 1) = 45, 4 3 â = 14; apply such simplifications in the solution of problems. M N.03-Number Sense and Operations ~ Find the approximate value for solutions to problems involving square roots and cube roots without the use of

19 a calculator, e.g., à 32-1 » 2.8. M N.04-Number Sense and Operations ~ Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers. M P.01-Patterns, Relations and Algebra ~ Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), linear, quadratic, and exponential functional relationships. M P.02-Patterns, Relations and Algebra ~ Demonstrate an understanding of the relationship between various representations of a line. Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a description of the line, e.g., by using the â œpoint-slopeâ or â œslope y- interceptâ formulas. Explain the significance of a positive, negative,

20 zero, or undefined slope. M P.03-Patterns, Relations and Algebra ~ Add, subtract, and multiply polynomials. Divide polynomials by monomials. M P.04-Patterns, Relations and Algebra ~ Demonstrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms; factoring (e.g., a2â b2= (a + b)(a â b), x2+ 10x + 21 = (x + 3)(x + 7), 5x4+ 10x3â 5x2= 5x2(x2+ 2x â 1)); identifying and canceling common factors in rational expressions; and applying the properties of positive integer exponents. M P.05-Patterns, Relations and Algebra ~ Find solutions to quadratic equations (with real roots) by factoring, completing the square, or using the quadratic formula. Demonstrate an understanding of the equivalence of the methods. M P.06-Patterns, Relations and Algebra ~ Solve equations and inequalities including those involving

21 J u n e Right Triangle Trigonometry draw and measure two and threedimensional Content Skills Assessments Lessons Definitions of sine, cosine, and tangent of an acute angle of a right Identify the sine, cosine, and tangent ratios of an acute angle of Homework 6/1/2013 Quizzes 6/1/2013 Tests 6/1/2013 Learning Benchmarks absolute value of linear expressions (e.g., x â 2 > 5) and apply to the solution of problems. M P.07-Patterns, Relations and Algebra ~ Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate. M P.08-Patterns, Relations and Algebra ~ Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. Students will know and be able to apply trigonometric ratios to solve Standards M M.04- Measurement ~ Describe the effects of

22 Do I use the most effective tool to determine and calculate measurements? logically writing as well as orally? triangle. Solve for sides and angles of a right triangle. Applications including angle of elevation and angle of depression a right triangle. Solve right triangle problems using the sine, cosine, and tangent ratios. Use trigonometry to solve an applied problem. Geometers' Sketchpad Labs 6/1/2013 right triangles. approximate error in measurement and rounding on measurements and on computed values from measurements. M N.04- Number Sense and Operations ~ Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers. M G.01- Geometry ~ Define the sine, cosine, a