mps algebra/geometry syllabus template - … docs/yr6_worddocs/hs_curriculu… · web view(algebra...

Milwaukee Public SchoolsCurriculum Framework

forHigh School Mathematics

Foundation Level(Algebra 1 and Geometry 1)

Draft 08/25/08

Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.

1

Introduction

This MPS Curriculum Framework for High School Mathematics, Foundation Level (Algebra 1 and Geometry 1) is based on the nineteen (19) MPS Foundation Level Learning Targets. These targets represent the Wisconsin mathematics process standard (A) and the Wisconsin content standards of number operations and relationships (B), geometry (C), measurement (D), statistics and probability (E) and algebra (F). These learning targets provide the context in which students can develop the knowledge and skills needed for a solid foundation in algebra and geometry. The nineteen learning targets (revised in summer 2008: Version 2.2) are aligned to state descriptors. The Wisconsin Assessment Framework for 10th grade was used for the first thirteen (13) learning targets. State standards for 12th grade were used for the remaining learning targets.

The first learning target addresses process skills: reasoning, using vocabulary, connecting math to real world applications, and communicating mathematical ideas. These process skills are to be continuously reinforced throughout the implementation of the Foundation Level courses. Learning targets two through thirteen are to be covered prior to November 1 of the second year, in preparation for the state of Wisconsin Knowledge and Concepts Examination. These thirteen targets (*in the following document),

Draft 08/25/08


2

including Learning Target 1, integrate the process and content standards related to the Wisconsin Assessment Framework for 10th grade. Learning targets fourteen through nineteen inform the content for the remainder of the second year math course.

For each learning target, a set of benchmarks (assessable specifications) is listed in a numerical sequence i.e. benchmark 2.1 represents the first benchmark for Learning Target 2. Every attempt was made to sequence the benchmarks for each target so that both teacher and student can determine student progress. Although the benchmarks are numbered, this does not designate a specific order of teaching. The specific pacing guides (designed in the summer of 2008) for the Foundation Level courses provide the sequencing for the benchmarks aligned with the textbook adopted in the spring 2008.

Reinforcing mathematical process skills, Learning Target 1, and acknowledging the fact that MPS schools are to implement instructional strategies to build mathematical vocabulary, Benchmark 1.8 was specifically designed: students will be able to communicate the MPS Academic Vocabulary for mathematics in oral and written presentations using literacy strategies, e.g. graphic organizers, vocabulary cloze, and word splash activities and cause-effect and similarities-differences diagrams. Under the MPS DIFI improvement plan, implemented in the fall of 2008, Marzano’s Six-Step Vocabulary Process is to be implemented.

A key criterion for the benchmarks was to provide a variety of thinking levels for each target from lower level thinking skills (knowledge and recall) to higher level thinking skills (evaluate and synthesize ideas and create models). MPS mathematical thinking classification levels were created in 2005 to analyze the depth of thinking a student is expected to demonstrate when completing an assessment. An overall depth of thinking must be associated with each benchmark in order to accurately interpret student achievement. It is important that analyzing the depth of thinking be part of the student feedback process, an important component of the MPS mathematical framework.

Specific course codes, listed in the Instructional Sequence column, have been given for the foundation level courses: For blocked schools, the first year instructional sequence includes RC111: Math Investigations I; MA211: Algebra (semester one); MA221: Algebra (semester two); and RC121: Math Investigations II. For schools on a regular teaching schedule, the instructional sequence includes MA211: Algebra (semester one) and MA221: Algebra (semester two). Block and regular instructional sequences for the second year are the same: MA301: Geometry (semester one) and MA311: Geometry (semester two). In the summer of 2008, pacing guides for the newly adopted Key Curriculum Press textbooks of Discovering Algebra and Discovering Geometry were drafted. These pacing guides will be under revision during the 2008-09 academic year as teachers use these guides and the textbooks.

Draft 08/25/08


3

Using this curriculum framework necessitates a strong commitment to the use of technology, from graphing calculators to computers and the newest in software. However, we are aware that not all schools are similarly equipped with the most recent developments. We can only encourage that technology be integrated to the extent possible in each classroom. The benchmarks for Learning Target 2, using a variety of mathematical and technological tools, are integrated throughout the pacing guides for these courses. A recommended school policy on the purchase and use of calculators at the high school has been drafted for fall 2008.

The MPS initiative that all high school teachers use the ESIS grade book was implemented in the fall of 2008. The learning targets were used as “categories” in the ESIS framework and the benchmarks are listed under “assignment types” as summative assessments. Each category was given a one or two word indicator which summarized the key content of that learning target. Similarly, each benchmark under summative assessments is summarized by a one to two word phrase. ESIS grade book also requires that categories (learning targets) be aligned to specific course codes. The learning targets listed for each course code represent the time frame when all, or the majority of benchmarks, will have been taught.

MPS teachers designed this curriculum framework for their colleagues. The framework was reviewed by educational faculty from the University of Wisconsin – Milwaukee. A framework is a constant work in progress and as such we hope that this framework will be revisited and revised. Reflections by teachers as they use this framework will be valuable and needed as this framework is implemented in the MPS high school classrooms.

Foundation LevelLearning Target 1*: Process

Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways, e.g. using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.

Topics Covered: Mathematical reasoning and communication; MPS Mathematics Academic Vocabulary and literacy strategies.

10th Grade Assessment Framework*/12th Grade Standards

Benchmarks: Students will be able to TL** Instructional Sequence

A.1*Use reasoning and logic to perceive patterns, formulate questions, identify relationships, pose problems, make and test

1.1 Defend, orally or in writing, the reasonableness of mathematical and real-world solutions.

3 Block RegularRC111 MA211MA211 MA221

Draft 08/25/08


4

conjectures, and evaluate and justify strategies.A.2*Communicate mathematical ideas and reasoning using the vocabulary of mathematics in a variety of ways e.g. using words, numbers, symbols, pictures, charts, tables, diagrams, graphs and models.A.3* Connect mathematics to the real-world as well as within mathematics.A.4*Create and use representations to organize, record, and communicate mathematical ideas.A.5* Solve and analyze routine and non-routine problems.A.12.1. Use reason and logic to evaluate information, perceive patterns, identify relationships, formulate questions, pose problems, and make and test conjectures and pursue ideas that lead to further understanding and deeper insight.

10th Grade Assessment Framework/12th Grade Standards

A.12.2. Communicate logical arguments and clearly show why a result does or does not make sense; why the reasoning is or is not valid, and an understanding of the difference between examples that support a conjecture and a proof of the conjecture.A.12.3. Analyze non-routine problems and arrive at solutions by various means, including models and simulations, often starting with provisional conjectures and progressing, directly or indirectly, to a

1.2 Determine whether or not the reasoning applied to mathematical and real- world problems make sense.

1.3 Write and solve their own mathematical and real-world application problems.

1.4 Write, using appropriate mathematical vocabulary, a defense of their own thinking in the solving of constructed response items in a test.

1.5. Design a PowerPoint or other computer-based application to demonstrate the connectedness of mathematics to the real-world.

1.6. Respond to feedback on classroom assessments based on standards which was written by the teacher and which uses a scoring rubric.

1.7 Read and interpret, in writing, charts, tables, diagrams, graphs, and models.

1.8 Communicate the MPS Academic Vocabulary for mathematics in oral and written presentations using literacy strategies e.g. graphic organizers, vocabulary cloze and word splash activities, and cause- effect and similarities-differences diagrams.Benchmarks: Students will be able to:

4

3

3

4

3

3

2

TL

MA221 MA301RC121 MA311MA301MA311

Instructional Sequence

Draft 08/25/08


5

solution, justification, or counter-example.A.12.4. Develop effective oral and written presentations employing correct mathematical terminology, notation, symbols, and conventions for mathematical arguments and display of data.A.12.5. Organize work and present mathematical procedures and results clearly, systematically, succinctly, and correctly. A.12.6. Read and understand mathematical texts and other instructional materials and writing about mathematics, e.g., articles in journals, mathematical ideas as they are used in other contexts. * 10th Grade Assessment Framework Descriptors No * State 12th grade Standards ** TL means Thinking Levels as defined by MPS 2005

Foundation Level Learning Target 2*: Measurement

Use a variety of mathematical and technological tools to determine measurements directly (ruler, protractor, compass) and to check reasonableness of answers. When students apply technology, e.g. computers and graphing calculators, they will interpret results appropriately.

Topics Covered: Measurement, estimation, technology and use of math tools e.g. protractor, ruler.

Vocabulary: estimate, dimension, conversion, length, degree, centimeter, kilometer, metric unit, meter, inch, foot, yard, mile, compass, straightedge, protractor.

Draft 08/25/08


6


Benchmarks: Students will be able to TL Instructional Sequence

B.6* Determine reasonableness of answers.D2.* Select and use tools with appropriate degree of precision to determine measurements directly.

2.1 Estimate measurements with precision, using appropriate units.

2.2 Measure lengths using a metric/English ruler (to the appropriate degree of tenths of cm and sixteenths of an inch).

2.3 Measure angles using a protractor (to appropriate degrees).

2.4 Justify reasons to interpret reasonableness of answers to mathematical and real-world applications.

1

2

2

4

Block RegularRC111 MA211MA211 MA221MA221 MA301RC121 MA311MA301MA311

Foundation LevelLearning Target 3*: Data Analysis

Use data in a variety of formats to summarize, predict, and analyze real-world applications.

Topics Covered: Use of data in various representations; finding measures of variation and measures of central tendency; use of data to make predications.

Vocabulary: Statistics: survey, sample, population, sampling techniques, validity, mean, median, mode, graph, range, standard deviation, data, scatter plot, percentiles, box and whisker plot, line of best fit, outliers, histogram, quartiles, stem and leaf, inter-quartile range, outlier, bias, measures of central tendency.Draft 08/25/08


7


Benchmarks: Students will be able to TL Instructional Time

E.1*Organize, display, compare and interpret data in a variety of ways in mathematical and real-world contexts, e.g. histograms, line graphs, stem-and-leaf plots, scatter plots, box and whiskers, bar charts, Venn diagrams, tables and circle graphs.E.2* Interpret, analyze and make predictions from organized and displayed data, e.g. measures of central tendency, measures of variation such as standard deviation, mean, median, mode, range, dispersion, outliers, line of best fit, percentiles.E.3* Analyze, evaluate and critique methods and conclusions of statistical experiments, e.g. randomness, sampling techniques, surveys.

3.1 Organize information into tables and stem-and-leaf plots.3.2 Create histograms and describe the distribution.3.3 Create and interpret bar graphs and circle graphs.3.4 Determine the mean, median and mode of a set of data.

3.5 Calculate the 5 number summary (quartiles) and create a box and whisker plot.3.6 Use measures of center and measures of variation to interpret, analyze and make

predications from the data.3.7 Display and interpret data using line graphs and scatter plots.3.8 Use the line of best fit to make predictions from data on a graph.

3.9 Display and interpret data using Venn diagrams.3.10 Compare and contrast two sets of data using measures of central tendency

from a box and whisker plot and a stem and leaf plot.3.11 Choose a graph given a set of data and justify its appropriateness.

2332

12

43

33¾

4

Block RegularRC111 MA211

Foundation LevelLearning Target 4*: Probability

Use a variety of counting methods to identify all possible occurrences of events and apply this information to analyze, critique, and predict the results of statistical experiments.

Topics Covered: Probability: Experiments, counting methods, probability of events.

Vocabulary: probability, permutations, combinations, reasonableness, conditional probability, theoretical probability, experimental probability, dependent events, independent events, bias, randomness.Draft 08/25/08


8


Benchmarks: Students will be able to TL Instructional Time

E.3* Analyze, evaluate and critique methods and conclusions of statistical experiments, e.g. randomness, sampling techniques, surveys.E.4* Determine the likelihood of occurrence of simple and complex events, e.g., combinations and permutations, fundamental counting principle, experimental vs. theoretical probability and independent, dependent and conditional probability.

4.1 Determine the experimental probability of an event.4.2 Determine the theoretical probability of an event.4.3 Determine the probability of independent events.4.4 Determine the likelihood of complex events using dependent and/or conditional probability.4.5 Compare the results of an experiment to the theoretical

probability.4.6 Apply the fundamental counting principle to real-world

applications.4.7 Use permutations and combinations.

2 2 2 2

4

2

2


Foundation LevelLearning Target 5*: Number Operations

Compare, perform, explain and evaluate mathematical operations (+, -, *, /, exponents, roots) and properties on real numbers, emphasizing negative and positive numbers; ratios, proportions and percents; and exponents and roots in mathematical and real-world applications.

Topics Covered: Number System: Order of operations, properties of real numbers, expressions, proportions, percents, roots.

Vocabulary: integer, ratio, proportion, percent, distributive property, associative properties, commutative properties, identity properties, inverse properties, expression, exponent, power, root, absolute value real numbers, transitivity.Draft 08/25/08


9



B.1* Compare and order real numbers.B.2* Analyze and solve problems using percents.B.3* Apply proportional reasoning and ratios in mathematical and real-world contexts.B.4*Compare, perform and explain operations on real numbers with and without context, e.g. transitivity, rate of change, exponential functions, scientific notation, roots, powers, reciprocals, absolute value, ratios, proportions, percents.B.5* Select and use appropriate properties, computational procedures, and modes of representation with and without context, e.g. simple and compound interest, commission, percents, proportions.F.6* Demonstrate understanding of properties by evaluating and simplifying expressions.

5.1 Solve problems using integers and absolute values.5.2 Solve problems with fractions, decimals and percents.5.3 Solve problems using ratios and proportions.5.4 Solve real-world application problems using scale factors and scale drawings.5.5 Solve problems involving exponents and roots.5.6 Express numbers using scientific notation and perform operations, using the laws of exponents.5.7 Identify the properties of real numbers.5.8 Use the order of operations to evaluate and simplify expressions.5.9 Simplify expressions using the commutative, associative and distributive properties.5.10 Translate verbal expressions into algebraic expressions.5.11 Simplify a radical.

2234

32

12

2

22


Foundation LevelLearning Target 6*: Applied Formulas Identify, describe and use formulas to solve real-world measurement problems such as interest, perimeter, area and volume.

Topics Covered: Formulas: interest, commissions, distance, area, perimeter, circumference, volume.

Vocabulary: variable, formula, substitution, area, perimeter, circumference, volume, interest, commission, prism, quadrilateral, variable, metric units, meter, gram, liter, length, volume, weight, capacity, square unit, cubic unit, polygon, triangle, right triangle, acute triangle, isosceles triangle, scalene triangle, equilateral triangle, obtuse triangles, circle, chord, diameter, radius, tangent, arcs in circles, simple interest, compound interest.Draft 08/25/08


10



B.5*Select and use appropriate properties, computational procedures and modes of representation with and without context e.g. simple and compound interest, commission, percents, proportions.D.3*Determine the perimeter/area of two-dimensional figures.D.4*Determine the surface area/volume of three-dimensional figures.D.7*Use formulas in applications, e.g. distance formula, simple and compound interest.

6.1 Use formulas in real-world applications, e.g. simple and compound interest, commission, distance.

6.2 Calculate the area, perimeter and/or circumferences of a triangle, quadrilateral and a circle.

6.3 Calculate the volume of rectangular prisms in real-world applications.

6.4 Solve for any variable in a mathematical formula.

3

3

3

2


Foundation LevelLearning Target 7*: Representations

Create and use tables, graphs, equations and formulas to describe relationships between variables.

Topics Covered: Linear Functions: using tables, graphs (slopes and intercepts) and equations, patterns of change, direct and inverse variation.

Vocabulary: graph, scale, equation, table, slope, intercept(s), parallel, perpendicular, coordinates, coordinate system, rate of change, domain, range, function(s), variable, slope-intercept, point slope, direct variation.

Draft 08/25/08


11



F.1* Describe, recognize, interpret and translate graphical representations of mathematical and real-world phenomena on coordinate grids, e.g., slope, intercepts, rate of change, linear and non-linear functions, and quadratic, exponential and constant functions.F.2*Analyze, generalize and represent patterns of change, e.g., direct and inverse variations, including numerical sequences, patterns to a given term, algebraic expressions and equations.F.5*Translate between different representations and describe the relationship among variable quantities in a problem, e.g. tables, graphs, functional notations, formulas.

7.1 Create tables, including real-world data, using equations and graphs.7.2 Create graphs, including real-world data, using equations and tables.7.3 Identify the domain and range for a relation given a set of ordered pairs, a

table or a graph.7.4 Determine from a set or ordered pairs, a table or a graph whether or not a

relation is a function.7.5 Interpret the meaning of tables, graphs and equations using data from real-

world applications.7.6 Find and describe intercepts on a graph.7.7 Find and describe slopes as constant rates of change.7.8 Describe the relationship between the slopes of parallel and perpendicular

lines.7.9 Write an equation from tables and graphs using real-world data.7.10 Describe patterns of change from a table of ordered pairs.7.11 Use formulas to calculate slope and intercepts from a set of ordered pairs.7.12 Write a linear equation to represent a pattern in which there is a constant rate of change between variables.7.13 Identify the difference between direct and inverse variations in tables, graphs, and equations.

112

2

3

233

2242

2

Block RegularMA211 MA211

Foundation LevelLearning Target 8*: Coordinate Plane

Use the two-dimensional coordinate plane to analyze, generalize and represent algebraic properties in mathematical and real-world applications.Topics Covered: Coordinate plane: distance and midpoint formulas, horizontal and vertical lines.Vocabulary: symmetry, midpoint, segment, direct variation, inverse variation, axis of symmetry, bisector, perpendicular, parallel, altitude, angle bisector. Pythagorean Theorem.10th Grade Assessment Framework*/12th Grade Standards


Draft 08/25/08


12

C.7* Use the two-dimensional rectangular coordinate system to describe and characterize properties of geometric figures. Identify and apply symmetry about an axis.C.8* Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships (e.g. slope, intercepts, parallelism, and perpendicularity, Pythagorean Theorem, distance formula).F.1* Describe, recognize, interpret and translate graphical representations of mathematical and real-world phenomena on coordinate grids, e.g. slope, intercepts, rate of change, linear and non-linear functions, and quadratic, exponential and constant functions.F2* Analyze, generalize and represent patterns of change, e.g. direct and inverse variations, including numerical sequences, patterns to a given term, algebraic expressions and equations.

8.1 Determine if lines and segments drawn on a coordinate graph are parallel or perpendicular.

8.2 Draw the line of symmetry of a graph (if it exists).

8.3 Use a coordinate plane and the distance and midpoint formulas to determine lengths and midpoints of segments.

8.4 Use a coordinate plane and the distance and midpoint formulas to determine the lengths and midpoints of the sides of triangles.

8.5 Write and graph an equation of a horizontal and a vertical line.

8.6 Analyze graphs of linear, quadratic and exponential functions to determine how slopes and intercepts affect rates of change.

2

3

2

2

1

4


Foundation LevelLearning Target 9*: Modeling

Model and solve mathematical and real-world applications that can be represented by linear equations and systems of equations, linear inequalities, and quadratic equations.

Topics Covered: Solving equations: One, two and multi-step equations; inequalities; systems; quadratics, properties of equality.Vocabulary: equation, inverse, matrices, roots, symmetric, transitive, reflexive, systems of equations, vertex, minimum, maximum, Substitution, inequality, velocity10th Grade Assessment Benchmarks: Students will be able to TL Instructional Sequence

Draft 08/25/08


13

Framework*/12th Grade StandardsF.3* Solve linear and quadratic equations, linear inequalities and systems of linear equations and inequalities.F.4* Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations and inequalities, e.g., linear, exponential, quadratic.F.7* Demonstrate understanding of properties by solving linear and quadratic equations, linear inequalities, and systems of linear equations and inequalities with one or two variables.

9.1 Solve one-step equations using inverse operations.9.2 Solve two-step equations using inverse operations and explain the meaning of the solution in context.9.3 Solve multi-step equations using inverse operations and explain the meaning of the solution in context. 9.4 Solve linear inequalities in one or two variables and graph the results.9.5 Solve and graph absolute value equations and inequalities.9.6 Solve a system of linear equations and explain the meaning

of the solution in context (methods: graphs, table, substitution, elimination, or matrices).

9.7 Solve a quadratic equation by finding the roots and identifying the minimum and maximum of a quadratic equation.

9.8 Solve linear equations, inequalities, quadratic equations and systems of linear equations to real-world applications.9.9 Model real-world situations with linear equations, systems

of equations, and inequalities.

22

3

3

34

3

3


Foundation Level Learning Target 10*: Functions

Evaluate information, analyze patterns, identify relationships, and represent them using algebraic expressions, functions, and equations, e.g., linear, exponential and quadratic, recognizing that a family of functions can model a variety of real-world applications.

Topics Covered: Algebraic Relations: Patterns, graphing inequalities and systems of equations, writing equations for linear, quadratic and exponential equations.

Draft 08/25/08


14

Vocabulary: pattern, inequality, model, quadratic, exponential function, analyze, acceleration, density. 10th Grade Assessment Framework*/12th Grade Standards


Draft 08/25/08


15

F.2* Analyze, generalize and represent patterns of change, e.g., direct and inverse variation, including numerical sequences, patterns to a given term, algebraic expressions and equations.F.4* Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities, e.g., linear, exponential, quadratic.

10.1 Recognize the characteristics of linear, quadratic and exponential families of functions.10.2 Identify the characteristics of an inequality graph.

10.3 Analyze graphs that represent a given real world applications.10.4 Write equations for linear, quadratic and exponential patterns.

10.5 Identify and interpret the intersection of a system. 10.6 Interpret the properties of linear and quadratic functions.

10.7 Identify a pattern in a numerical sequence and complete the pattern to a given term.10.8 Create models and justify strategies for a variety of real-world applications using linear, exponential and quadratic equations.

3

3

3

2

33

2

3/4


Foundation LevelLearning Target 11*: Right Triangles

Explain and use the Pythagorean Theorem and right triangle trigonometry as models to solve a variety of right triangle problems in real-world applications.

Topics Covered: Right triangles.

Vocabulary: Triangles, Pythagorean Theorem, right, obtuse, acute, sine, cosine, tangent, elevation, depression, trigonometry functions, clinometer.

10th Grade Assessment Benchmarks: Students will be able to TL Instructional Sequence

Draft 08/25/08


16

Framework*/12th Grade StandardsC2* Present convincing geometric arguments by means of informal proof, counter-examples or other logical means.C.3* Model problems using the Pythagorean Theorem and right triangle trigonometry.C.4*Use proportional reasoning to solve congruence and similarity problems, e.g., scale drawings and similar geometric figures.D.6*Use right triangle trigonometric functions and the Pythagorean Theorem to solve right-triangle problems.

11.1 Apply the Pythagorean Theorem to find side lengths of a right triangle in mathematical and real-world applications.

11.2 Determine if a triangle is right, obtuse or acute by using the Pythagorean Theorem.

11.3 Solve right triangle problems using trigonometric ratios.

11.4 Use trigonometric ratios to find the angle of elevation or the angle of depression in real world applications.

2

3

3

4


Foundation LevelLearning Target 12*: Lines and Angles

Identify and apply the definitions related to lines and angles in order to use them to solve problems and perform basic geometric constructions.

Topics covered: Lines: angles; parallel and perpendicular; proofs.

Vocabulary: line, ray, line segment, plane, parallel, perpendicular, angle, complementary angle, supplementary angle, linear pair, vertical angles, transversal alternate exterior, alternate interior, corresponding, consecutive interior, proof, collinear, coplanar, endpoint, congruent, vertex, counterexample, right angle, acute angle, obtuse angle, circumcenter, incenter, centroid, orthocenterDraft 08/25/08


17



C.1* Identify, describe and analyze properties of figures, relationships among figures and relationships among their parts.C.2* Present convincing arguments by means of informal proof, counter-examples or other logical means.

12.1 Identify and name points, lines, rays, segments and planes.

12.2 Name and classify angles.

12.3 Identify and use angle-pair relationships in mathematical and real-world applications.

12.4 Classify and communicate the differences between pairs of lines.

12.5 Classify the types of angles formed by two lines and a transversal.

12.6 Prove statements about segments, lines, angles and angle relationships by using properties, postulates, and theorems.

12.7 Perform basic geometric constructions.

1

2

3

3

2

4

3


Foundation LevelLearning Target 13*: Classify Polygons

Classify and describe polygons and 3-dimensional figures.

Topics covered: Polygons: 3-dimensional figures.

Vocabulary: polygon, acute, obtuse, scalene, equilateral, isosceles, prism, pyramid, cone, cylinder, sphere, convex, concave, polyhedron, displacement, density, orthographic drawing.



Draft 08/25/08


18

C.1* Identify, describe and analyze properties of figures, relationships among figures and relationships among their parts. C.6* Visualize 3-dimensional figures in problem-solving situationsC.7* Use the two-dimensional rectangular coordinate system to describe and characterize properties of geometric figures. Identify and apply symmetry about an axis.C.8* Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships (e.g. slope, intercepts, parallelism and perpendicularity, Pythagorean Theorem, distance formula).

13.1 Classify polygons by sides and angles.

13.2 Classify triangles by sides and angles.

13.3 Classify quadrilaterals by their parts.

13.4 Describe properties of a given polygon.

13.5 Describe properties of quadrilaterals.

13.6 Describe properties of other polygons.

13.7 Classify geometric properties by using the coordinate system (e.g. distance formula, slope).

13.8 Identify 3-dimensional objects (e.g. prisms, pyramids, cones, cylinders and spheres).

2

2

2

3

3

3

3

2


Foundation LevelLearning Target 14: Analyze Polygons

Use and analyze geometric relationships and properties of polygons and 3-dimensional figures to solve mathematical and real-world applications.

Topics Covered: Polygons: Sides and angles in triangles and polygonsVocabulary: angles, interior angle, exterior angle, vertical angle, polygon, 3-dimensional, similarity, similar polygons.



Draft 08/25/08


19

C.12.1 Identify, describe and analyze properties of figures, relationships among figures and relationships among their parts by constructing physical models, drawing precisely with paper-and-pencil, hand calculators, and computer software, using appropriate transformations, and using reason and logic.C.12.2 Use geometric models to solve mathematical and real-world problems. C 12.3 Present convincing arguments by means of demonstration, informal proof, counter-examples or any other logical means to show the truth of statements (e.g. these two triangles are not congruent) and generalizations (e.g., the Pythagorean theorem holds for all right triangles).D.5* Solve for angles and segments in similar polygons and arcs in circles.

14.1 Determine if lengths of three segments can form a triangle.

14.2 Determine the range in which the length of the third side of a triangle must be given the lengths of two sides.

14.3 Find the measures of segments in similar polygons.

14.4 Find the measures of each interior and exterior angle of a regular polygon.

14.5 Find the sum of the measures of the interior and exterior angles of a convex polygon.

14.6 Solve problems involving real-world applications using the relationships between pairs of angles.

14.7 Make a two-dimensional representation of a 3-dimensional object.

3

3

2

2

2

3

3


Foundation LevelLearning Target 15: Congruence/Similarity

Apply the basic theorems of congruence and similarity to solve mathematical and real-world applications.

Topics covered: Congruence, similarity.

Vocabulary: ASA, SSS, SAS, HL, AA, congruent, similar, similarity.10th Grade Assessment Framework*/12th Grade Standards


Draft 08/25/08


20

C.12.1 Identify, describe, and analyze properties of figures, relationships among figures, and relationships among their parts by constructing physical models, drawing precisely with paper-and pencil, hand calculators, and computer software, using appropriate transformations, and using reason and logic.C 12.3 Present convincing arguments by means of demonstration, informal proof, counter-examples or any other logical means to show the truth of statements (e.g. these two triangles are not congruent) and generalizations (e.g., the Pythagorean theorem holds for all right triangles).C.12.5 Identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent). .D12.3 Determine measurements indirectly, using proportional reasoning.F.12.4 Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations and inequalities.

15.1 Identify congruent and similar polygons.

15.2 Justify congruency or similarity of polygons by using formal and informal proofs.

15.3 Prove two triangles are congruent using coordinate methods (e.g. distance and slope formulas).

15.4 Solve real-world applications using the properties of congruency and similarity.

2

3

4

4


Foundation LevelLearning Target 16: Transformations

Apply transformations and their compositions to analyze geometric figures and create designs.

Topics Covered: Transformations and tessellations.

Vocabulary: transformation, tessellation, image, pre-image, symmetry, representations, reflection, rotation, isometry, isometrics, translation, axis of symmetry

Draft 08/25/08


21



C.12.1 Identify, describe, and analyze properties of figures, relationships among figures, and relationships among their parts by constructing physical models, drawing precisely with paper-and- pencil, hand calculators, and computer software, using appropriate transformations (e.g., translations, rotations, reflections, enlargements), and using reason and logic.C.12.2 Use geometric models to solve mathematical and real-world problems. C.12.4 Use the two-dimensional rectangular coordinate system and algebraic procedures to describe and characterize geometric properties and relationships such as slope, intercepts, parallelism, and perpendicularity.C.5* Use transformations and symmetry to solve problems.

16.1 Plot and label geometric figures using a coordinate plane.

16.2 Perform transformations using triangles in a coordinate plane.

16.3 Identify, given an image and pre-image, the transformation that has taken place as a reflection, rotation, or translation.

16.4 Determine whether a figure has point symmetry, line symmetry or neither.

16.5 Identify tessellations in art, construction and nature.

16.6 Design a real-world application of transformations and communicate the process used in the design.

2

3

2

2

3

4


Foundation LevelLearning Target 17: Circles

Use properties of circles to solve mathematical and real-world applications.

Topics covered: Circles.

Vocabulary: chord, secant, tangent, arc, sector, inscribed, central angle.

Draft 08/25/08


22



C.12.1 Identify, describe, and analyze properties of figures, relationships among figures, and relationships among their parts by constructing physical models, drawing precisely with paper-and pencil, hand calculators, and computer software, using appropriate transformations (e.g., translations, rotations, reflections, enlargements), and using reason and logic.C.12.2 Use geometric models to solve mathematical and real-world problems. D.12.3 Determine measurements indirectly using geometric relationships and properties of circles and polygons (e.g. size of central angles, area of a sector of a circle).

17.1 Determine circumference and area of a circle.

17.2 Determine measures of inscribed and central angles.

17.3 Determine arc lengths and areas of sectors of circles.

17.4 Write and solve equations to find the measures of angles formed by chords, secants, and tangents.

17.5 Calculate lengths of chord, tangent and secant segments.

17.6 Write an equation of a circle and graph a circle from its equation.

17.7 Solve real-world applications of circles.

2

3

3

3

3

3

4


Foundation LevelLearning Target 18: Applied Geometry

Use perimeter, area, volume and surface area to solve real-world applications.

Topics covered: Measurements of 2 and 3 dimensional figures.

Vocabulary: perimeter, area, volume, surface area, degree, cubic units, square units, faces, bases, edge, lateral area, perspective, concurrency

Draft 08/25/08


23



C.12.1 Identify, describe, and analyze properties of figures, relationships among figures, and relationships among their parts by constructing physical models, drawing precisely with paper-and pencil, hand calculators, and computer software, using appropriate transformations (e.g., translations, rotations, reflections, enlargements), and using reason and logic.C.12.2 Use geometric models to solve mathematical and real-world problems.D.12.3Determine measurements indirectly using geometric formulas to derive lengths, areas, or volumes or shapes and objects.

18.1 Determine the perimeter/circumference and area of quadrilaterals, triangles and other polygons, using real-world applications.18.2 Determine the volume and lateral area and total surface area of spheres, prisms, pyramids, cylinders and cones.18.3 Use volume, lateral area and surface area of 3-dimensional figures to solve real-world application problems.18.4 Solve real-world application problems for missing lengths in

special right triangles.18.5 Compare perimeters and areas of similar 2-dimensional figures using proportions.18.6 Describe how a change in one measurement affects other measurements of the object.18.7 Solve real-world application problems using scale drawings, perspective drawings, blueprints, and/or computer drawings as models.18.8 Make a model of a 3-dimensional figure from a 2-dimensional drawing.

2

2

3

3

3

3

3

4


Foundation LevelLearning Target 19:

Use increased rigor in justifying conclusions to mathematical and real-world applications and in verifying the truth of geometric theorems.

Topics covered: Conjectures, proofs

Draft 08/25/08


24

Vocabulary: conjecture, counterexample, deductive logic, inductive logic, proof, theorem, postulate, syllogism, hypothesis, conclusion, converse, inverse, contra positive, paragraph proof, flow-chart, coordinate proof., Venn diagram, justify, strategy, reasonableness,, representations, negation.10th Grade Assessment Framework*/12th Grade Standards


A.12.1 Use reason and logic to evaluate information, perceive patterns, identify relationships, formulate questions, pose problems, and make and test conjectures.B.12.5 Create and critically evaluate numerical arguments presented in a variety of classroom and real-world situations (e.g., political, economic, scientific, social).C.12.3 Students will present convincing arguments by means of demonstration, informal proof, counter examples or any other logical means to show the truth of statements and generalizations.

19.1 Identify the converse, inverse and contra positive of a conditional statement and their relative truth value.

19.2 Translate short verbal arguments into symbolic form.

19.3 Write conjectures using characteristics, postulates and theorems of geometric figures.

19.4 Use and interpret Venn diagrams.

19.5 Diagram conditional statements to solve logic puzzles.

19.6 Use valid forms of inductive and deductive reasoning to draw conclusions and make conjectures.

19.7 Select and use various types of reasoning and methods to prove characteristics and properties of algebraic models and geometric figures.

2

2

3

3

3

3

4

Regular BlockMA311 MA311

Draft 08/25/08


25

mps algebra/geometry syllabus template - … docs/yr6_worddocs/hs_curriculu… · web view(algebra...

Documents