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Course Overview

Locally Developed Mathematics

Identifying Information

Grade 10 Mathematics: locally developed optional course

Writers: Shirley Scott, District School Board of Niagara,Steve Etienne, District School Board of Niagara, Mary-Beth Fortune, Peel District School Board

Description/Rationale

This Grade 10 Mathematics – a locally developed optional course, is designed to provide additional experiences in mathematics that may help the student in the Grade 11 Workplace Mathematics course. The students for whom this course is designed will have had varying degrees of success in learning mathematics. They are students from the Grade 9 Essential Mathematics course who intend to take the Grade 11 Workplace Mathematics course. They are students who have experienced significant difficulty in previous mathematics courses and may not be ready to work at the level demanded by the Grade 11 course. Students need to continue reinforcing and developing skills from Grade 9 and to continue building the necessary base for success in Grade 11. Repetition of skills, including repeated exposure to technology, in a diversity of contexts, is an important strategy to use since students may take longer to consolidate skills and concepts.

In order for students to complete their work thoroughly, and to achieve an appropriate level of understanding and a mastery of skills, it is beneficial for them to have more time to complete the assignments in a structured, well-organised environment. Students should be encouraged to work in pairs or in small groups, but increasing independence is the goal. This does not imply that a formal co-operative learning structure must be in place. At this level, students often find comfort and confidence when allowed to sit near a friend as they both complete the same assignment.

The Grade 11 Workplace course requires that students spend time solving authentic problems and using technology. A comfort level must be reached in these areas so that students are more willing to take risks and to try to solve authentic problems. Providing opportunities to work with mathematics within a real-life context of high student interest provides a vehicle that can help to make this happen. This context helps the students develop a strategy and apply it, allowing them to complete a solution which otherwise might be very abstract and intimidating.

The course assumes that students have had Grade 9 experience in:

Number Sense

· applying strategies for mental mathematics and estimation;

· developing understanding of percent through the use of activities involving concrete materials, models, and diagrams;

· solving simple problems involving percent drawn from familiar applications;

· using ratios to express the relationships among quantities illustrated by models, diagrams, or concrete materials;

· solving simple problems involving proportions;

· calculating rates in applications drawn from familiar experiences;

· solving simple problems involving rates.

Calculator Use

· using a calculator effectively;

· judging the reasonableness of answers to problems by considering likely results;

· judging the reasonableness of answers produced by a calculator or computer, using mental mathematics and estimation.

Data Management

· collecting, organising, and analysing data involving one variable;

· understanding sampling and surveying;

· displaying data, using appropriate graphs;

· describing trends observed in data;

· explaining findings;

· answering questions about data.

Measurement

· measuring lengths accurately, using the metric system;

· using metric prefixes appropriately in measurement and estimation activities;

· investigating the relationships between the perimeter and area of a rectangle (e.g., 56 m of fencing are available to fence a rectangular region. What is the maximum area that can be fenced?);

· solving simple problems drawn from students’ experiences, using the formulas for the area of a rectangle, a square, a triangle, and a circle;

· developing understanding of the concept of volume, using concrete materials;

· solving simple problems involving the volume of a rectangular prism.

Communication

· communicating solutions in oral and/or written form;

· using appropriate terminology, symbols and form in communicating solutions.

Expectations and support activities relating to these experiences are found in the course profile for the Locally Developed Grade 9 Essential Mathematics course, released in 1999 and available at www.curriculum.org.

Unit Titles (Time + Sequence)

Unit 1	Sports and Leisure	20 hours
Unit 2	Trends in Society	20 hours
Unit 3	Home Entertainment	25 hours
Unit 4	Construction	18 hours
Unit 5	Packaging	15 hours
Unit 6	Summative Assessment and Evaluation Activities	12 hours

Unit Descriptions

Unit 1: Sports and Leisure

Time: 20 hours

Description

Students examine and apply geometric properties and relationships by investigating sports and leisure activities. The sporting world is rich with applications of, and opportunities to use angle properties, parallel lines, the Pythagorean theorem, and measurement formulas. Opportunities for the consolidation of a variety of numeracy skills abound. Students practise estimation skills and judge the reasonableness of answers throughout the unit.

Overall Expectations: PRV.01, .02, MEV.01, .02, .04, GPV.01, .02.

Specific Expectations: PR 1.01, 1.02, 2.01, 2.02, 2.03, 2.04, 2.05, 2.07, ME 1.01, 1.02, 1.03, 2.05, 4.01, 4.02, 4.03, 4.04, GP 1.02, 1.03, 1.04, 1.05, 2.01, 2.03, 2.04.

Unit 2: Trends in Society

Time: 20 hours

Description

Students collect primary data for the purpose of discovering present trends and the making of predictions of future outcomes. Students use appropriate equipment and/or technology to collect, organise, display, and aid in the analysis of data. As a result of this analysis, students interpolate and extrapolate from the data. Opportunities for students to practise estimation skills and to judge the reasonableness of answers are provided throughout the unit.

Overall Expectations: PRV.02, MEV.04.

Specific Expectations: PR 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, ME 4.01, 4.02, 4.03, 4.04.

Unit 3: Home Entertainment

Time: 25 hours

Description

Students investigate mathematical principles and applications in the context of real-life situations. They develop a greater understanding of fixed and variable rates in a financial context. Students use measurement and data collection skills to enhance their understanding of design, scale diagrams, and proportionality. The Pythagorean theorem is applied to solve real-life problems. By using appropriate technology and/or traditional methods, students construct, read and interpret charts and tables, as well as identify relationships, make inferences and communicate observations. Opportunities for students to practise estimation skills and to judge the reasonableness of answers are provided throughout the unit.

Overall Expectations: PRV.01, .02, MEV.01, .02, .04, GPV.02.

Specific Expectations: PR 1.01, 1.02, 2.01, 2.02, 2.04, 2.05, 2.07, ME1.03, 2.05, 4.01, 4.02, 4.03, 4.04, GP 2.01, 2.03, 2.04.

Unit 4: Construction and Design

Time: 18 hours

Description

Students extend their study of measurement and geometry within the contextual framework of construction, e.g., fencing, roofing, and concrete work. Students explore some of the financial aspects relating to construction, e.g., cost of materials and labour, taxes. Students use mental mathematics and estimation to ensure that their calculations, use of technology, and problem-solving strategies produce reasonable results.

Overall Expectations: PRV.01, MEV.01, .02, .03, .04, GPV.01, .02.

Specific Expectations: PR 1.01, 1.02, ME 1.02, 2.01, 2.02, 2.03, 2.04, 2.05, 3.01, 3.02, 3.04, 4.01, 4.02, 4.03, 4.04, GP 1.01, 1.04, 1.05, 2.01, 2.02, 2.04.

Unit 5: Packaging

Time: 15 hours

Description

Students investigate the relationships between the surface area and the volume of cylinders and rectangular prisms through the use of concrete materials, drawings, and technology. Students construct square-based prisms to determine optimal values between variables. Opportunities for students to practise estimation skills and to judge the reasonableness of answers are provided throughout the unit.

Overall Expectations: PRV.01, .02, MEV.02, .03, .04, GPV.02.

Specific Expectations: PR 1.01, 1.02, 2.01, 2.03, 2.04, 2.06, 2.07, ME 2.02, 2.03, 2.04, 2.05, 3.01, 3.02, 3.03, 3.04, 3.05, 4.01, 4.02, 4.03, 4.04., GP 2.01, 2.03, 2.04.

Unit 6: Summative Assessment and Evaluation Activities

Time: 12 hours

Description

This summative assessment and evaluation unit involves students performing tasks which are assessed and evaluated over a period of several days. Students have more than one opportunity to demonstrate their ability to make calculations and to organise, to display, and to analyse data. Students apply appropriate measurement skills to consolidate the meaning and the use of proportionality. Students communicate results and reasoning. Throughout the unit, students judge the reasonableness of their answers.

Overall Expectations: PRV.01, .02, MEV.01, .02, .03, .04, GPV.01, .02.

Specific Expectations: PR1.02, 2.01, 2.02, 2.04, 2.05, 2.06, 2.07, ME 1.03, 2.02, 2.04, 2.05, 3.01, 3.02, 3.04, 4.01, 4.02, 4.03, 4.04, GP 1.02, 1.03, 1.05, 2.01, 2.04.

Course Notes

The activities in this course are presented in a non-threatening, contextual format that encourages students to try to make sense of the mathematics and to apply it in an understandable and useful manner. The teacher and students work closely together in a structured, welcoming environment to develop skills by solving authentic problems. Variety and flexibility of teaching style and method are important within the structured setting.

Students are provided with opportunities to

· work in an environment where they feel secure;

· take risks;

· learn through a wide variety of classroom experiences;

· learn mathematics in real-life contexts;

· learn through the use of technology;

· improve their organisational skills;

· improve their estimation skills;

· improve their ability to judge the reasonableness of answers;

· communicate effectively with the language of mathematics;

· demonstrate their achievement of the course expectations in a variety of ways.

Teaching/Learning Strategies

Opportunities are provided throughout the course to use a wide variety of teaching and/or learning strategies. It is critical for student success that the teacher has ongoing, direct interaction with the student and provides immediate feedback on a continual basis. This is not an exhaustive list and teachers may have other strategies to include:

· Brainstorming

· Case study

· Collaborative learning/co-operative learning/learning partners

· Community involvement

· Conferencing/interviewing

· Context-based learning

· Demonstration

· Direct teaching

· Discussion

· Field trip

· Investigation/inquiry/research

· Learning centres

· Model making

· Open-ended questions

· Oral communication/read aloud/read along

· Simulation

· Technology-assisted learning/manipulatives

· Written communication/journal

Assessment and Evaluation

Assessment is a systematic process of collecting information or evidence about student learning. Evaluation is the judgement a teacher makes about the assessments of student learning based on established criteria. This profile provides specific examples of assessment strategies and tools, and general statements about how these assessments might be used in evaluation. Evaluation requires that the teacher not simply average marks. In forming an evaluative judgement, the teacher should consider students’ performances in all Categories of the Achievement Chart for Mathematics.

It is important to note that assessment and evaluation are criterion referenced, comparing student performance to the Ministry standard, not to other students. Level 3 is defined as the provincial standard. A student achieving at this level is prepared for work in the Grade 11 Workplace course. Level 4 performance requires a consistent, but not constant, pattern of well-communicated higher level thinking and not simply technically correct solutions. Level 4 does not require a student to perform beyond grade level expectation.

Assessment and evaluation strategies and tools must address the variety of teaching and learning styles as well as the variety of expectations. Assessment should be used to gather information for diagnostic, formative and summative purposes. A balanced assessment and evaluation program is based on the provincial curriculum expectations and the achievement levels. For example:

· assess and evaluate Knowledge/Understanding through tests, quizzes, and observation of performance tasks;

· assess and evaluate Thinking/Inquiry/Problem Solving in varied settings through performance assessment, observation, and conferencing;

· assess and evaluate Communication through journals, discussions, performance assessments, observations, and presentations;

· assess and evaluate Application in varied settings through tests, quizzes, and performance assessments;

· assess Learning Skills, through journals, portfolios, and observations.

Assessment and Evaluation tools to be used throughout the course include:

· the four-level Achievement Chart for Mathematics;

· checklists;

· rating scales;

· anecdotal comments;

· marking schemes;

· rubrics.

When teachers use a variety of these assessment tools, it is necessary to ensure that a consistent standard is maintained. That is, a 70-79% performance using an objective marking scheme should be equivalent to a Level 3 performance. Teachers may find it more appropriate to use rubrics to assess Inquiry/Problem Solving and Communication, and objective scales for Knowledge/Understanding and Application, as they are beginning to gather data in the Categories of the Achievement Chart. In doing so, it is important that they keep in mind that Level 3 and 70-79% are the provincial standard. Performance tasks and tests should be set with the Expectations in the policy document as the criteria for this standard.

A selection of these tools is designed for this course profile to accompany specific assessment and evaluation activities. Teachers are encouraged to use them to develop similar tools for other assessment and evaluation activities. Some suggestions for increasing scoring consistency include:

· involving other teachers in the creation of assessment and evaluation tools;

· involving students, whenever appropriate, in the setting of criteria;

· gathering exemplars of student work at the four levels, so that teachers and students can get a better image of the performance expected at each level.

Assessment of the Expectations, using the four levels of the Achievement Chart, is ongoing throughout the Course Profile. A summative performance activity and/or summative paper and pencil questions are provided for each unit. Assessment tools are designed to allow students to demonstrate performance at the full range of student learning (Levels 1 to 4).

It should be noted that:

· Tests that include only questions that ask students to perform algorithms and to apply their knowledge do not necessarily offer an opportunity for students to demonstrate Level 4 performance.

· It is often easier to pose questions with the expectation of Level 1 to 4 responses in the Inquiry/Problem Solving and Communication Categories of the Achievement Chart than the Knowledge/Understanding and routine Application Categories.

· Teachers must expand their understanding of Applications to include non-routine applications. This newer view of Applications requires a shift from thinking of them as being tied to specific content, to applications of mathematics in general.

· The issue of Communication is complex. Teachers need to ask students to communicate their understanding of their knowledge, their stages of thought in an inquiry, and their process of applying mathematics to a problem, in order to assess Level 1 to 4 performances in the other three Categories of the Achievement Chart. Then, they need to report on the Communications Category separately from those categories.

· The expectations of the course include a wide range of skills, all of which must be addressed. Students who have not demonstrated the expected level of achievement earlier in the course will require more learning opportunities. Students should be given repeated opportunities to demonstrate acquisition and retention of the necessary skills as determined by the course expectations.

This profile contains more assessment suggestions than would be reasonable for any teacher to use in one course. The expectation is that teachers will try a variety of strategies and tools so that an informed decision can be made about which of these works best, for them, in the various Categories of the Achievement Chart.

Accommodations

Appropriate accommodations should be part of the planning of each unit activity with respect to the particular students in the class and their specific needs. Instructional, assessment, and evaluation activities must take into account the strengths, needs, learning expectations, and accommodations as identified in the Individual Education Plan (IEP) whether students are formally identified or not (Regulation 181/98).

Accommodation to curriculum, instruction, assessment, and evaluation may include, but are not limited to the following:

Accommodations for students with learning disabilities:

· allow more time for learning and for completion of activities, e.g., some students may require greater time to become comfortable with the technology emphasised in this course profile before they are able to demonstrate their understanding of a concept;

· allow the use of specialised equipment and assistance, e.g., some students may require calculators with large keys or calculators that are capable of fraction manipulation;

· provide specialised instructional aids, e.g., some students may require pre-completed portions of an activity so that they can focus on the important concepts;

· use varied assessment and evaluation strategies;

· encourage the use of available adaptive technologies to assist students, e.g., students may require opportunities outside of regular class time to use new technologies such as dynamic geometry software;

· provide extensive student/teacher conferencing;

· allow students to work with a partner;

· provide a list of terminology (possibly simplified) before an activity begins;

· provide oral preplanning of activities with students;

· allow alternate formats for the completion of assignments;

· provide adjusted handouts, e.g., some students will benefit from written, visually appealing materials that are in a large font and not clustered on a page;

· keep manipulatives, grid paper, formula sheets and other aids available for needs that arise;

· provide alternate settings, e.g., resource room where students can receive assistance with problems that are language-based;

· contact parent/guardian for support and suggestions.

Accommodations for ESL/ESD students:

· work with partners, peer tutors, or classmates who share the same linguistic background;

· provide extensive student/teacher conferencing;

· use peer conferencing to reinforce instructions/information;

· ask an ESL/ESD teacher to review questions, assignments, or assessment instruments;

· provide sets of reference notes, outlines of critical information, and models of charts, timelines, or diagrams;

· reinforce main ideas by using think, pair, share;

· pair written instruction with verbal instructions;

· use key visuals to illustrate definitions for the student;

· simplify instructions;

· highlight and/or make a dictionary of key words or phrases;

· brainstorm in groups in first language, if English is limited;

· provide opportunities for students to practise oral presentation skills;

· provide visual/auditory cues.

Resources

Airasian, P.W., Classroom Assessment. New York: McGraw-Hill, 1994.

Andrini, B., Cooperative Learning and Mathematics: A Multi-Structural Approach. California: Resources for Teachers. 1991.

Baker, E., Making Performance Assessment Work: The Road Ahead. Educational Leadership 51, (1994): 6:58-62.

Burz, H.L. and K. Marshall. Performance-Based Curriculum for Mathematics. California: Sage, 1996.

Charles, L. and M.R. Brummet. Connections 8: Linking Manipulatives to Mathematics. California: Creative Publications, 1996.

Countryman, J. Writing to Learn Mathematics. Portsmouth: Heinemann. 1992.

Elchuck, L., et al. Interactions 8 (Blackline Masters and Professional Assessment Handbook). Scarborough: Prentice Hall. 1997.

Flewelling, G. and C. Lemenchick. Mathematics Assessment Activities 8A. Vancouver: Gage. 1997.

Flowers, L. and J. O’Connell. Math Across the Curriculum. California: Frank Schaffer Publications. 1994.

Harper, Mark, K. O’Connor, and M. Simpson. Quality Assessment: Fitting the Pieces Together. Toronto: OSSTF, 1999.

Hibbard, K.M., et al. A Teacher’s Guide to Performance-Based Learning and Assessment. Alexandria, VA: Association for Supervision and Curriculum Department. 1996.

Kulm, G. (Ed.) Assessing Higher Order Thinking in Mathematics. Washington: American Association for the Advancement of Science. 1991.

Lambdin. D.V., et al. Emphasis on Assessment: Readings from NCTM’s School-Based Journals. Reston, VA: National Council of Teachers of Mathematics. 1996.

Lappin, G., et al. Data About Us - Teacher’s Guide. California: Dale Seymore Publications. 1998.

McTighe, J. “What Happens Between Assessments?” Educational Leadership 54, 4:6 - 12. 1996.

National Council of Teachers of Mathematics. Assessment Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics. 1995.

O’Neil, J. “Putting Performance Assessment to the Test.” Educational Leadership 49, 8:14-19. 1992.

Romberg, T.A. (Ed.) “Reform in School Mathematics and Authentic Assessment” New York: State University of New York Press.

Romberg, T.A. (Ed.) Mathematics Assessment and Evaluation: Imperatives for Mathematics Educators. New York: State University of New York Press.

Silver, E.A., et al. Thinking Through Mathematics: Fostering Inquiry and Communication in Mathematics Classrooms. New York: College Entrance Examination Board. 1990.

Stepien, W. and S. Gallagher. “Problem-Based Learning: As Authentic As It Gets.” Educational Leadership 50, 7:25-28.

Course Evaluation

Course improvement should be viewed as an ongoing, collaborative process among mathematics teachers. As new resources, new technology, and new insights about the programs develop, teachers must adapt their programs to better serve the needs of their students.

To meet these goals, teachers should evaluate the effectiveness of their courses using a variety of information sources. While students’ performances on summative tasks are obvious indicators of success, many other sources exist. These include student feedback, parental feedback, and the performance of students in subsequent mathematics courses.

Anecdotal evidence can be gathered from observing the following indicators:

· care taken by the student in completing work;

· students’ efforts to seek help when needed;

· students’ growth in independence and persistence when completing tasks.

The School Board must apply to the Ministry of Education every three years for re-approval to offer this locally developed optional credit course.

Coded Expectations, Locally Developed Mathematics, Grade 10 - Public

Patterns and Relationships

Overall Expectations

PRV.01

– solve simple problems using patterning strategies as they arise in activities throughout the course;

PRV.02

– determine relationships between two variables by collecting and analysing data.

Specific Expectations

Solving Problems Using Patterning Strategies

PR1.01

– describe simple number patterns using language in oral and/or written form;

PR1.02

– identify and extend simple patterns in problem solving situations.

Determining Relationships Between Two Variables

PR2.01

– analyse information displayed in graphs and tables drawn from a wide variety of sources;

PR2.02

– formulate an hypothesis about a relationship between two variables;

PR2.03

– collect data using appropriate equipment and/or technology (e.g., measuring tools, graphing calculators, scientific probes);

PR2.04

– organise, display, and analyse data, using appropriate techniques and technology (e.g., graphing calculators, spreadsheets);

PR2.05

– describe trends and relationships observed in data and compare them to the original hypotheses (e.g., Are the data scattered or do they cluster around the shape of a straight line or a smooth curve? What does it mean if the data cluster around a straight line? Can a straight line be used to make predictions? Identify any outlying data points and provide explanations for them. Is the outcome of the experiment consistent with the original hypothesis? Why or why not?);

PR2.06

– explain clearly the procedure for and the findings of an experiment, by using a variety of mathematical forms (e.g., oral or written explanations, formulas, charts, tables, graphs);

PR2.07

– solve and/or pose extending problems related to the design or the findings of an experiment (e.g., Repeat the experiment under different conditions. Will the results be the same? Why or why not?).

Measurement

Overall Expectations

MEV.01

– solve simple problems involving the Pythagorean theorem;

MEV.02

– estimate and measure lengths in the metric and the imperial systems;

MEV.03

– solve problems involving the measurement of three-dimensional objects;

MEV.04

– demonstrate an ability to use technology effectively when solving problems drawn from a broad range of familiar experiences.

Specific Expectations

Solving Simple Problems Involving the Pythagorean Theorem

ME1.01

– illustrate the Pythagorean theorem, using concrete models;

ME1.02

– use the Pythagorean theorem to construct right angles in practical situations (e.g., the 3,4,5 triangle used by carpenters);

ME1.03

– solve simple problems drawn from familiar applications, using the Pythagorean theorem.

Estimating and Measuring Lengths in Metric and in Imperial

ME2.01

– compare, order, and represent (with and without concrete materials and drawings) fractions with denominators 2, 4, 8, 10, and 16, within the context of measurement ;

ME2.02

– demonstrate an understanding of the relationships among some imperial measures of length (e.g., inches, feet, and yards);

ME2.03

– measure and report lengths accurately, using inches, feet, and yards;

ME2.04

– use estimation and measurement of imperial lengths in applications drawn from other subjects (e.g., technology);

ME2.05

– estimate and measure lengths in the metric system within familiar applications.

Solving Problems Involving the Measurement of Three-dimensional Objects

ME3.01

– substitute into and evaluate measurement formulas involving exponents as the need arises in problem solving;

ME3.02

– state appropriate units when communicating answers to measurement problems;

ME3.03

– construct a variety of square-based prisms for a given volume and determine the minimum surface area for the given volume;

ME3.04

– solve simple problems drawn from familiar applications, using the formulas for the surface area and the volume of a prism and a cylinder;

ME3.05

– demonstrate an understanding of the significance of optimal measure within the application of packaging (e.g., Construct three different boxes that hold 1000 cm3 and compare the cost of the materials).

Using Technology Effectively

ME4.01

– use a scientific calculator effectively in applications throughout the course;

ME4.02

– select the most appropriate method for calculation when solving problems (e.g., use mental mathematics or estimation, use a calculator, use a pencil/paper computational method);

ME4.03

– judge the reasonableness of answers to problems by considering likely results;

ME4.04

– judge the reasonableness of answers produced by a calculator or computer, using mental mathematics and estimation.

Geometry and Proportionality

Overall Expectations

GPV.01

– demonstrate an understanding of the properties of sides and angles in triangles and parallel lines, through investigations using concrete materials and appropriate technology;

GPV.02

– solve problems drawn from a variety of applications, using proportional reasoning.

Specific Expectations

Properties of Triangles and Parallel Lines

GP1.01

– illustrate the meanings of key terms associated with angles and triangles by constructing diagrams (e.g., acute angle, obtuse angle, scalene triangle, isosceles triangle, equilateral triangle, right triangle, perpendicular lines, parallel lines);

GP1.02

– estimate the measures of angles ;

GP1.03

– determine the measures of angles, using appropriate tools;

GP1.04

– determine, through investigation, some of the properties of the angles of triangles and parallel lines;

GP1.05

– solve simple geometric problems;

Solving Problems, Using Proportional Reasoning

GP2.01

– solve problems drawn from familiar applications involving percent, rate, ratio, proportion, and scale;

GP2.02

– determine some properties of similar right triangles, using appropriate technology (e.g., spreadsheets, dynamic geometry software);

GP2.03

– solve problems involving scale, proportionality and similar figures drawn from familiar applications (e.g., scaling down the dimensions of a ball diamond for T-ball, building models in construction projects)

GP2.04

– communicate solutions to problems and the results of investigations, using appropriate terminology, symbols, and form.

Acknowledgements

Description/Rationale

Unit Titles (Time + Sequence)

Unit Descriptions

Unit 1: Sports and Leisure

Unit 2: Trends in Society

Unit 3: Home Entertainment

Unit 4: Construction and Design

Unit 5: Packaging

Unit 6: Summative Assessment and Evaluation Activities

Course Notes

Teaching/Learning Strategies

Assessment and Evaluation

Accommodations

Resources

Course Evaluation

Patterns and Relationships

Overall Expectations

Specific Expectations

Measurement

Overall Expectations

Specific Expectations

Geometry and Proportionality

Overall Expectations

Specific Expectations