Here you will find the curriculum map for this unit of work. It will give you information about what you will be studying, questions you should be able to answer as you work through the unit, and some useful websites.

Covering and Surrounding

2-Dimensional Measurement

Topics Covered

Perimeter and area of rectangles, triangles, parallelograms and circles
Perimeter and area of irregular shapes

Essential Questions

1. How is mathematics used to measure, quantify, calculate, manipulate, and compare situations, events, processes, changes, trends, and phenomena?
2. How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations and/or solve problems?
5. “When are we ever going to use this?”

Questions that support students in determining responses to the above EQs

• How do I know whether area or perimeter is involved?
• What attributes of a shape are important to measure?
• What am I actually finding when I find A and P?
• What relationships involving A, P or both will help solve particular problems?
• How can I find A and P of an irregular shape?

Standards Addressed & Benchmarks Assessed

Standard 1: Number and Operations

1.1 Students should understand numbers, ways of representing numbers, relationships among numbers, and number systems
1.1.4 Understand and use ratios and proportions to represent quantitative relationships
1.3 Students should compute fluently and make reasonable estimates

Standard 2: Algebra

2.1 Students should understand patterns, relations, and functions
2.1.1 Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules
2.2 Students should represent and analyse mathematical situations and structures using algebraic symbols
2.2.1 Develop an initial conceptual understanding of different uses of variables;
2.3 Students should use mathematical models to represent and understand quantitative relationships
2.3.1 Model and solve contextualized problems using various representations, such as graphs, tables, and equations

Standard 3: Geometry

3.1 Students should be able to analyze characteristics and properties of two-dimensional geometric shapes and develop mathematical arguments about geometric relationships
3.1.1 Precisely describe, classify, and understand relationships among types of two-dimensional objects using their defining properties
3.4 Students should use visualization, spatial reasoning, and geometric modeling to solve problems
3.4.5 Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

Standard 4: Measurement

4.1 Students should understand measurable attributes of objects and the units, systems, and processes of measurement
4.1.1 Understand both metric and customary systems of measurement
4.1.2 Understand relationships among units and convert from one unit to another within the same system
4.1.3 Understand, select, and use units of appropriate size and type to measure angles, perimeter, area
4.2 Students should apply appropriate techniques, tools, and formulae to determine measurements
4.2.5 Solve problems involving scale factors, using ratio and proportion

Standard 6: Problem Solving

6.1 Build new mathematical knowledge through problem solving
6.2 Solve problems that arise in mathematics and in other contexts
6.3 Apply and adapt a variety of appropriate strategies to solve problems
6.4 Monitor and reflect on the process of mathematical problem solving

Standard 8: Communication

8.1 Organize and consolidate their mathematical thinking through communication
8.2 Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
8.3 Analyse and evaluate the mathematical thinking and strategies of others
8.4 Use the language of mathematics to express mathematical ideas precisely

Standard 9: Connections

9.1 Recognize and use connections among mathematical ideas
9.2 Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
9.3 Recognize and apply mathematics in contexts outside mathematics

Standard 10: Representations

10.1 Create and use representations to organize, record, and communicate mathematical ideas
10.2 Select, apply, and translate among mathematical representations to solve problems
10.3 Use representations to model and interpret physical, social, and mathematical phenomena

Skills Emphasized

At the conclusion of this unit, students should be able to do the following:
Relate area to covering a figure
Relate perimeter to surrounding a figure
Measure and compute A and P of a figure/shape
Know that P and A can vary while the other remains fixed
Demonstrate that the A of a triangle or parallelogram is related to A of a rectangle
Utilise formulae and procedures for finding A and P of rectangles, parallelograms, triangles and circles
Utilise techniques for estimating A and P of irregular shapes
Use P and A to answer practical questions

Assessment

Bookwork, class work, discussion, Q & A sessions, hands-on problem solving
unit project, quizzes/tests, Application, Connection, Extension problems

Academic achievement Critical thinking Effective communication Involved citizenship Self-directed learning

Differentiation Strategies

The usual array of sound pedagogical methodologies as built into CMP2:

Individual and collaborative activities

Evaluation activities – see above

Website: http://www.internet4classrooms.com/di.htm
This website acts as a directory for a plethora of information on Learning Styles, Instructional Theory, Practical Classroom Tips…

Cross-curricular and Information and Technological Literacy Integration

Covering & SurroundingCurriculum MapHere you will find the curriculum map for this unit of work. It will give you information about what you will be studying, questions you should be able to answer as you work through the unit, and some useful websites.Covering and Surrounding2-Dimensional Measurement

Perimeter and area of rectangles, triangles, parallelograms and circlesTopics CoveredPerimeter and area of irregular shapes

1. How is mathematics used to measure, quantify, calculate, manipulate, and compare situations, events, processes, changes, trends, and phenomena?Essential Questions2. How are spatial relationships, including shape and dimension, used to draw, construct, model, and represent real situations and/or solve problems?

5. “When are we ever going to use this?”

• How do I know whether area or perimeter is involved?Questions that support students in determining responses to the above EQs• What attributes of a shape are important to measure?

• What am I actually finding when I find A and P?

• What relationships involving A, P or both will help solve particular problems?

• How can I find A and P of an irregular shape?

Standards Addressed & Benchmarks Assessed

1.1 Students should understand numbers, ways of representing numbers, relationships among numbers, and number systemsStandard 1: Number and Operations1.1.4 Understand and use ratios and proportions to represent quantitative relationships

1.3 Students should compute fluently and make reasonable estimates

2.1 Students should understand patterns, relations, and functionsStandard 2: Algebra2.1.1 Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules

2.2 Students should represent and analyse mathematical situations and structures using algebraic symbols

2.2.1 Develop an initial conceptual understanding of different uses of variables;

2.3 Students should use mathematical models to represent and understand quantitative relationships

2.3.1 Model and solve contextualized problems using various representations, such as graphs, tables, and equations

3.1 Students should be able to analyze characteristics and properties of two-dimensional geometric shapes and develop mathematical arguments about geometric relationshipsStandard 3: Geometry3.1.1 Precisely describe, classify, and understand relationships among types of two-dimensional objects using their defining properties

3.4 Students should use visualization, spatial reasoning, and geometric modeling to solve problems

3.4.5 Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

4.1 Students should understand measurable attributes of objects and the units, systems, and processes of measurementStandard 4: Measurement4.1.1 Understand both metric and customary systems of measurement

4.1.2 Understand relationships among units and convert from one unit to another within the same system

4.1.3 Understand, select, and use units of appropriate size and type to measure angles, perimeter, area

4.2 Students should apply appropriate techniques, tools, and formulae to determine measurements

4.2.5 Solve problems involving scale factors, using ratio and proportion

6.1 Build new mathematical knowledge through problem solvingStandard 6: Problem Solving6.2 Solve problems that arise in mathematics and in other contexts

6.3 Apply and adapt a variety of appropriate strategies to solve problems

6.4 Monitor and reflect on the process of mathematical problem solving

8.1 Organize and consolidate their mathematical thinking through communicationStandard 8: Communication8.2 Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

8.3 Analyse and evaluate the mathematical thinking and strategies of others

8.4 Use the language of mathematics to express mathematical ideas precisely

9.1 Recognize and use connections among mathematical ideasStandard 9: Connections9.2 Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

9.3 Recognize and apply mathematics in contexts outside mathematics

10.1 Create and use representations to organize, record, and communicate mathematical ideasStandard 10: Representations10.2 Select, apply, and translate among mathematical representations to solve problems

10.3 Use representations to model and interpret physical, social, and mathematical phenomena

At the conclusion of this unit, students should be able to do the following:Skills EmphasizedRelate area to covering a figure

Relate perimeter to surrounding a figure

Measure and compute A and P of a figure/shape

Know that P and A can vary while the other remains fixed

Demonstrate that the A of a triangle or parallelogram is related to A of a rectangle

Utilise formulae and procedures for finding A and P of rectangles, parallelograms, triangles and circles

Utilise techniques for estimating A and P of irregular shapes

Use P and A to answer practical questions

Bookwork, class work, discussion, Q & A sessions, hands-on problem solvingAssessmentunit project, quizzes/tests, Application, Connection, Extension problems

Dale Seymour Publications/Pearson Ed Connected Mathematics 2:ResourcesCovering & SurroundingWorksheets provided with course materials

Manipulatives provided with course materials

Geometer’s Sketchpadsoftwarehttp://mathematicsgradesix.wikispaces.com/ M'KIS grade 6 wiki

http://phschool.com/ activities/support for CMP2

http://phschool.com/cmp2/ website for teachers, students, parents for CMP2

http://www.emints.org/ethemes/resources/S00001378.shtml brilliant!!!

http://www.brainpop.com/math/seeall/ for information and fun activities - see Librarian for username and password

http://dictionary.reference.com …. To enrich glossary; provide links on wiki project page

Academic achievement Critical thinking Effective communication Involved citizenship Self-directed learningESLRs Applied

The usual array of sound pedagogical methodologies as built into CMP2:Differentiation StrategiesWebsite:http://www.internet4classrooms.com/di.htm

This website acts as a directory for a plethora of information on Learning Styles, Instructional Theory, Practical Classroom Tips…

Cross-curricular and Information and Technological Literacy IntegrationWebsites– see aboveGeometer’s SketchpadsoftwareBloom’s Taxonomy– knowledge, comprehension, application, analysis, evaluation

Standard 1Language Arts Standards & BenchmarksStandard 2

Standard 3

Standard 7

Standard 8

Standard 1Information Literacy Standards & BenchmarksStandard 2

Standard 4

Standard 1Technological Literacy Standard & BenchmarksStandard 2

Standard 3

Standard 4

Standard 5

Standard 6

Standard 7