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Geometry: WebConnects
WEBCONNECTS, or Internet links, are described in the margin of the Background and Strategies Book and the Guide to the Developmental Map. These links extend the discussion from the books to the Internet.

The links listed direct to sites outside of Nelson Education Ltd. which implies neither responsibility for, nor approval of, the information contained in those other Web sites on the part of Nelson Education Ltd. You may close the new browser window to return to Nelson or simply return to http://www.prime.nelson.com.

Background and Strategies Webconnects
Guide to the Developmental Map Webconnects

Background and Strategies Table of Contents 

Section 1: Introduction
Section 2: Instructional Issues Around Teaching Geometry
Section 3: Content Issues in Learning About Geometry
Section 4: Developing Spatial Sense
Section 5: Problem Solving in Geometry
Section 6: Communication in Geometry
Section 7: Assessment and Evaluation in Geometry
Section 8: Differentiating Instruction in Geometry

Section 1: Introduction

Geometry Connections to Other Subject Areas (p. 6)

Geometric Sculptures offers a connection between geometry and visual arts: symmetry and shapes are integral to the sculptures of George W. Hart. While the sculptures are fairly sophisticated, students will be able to identify shapes and symmetry in some pieces and may be interested in making their own polyhedron art. See Polyhedron Activities.

Geometry in Art Lessons, from the NCTM Illuminations Lessons site, offers a connection between geometry and visual arts—shapes and lines in the art of Wassily Kandinsky. Students use the Internet to research the Russian artist, identify geometric shapes and lines in his works, and design their own piece of art using Kandinsky’s techniques and their knowledge of geometry.

Graphic Design, from the PBS Teachers site, offers a connection between geometry and visual arts—symmetry in corporate logos. It offers, among others, the activity Using Symmetry to Create Corporate Logos where students describe types of symmetry, categorize symmetric figures based on type of symmetry, and create figures using different type of symmetry.

Making a Kaleidoscope offers a connection between geometry and science— symmetry in a kaleidoscope. It provides directions for making a kaleidoscope.

Making Snowflakes offers a connection between geometry and science— symmetry of snowflakes. Students cut paper virtually and create unique snowflakes. There is a gallery of virtual snowflakes.

 

Section 2: Instructional Issues Around Teaching Geometry

Technology Resources (p. 38)

BBC KS2 Bitesize Maths offers interactive activities, fact sheets, tests, and printable worksheets.

Math Central, from the University of Regina, features teaching resources including links to activities, mathematics glossaries, and Quandaries and Queries.

Mathematically Sane provides links to balanced, research-based information about mathematics teaching and learning.

The Math Forum, from Drexel University, features Ask Dr. Math and an Internet Mathematics Library. It offers both student and teacher areas with links to Web sites with activities and problems. Some useful geometry links are Tessellation Tutorials and Printable Dot Paper.

Math Playground offers varied and abundant practice of math skills for students in Grades K–6.

The National Council of Teachers of Mathematics (NCTM) site provides information about the organization, its conferences, and its publications. Principles and Standards for School Mathematics is available here as are problems, activities for home and school, applets, and lessons.

 

The National Library of Virtual Manipulatives for Interactive Math, from Utah State University, is a source of applets for learning mathematics. It is categorized by grade level and strand. It offers several Geometry Virtual Manipulatives.

 

NCTM Illuminations provides activities and resources that are appropriate for teachers at various grade levels to use as they reflect on, plan for, and implement NCTM Standards–based mathematics education in their classrooms. Useful geometry links are Cube Nets and Isometric Drawing Tool.

 

Section 3: Content Issues in Learning About Geometry

Identifying, Naming, and Classifying Shapes (p. 41)

Shapes Buddies provides worksheets and paper crafts related to 2-D shapes.

Shapes Theme Page provides many worksheets and colouring activities involving 2-D and 3-D shapes.

Shapes Worksheets provides several worksheets and colouring activities involving 2-D shapes.

 

2-D and 3-D Shapes: Appropriate Technology (p. 93)

Building a Box Lesson, from the NCTM Illuminations Lessons site, offers a specific activity for using Cube Nets.

Cube Nets, from the NCTM Illuminations Tools site, presents assorted nets from which students must select the possible cube nets.

Cutting Corners, from the NCTM Illuminations Tools site, is a dissecting applet with activity suggestions. Students dissect a square, an equilateral triangle, or an isosceles trapezoid and slide, flip, and/or turn the resulting shapes to compare them, such as for congruence.

Developing Geometric Understandings and Spatial Skills through Tangram Puzzles Lesson, from the NCTM Illuminations Lessons site, offers an activity where students choose a picture and use all seven tangram pieces to fill in the outline. They describe and visualize what figures look like when they are transformed through rotations or flips or are put together or taken apart in different ways.

Geometric Solids, from the NCTM Illuminations Tools site, allows students to view assorted 3-D shapes from different perspectives and count the number of faces, edges, and vertices. When holding down the Shift key as each component is clicked, the component is marked to facilitate counting.

Geometry and Spatial Sense offers lesson plans and animated examples of some concepts.

Geometry of 3-D Drawing, a Math Forum site, discusses how to draw 3-D shapes so that they appear to be three-dimensional. Follow links to Isometric Drawings and Perspective Drawing.

Geometry Virtual Manipulatives, from Utah State University’s National Library of Virtual Manipulatives for Interactive Math, offers many excellent applets for interactive geometry activities at all grade levels.

Isometric Drawing Tool, from the NCTM Illuminations Tools site, allows students to draw cube structures on isometric dot paper virtually, using cubes or faces of cubes.


Lines, Line Segments, Rays, from the NCTM Illuminations Tools site, is an interactive dictionary of these geometry concepts.

Pattern Block Applet allows students to move patterns blocks on an isometric grid to create patterns or to combine shapes. The pattern block shapes can be selected, moved onto the grid, and rotated as desired.  

Pentominoes Puzzle Applet challenges students to tile a surface with the pentominoes.

Perspective Lesson, from the NCTM Illuminations Lessons site, offers an activity using Geometric Solids.

Polyhedrons and Their Nets provides a discussion about regular and other polyhedrons, their faces, and where they occur in nature. Assorted possible nets for each are presented from which students select which are nets, and nets with gluing tabs are available to print out.

Printable Dot Paper, a Math Forum site, offers several sizes of printable dot paper that looks like geoboards.

Properties of Rectangles and Parallelograms Lesson, from the NCTM Illuminations Lessons site, offers an activity where students identify, compare, and analyze attributes of rectangles and more general parallelograms through physical and mental manipulation. Students use dynamic software to examine the properties of rectangles and parallelograms, and identify what distinguishes a rectangle from a more general parallelogram.

Puzzle Corner, from the AIMS site, offers over 100 interesting puzzles that can help students learn to enjoy puzzles and the mathematics behind them. The puzzles are categorized by type and are listed in order of increasing difficulty within each category. Solutions are available.

Regular Polyhedrons, a Math Forum site, allows students to view regular polyhedrons from different perspectives. It tells the number of edges and vertices for the number of faces on the selected polyhedron.

Sagwa Tangram Puzzles offers tangram puzzles classified as easy and hard, with hints.

Shape Cutter Tool, from the NCTM Illuminations Tools site, allows students to dissect a shape and combine the new shapes to make another shape. Students draw a shape on square dot paper, cut the shape, and use slides, turns, and/or flips to combine the resulting shapes to create a new shape.

Shape Makers, from the AIMS site, provides shapes that can be printed, cut out, and combined to create specific shapes.

Shape Tool, from the NCTM Illuminations Tools site, is a combination of several Illuminations tools. Students either make their own shapes by drawing line segments or use given shapes, which they can dissect, rotate, flip, and turn to compare or make new shapes.

Tangram Puzzles provides tangram pieces that can be printed and cut out, and three sets of challenging puzzle to solve. Solutions are available.

 

Location and Movement: Appropriate Technology (p. 93)

Directional Language suggests students identify a local landmark and write directions in terms of paces and turns. The activity can be modified to use language students are learning—left and right, compass directions, or 1/4 turns clockwise and counterclockwise.

The Geometer’s Sketchpad is the Key Curriculum Press site where teachers can get information about this dynamic geometry software and other products.

Get the Turtle to the Pond Lesson, from the NCTM Illuminations Lessons site, offers a creative problem-solving activity where students use directional language as well as estimating length and angle measure to enter a sequence of Logo commands to help the turtle get to the pond.

Geometry Virtual Manipulatives, from Utah State University’s National Library of Virtual Manipulatives for Interactive Math, offers many excellent applets for interactive geometry activities at all grade levels.

MSW Logo provides links to Logo software and Logo activities.

Paper Mosaics shows samples of origami tessellations, provides patterns and instructions for creating some tessellations by hand, and offers links to software that will make patterns for origami tessellations.

Pattern Block Applet allows students to move patterns blocks on an isometric grid to create patterns or to combine shapes. The pattern block shapes can be selected, moved onto the grid, and rotated as desired.  

Tessellation Tutorials, a Math Forum site, offers assorted activities for investigating tessellations using various software, such as Claris Works and The Geometer’s Sketchpad.

Totally Tessellated offers examples and explanations of many tessellations, including works by Escher, mosaics, and tiling with regular polygons and non-regular polygons.

Transformations, from the MathsNet site, offers several transformation applets. Basic reflection, Basic translation, An illustration (of rotations), and Half turns demonstrate some basics about transformations. Drawing with Rotations and Drawing with Reflections allow students to create symmetrical shapes.

 

Section 5: Problem Solving in Geometry

Sources of Other Problems (p. 158)

Figure This, an NCTM site, offers problems called Challenges for Families, with hints. Problems are indexed by title and by math topic (see Math Index). Both quick answers and full solutions are provided.

Math Mountain offers many problems for students in Grades 2–3 and 4–5 with hints and solutions. It also has links to its archived problems and to Web sites with math problems, puzzles, and tips.

NRICH, from University of Cambridge, focuses on a different topic each month. It offers many problems on the topic at various levels. Students are invited to submit solutions. As well, links to archived problems are provided.

Math Contest, from Columbus State University, offers weekly problems such as Elementary Math Brain Teaser and Middle School Madness, and invites students to submit answers. Those who answer correctly get their names posted. Students can also submit answers to past problems.

Puzzle Corner, from the AIMS site, offers over 100 interesting puzzles that can help students learn to enjoy puzzles and the mathematics behind them. The puzzles are categorized by type, such as dissecting, and are listed in order of increasing difficulty within each category. Solutions are available.

Word Problems for Kids, from St. Francis Xavier University, offers challenging, non-traditional problems for students in Grades 5–12. In addition to answers, hints are available.

 

Section 6: Communication in Geometry

Reading Opportunities in Mathematics (p. 171)

Children's Literature with Mathematical Possibilities lists children’s literature books by math topic. The topics are classification, counting, addition and subtraction, multiplication, fractions, big numbers, geometry, measurement, and general. The information provided includes author, date, title, and publisher.

The Mathematics Council of the Alberta Teachers' Association (MCATA) Mathematics and Literature site lists children’s literature books for three math strands—number concept, shape and space, and data analysis—and general reference. The information provided includes author, title, publisher, and date.

Mathematics Vocabulary and Symbols (p. 175)

A Maths Dictionary for Kids has definitions with examples in student-friendly language.

The Mathematics Glossary – Middle Years has definitions from the Saskatchewan Education document Mathematics 6–9: A Curriculum Guide for the Middle Level. The definitions were designed to be meaningful to middle-level mathematics teachers. Some definitions have examples.

The Math Dictionary offers concise definitions of mathematical terms. Some definitions have links to illustrated examples.

 

Section 7: Assessment and Evaluation in Geometry

 Other Resources (p. 200)

The Kid-Friendly Problem Solving Rubric is a seven-level problem solving rubric in student language.

 The Math Problem Solving Rubric is a five-criteria, four-level problem solving rubric for teachers.  

Principles for Fair Student Assessment is an assessment document from the University of Alberta Faculty of Education Web site.

 

Section 8: Differentiating Instruction in Geometry

Strategies for Motivated and Gifted Students (p. 215)

Aunty Math offers challenging problems for students in Grades K–5. Students are invited to submit their solutions. There are options for more difficult or easier problems as well as tips for teachers and parents.

BrainDen offers geometric puzzles which are quite challenging. Several are dissecting problems. Solutions are available.

Explore Your Knowledge offers questions for students in Grades 4 and 8. The questions are from the Trends in International Mathematics and Science Study (TIMSS). Students must select the subject, their grade, and the number of questions they want to try. Answers are provided.

Figure This, an NCTM site, offers problems called Challenges for Families, with hints. Problems are indexed by title and by math topic (see Math Index). Both quick answers and full solutions are provided.

Geometry Problems and Puzzles, a Math Forum site, offers links to challenging geometry problems and puzzles.

MATHCOUNTS is a coaching and competition program for middle school. Even without registering your school to participate, you can take advantage of several free problem-solving features. There is a problem of the week, with the solution provided the next week, links to archived problems, and links to Web sites with math problems.

Math Mountain offers many problems for students in Grades 2–3 and 4–5 with hints and solutions. It also has links to its archived problems and to Web sites with math problems, puzzles, and tips.

Math Olympiads for Elementary and Middle Schools offers contests for Grades 4–6 and 7–8. Before registering a team of students, you can view a sample test at each level online. There is also a problem of the month, with the solution provided the next month.

NRICH, from University of Cambridge, focuses on a different topic each month. It offers many problems on the topic at various levels. Students are invited to submit solutions. As well, links to archived problems are provided.

Math Contest, from Columbus State University, offers weekly problems such as Elementary Math Brain Teaser and Middle School Madness. Students are invited to submit answers. Those who answer correctly get their names posted. Students can also submit answers to past problems.

Word Problems for Kids, from St. Francis Xavier University, offers challenging, non-traditional problems for students in Grades 5–12. In addition to answers, hints are available.

 

Guide to the Developmental Map Table of Contents

Section 1: Introduction
Section 2: Phases of Development in Geometry

Section 1: Introduction

How PRIME Complements Curriculum (p. 4)

Curriculum correlations that relate CAMET (Council of Atlantic Ministers of Education and Training) Kindergarten to Grade 6 curriculums to the Developmental Map are provided to show how each developmental map relates to and complements curriculum.

Curriculum correlations that relate Ontario Kindergarten to Grade 6 curriculums to the Developmental Map are provided to show how each developmental map relates to and complements curriculum.

Curriculum correlations that relate WNCP (Western and Northern Curriculum Protocol) Kindergarten to Grade 6 curriculums to the Developmental Map are provided to show how each developmental map relates to and complements curriculum.

Section 2: Phases of Development in Geometry

Supporting Students in Phase 1, Special Approaches for Older Students (p. 35)

Geometric Solids, from the NCTM Illuminations Tools site, allows students to view assorted 3-D shapes from different perspectives. In this phase, students might move the shape to view it from different perspectives and simply match it with a concrete model.

Geometry Virtual Manipulatives, from Utah State University’s National Library of Virtual Manipulatives for Interactive Math, offers many excellent applets for interactive geometry activities. In this phase, students might try Attribute Blocks, Geoboard, Lady Bug Mazes, Pattern Blocks, or others.

Pattern Block Applet allows students to move pattern blocks on an isometric grid to create patterns or to combine shapes. The pattern block shapes can be selected, moved onto the grid, and rotated as desired.

Supporting Students in Phase 2, Special Approaches for Older Students (p. 55)

Cutting Corners, from the NCTM Illuminations Tools site, is a dissecting applet with activity suggestions. Students dissect a square, an equilateral triangle, or an isosceles trapezoid and slide, flip, and/or turn the resulting shapes to compare them.

Geometric Solids, from the NCTM Illuminations Tools site, allows students to view assorted 3-D shapes from different perspectives. In this phase, students might move the shape to view it from different perspectives and match its faces to concrete 2-D shapes.

Geometry Virtual Manipulatives, from Utah State University’s National Library of Virtual Manipulatives for Interactive Math, offers many excellent applets for interactive geometry activities. In this phase, students might try Attribute Blocks, Geoboard, Lady Bug Mazes, Pattern Blocks, Tangrams, Transformations–Reflections, Transformations–Translations, or others.

Pattern Block Applet allows students to move patterns blocks on an isometric grid to create patterns or to combine shapes. The pattern block shapes can be selected, moved onto the grid, and rotated as desired.  

Sagwa Tangram Puzzles offers tangram puzzles classified as easy and hard, with hints. In this phase, students might try the easy ones.

Shape Cutter Tool, from the NCTM Illuminations Tools site, allows students to dissect a shape and combine the new shapes to make another shape. Students draw a shape on square dot paper, cut the shape, and use slides, turns, and/or flips to combine the resulting shapes to create a new shape.

Supporting Students in Phase 3, Special Approaches for Older Students (p. 82)

Building a Box Lesson, from the NCTM Illuminations Lessons site, offers an activity using Cube Nets.

Cube Nets, from the NCTM Illuminations Tools site, folds a net of a cube virtually, and presents assorted possible nets from which students select which are nets.

Cutting Corners, from the NCTM Illuminations Tools site, is a dissecting applet with activity suggestions. Students dissect a square, an equilateral triangle, or an isosceles trapezoid and slide, flip, and/or turn the resulting shapes to compare them, such as for congruence.

Developing Geometric Understandings and Spatial Skills through Tangram Puzzles Lesson, from the NCTM Illuminations Lessons site, offers an activity where students choose a picture and use all seven tangram pieces to fill in the outline. They describe and visualize what figures look like when they are transformed through rotations or reflections or are put together or taken apart in different ways.

Geometric Solids, from the NCTM Illuminations Tools site, allows students to view assorted 3-D shapes from different perspectives and count the number of faces, edges, and vertices. By holding down the Shift key as each component is selected, the component is marked to facilitate counting.

Geometry Virtual Manipulatives, from Utah State University’s National Library of Virtual Manipulatives for Interactive Math, offers many excellent applets for interactive geometry activities. In this phase, students might try Congruent Triangles, Geoboard, Pattern Blocks, Pentominoes, Platonic Solids, Tangrams, Transformations–Reflections, Transformations–Rotations, Transformations–Reflections, or others.

Pattern Block Applet allows students to move patterns blocks on an isometric grid to create patterns or to combine shapes. The pattern block shapes can be selected, moved onto the grid, and rotated as desired.  

Perspective Lesson, from the NCTM Illuminations Lessons site, offers an activity using Geometric Solids.

Polyhedrons and Their Nets provides a discussion about regular and other polyhedrons, their faces, and where they occur in nature. Assorted possible nets for each are presented from which students select which are real nets, and nets with gluing tabs are available to print out.

Sagwa Tangram Puzzles offers tangram puzzles classified as easy and hard, with hints.

Shape Cutter Tool, from the NCTM Illuminations Tools site, allows students to draw, dissect, and combine shapes. Students draw a shape on square dot paper, cut the shape, and use slides, turns, and/or flips to combine the resulting shapes to create a new shape.

Supporting Students in Phase 4, How Parents Can Help (p. 110)

Developing Geometric Understandings and Spatial Skills through Tangram Puzzles Lesson, from the NCTM Illuminations Lessons site, offers an activity where students choose a picture and use all seven tangram pieces to fill in the outline. They describe and visualize what figures look like when they are transformed through rotations or reflections or are put together or taken apart in different ways.

Geometric Sculptures offers a connection between geometry and visual arts: symmetry and shapes are integral to the sculptures of George W. Hart. While the sculptures are fairly sophisticated, students will be able to identify shapes and symmetry in some pieces and may be interested in making their own polyhedron art. See Polyhedron Activities.

Geometry in Art Lessons, from the NCTM Illuminations Lessons site, offers a connection between geometry and visual arts—shapes and lines in the art of Wassily Kandinsky. Students use the Internet to research the Russian artist, identify geometric shapes and lines in his works, and design their own piece of art using Kandinsky’s techniques and their knowledge of geometry.

Graphic Design, from the PBS Teachers site, offers a connection between geometry and visual arts—symmetry in corporate logos. It offers, among others, the activity Using Symmetry to Create Corporate Logos where students describe types of symmetry, categorize symmetric figures based on type of symmetry, and create figures using different type of symmetry.

Paper Mosaics shows samples of origami tessellations, provides patterns and instructions for creating origami tessellations by hand, and offers links to software that will make patterns for origami tessellations.

Pentominoes Puzzle Applet challenges students to tile a surface with the pentominoes.

Sagwa Tangram Puzzles offers tangram puzzles classified as easy and hard, with hints.

 

Totally Tessellated offers examples and explanations of many tessellations, including works by Escher, mosaics, and tiling with regular polygons and non-regular polygons.

 

Consolidating and Extending Phase 4, Instructional Focus (p. 112)

Building a Box Lesson, from the NCTM Illuminations Lessons site, offers an activity using Cube Nets.

 

Cube Nets, from the NCTM Illuminations Tools site, folds a net of a cube virtually, and presents assorted possible nets from which students select which are nets.

 

Cutting Corners, from the NCTM Illuminations Tools site, is a dissecting applet with activity suggestions. Students dissect a square, an equilateral triangle, or an isosceles trapezoid and slide, flip, and/or turn the resulting shapes to compare them, such as for congruence.

 

Developing Geometric Understandings and Spatial Skills through Tangram Puzzles Lesson, from the NCTM Illuminations Lessons site, offers an activity where students choose a picture and use all seven tangram pieces to fill in the outline. They describe and visualize what figures look like when they are transformed through rotations or reflections or are put together or taken apart in different ways.

 

Geometric Solids, from the NCTM Illuminations Tools site, allows students to view assorted 3-D shapes from different perspectives and count the number of faces, edges, and vertices. By holding down the Shift key as each component is selected, the component is marked to facilitate counting.

 

Geometry of 3-D Drawing, a Math Forum site, discusses how to draw 3-D shapes so that they appear to be three-dimensional. Follow links to Isometric Drawings and Perspective Drawing.

 

Geometry Virtual Manipulatives, from Utah State University’s National Library of Virtual Manipulatives for Interactive Math, offers many excellent applets for interactive geometry activities. In this phase, students might try Congruent Triangles, Geoboard, Platonic Solids, Platonic Solids–Slicing, Pentominoes, Polyominoes,Tangrams, Transformations–Reflections, Transformations–Rotations, Transformations–Translations, or others.

 

Get the Turtle to the Pond Lesson, from the NCTM Illuminations Lessons site, offers a creative problem-solving activity where students use directional language as well as estimating length and angle measure to enter a sequence of Logo commands to help the turtle get to the pond.

 

Isometric Drawing Tool, from the NCTM Illuminations Tools site, allows students to draw cube structures on isometric dot paper virtually, using cubes or faces of cubes.

 

Paper Mosaics shows samples of origami tessellations, provides patterns and instructions for creating origami tessellations by hand, and offers links to software that will make patterns for origami tessellations.

 

Pentominoes Puzzle Applet challenges students to tile a surface with the pentominoes.

 

Perspective Lesson, from the NCTM Illuminations Lessons site, offers an activity using Geometric Solids.

 

Polyhedrons and Their Nets provides a discussion about regular and other polyhedrons, their faces, and where they occur in nature. Assorted possible nets for each are presented from which students select which are really nets, and nets with gluing tabs are available to print out.

 

Sagwa Tangram Puzzles offers tangram puzzles classified as easy and hard, with hints.

 

Shape Cutter Tool, from the NCTM Illuminations Tools site, allows students to draw, dissect, and combine shapes. Students draw a shape on square dot paper, cut the shape, and use slides, turns, and/or flips to combine the resulting shapes to create a new shape.

 

Tessellation Tutorials, a Math Forum site, offers assorted activities for investigating tessellations using various software, such as Claris Works and The Geometer’s Sketchpad.

 

Totally Tessellated offers examples and explanations of many tessellations, including works by Escher, mosaics, and tiling with regular polygons and non-regular polygons.

 

Transformations, from the MathsNet site, offers several transformation applets. Basic reflection, Basic translation, An illustration (of rotations), and Half turns demonstrate some basics about transformations. Drawing with Rotations and Drawing with Reflections allow students to create symmetrical shapes.