Save this PDF as:

Size: px
Start display at page:

Transcription

5 Help children break free of these limitations by using a wide range of good examples and nonexamples. To do so, try these tactics: Vary the size, material, and color of examples. For rectangles and triangles, vary their orientation and dimensions, such as the rectangles in figure 1. For triangles, vary their type, including scalene no sides equal in length and obtuse one angle larger than 90 degrees. Compare examples with nonexamples to focus children s attention on the essential attributes (see fig. 3). Encourage children to change shapes dynamically. FIGURE 4 Manipulating a category of shape in Math Van Math Van (McGraw-Hill School Division 1997) allows children to draw and manipulate a certain kind, or category, of shape. Here children defined an isosceles triangle. The double-color on the two equal sides represents their equality (a). Children can slide, turn, or flip this triangle. They can also distort it, but no matter how they do, it remains an isosceles triangle [(b) and (c)]. FIGURE 3 Tricky Triangles The Tricky Triangles sheet includes triangles (shapes 1 5) and nontriangles (shapes 6 10) that are paired to encourage contrasts. For example, shape 1 is a triangle, but shape 6 is not a triangle because it is not closed. Shape 2 does not have a horizontal base and is not symmetric, but it is a triangle; however, shapes 7 and 8 are not triangles, because they have four sides. (a) (b) (c) 486 TEACHING CHILDREN MATHEMATICS

6 For example, some computer programs allow children to manipulate a figure, such as an isosceles triangle, in many ways, but it always stays an isosceles triangle (see figs. 4a, 4b, and 4c). Matching activities to children s level of thinking about shapes Children at the prerecognition level might best work with shapes in the world. Help these children understand the relevant and irrelevant for example, orientation, size, color attributes of shapes with such activities as the following: Identifying shapes in the classroom, school, and community Sorting shapes and describing why they believe that a shape belongs to a group Copying and building with shapes using a wide range of materials Children at the visual level also can measure, color, fold, and cut shapes to identify their attributes. For example, they might engage in the following activities: Describing why a figure belongs or does not belong to a shape category Folding a square or rhombus in various ways to determine its symmetries and the equality of its angles and sides Drawing shapes with turtle geometry, which helps children approach shapes actively but with precise mathematical commands and measurements; or having children give commands to a child-turtle who walks the path Using a right-angle tester to find angles in the classroom equal to, larger than, or smaller than a right angle Using computers to find new ways to manipulate (fig. 5a) and make (fig. 5b) shapes (Clements and Meredith 1998) Discussing such general categories as quadrilaterals, or four-sided shapes, and triangles, counting the sides of various figures to choose the category in which they belong Conclusions An adult s ability to instantly see shapes in the world is the result, not the origin, of geometric knowledge. The origin is our early active manipulation of our world. Young children learn a lot about shapes. Geometry instruction needs to begin early. Our research and that of Gagatsis and Patronis (1990) show that young children s concepts about shapes stabilize by six years of age but that these concepts are not necessarily accurate. We can do a lot as teachers to supplement curricula that too often are part of the problem rather than the solution. References Clements, Douglas H. Longitudinal Study of the Effects of Logo Programming on Cognitive Abilities and Achievement. Journal of Educational Computing Research 3 (1987): Clements, Douglas H., and Michael T. Battista. The Development of a Logo-Based Elementary School Geometry Curriculum. Final Report: NSF Grant No. MDR Buffalo, N.Y./Kent, Ohio: State University of New York at Buffalo/Kent State University, 1992a. FIGURE 5 Manipulating shapes in the Shapes program The Shapes program (Clements and Meredith 1998) allows children to manipulate shapes in ways not possible with usual pattern blocks, such as to define new units-of-units, which would turn and duplicate together. They can enlarge or shrink shapes, as Leah did in making her snow person (a). They can hammer shapes to decompose them into parts (b). (a) (b) APRIL

7 . Geometry and Spatial Reasoning. In Handbook of Research on Mathematics Teaching and Learning, edited by Douglas A. Grouws, New York: Macmillan, 1992b. Clements, Douglas H., and Sue McMillen. Rethinking Concrete Manipulatives. Teaching Children Mathematics 2 (January 1996): Clements, Douglas H., and Julie Sarama Meredith. Shapes Making Shapes. Palo Alto, Calif.: Dale Seymour Publications, Clements, Douglas H., Sudha Swaminathan, Mary Anne Zeitler Hannibal, and Julie Sarama. Young Children s Concepts of Shape. Journal for Research in Mathematics Education 30 (March 1999): Gagatsis, A., and T. Patronis. Using Geometrical Models in a Process of Reflective Thinking in Learning and Teaching Mathematics. Educational Studies in Mathematics 21 (1990): Hannibal, Mary Anne. Young Children s Developing Understanding of Geometric Shapes. Teaching Children Mathematics 5 (February 1999): Kay, Cynthia S. Is a Square a Rectangle? The Development of First-Grade Students Understanding of Quadrilaterals with Implications for the van Hiele Theory of the Development of Geometric Thought. Dissertation Abstracts International 47 (1987): 2934A. University Microfilms No. DA McGraw-Hill School Division. Math Van. New York: McGraw- Hill, Software. Sarama, Julie, Douglas H. Clements, and Elaine Bruno Vukelic. The Role of a Computer Manipulative in Fostering Specific Psychological/Mathematical Processes. In Proceedings of the Eighteenth Annual Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education, edited by E. Jakubowski, D. Watkins, and H. Biske, Columbus, Ohio: ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Thomas, Betsy. An Abstract of Kindergarten Teaching s Elicitation and Utilization of Children s Prior Knowledge in the Teaching of Shape Concepts. Unpublished manuscript, School of Education, Health, Nursing, and Arts Professions, New York University, van Hiele, Pierre M. The Child s Thought and Geometry. In English Translation of Selected Writings of Dina van Hiele- Geldof and Pierre M. van Hiele, edited by D. Fuys, D. Geddes, and R. Tischler, Brooklyn, N.Y.: Brooklyn College, School of Education, 1959/1985. ERIC Document Reproduction Service No Time to prepare this material was partially provided by two National Science Foundation Research Grants: NSF MDR , An Investigation of the Development of Elementary Children s Geometric Thinking in Computer and Noncomputer Environments, and ESI , Building Blocks Foundations for Mathematical Thinking, Pre-Kindergarten to Grade 2: Research-based Materials Development. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation. We also extend our appreciation to Julie Jacobs Henry for her suggestions regarding the article. 488 TEACHING CHILDREN MATHEMATICS

Performance Assessment Task Which Shape? Grade 3. Common Core State Standards Math - Content Standards

Performance Assessment Task Which Shape? Grade 3 This task challenges a student to use knowledge of geometrical attributes (such as angle size, number of angles, number of sides, and parallel sides) to

Activities Grades K 2 THE FOUR-SQUARE QUILT. Put triangles together to make patterns.

Activities Grades K 2 www.exploratorium.edu/geometryplayground/activities THE FOUR-SQUARE QUILT Put triangles together to make patterns. [45 minutes] Materials: Four-Square Quilt Template (attached) Triangle

CONSTRUCTING TASK: SHAPE SORTER Adapted from Activity 8.1 in Teaching Student Centered Mathematics 3-5, by John Van de Walle and LouAnn Lovin

CONSTRUCTING TASK: SHAPE SORTER Adapted from Activity 8.1 in Teaching Student Centered Mathematics 3-5, by John Van de Walle and LouAnn Lovin STANDARDS FOR MATHEMATICAL CONTENT MCC3.G.1 Understand that

Constructing Symmetrical Shapes

07-NEM5-WBAns-CH07 7/20/04 4:36 PM Page 62 1 Constructing Symmetrical Shapes 1 Construct 2-D shapes with one line of symmetry A line of symmetry may be horizontal or vertical 2 a) Use symmetry to complete

Geometry and Spatial Sense

Geometry and Spatial Sense Diagnostic Assessment Grade Level: Appropriate for grades 4-6 Assessing the Students Levels of Thinking Based on the van Hiele Model The Rationale The Van Hiele Theory According

van Hiele, Pierre M. Developing Geometric Thinking through Activities That Begin with Play. Teaching Children Mathematics 6 (February 1999):

van Hiele, Pierre M. Developing Geometric Thinking through Activities That Begin with Play. Teaching Children Mathematics 6 (February 999): 0 6. Developing Geometric Thinking through Activities That Begin

Properties of Polygons Objective To explore the geometric properties of polygons.

Properties of Polygons Objective To explore the geometric properties of polygons. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

Kindergarten to Grade 3. Geometry and Spatial Sense

Kindergarten to Grade 3 Geometry and Spatial Sense Every effort has been made in this publication to identify mathematics resources and tools (e.g., manipulatives) in generic terms. In cases where a particular

Activities Grades 3 5 ROTATING STRING SHAPES. Make multi-sided shapes with string. [45 minutes]

Activities Grades 3 5 www.exploratorium.edu/geometryplayground/activities ROTATING STRING SHAPES Make multi-sided shapes with string. [45 minutes] Materials: String, about 2.5 meters (8 feet) long, tied

1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?

Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.

Geometry Is A Verb: Making Elementary School Geometry Come Alive

Geometry Is A Verb: Making Elementary School Geometry Come Alive Tad Watanabe Kennesaw State University twatanab@kennesaw.edu http://science.kennesaw.edu/~twatanab/geometry.pdf Geometry: NCTM Focal Points

Geometry Vocabulary Booklet

Geometry Vocabulary Booklet Geometry Vocabulary Word Everyday Expression Example Acute An angle less than 90 degrees. Adjacent Lying next to each other. Array Numbers, letter or shapes arranged in a rectangular

Estimating Angle Measures

1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

Consolidation of Grade 6 EQAO Questions Geometry and Spatial Sense

Consolidation of Grade 6 EQAO Questions Geometry and Spatial Sense Compiled by Devika William-Yu (SE2 Math Coach) Overall Expectations GV1 Classify and construct polygons and angles GV2 GV3 Sketch three-dimensional

acute angle acute triangle Cartesian coordinate system concave polygon congruent figures

acute angle acute triangle Cartesian coordinate system concave polygon congruent figures convex polygon coordinate grid coordinates dilatation equilateral triangle horizontal axis intersecting lines isosceles

Featured Mathematical Practice: MP.5. Use appropriate tools strategically. MP.6. Attend to precision.

Domain: Geometry 4.G Mathematical Content Standard: 1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.

SHAPE, SPACE AND MEASURES

SHPE, SPCE ND MESURES Pupils should be taught to: Understand and use the language and notation associated with reflections, translations and rotations s outcomes, Year 7 pupils should, for example: Use,

Chapter 18 Symmetry. Symmetry of Shapes in a Plane 18.1. then unfold

Chapter 18 Symmetry Symmetry is of interest in many areas, for example, art, design in general, and even the study of molecules. This chapter begins with a look at two types of symmetry of two-dimensional

Geometry of 2D Shapes

Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles

A Teacher Resource Package for the Primary Grades

A Teacher Resource Package for the Primary Grades Notes for Teachers: These are intended to be a starting point to help your class apply what they have learned in the Geometry and Spatial Sense strand

Chapter 17. Geometric Thinking and Geometric Concepts. T he geometry curriculum in grades K 8 should provide an

Chapter 17 Geometric Thinking and Geometric Concepts T he geometry curriculum in grades K 8 should provide an opportunity to experience shapes in as many different forms as possible. These should include

Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) August-September (12 days) Unit #1 : Geometry

Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Common Core and Research from the CCSS Progression Documents Geometry Students learn to analyze and relate categories

Performance Assessment Task Symmetrical Patterns Grade 4. Common Core State Standards Math - Content Standards

Performance Assessment Task Symmetrical Patterns Grade 4 The task challenges a student to demonstrate understanding of the concept of symmetry. A student must be able to name a variety of two-dimensional

Session 6 Area. area midline similar figures

Key Terms in This Session Session 6 Area Previously Introduced scale factor New in This Session area midline similar figures Introduction Area is a measure of how much surface is covered by a particular

EL EM EN TA RY S CH OOL Geometry Lesson Plans. A Practical Guide For Educators:

EL EM EN TA RY S CH OOL Geometry Lesson Plans A Practical Guide For Educators: Introduction This is a set of lesson plans that complement the app Shapes - 3D Geometry Learning on the ipad or Android tablet.

parallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect

parallel lines lines that stay same distance from each other forever and never intersect perpendicular lines lines that cross at a point and form 90 angles intersecting lines vertices lines that cross

Problem of the Month The Shape of Things

Problem of the Month The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:

Grade 4 - Module 4: Angle Measure and Plane Figures

Grade 4 - Module 4: Angle Measure and Plane Figures Acute angle (angle with a measure of less than 90 degrees) Angle (union of two different rays sharing a common vertex) Complementary angles (two angles

Jelly Beans. The Pythagorean Theorem with. Jeong Oak Yun and Alfinio Flores

pprinciples and Standards for School Mathematics advocates an experimentation approach to middle-grades geometry study (NCTM 2000). Students are asked to explore and examine a variety of geometric shapes

Grade 8 Mathematics Geometry: Lesson 2

Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

Begin recognition in EYFS Age related expectation at Y1 (secure use of language)

For more information - http://www.mathsisfun.com/geometry Begin recognition in EYFS Age related expectation at Y1 (secure use of language) shape, flat, curved, straight, round, hollow, solid, vertexvertices

Shape and Space. General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships.

Shape and Space General Curriculum Outcome E: Students will demonstrate spatial sense and apply geometric concepts, properties and relationships. Elaboration Instructional Strategies/Suggestions KSCO:

Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons

Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons I. ABSTRACT This unit contains lessons that focus on geometric

Line Segments, Rays, and Lines

HOME LINK Line Segments, Rays, and Lines Family Note Help your child match each name below with the correct drawing of a line, ray, or line segment. Then observe as your child uses a straightedge to draw

CARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM

GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write

Problems using a square 9-pin geoboard

Problems using a square 9-pin geoboard The 9-pin geoboard can be used with learners of all ages, from making and talking about shapes with younger pupils to working out the intersecting area of two overlapping

Shapes & Designs Notes

Problem 1.1 Definitions: regular polygons - polygons in which all the side lengths and angles have the same measure edge - also referred to as the side of a figure tiling - covering a flat surface with

NEW MEXICO Grade 6 MATHEMATICS STANDARDS

PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical

Line. A straight path that continues forever in both directions.

Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A

Grade 3 Core Standard III Assessment

Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse

Teaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons

CIRCLE FOLDING Teaching Guidelines Subject: Mathematics Topics: Geometry (Circles, Polygons) Grades: 4-6 Concepts: Property Diameter Radius Chord Perimeter Area Knowledge and Skills: Can specify defining

Lesson 7: Drawing Parallelograms

Student Outcomes Students use a protractor, ruler, and setsquare to draw parallelograms based on given conditions. Lesson Notes In Lesson 6, students drew a series of figures (e.g., complementary angles,

Unit 6. Five daily lessons. Year 3 Autumn term. Unit Objectives Year 3. Resources needed to teach this unit: Shape and space Reasoning about shapes

Unit 6 Shape and space Reasoning about shapes Five daily lessons Year 3 Autumn term Classify and describe 3-D and 2-D shapes, referring to reflective symmetry, faces, sides/edges, vertices, angles. (pages

Su.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)

MA.912.G.2 Geometry: Standard 2: Polygons - Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures

Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson

Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations

Math Buddies -Grade 4 13-1 Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Goal: Identify congruent and noncongruent figures Recognize the congruence of plane

Geometry Strategies for Middle School

Geometry Strategies for Middle School This Considerations Packet describes strategies middle school mathematics teachers can incorporate into their teaching of geometry. An overview of the van Hiele Model

PDM1-1 Sorting into Groups

PDM1-1 Sorting into Groups Page 175-176 Curriculum Expectations Ontario: km31, 1m5, 1m7, 1m46, 1m72 Western: kss2, 1SS2, [C,CN] Goals Students will sort objects according to different attributes using

Activity Set 3. Trainer Guide

Geometry and Measurement of Plane Figures Activity Set 3 Trainer Guide GEOMETRY AND MEASUREMENT OF PLANE FIGURES Activity Set 3 Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development

Marie has a winter hat made from a circle, a rectangular strip and eight trapezoid shaped pieces. y inches. 3 inches. 24 inches

Winter Hat This problem gives you the chance to: calculate the dimensions of material needed for a hat use circle, circumference and area, trapezoid and rectangle Marie has a winter hat made from a circle,

Session 7 Symmetry. coordinates reflection rotation translation

Key Terms for This Session Session 7 Symmetry Previously Introduced coordinates reflection rotation translation New in This Session: frieze pattern glide reflection reflection or line symmetry rotation

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

Planning Guide. Shape and Space (3-D Objects and 2-D Shapes) Specific Outcomes 2, 3

Mathematics Planning Guide Kindergarten 3-D Objects/2-D Shapes Shape and Space (3-D Objects and 2-D Shapes) Specific Outcomes 2, 3 This Planning Guide can be accessed online at: http://www.learnalberta.ca/content/mepgk/html/pgk_3dobjects2dshapes/index.html

Classifying Shapes and Figures Grade Four

Ohio Standards Connection Geometry and Spatial Sense Benchmark E Use attributes to describe, classify and sketch plane figures and build solid objects Indicator 2 Describe, classify, compare and model

INFORMATION FOR TEACHERS

INFORMATION FOR TEACHERS The math behind DragonBox Elements - explore the elements of geometry - Includes exercises and topics for discussion General information DragonBox Elements Teaches geometry through

A Clever New CorelDRAW 12 Drawing Tool By Steve Bain

A Clever New CorelDRAW 12 Drawing Tool By Steve Bain Has anyone ever known you well enough to finish your sentences? Well, that's how the powerful new drawing tool in CorelDRAW 12 works. The new Smart

CLASSIFYING GEOMETRIC SHAPES

4 CLASSIFYING GEOMETRIC SHAPES INSTRUCTIONAL ACTIVITY Lesson 2 LEARNING GOAL Students will classify shapes according to single attributes. PRIMARY ACTIVITY Students will create groups of shapes that have

Finding Triangle Vertices

About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection

CHILDREN S ABILITY FOR USING DIFFERENT PLANE REPRESENTATIONS OF SPACE FIGURES *

CHILDREN S ABILITY FOR USING DIFFERENT PLANE REPRESENTATIONS OF SPACE FIGURES * Angel Gutiérrez Departamento de Didáctica de la Matemática Universidad de Valencia Apartado 22045. 46071 - Valencia (Spain)

Decomposing and Recomposing Shapes Warm-Up Name

Decomposing and Recomposing Shapes Warm-Up Name CST/Grade 2 MG 2.2 CST/Grade 2 MG 2.2 Look at the three triangles. Which of the following shapes can be made from the three triangles? These two shapes can

Progressions for the Common Core State Standards in Mathematics (draft)

Progressions for the Common Core State Standards in Mathematics (draft) cthe Common Core Standards Writing Team 23 June 2012 1 K 6, Geometry Overview Like core knowledge of number, core geometrical knowledge

1 st Grade Mathematics Unit # 5: Composing and Partitioning Shapes/Time Pacing: 15 days Unit Overview 1 In lessons 1-3, students identify the defining parts, or attributes, of two- and three-dimensional

Discovering Math: Exploring Geometry Teacher s Guide

Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional

PRACTICAL GEOMETRY SYMMETRY AND VISUALISING SOLID SHAPES NCERT

UNIT 12 PRACTICAL GEOMETRY SYMMETRY AND VISUALISING SOLID SHAPES (A) Main Concepts and Results Let a line l and a point P not lying on it be given. By using properties of a transversal and parallel lines,

E XPLORING QUADRILATERALS E 1 Geometry State Goal 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. Statement of Purpose: The activities in this

Shape Hunting This problem gives you the chance to: identify and describe solid shapes

Shape Hunting This problem gives you the chance to: identify and describe solid shapes Detective Sherlock Shapehunter tracks down solid shapes using clues provided by eyewitnesses. Here are some eyewitness

N Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Performance Assessment Task Swimming Pool Grade 9 The task challenges a student to demonstrate understanding of the concept of quantities. A student must understand the attributes of trapezoids, how to

Session 9 Solids. congruent regular polygon vertex. cross section edge face net Platonic solid polyhedron

Key Terms for This Session Session 9 Solids Previously Introduced congruent regular polygon vertex New in This Session cross section edge face net Platonic solid polyhedron Introduction In this session,

Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base)

GEOMETRY Vocabulary List Geometry Altitude- the perpendicular distance from the vertex to the opposite side of the figure (base) Face- one of the polygons of a solid figure Diagonal- a line segment that

Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

Algebra Geometry Glossary. 90 angle

lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

Math Mammoth Geometry 1 Contents

Math Mammoth Geometry 1 Contents Introduction... 4 Review: Area of Rectangles... 8 Review: Area and Perimeter... 13 Lines, Rays, and Angles... 17 Measuring Angles... 22 Drawing Angles... 27 Angle Problems...

Problem of the Month: Cutting a Cube

Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:

3. Relationship between this Unit and the Principles and Standards for School Mathematics (NCTM 2000). This Unit

4 th Grade Mathematics Lesson Plan April 16-18, 2002 Brewer Island School, San Mateo, CA Instructor: Akihiko Takahashi 1. Title of Unit: Finding the Area of Shapes 2. Goal: a. To deepen students understanding

Rep-Tiles Mela Hardin

Rep-Tiles Mela Hardin Introduction & Background In this activity, we want students to discover and explore algebraic expressions through a special kind of tiling of the plane. This activity is geared towards

Explorations with Shapes Kindergarten

Ohio Standards Connections Geometry and Spatial Sense Benchmark C Sort and compare twodimensional figures and threedimensional objects according to their characteristics and properties. Indicator 1 Identify

Grade 1 Geometric Shapes Conceptual Lessons Unit Outline Type of Knowledge & SBAC Claim Prerequisite Knowledge:

Grade 1 Geometric Shapes Conceptual Lessons Unit Outline Type of Knowledge & SBAC Claim Prerequisite Knowledge: Standards: Lesson Title and Objective/Description Shape names: square, rectangle, triangle,

Which Shape? Student Task Core Idea 4 Geometry and Measurement

Which Shape? Student Task Core Idea 4 Geometry and Measurement Identify circles, triangles, and squares among a collection of shapes. Identify two attributes of all triangles. Recognize and use characteristics,

Target To know the properties of a rectangle

Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles

Analysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 5-50 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website

Analysis in Geometry By Danielle Long Grade Level: 8 th Time: 5-50 minute periods Technology used: Geometer s sketchpad Geoboards NLVM website 1 NCTM Standards Addressed Problem Solving Geometry Algebra

1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

NCTM STANDARD 1: Numbers and Operations Kindergarten Grade 2 1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Kindergarten Grade One Grade Two 1. Count

8 PAGE INSERT ELEMENTARY MATH O N T A R I O ASSOCIATION FOR M A T H E M A T I C S E D U C A T I O N Volume 50 Number 3 March 2012 GEOMETRIC TRANSFORMATIONS TABLE OF CONTENTS Abacus Editor Greetings......

37 Basic Geometric Shapes and Figures

37 Basic Geometric Shapes and Figures In this section we discuss basic geometric shapes and figures such as points, lines, line segments, planes, angles, triangles, and quadrilaterals. The three pillars

Marie has a winter hat made from a circle, a rectangular strip and eight trapezoid shaped pieces. y inches. 3 inches

Winter Hat This problem gives you the chance to: calculate the dimensions of material needed for a hat use circle, circumference and area, trapezoid and rectangle Marie has a winter hat made from a circle,

Geometry. Unit 1. Transforming and Congruence. Suggested Time Frame 1 st Six Weeks 22 Days

Geometry Unit 1 Transforming and Congruence Title Suggested Time Frame 1 st Six Weeks 22 Days Big Ideas/Enduring Understandings Module 1 Tools of geometry can be used to solve real-world problems. Variety

Objective. Materials. Find the areas of parallelograms and trapezoids. Discover shortcut ways of finding the areas of parallelograms and trapezoids.

. Objective To use Geoboard to determine the areas of quadrilaterals between parallel lines Activity 4 Materials TI-73 Student Activity pages (pp. 41 45) Slide Along In this activity you will Find the

Constructing Geometric Solids

Constructing Geometric Solids www.everydaymathonline.com Objectives To provide practice identifying geometric solids given their properties; and to guide the construction of polyhedrons. epresentations

In our years of teaching geometry, the greatest challenge has been getting students to STUDENT REASONING IMPROVING IN GEOMETRY

IMPROVING STUDENT REASONING IN GEOMETRY Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof. Bobson Wong and Larisa Bukalov In our years of teaching

Warning! Construction Zone: Building Solids from Nets

Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have

Building a Bridge to Academic Vocabulary in Mathematics

Building a Bridge to Academic Vocabulary in Mathematics AISD Elementary Mathematics Department How Students Develop a Repertoire of Academic English in Mathematics Developed and researched by the AISD

Lesson 1: Exploring Polygons

Lesson 1: Exploring Polygons Objectives: Students will be able to identify whether a given shape is a polygon using the properties of polygons. Students will be able to identify and name polygons that

Which two rectangles fit together, without overlapping, to make a square?

SHAPE level 4 questions 1. Here are six rectangles on a grid. A B C D E F Which two rectangles fit together, without overlapping, to make a square?... and... International School of Madrid 1 2. Emily has

Problem of the Month: William s Polygons

Problem of the Month: William s Polygons The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common

To analyze students geometric thinking, use both formative and summative assessments and move students along the van Hiele model of thought.

van Hiele Rev To analyze students geometric thinking, use both formative and summative assessments and move students along the van Hiele model of thought. M. Lynn Breyfogle and Courtney M. Lynch When you

Shape Dictionary YR to Y6

Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use

4 Mathematics Curriculum

Common Core 4 Mathematics Curriculum G R A D E GRADE 4 MODULE 4 Table of Contents GRADE 4 MODULE 4 Angle Measure and Plane Figures Module Overview... i Topic A: Lines and Angles... 4.A.1 Topic B: Angle

Fractions In Action! Dawn Jesse

Fractions In Action! Dawn Jesse Fractions In Action Dawn Jesse Fractions In Action is an interactive activity that consists of direct instruction, cooperative learning and is inquire based. As the students

Kindergarten Math I can statements

Kindergarten Math I can statements Student name:. Number sense Date Got it Nearly I can count by 1s starting anywhere from 1 to 10 and from 10 to 1, forwards and backwards. I can look at a group of 1 to

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,

Hint for success: When tested in groups of students grade 3 and younger, this activity worked best as a centers activity.

Activities Grades 3 5 www.exploratorium.edu/geometryplayground/activities MAKING A TRANSLATION TESSELLATION Background: What is a tessellation? Suppose you wanted to cover a floor with tiles. You could