Polygon Puzzlers - Queen's UniversityThe Bermuda Triangle Puzzlehedz Inc. ... The Culminating Task Including: October 2001 Written by: Kelly Healey, Jennifer Roberts, Diane Muckleston

Reconnecting the Pieces Puzzlehedz Inc. ... The Culminating Task

Tools of the TradePuzzlers R UsAll the Angles

Classification Contest ... Riddles Congruency Concentration

Puzzlemakers in Training 1 ... Simply Symmetrical The Bermuda Rectangle ... Exploring Coordinate

SystemsTransformation Twister Pentomino Puzzlers

Puzzlemakers in Training 2 ... The Bermuda TrianglePuzzlehedz Inc. ... The Culminating Task

Including:

October 2001

Written by:

Kelly Healey, Jennifer Roberts, Diane Muckleston (Project Leader)

Polygon PuzzlersGeometry and Spatial Sense

Length of Unit: approximately: 22.5 hours

A Unit for Grade 4/5

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Oct 26, 2001 at 11:07:44 AM

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York Region District School Board

Polygon PuzzlersGeometry and Spatial Sense A Unit for Grade 4/5

Kelly Healey, Jennifer Roberts, Diane Muckleston (Project Leader)

York Region District School Board

A Unit for Grade 4/5Written by:

This unit was written using the Curriculum Unit Planner, 1999-2001, which Planner was developed in the province ofOntario by the Ministry of Education. The Planner provides electronic templates and resources to develop and share unitsto help implement the new Ontario curriculum. This unit reflects the views of the developers of the unit and is notnecessarily those of the Ministry of Education. Permission is given to reproduce this unit for any non-profit educationalpurpose. Teachers are encouraged to copy, edit, and adapt this unit for educational purposes. Any reference in this unitto particular commercial resources, learning materials, equipment, or technology does not reflect any officialendorsements by the Ministry of Education, school boards, or associations that supported the production of this unit.

AcknowledgementsThe developers are appreciative of the suggestions and comments from colleagues involved through theinternal and external review process.

Participating Lead Public School Boards:Mathematics, Grades 1-8Grand Erie District School BoardKawartha Pine Ridge District School BoardRenfrew District School Board

Science and Technology, Grades 1-8Lakehead District School BoardThames Valley District School BoardYork Region District School Board

Social Studies, History and Geography, Grade 1-8Renfrew District School BoardThames Valley District School BoardYork Region District School Board

The following organizations have supported the elementary curriculum unit project through team building andleadership:

The Council of Ontario Directors of EducationThe Ontario Curriculum CentreThe Ministry of Education, Curriculum and Assessment Policy Branch


Polygon Puzzlers Page 1

Geometry and Spatial Sense A Unit for Grade 4/5

Task ContextStudents will explore the world of recreational mathematics from the perspective of a puzzlemaker employedby Puzzlehedz Incorporated. All subtasks are designed to develop the key concepts necessary for thedesign, construction, analysis, and subsequent redesign of a geometric puzzle.

This unit addresses most of the expectations for Geometry and Spatial Sense for Grades 4/5. Expectationsat both grade levels related to three-dimensional geometry and the use of a protractor to measure and/orconstruct angles are not included in this unit. Teachers are encouraged to introduce the use of a protractoronce students have developed an understanding of angle and angle size as related to a square angle.

This is a combined grade unit. Each subtask, as well as the culminating task, is designed to enable teachersto provide one focus for concept development for his/her class. Students of both grades will be working withthe same materials and supporting each other's learning through the use of partner and small group activities.Achievement of grade specific expectations will be differentiated through the use of a task specific rubric.

Task SummaryStudents will explore two-dimensional geometry as well as transformational and coordinate geometry throughinvestigations with polygon puzzles such as, tangrams, pentominoes, etc. They will apply their learning tothe design, construction, analysis, and subsequent redesign of a geometric puzzle.

Each subtask is designed to cumulatively build the knowledge and skills necessary for the culminating task.In subtasks 8 and 12, students work on activities that focus on the learning to that point and are appropriatetimes to use self and/or peer assessment.

This is a combined grade unit. Differentiation appropriate to each grade is described in each subtask, wherenecessary. In order to facilitate parents' understanding of this process, sample letters are provided.

Culminating Task AssessmentStudents apply their learning to the design and construction of a geometric puzzle. Students have access toany of the manipulatives they explored in Subtask 3 (pattern blocks, attribute blocks, tangrams, polygon tiles,colour tiles, and pentominoes) to help them create a puzzle design on coordinate grid paper. Students designa blueprint and a set of directions for the educational puzzle to meet certain design requirements which arespecific to their grade. In pairs, students test a draft version of their puzzle and directions. A partner asksquestions for clarification and the student Puzzlemaker records these clarifications for later revision. Thestudent Puzzlemaker also views and analyses the puzzle created by their partners. Finally, the studentsrevise their products and written instructions to create their final product. Each student's prototype is thenfield tested by an adult at home and a student in class.

Links to Prior KnowledgeStudents are expected to have a basic understanding of the related concepts from previous grades inGeometry and Spatial Sense i.e. names of two-dimensional shapes, attributes of two-dimensional shapes,congruency, symmetry, transformations, coordinate systems, angles (Grade 5 only), and similarity (Grade 5only).

In Subtask 1, students brainstorm, summarize, and discuss their understanding of concepts from theprevious grade prior to participating in Activity 1. This provides the opportunity to activate prior knowledgebefore the initial assessment. This initial assessment can be used to determine students' understanding oftwo-dimensional shapes, symmetry, similar and congruent shapes, as well as transformations. This will alsoallow the teacher to gauge if the subtasks provided are sufficient to engage students at an appropriate level.

Unit Overview

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Suggestions for adaptations to the learning experiences are included in each subtask.

Considerations

Notes to Teacher1. Combined GradesWhere expectations for Grade 4 and 5 differ, these differentiations are made within the activity. For example,in Subtask 7, the Grade 4 Puzzlemakers are asked to identify lines of symmetry within their design, while theGrade 5 Puzzlemakers are asked to create a design with one line of symmetry.

2. TimeFor the purpose of this unit a math lesson is defined as a 50 minute period. A subtask may contain more thanone lesson and where this occurs, the suggested time is given as multiples of 50 minutes.

3. ManipulativesThroughout this unit, student will be using appropriate manipulatives.

Teachers may wish to supplement their stores of gameboards and two-dimensional puzzles by askingstudents to bring in examples of their favourite games and/or puzzles.

4. Instructional StrategiesEach subtask in this until follows a similar instructional pattern:1. Teacher Input - The teacher poses a problem to be investigated and solved or a question to be answered.2. Class Discussion - The class brainstorms and discusses approaches to the investigation.3. Cooperative Group and Partner Work - The students work in pairs, small groups or individually to carry outthe investigation. The teacher acts as a facilitator, moving from group to group, asking guiding questions orgiving prompts.4. Whole Group - The teacher periodically brings the class together to talk about successes and difficulties.5. Cooperative Group and Partner Work - The class continues to work to reflect on, refine, and revise theirown work.6. Closure - The class shares and reports its findings. Students are encouraged to ask questions of eachother.7. Communication - Students communicate their findings and reflect upon the process. This may be a math journal entry, a definition in their personal math dictionary, or a chart paper summary.8. Application - Students apply their learning to individual tasks.

* Note - Cooperative LearningIn a combined grade class, the use of cooperative learning strategies provides the opportunity for students tosupport each other's learning in a structured environment. If you are using cooperative learning for the firsttime, an excellent resource is Cooperative Learning: Where Heart Meets Mind by Barrie Bennett, CarolRolheiser-Bennett and Laurie Stevahn (ISBN 0-9695388-0-4) or refer to the Teacher Companions in theCurriculum Planner.

5. Assessment StrategiesSuggestions for assessment are provided in each subtask. A variety of assessment tools are used:anecdotal comments, checklists, student and teacher rubrics, as well as samples of frameworks that can beused for peer and self-assessment. Because the purpose of assessment is to improve student learning,explicit feedback by teacher and peers is an integral part of the assessment process. Students shouldalways be able to identify what they know now, that they didn't know before.

6. AdaptationsIn order to meet the needs of all students, teachers will need to make changes to the learning experiences,assessment, and evaluation strategies. These changes should reflect an inclusive classroom withconsiderations for culture, gender, learning style and accommodation and/or modifications for special needsstudents including ESL/ELD. Suggestions for changes to the activities are included in each subtask.


7. Use of TechnologySeveral of the subtasks provide the opportunity for the use of Ministry licensed software. Specificrecommendations are made in the resource section of the appropriate subtasks.

8. Cross-Curricular LinksThe culminating task involves the design of a geometric puzzle. This may provide an opportunity for across-curricular link to visual art and/or social studies. At the Grade 4 level, students could design a medievalknight's shield during 'Medieval Times'; while at the Grade 5 level, students could design a pattern for a vaseor other type of pottery during their study of 'Early Civilizations.'The communication component of writing instructions also provides the opportunity to focus on the text formof procedures.



Subtask List Page 1List of Subtasks

Reconnecting the Pieces This initial subtask can be used to determine students' understanding of two-dimensional shapes,symmetry, similar and congruent shapes, and transformations. Students describe the design of avariety of familiar game boards, such as checkers, Chinese checkers, and backgammon, in terms oftheir use of two-dimensional geometry. To activate prior learning, students initially work in small groupsto brainstorm what they notice about the use of geometry in games. Each group is then responsible fororganizing and summarizing the brainstormed ideas and sharing their analysis with the class. Studentsare encouraged to ask questions of other students in order to clarify the concepts. Finally, studentsuse these concepts in their analysis of game boards.

1

Puzzlehedz Inc. ... The Culminating Task Students are introduced to the design specifications and written requirements of the culminating task:creating an educational geometric puzzle for Puzzlehedz Incorporated. They then complete the firsttwo columns of a KWL chart (know, want/need to know, learn); the final column of the chart iscompleted in Subtask 13. The importance of using effective mathematical language throughout the unitand in the culminating task is illustrated by playing a game, 'What's My Design.' In this game, studentscreate a design from a few polygon tiles and write a riddle to help another pair recreate the design.Finally, students discuss what made the design easy or difficult to recreate. Students have anopportunity to revise their KWL chart.

2

Tools of the TradeStudents explore the tools (e.g., pattern blocks, attribute blocks, tangrams, polygon tiles, and colourtiles ) that will be available for them to use during the culminating task. Initially they work in smallgroups, focusing on one manipulative, then share their findings with other students. Finally, studentsexplore at least one other manipulative. Students are given a guiding question to focus theirexploration.

3

Puzzlers R UsStudents begin to examine the world of recreational mathematics by playing the strategy game of Hex.First students are challenged to create the instructions for a game that could be played on a tiledgameboard of hexagons. They then compare their game to the game of Hex. Next students play Hex bycreating a continuous path across a gameboard of tiled hexagons. The players must think about movesthat allow them to complete their pathway as well as moves that keep their partner from completingtheir path. Finally, students record the instructions for Hex as a model for the future writing ofinstructions in later subtasks.

4

All the AnglesStudents explore angles using the hands on a clock as a referent. Students model 3 o'clock or 90degrees using a pipe cleaner and locate examples of this angle in the room. Next students locateangles bigger or smaller than 90 degrees. Finally students create polygons on geoboards, cut them out,and label the angles within the polygons. Polygons are then stored in an envelope for use in Subtask 6.

5

Classification Contest ... Riddles Students use their knowledge of the attributes of two-dimensional shapes, including angles, to have aclassification contest. Students work in teams to group polygons in as many ways as possible.Students share their sorting and generate a class list of all the ways polygon tiles can be grouped.Using the class list as reference, students write a mathematical riddle to describe a randomlyselected polygon shape. Students then challenge a partner to solve their polygon riddle.

6

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Subtask List Page 2List of Subtasks

Congruency Concentration Students acquire their own knowledge of similar and congruent shapes and then play aconcentration-style game where the person who matches the most pairs of congruent or similarshapes wins the game. They then construct additional congruent game cards in a variety of ways, cutand match, transparent mirror (Mira), and geoboards.

7

Puzzlemakers in Training 1 ... Simply Symmetrical Students use a variety of polygons to create a jigsaw puzzle design. The Grade 4 Puzzlemakers areasked to identify lines of symmetry within their design, while the Grade 5 Puzzlemakers are asked tocreate a design with one line of symmetry. This task allows students to demonstrate and assess theirown understanding of symmetry as well as the attributes of polygons, including similar and congruentshapes.

8

The Bermuda Rectangle ... Exploring Coordinate Systems Students relate plotting coordinates on a grid to the game of battleship. They then use their knowledgeto play a battleship-style coordinate game where students work in pairs to hide and locate aquadrilateral.

9

Transformation Twister Students construct their own knowledge of transformations using their bodies to create translations,reflections, and rotations in a large open space such as a gym, hallway, or library resource centre.One student spins a spinner labelled with each type of transformation while another student recordsthe position of each player on chart paper using stick figure drawings. Students then work as a classto label the chart paper drawings as "translations," "reflections," or "rotations." Students finally work inpairs to play a strategy-style game where the goal is to transform a polygon shape from start to home.

10

Pentomino PuzzlersStudents use their knowledge of congruent shapes and transformations to find all the possiblecombinations of five squares to create pentominoes. They then work cooperatively to solve a varietyof pentomino challenges.

11

Puzzlemakers in Training 2 ... The Bermuda Triangle Students apply their knowledge of coordinate systems and transformations from previous activities tocreate a gameboard for the Bermuda Triangle Edition of Puzzlehedz Inc. Students create and followdirections for transforming a variety of polygon tiles such as a tangram triangle and pattern blockrhombus or trapezoid on a coordinate grid. This task allows students to demonstrate and assess theirown understanding of transformations and coordinates as well as their use and clarity of mathematicallanguage.

12

Puzzlehedz Inc. ... The Culminating TaskStudents apply their learning to the design and construction of a geometric puzzle. Students haveaccess to any of the manipulatives they explored in Subtask 3 (pattern blocks, attribute blocks,tangrams, polygon tiles, colour tiles, and pentominoes) to help them create a puzzle design oncoordinate grid paper. Students design a blueprint and a set of directions for the educational puzzle tomeet certain design requirements which are specific to their grade. In pairs, students test a draftversion of their puzzle and directions. A partner asks questions for clarification and the studentPuzzlemaker records these clarifications for later revision. The student Puzzlemaker also views andanalyses the puzzle created by their partners. Finally, the students revise their products and writteninstructions to create their final product. Each student's prototype is then field tested by an adult athome and a student in class.

13

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Polygon Puzzlers Subtask 1Reconnecting the Pieces

Geometry and Spatial Sense A Unit for Grade 4/5 mins100

Expectations4m61 A • solve problems using geometric models;4m62 A • investigate the attributes of three-dimensional

figures and two-dimensional shapes using concretematerials and drawings;

5m65 A • identify, describe, compare, and classify geometricfigures;

4m65 A • understand key concepts in transformationalgeometry using concrete materials and drawings;


4m66 A • describe location and movements on a grid;5m90 A – demonstrate an understanding of coordinate

systems on maps and grids.4m73 A – identify similar and congruent figures using a

variety of media;5m77 A – demonstrate an understanding of congruent

figures;4m84 A – draw lines of symmetry on two-dimensional

shapes;5m89 A – construct two-dimensional shapes with one line of

symmetry;5m88 A – explore tiling patterns that cover a plane;4m67 A • use language effectively to describe geometric

concepts, reasoning, and investigations, andcoordinate systems.

5m70 A • use mathematical language effectively to describegeometric concepts, reasoning, and investigations,and coordinate systems.

DescriptionThis initial subtask can be used to determine students' understanding of two-dimensional shapes, symmetry,similar and congruent shapes, and transformations. Students describe the design of a variety of familiar gameboards, such as checkers, Chinese checkers, and backgammon, in terms of their use of two-dimensionalgeometry. To activate prior learning, students initially work in small groups to brainstorm what they notice aboutthe use of geometry in games. Each group is then responsible for organizing and summarizing thebrainstormed ideas and sharing their analysis with the class. Students are encouraged to ask questions ofother students in order to clarify the concepts. Finally, students use these concepts in their analysis of gameboards.

GroupingsStudents Working As A Whole ClassStudents Working In Small GroupsStudents Working Individually

Teaching / Learning StrategiesBrainstormingClassifyingThink Aloud

Assessment* Collect students' individual performancetasks and record your observations on BLM01.3 Diagnostic Checklist.* Put a check mark under each concept thata student accurately labels and an x underthe concepts that are not identified at all ornot identified accurately.* Write any other observations that youmade during the process in the notessection (i.e., only identifies squares andtriangles).

Assessment StrategiesPerformance Task

Assessment Recording DevicesChecklistAnecdotal Record

Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONWhole Class Brainstorming* Ask students "How is geometry used in the design of games?" (i.e., design of game board, design ofpieces, design of box, use of shapes, etc.) Answers will vary; accept all possible answers.

COOPERATIVE GROUP WORKSmall Group Classifying* Give each group of two or three a game board.

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* Ask students to brainstorm, on strips of chart paper, as many different geometric words as they can todescribe what they notice about the use of geometry on the face of their game board.* Prompt groups that are only focusing on shape by asking, "What other ways can we use geometric terms todescribe the face of a game board?" (e.g., symmetry, congruent, angles).* Trade game boards with a group nearby and continue to brainstorm.* Ask students to sort the geometric words into groups and give each group a name.

WHOLE GROUPWhole Group Classifying* Select one student from each group to share their sorting with the class (e.g., person who has the nextbirthday).* Make a master list on chart paper of all the categories, concepts, and words presented.* Review the list as a class and delete any categories that are not related to geometry (e.g., colour) or thatare not related to the design on the face of the game board (i.e., words that relate to three dimensions).* Prompt students to add any categories that may be missing. At this point, students may not fully understandall of the categories as this is a diagnostic assessment.* Inform students that they will be exploring these terms throughout the unit and will only be expected to usethe terms today with which they are familiar.

CLOSURE/COMMUNICATIONWhole Class Learning Log/Journal* Tell students that today they will be writing their journal as a class based on a framework that they aregoing to use several times throughout the unit. We are going to call it "Puzzlemaster's Journal Framework."Explain that you are going to follow the framework today as you create the first journal entry with them. HavePuzzlemaster's Journal Framework outline on chart paper.* Read section one of the math journal outline, "What we did..." Ask students, "What did we do today?" Thenmodel how to write a topic sentence (e.g., "Today we looked at different games and how geometry wasused to design them").* Ask students, "What was the first thing we did?" Accept all student input, then model how to write thesecond sentence (e.g., "First we worked in groups to look at a game board and made a list of all thegeometric words we could think of").* Continue by asking, "What did we do next?" and model how to write the sentence until you have thecomplete description of what was accomplished in class.* Read through Section 2 of the math journal outline, "What you thought ..." Ask a variety of students for theiropinions and select one as your example. Model for students how to write the topic sentence for the oneselected (e.g., "It reminded me of a game I have at home that I haven't played in a long time.").* Depending on the topic sentence, ask students "What was fun, interesting, or boring about this activity?"and model how to write the next sentence (e.g., "I enjoyed looking at the different game boards.")* Continue asking for input until you have used all of the class's ideas.* Read through Section 3 of the math journal outline "What you learned..." Ask students "What did you learn?"Ask a variety of students for their opinions and using these ideas, model how to write the final paragraph,using the same procedure as before (e.g., "I learned that there is a lot of geometry in games. I also learnedthat I can work well in a group. Wouldn't game boards be boring if there weren't so many shapes to choosefrom?").* Have students copy or create their first math journal based on Puzzlemaker's Journal Framework BLM 01.1.* Ask students to keep the framework in their math journal for use later in the unit.

APPLICATIONIndividual Diagnostic Assessment* Give students photocopies of game boards.* Tell students they are going to label as many geometric features and properties as they can. Remindstudents they can refer to the list they brainstormed together.




Resources

* Do not prompt students or have them share ideas at this time, as it is an assessment of what studentsalready know.* Tell students to hand in their sheet when it is completed.

Adaptations * Refer back to the checklist before beginning each subtask to identify students who may need additionalsupport, such as remediation or enrichment. Note that suggestions for remediation, consolidation, and enrichmentwill be provided in the adaptation section of all of the tasks (i.e., before beginning Subtask 7, note that students x,y, and z demonstrated no knowledge of congruency and may need remediation for the task).

BLM 01.1 Puzzlemaker's JournalFramework

BLM 01.1 Journal.cwk

BLM 01.3 Diagnostic Checklist BLM 01.3 Diagnostic.cwk

chart paper strips 10

markers 2

gameboards 1

Notes to Teacher1. Prior to beginning this unit, collect or borrow a variety of game boards from around the school or ask studentsto bring them in.2. Decide whether you want your students to have access to the new vocabulary at the beginning of the unit orwhether you want to build the new vocabulary as the concept is taught.3. Journal Writing can be done in students' math notebooks, in a separate math journal book or on sheets ofpaper. See BLM 01.1 for sample framework for this subtask.

Teacher Reflections


Polygon Puzzlers Subtask 2Puzzlehedz Inc. ... The Culminating Task


Expectations4m62 A • investigate the attributes of three-dimensional



4m67 A • use language effectively to describe geometricconcepts, reasoning, and investigations, andcoordinate systems.


4m80 A – discuss ideas, make connections, and articulatehypotheses about geometric properties andrelationships;

5m85 A – discuss ideas, make conjectures, and articulatehypotheses about geometric properties andrelationships;

DescriptionStudents are introduced to the design specifications and written requirements of the culminating task: creatingan educational geometric puzzle for Puzzlehedz Incorporated. They then complete the first two columns of aKWL chart (know, want/need to know, learn); the final column of the chart is completed in Subtask 13. Theimportance of using effective mathematical language throughout the unit and in the culminating task isillustrated by playing a game, 'What's My Design.' In this game, students create a design from a few polygontiles and write a riddle to help another pair recreate the design. Finally, students discuss what made thedesign easy or difficult to recreate. Students have an opportunity to revise their KWL chart.

GroupingsStudents Working In PairsStudents Working As A Whole ClassStudents Working Individually

Teaching / Learning StrategiesThink / Pair / ShareConcept ClarificationDiscussion

Assessment* Observe students during the riddle writingactivity and record anecdotal informationabout the clarity of language. Use ahighlighter to indicate those students whorequire intervention, enrichment,consolidation, or remediation. Students willhave another opportunity to write riddles inSubtask 6. See BLM 02.6 for a sample ofanecdotal record format.

Assessment StrategiesObservation

Assessment Recording DevicesAnecdotal Record

Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONThink/Pair/Share* Provide students with a copy of 'Calling All Grade 4 Puzzlemakers!" or "Calling All Grade 5 Puzzlemakers!"(BLMs 13.1 and 13.2) or show Grade 4 an overhead annotated to include differences for Grade 5.* Ask students to read it silently to themselves to find out what it is they are going to have to do at the end ofthe unit as a final assessment. Next ask them to turn to their neighbour and share their understanding of theculminating task. Ask partners to share with the whole group.* Repeat this process. Ask students to read on to find out what the three steps are that they are going tohave to complete.* Invite students to ask questions to clarify the task and the requirements. Summarize the steps in the task onchart paper. Tell students that each of the activities that they are going to do in the next few weeks willprepare them for the assignment.




* Explain the assessment process: peer trial and revision, peer assessment, home feedback, and teacherassessment.* Share the peer assessment rubric (BLM 13.3) with the students. Link each of the categories in the rubric toone of the steps in the task.* Tell students that you are going to use a similar rubric.* Wait while each student places each BLM in a folder or envelope that will house all their work for this unit.

COOPERATIVE GROUP WORKSmall Group Classifying* Model the use of a KWL chart for an imaginary student.* Invite students to work together to fill out the first two columns of the chart. Although they are encouragedto talk to each other about what they feel they know and do not know, each student's KWL chart shouldreflect their own strengths and weakness.

WHOLE GROUPWhole Class Concept Clarification* Explain that as Puzzlemakers they have a variety of tools that they will be able to use. Each tool, regardlessof the shape or size, has one common characteristic: they are all polygons. Introduce the concept of apolygon through concept attainment.* Present "yes" and "no" examples (see BLM 02.2 for examples)* Ask students to turn to a partner and discuss what the "yes" examples have in common.* Present test examples one at a time and ask students to indicate whether they think each is a "yes" or a"no." Provide students with the answer.* Ask students to turn to a partner and discuss a possible definition for a polygon.* Share ideas and construct a definition on chart paper of a polygon.

CLOSUREWhole Class Discussion.* Ask students, "Now that we have a common understanding of a polygon, how will you, as Puzzlemakers,differentiate one polygon from another?" (We call them by a different name.)* Prompt students to recognize that a polygon's name is determined by the number of its sides.

* After this activity, students should have an understanding of the following:1. A polygon is any closed two-dimensional figure formed by three or more line segments.2. A polygon is named according to the number of sides. (See BLM 02.3 Glossary)

COMMUNICATIONIndividual Math Dictionary * Ask students to add the definition of polygon to their math dictionaries. Ask them to include a diagram of anexample and a non example for polygon as well as two examples of each type of polygon.

APPLICATIONPartner Peer Practice* Tell students that they are going to practise using their new mathematical vocabulary by playing the game,'What's My Design?'* Ask pairs of students to choose three or four polygon tiles, create a design and write a riddle for recreatingthe design. Example: "I am made of a hexagon, a triangle and a quadrilateral. My final shape looks like aclown. I have a head of a hexagon, a hat of a triangle and a body of a quadrilateral. What do I look like?"* Ask students to place the tiles and a tracing of the design inside a brown paper bag and attach the riddlewith a paper clip to the outside of the bag.* Students bring their completed 'What's My Design?' bag to a central location and select a different one to try.




Resources

* Ask students to use recording sheet (BLM 02.4) to keep track of their work.Whole Class Discussion* Prompt students to recognize that the success of recreating the design is directly related to the correct,clear use of mathematical language. Ask questions such as: "Was it easier to create or solve the riddles?"and "Tell me why."* Ask students if anyone would like to revise their KWL chart based on this discussion.

Homework/Homelinks* Send The FourFive Math Corner letter (BLM 02.5) home to parents.*Ask students to share the letter and their initial math dictionary entry on polygons with their parents.

AdaptationsEnrichment* Pose the following challenge: "Choose three polygons that have the same name but are different in someway. Create a design and riddle. Trade with a partner. What made the riddle hard or easy to solve? " What doyou know now?"

Consolidation* Pose the following challenge: "Create a design and riddle as you did previously. Trade with a partner andwatch as they try to recreate your design. Revise your riddle if necessary."

Remediation* Model the creation of a three polygon design and think aloud while writing the riddle.* Give students a similar but slightly different challenge to do together. Share the process, teacher andstudents thinking aloud.* Allow students to work together in twos or threes to create another design and riddle. Guide students byprompting them to use the strategies you developed together.* Ask students to create a design and riddle independently.

BLM 02.1 KWL Chart BLM 02.1 KWL Chart.cwk

BLM 02.2 Polygon Data Set BLM 02.2 Polygon Data Set.cwk

BLM 02.4 What's my Design? BLM 02.4 What's my Design.cwk

BLM 02.5 The FourFive Math Corner BLM 02.5 Math Corner.cwk

BLM 02.6 Anecdotal Observations BLM 02.6 Anecdotal.cwk

BLM 02.7 Polygon Puzzlers TrackingSheet

BLM 02.7 Polygon.cwk

folder or envelope 1

paper bags 1

polygon tiles 1




Notes to Teacher1. Students will need a folder or envelope in which to keep all their work during the unit.

2. You may or may not want to share the teacher rubric at this time.

3. 'What's My Design?' game - Number the bags with a magic marker so that students can keep track of thebags they have tried.

4. Concept Attainment/Concept Clarification: This instructional strategy can be used to teach or clarifyconcepts. In this subtask, it is used to teach the concept of polygon. See Beyond Monet: The ArtfulScience of Instructional Integration by Bennett and Rolheiser or Models of Teaching by Joyce and Weil forfurther information on this model of teaching.

Teacher Reflections


Polygon Puzzlers Subtask 3Tools of the Trade







DescriptionStudents explore the tools (e.g., pattern blocks, attribute blocks, tangrams, polygon tiles, and colour tiles )that will be available for them to use during the culminating task. Initially they work in small groups, focusingon one manipulative, then share their findings with other students. Finally, students explore at least one othermanipulative. Students are given a guiding question to focus their exploration.

GroupingsStudents Working In Small GroupsStudents Working As A Whole ClassStudents Working Individually

Teaching / Learning StrategiesBrainstormingNumbered HeadsDiscussion

AssessmentObserve students during the explorationactivity and record anecdotal information.Are they building with the materials, makingpictures, sorting, or seeing relationships?Listen for the use of mathematical language.Use a highlighter to indicate those studentswho require intervention, enrichment,consolidation, or remediation.In Subtask 5, students will have anopportunity to sort polygon tiles in as manyways as possible. See BLM 02.6 for asample of an anecdotal record format.



Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONBrainstorm - Whole Class* Explain that as puzzlemakers for Puzzlehedz Inc., they are going to have a variety of tools to use and thatthere are going to be many opportunities to use them before they have to make their final product.* Ask, "What would you want to know about these tools, before you had to use them?" Record ideas onchart paper. As you record the first idea, ask the student who gave the first idea to select the secondperson, and so on. You may also want to ask them to choose a girl if they are a boy, and vice versa.* Prompt students to realize that they need to know what the tools do and what they do not do.

COOPERATIVE GROUP WORKSmall Group Brainstorming




* Form groups according to the number and types of manipulatives you have. You may have more than onegroup working with the same manipulative.* Give each group of students time to explore the manipulative, focusing on what it does and does not do.* Provide each group of students with chart paper and markers to record its findings.* Tell students that each group will have a chance to share its findings and the reporter will be determined byrolling a dice. They therefore all need to be prepared to share their group's findings.

WHOLE CLASSNumbered Heads - Class Discussion* Number each group and each person within the group.* Ask each group to share: the first roll of the dice determines the group number and the second roll of thedice determines the reporter.* Ask class, "From what you have learned about each manipulative, which do you think could be themost/least valuable to you as a Puzzlemaker?"

COOPERATIVE PARTNER WORKCollaborative/Cooperative Learning* Give students time to explore a different manipulative, encouraging them to extend the list of do's and don'tsfrom the previous group.

CLOSUREWhole Class Discussion* Ask students to share any further findings about each of the manipulatives.* Post chart paper summaries around the room, where they can be referred to or added to during the unit.

COMMUNICATIONIndividual Learning Log/Journal* Ask students to write a response based on Puzzlemaker's Journal Framework (BLM 01.1)

APPLICATIONHomework/Homelinks* Ask students to take home their baggie of tangrams to share with someone at home. (BLM 03.1 TangramTemplate)* Consider using challenges such as1. How many different ways are there to make the large triangle with the smaller pieces?2. How many different ways can you make a square using some or all of the tangram pieces?3. How many different polygons can you make using the two small and one medium-sized triangle?4. How many different ways are there to make a triangle using some or all of the tangram pieces?* Ask students to sketch any solutions to these challenges on tangram paper (BLM 03.2)

AdaptationsIf you feel students need more time to explore the tools:Enrichment* Pose the following challenge: "Use pattern blocks and see if you can make a larger hexagon, using onlyhexagons, a larger triangle using only triangles."Consolidation* Pose the following challenge: "Use one of the manipulatives that you haven't yet had a chance to exploreand try some of the ideas that are listed on the chart paper. See if you agree or if there are new ideas youcould add."Remediation -




Resources

* Using a geoboard as the tool, model creating a shape and think aloud, "I've just made a triangle. I wonderwhat other shapes I could make, how many sizes of triangles I could make, and how many triangles of thesame size I could make."* Share the process, teacher and students thinking aloud as you try one of the "I wonders."* Allow students to work together in twos or threes to solve a challenge such as, "I wonder how manysquares I could make on the geoboard." Guide students by prompting them to use the strategies youdeveloped together.* Ask students to solve a challenge independently.

BLM 03.1 Tangram Template BLM 03.1 Tangram Template.cwk

BLM 03.2 Tangram Paper BLM 03.2 Tangram Paper.cwk

Grandfather Tang's Story Ann Tompert

Three Pigs, One Wolf and Seven MagicShapes

Grace MacCarone and David Neuhaus

pattern blocks bin

tangrams 1

colour tiles bin

geoboards 1

polygon tiles bin

Notes to Teacher1. Polygonal tiles are available for purchase from a variety of educational suppliers.2. Make a set of tangrams for each student: photocopy the tangram template (BLM 03.1) onto cover stock; cutwith a paper cutter and store in baggies.3. Students may like to create a character(s) from a familiar story from tangram pieces.

Teacher Reflections


Polygon Puzzlers Subtask 4Puzzlers R Us


Expectations4m75 A – discover geometric patterns and solve geometric

puzzles with and without the use of computerapplications;

5m81 A – use a computer application to explore and extendgeometric concepts;

5m88 A – explore tiling patterns that cover a plane;4m67 A • use language effectively to describe geometric



4m78 A – recognize and describe the occurrence andapplication of geometric properties and principles inthe everyday world;

5m83 A – recognize and explain the occurrence andapplication of geometric properties and principles inthe everyday world;

DescriptionStudents begin to examine the world of recreational mathematics by playing the strategy game of Hex. Firststudents are challenged to create the instructions for a game that could be played on a tiled gameboard ofhexagons. They then compare their game to the game of Hex. Next students play Hex by creating acontinuous path across a gameboard of tiled hexagons. The players must think about moves that allow themto complete their pathway as well as moves that keep their partner from completing their path. Finally, studentsrecord the instructions for Hex as a model for the future writing of instructions in later subtasks.


Teaching / Learning StrategiesBrainstormingCollaborative/cooperative LearningDiscussion

Assessment* Observe students to determine whether ornot they are using an effective strategy toplay the game. Use a highlighter to indicatethose students who require intervention,enrichment, consolidation, or remediation.


Assessment Recording DevicesChecklist

Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONBrainstorm - Whole Class* Explain that as puzzlemakers for Puzzlehed Inc., they are going to work in an area of mathematics called'recreational mathematics.' For hundreds of years, mathematicians have created puzzles for entertainmentthat use mathematical principles. Today you are going to examine and play a game called 'Hex' which wascreated twice by mathematicians in two different parts of the world. This game is played on a board thatlooks like a tiled floor of hexagons. (Show BLM 04.1)* Pose the following question, "What might the goal and rules of the game be for a game played using agameboard only of hexagons? Think about the games you know such as checkers, Chinese Checkers etc. tohelp you decide.* Brainstorm possible ideas and record on chart paper.

COOPERATIVE PARTNER WORKCollaborative/Cooperative Learning* Instruct students to try a variety of approaches for the next 10 minutes. ( BLM 04.1 HEX Gameboard)

WHOLE CLASS




Whole Group Discussion* Ask students to share or demonstrate what they tried, what worked and what did not.* Prompt students to state the goal of the game and the rules they created.* Script possible instructions for one of the successful games. See Puzzlemaker's Instruction Framework -BLM 04.2

COOPERATIVE PARTNER WORKCollaborative/Cooperative Learning* Ask all students to go back and try one of the successes and note any changes they make.

CLOSUREWhole Class Discussion* Ask students to share their results. Are there revisions that need to occur?* Present instructions for 'Hex' and ask, "What do you notice that is the same or different about our game andthe game of 'Hex'?"*Prompt students to notice the similarity in the frameworks and tell them that whenever they are writinginstructions for a game or puzzle, they will be expected to use this framework.

COMMUNICATIONIndividual Learning Log/Journal* Provide students with a copy of the framework for their "Puzzlehedz" folder or journal. (BLM 04.2)* Ask students to use the framework to make a model of puzzle instructions by writing the instructions for'Hex' or the class game.

APPLICATIONPartner Work* Challenge students to play the game of 'Hex' for the purpose of developing/recording strategies for winning.Whole Class Discussion* Share strategies and create a list of successful strategies for use during play at another time.Homework/Homelinks* Ask students to share the game of 'Hex' with someone at home and record all strategies on the back of thegameboard. (BLM 04.1 and 04.3 photocopied back to back.)* Share strategies next day and add any new strategies to the list. Store homework gameboard in'Puzzlehedz' folder or envelope.Computer Connection* Use an AppleWorks drawing document (Clarisworks) to explore/investigate whether some or all regularpolygon shapes can be used to make a tiled gameboard.

AdaptationsEnrichment*Pose the following challenge: "Based on your exploration of regular polygons using Appleworks, create atiled gameboard and game rules for a new game based on a regular polygon of your choice."

Consolidation* Pose the following question, "How would the instructions for the game of Hex change if you were using agameboard of tiled triangles?"* Have students create the gameboard using the large triangles from a set of attribute blocks or give eachstudent an equilateral triangle cut out of card stock to act as a template.* Instruct students to use Puzzlemaker's Instruction Framework BLM 04.2 as the template for the game'sinstructions.




Resources

Remediation* Play the game of Hex with this small group of students working in two teams. Ask each team to talk eachmove out loud before it is made. Encourage students to look ahead at their opponent's possible moves aswell as their own.

BLM 04.1 HEX Gameboard BLM 04.1 HEX Gameboard.cwk

BLM 04.2 Puzzlemaker's InstructionFramework

BLM 04.2 Puzzlemaker.cwk

BLM 04.3 HEX Rules and StrategySummary

BLM 04.3 HEX Rules.cwk

ClarisWorks 5.0 (English)

game pieces 30

Notes to Teacher1. In 1942, Piet Hein introduced the game during a lecture to university students at the Institute for TheoreticalPhysics, in Denmark. In 1948, John Nash, a graduate at Princeton University, and later a professor at theMassachusetts Institute of Technology, independently invented the same game.

2. Create a sample gameboard by taping pattern block hexagons in a diamond shape on a piece of bristolboard or chart paper.

3. Ensure that Puzzlemaker's Instructions for Hex are accurately completed as this entry will provide a model forfuture subtasks in which the writing of instructions is required. (Subtasks 7, 8, 11 & 12)

4. The individual challenge can be done using or tracing pattern blocks or by using AppleWorks (formerly calledClarisworks). Using a computer DRAW programme is very time consuming and is perhaps best suited as anadaptation for enrichment students.

Teacher Reflections


Polygon Puzzlers Subtask 5All the Angles


Expectations4m71 A – identify and sort quadrilaterals (e.g., square,

trapezoid);4m72 A – sort and classify two-dimensional figures according

to shape;5m75 A – sort polygons according to the number of sides,

angles, and vertices;5m76 A – classify two-dimensional shapes according to

angle and side properties (e.g., obtuse, scalene);4m77 A – use mathematical language to describe geometric

ideas (e.g., line, angle);5m82 A – use mathematical language to describe geometric

ideas (e.g., quadrilateral, scalene triangle);

DescriptionStudents explore angles using the hands on a clock as a referent. Students model 3 o'clock or 90 degreesusing a pipe cleaner and locate examples of this angle in the room. Next students locate angles bigger orsmaller than 90 degrees. Finally students create polygons on geoboards, cut them out, and label the angleswithin the polygons. Polygons are then stored in an envelope for use in Subtask 6.


Teaching / Learning StrategiesClassifyingWorking With ManipulativesReview

Assessment* Check students dictionaries, journals, andcollection of geoboard shapes to seewhether students were able to accuratelymatch the triangles and quadrilaterals withtheir definitions and whether or not theyseem to understand the concept of anangle. Record on a checklist. Use ahighlighter to indicate those students whorequire intervention, enrichment,consolidation, or remediation.

Assessment StrategiesLearning Log


Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONWhole Class Demonstration* Ask students, "What happens to the space between the hands on a clock as the time changes?" Acceptall possible answers.* Hold up a model of a clock with moving hands (BLM 05.1 Model of a Clock). Place the small hand on the 6and the long hand on the 12. Slowly move the long hand clockwise to 6 and back again.* Prompt students to notice that the amount of space between the two hands starts off large and gets smalleras you move towards the 6 and then gets larger again as you move back to the 12.* Tell them that the spread of the clock hands is the size of the angle. Place the hands of the clock at the 12and the 3.* Tell them that the spread between the clock hands sometimes forms a special kind of angle called a "squareangle" or "right angle." Angles can be measured in units called "degrees." The measure of a right angle is 90degrees.




COOPERATIVE GROUP WORKWhole Class Classifying* Supply each student with a pipe cleaner and ask them to form a 3 o'clock (right angle) with it by bending itin half and then moving the two arms out to the 3 o'clock position.* Tell them that their task is to take their square or right angle and find objects in the room that match the angle.* Demonstrate this by holding up a textbook and matching the pipe cleaner angle with one of the corners ofthe book.* Tell students that it is important to keep the pipe cleaner in the 3 o'clock (square or right angle) position.

WHOLE GROUPWhole Class Discussion* Ask students, "What were some of the things that you found that had square or right angles?"* Correct any misconceptions by having a student take their pipe cleaner and check.* Ask students "Do all of the objects in the room have square or right angles?"* Prompt students to recognize that some objects have angles that are smaller than a right angle and someobjects have angles that are larger.* Tell students that angles that have a measure smaller than a right angle are called "acute" angles and thatangles that have a measure greater than a right angle are called "obtuse" angles.* Ask students to recognize an object that has an acute angle, an angle with a measure less than 90degrees, and have a student check it with a pipe cleaner.* Ask students to recognize an object that has an obtuse angle, an angle with a measure greater than 90degrees, and have a student check it with a pipe cleaner.* Tell students to bend their pipe cleaner to form an acute angle or an angle with a measure less than a rightangle and hold it up. Correct any students who have not formed an acute angle.* Repeat this process for an obtuse angle.

COOPERATIVE GROUP WORKGroup Working With Manipulatives* Review the nature of an angle with students.* Identify that all polygons have at least three angles.* Hand out a geoboard to each student. (This could be done in partners if geoboards are limited.)* Tell students they are going to be using the geoboards to construct a variety of polygons. The Grade 5students will be constructing triangles and the Grade 4 students will be constructing quadrilaterals. At theend, you will ask them what they noticed about the angles in their polygons.* Model for students how to draw the shape they created on the geoboard on dot paper, by picking a startingpoint and counting the number of pegs to the next vertex and connecting the dots with a ruler.* Model how to label angles in as many ways as possible using a right angle as a reference: a "right" angle isequal to 90 degrees, an "obtuse" angle is greater in size than a right angle or > 90 degrees, and an "acute"angle is smaller in size than a right angle or < 90 degrees.* Ask students to cut out the polygons they create and store them in an envelope.* Watch for students who accidentally create polygons with more sides than they have been asked for, orstudents who are creating only regular polygons (i.e., squares, equilateral triangles) and encourage them tocreate shapes with sides of different lengths.

CLOSUREWhole Class Discussion* Use the following prompt to ensure students have a common understanding.1. What is an angle?2. What did you notice about the angles in triangles and quadrilaterals?

* After this activity students should have an understanding of the following:




Resources

1. An angle size is the spread of the angle's rays. Or, an angle size is how much one ray has rotated awayfrom the other ray. (Grades 4 and 5).2. All polygons have angles and it is possible for one polygon to have more than one type of angle (Grades 4and 5).3. There are different types of angles and a right angle can be used as a reference to determine the type ofangle: a right angle is equal to 90 degrees, an obtuse angle is greater in size than a right angle or > 90degrees and an acute angle is smaller in size than a right angle or < 90 degrees. See Notes to Teacher.

COMMUNICATIONIndividual Learning Log/JournalJournal* Ask students to use the Puzzlemaker's Journal Framework (BLM 01.1) to guide them in creating a responseto this activity.

Math DictionaryHave students add terms associated with this activity to their math dictionary.

APPLICATIONIndividual Review* Challenge students to review the definitions of mathematics terms associated with this activity in adictionary. For the different types of quadrilaterals and triangles identified, have them look at their dot papershapes and match the shapes to the definitions.* When students have found a match, they should label the shape on the back.* Remind students that sometimes a polygon can be classified in several different ways, e.g., a square canbe classified as a quadrilateral, a rectangle, a rhombus, and a parallelogram.* If students have a definition with no match, have them attempt to create a shape on the geoboard that fitsthe definition, cut it out, and add it to their collection of shapes.* Have students put their shapes back in the envelope to be used in Subtask 6.Computer Connection - The Geometer's Sketchpad* From the toolbox at the left side of the screen, click on tool #4, the "straight edge" tool. Hold and drag toselect the "segment" tool. Click and drag on the screen to create an angle.* Estimate the measure of the angle as >, <, or = 90 degrees. Select tool #5, or text tool, from the toolbox.Click and drag on the screen to create a text box. Type your estimate inside the text box.* Select the "arrow" tool; hold down the Shift key and click on each point of the angle so that the middlevertex is clicked second (e.g., in angle ABC, click on B second).* Go to the "Measure" menu and click on "angle." Compare the actual measure of the angle with your estimate.* Create a different angle and try again.

AdaptationsEnrichment* Challenge students to create shapes that will fit beside more than one definition.

Consolidation* Challenge students to continue to generate as many shapes as they can and create them in different waysand sizes.

RemediationRepeat the activity of going around the class with their pipe cleaners and give them immediate feedback asthey identify angles.




BLM 05.1 Model of a Clock BLM 05.1 Model of a Clock.cwk

pipe cleaners 1

geoboard dot paper approx.

envelope 1

scissors 1

geoboards 1

The Geometer's Sketchpad licensed software

Notes to Teacher1. The Grade 4 students need to understand the concept of "angle" in order to sort by shape, i.e., a square isdifferent to a rhombus, because the angles are different. Grade 4 students do not need to use specificvocabulary related to angles or to differentiate triangles based on angle and side properties.2. Model using the appropriate language for the Grade 4 students as well as for the Grade 5 students.Differentiate the students' use of correct mathematical language by grade level at the assessment level.

Teacher Reflections


Polygon Puzzlers Subtask 6Classification Contest ... Riddles


Expectations4m71 A – identify and sort quadrilaterals (e.g., square,

trapezoid);4m72 A – sort and classify two-dimensional figures according

to shape;5m75 A – sort polygons according to the number of sides,

angles, and vertices;5m76 A – classify two-dimensional shapes according to

angle and side properties (e.g., obtuse, scalene);4m77 A – use mathematical language to describe geometric

ideas (e.g., line, angle);5m82 A – use mathematical language to describe geometric

ideas (e.g., quadrilateral, scalene triangle);

DescriptionStudents use their knowledge of the attributes of two-dimensional shapes, including angles, to have aclassification contest. Students work in teams to group polygons in as many ways as possible. Students sharetheir sorting and generate a class list of all the ways polygon tiles can be grouped. Using the class list asreference, students write a mathematical riddle to describe a randomly selected polygon shape. Studentsthen challenge a partner to solve their polygon riddle.


Teaching / Learning StrategiesClassifyingDiscussionLearning Log/ Journal

Assessment*Observe students during the sorting activityand record anecdotal information aboutwhich categories students were able tosuccessfully or accurately sort their shapes.Make note of any student who requiresintervention, enrichment, consolidation, orremediation.

* Each day have three or four studentsshare their riddle with the class and see ifthe class can guess. If a student's riddlewas not clear, ask for peer suggestions forhow they could make it clearer. Record anyobservations in your anecdotal notes andallow students to try another riddle to showimprovement.

Assessment StrategiesObservationLearning Log


Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONWhole Class Discussion* Present students with one quadrilateral and one triangle.* Ask students, "What is similar about these two shapes?" Accept all possible answers.* Ask students, "What is different about these two shapes?" Accept all possible answers.* Ask students, "If we wanted to put these shapes together in a group, how could we describe the group?"* Ask students, "If we wanted to make sure these shapes were not in the same group, how could we




describe the two groups?"

COOPERATIVE GROUP WORKGroup Classifying* Divide students into groups of four to six students.* Present each group of students with a variety of polygons, including the shapes they made on dot paper inthe previous subtask.* Tell students they are going to participate in a classification contest and that the goal of the contest is to sortthe polygon shapes in as many ways and into as many groups as possible.* Have one student record the groupings onto a piece of chart paper.* The group that wins will be the group that has the greatest number of categories. This will probably be agroup that understands that any given shape can be grouped by a variety of attributes and can fit into manydifferent groups.

WHOLE GROUPWhole Class Brainstorming* Ask each group to give one of its categories and record it on chart paper.* Continue asking students until all groupings are recorded. Each part of the grouping should go on a differentline, e.g., shapes with only acute and obtuse angles, shapes with only right angles. If students think ofothers as they are sharing, these can be added as well.* Have students look at the list that has been recorded and ask if there are any categories that are not relatedto geometry, e.g., colour.* If any of the following categories are not listed, prompt students to include: acute angles, right angles,obtuse angles, triangles, quadrilaterals, (common polygon names, e.g., hexagon), three vertices, fourvertices, five vertices, six vertices, more than six vertices, three sides, four sides, five sides, six sides, morethan six sides, all sides equal, two sides equal, all sides unequal.

COOPERATIVE PARTNER WORKPairs Classifying* Cut into strips the group headings generated in the whole class brainstorming.* Number all the students as either a "one" or a "two." Tell the "ones" that they need to find a "two" and findan area in which to work.* Give pairs of students a variety of polygons, including the shapes they created with the geoboards in theprevious task.* Give students two pieces of string approximately 60 cm. long. Have them form two overlapping circles withthe pieces of string so that it looks like a Venn diagram.* Shuffle the strip headings and give two strips out to each pair randomly.* Have students place the heading at the top of each circle and remind them that the area in the middle is forshapes that fit both categories.* Tell students that when they have finished, they should show their teacher, return their strips, thenrandomly choose two more categories.* This task can continue until the teacher has had a chance to assess all students' work.* If it appears that most students are finishing at the same time, assess some students on their second orthird attempt.

CLOSUREWhole Class Discussion* Use the following prompt to ensure students have a common understanding: "What have you learned aboutsorting polygons?"* After this activity students should understand the following:1) Polygons can be sorted in a variety of ways including shape, size, number of sides, angles and vertices,type of angle, and length of sides.




Resources

2) Sometimes polygons can fit into more than one group or category.

COMMUNICATIONIndividual Journal Writing* After the class discussion ask students to apply what they have learned, by responding in their mathjournal. Use the Puzzlemaker's Journal Framework (BLM 01.1), to discuss what they did, what they thoughtof it, and what they learned.Math Dictionary* There should be no new words at this time, but if any terms come up that are not already included in thedictionary, they should be added at this time.

APPLICATIONIndividual Homework* Instruct students to create a mathematical riddle, using the list of categories generated as a class and theirmath dictionaries for one polygon shape.* You may want to model this as a class (e.g., "I have two equal angles, two of my connecting sides areequal, three acute angles, three sides, and two equal sides. I also have one line of symmetry. You will findme on a backgammon board. What am I?").

AdaptationsEnrichment* Have students place a third piece of string on the bottom in the middle of the other two circles, to create athird circle on the Venn diagram i.e., an area where all three circles overlap.* Have students choose three groups and compare their shapes with all three categories.

Consolidation* Have students continue choosing different groups to practise sorting and classifying their shapes.

Remediation* Provide individual guidance or direction to students who are having difficulty putting polygons in the rightgroup or do not recognize that some polygons fit in both. If these students are having difficulty with the tworandom groupings, give them groupings that originally went together, looking at the same attributes (e.g., rightangles, obtuse angles). You may want to separate the circles, until they can sort into separate categoriesindependently.

chart paper 5

markers 1

string 120 cm

variety of polygon shapes




Notes to TeacherPrior to the activity, if you do not have enough shapes, have students create a variety of polygons using thegeoboard activity from Subtask 4.

Teacher Reflections


Polygon Puzzlers Subtask 7Congruency Concentration


Expectations4m73 A – identify similar and congruent figures using a

variety of media;4m74 A – construct congruent figures in a variety of ways

(e.g., cutting and matching, using a geoboard);5m77 A – demonstrate an understanding of congruent

figures;5m80 A – demonstrate congruence of figures using paper

folding, reflections in a transparent mirror (Mira), andvarious computer applications;



4m79 A – discuss geometric concepts with peers andexplain their understanding of the concepts;

5m84 A – discuss geometric concepts with peers and usemathematical language to explain theirunderstanding of the concepts;

DescriptionStudents acquire their own knowledge of similar and congruent shapes and then play a concentration-stylegame where the person who matches the most pairs of congruent or similar shapes wins the game. They thenconstruct additional congruent game cards in a variety of ways, cut and match, transparent mirror (Mira), andgeoboards.

GroupingsStudents Working As A Whole ClassStudents Working In Small GroupsStudents Working In Pairs

Teaching / Learning StrategiesBrainstormingConcept ClarificationWorking With Manipulatives

Assessment*Observe students during the peer practiceconcentration game. By looking at theirpiles of matched cards, record on a checklistwhether students are able to independentlymatch congruent and similar cards. Use ahighlighter to indicate those students whorequire intervention, enrichment,consolidation, or remediation.

*Collect students' homework sketches ofcongruent and similar figures and record onthe checklist used above any changes instudents ability to identify congruent andsimilar figures.



Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONWhole Class Brainstorming* Ask students "How do you know if two shapes are the same or different?" or "How many ways are thereto compare shapes?"* Accept all possible answers and record them on chart paper or the chalk board.Whole Class and Small Group Concept Clarification** Introduce the concept of 'congruent' through concept attainment.* Present the following focusing statement: "One of the terms we use to describe pairs of shapes that havecharacteristics in common is 'congruent.' I'm going to show you some examples of shapes that are congruentand shapes that are not congruent. I'd like you to focus on what the congruent pairs of shapes have in




common. It has nothing to do with their colour or shading."* Present "yes" and "no" examples (see BLM 07.1 Congruent Figures Data Set for examples).* Ask students to discuss with a partner what the "yes" examples have in common.* Present test examples one at a time and ask students to indicate whether they think each is a "yes" or a"no." Provide students with the correct answer.* Ask students to discuss with a partner a possible definition for congruent.* Ask students, "What does it mean if two shapes are congruent?" Prompt students to come the realizationthat "congruent" means that an object is the same size and shape and that colour and design do not matter.* Share ideas and construct a definition on chart paper of congruent shapes.* Provide each group of students with a variety of polygon shapes, including some that are congruent (samesize and shape), some that are similar (same shape, but different size), and some that are neither congruentnor similar.* Ask students to work in their groups to find polygons that are congruent.* Correct any misconceptions students may have as you monitor the groups.

* Introduce the concept of "similarity" through concept attainment.* Present "yes" and "no" examples (see BLM 07.2 Similar Figures Data Set for examples).* Follow the same procedure as for congruent shapes above.* Ask students "What does it mean if two shapes are 'similar'?" Prompt students to come to the realization that"similar" means that an object is the same shape, but may differ in size but that colour and design do notmatter.*Ask students to work in their groups to find polygons that are similar.* Correct any misconceptions students may have as you monitor the groups.

COOPERATIVE PARTNER WORKPairs Peer Practice* Tell students to choose a polygon and collect the remainder of the shapes.* Tell the students to find a partner with a congruent shape. If any students cannot find a person with acongruent shape, the teacher should team the remaining students with partners. If there is an odd number,form a group of three.* Give each pair three copies of BLM 07.3 Congruency Concentration Game and have them cut out the cards.* Direct the students to put the blank cards aside for later use, then shuffle and place the remaining cards inan orderly fashion face down on the desk.* Inform students that they will be playing a concentration game. Explain that students take turns flipping overtwo cards. If the cards are congruent or similar they keep the match. If not, they place them in the originalposition. Explain that the goal of the game is to collect as many pairs of similar and congruent shapes aspossible. When all of the cards have been matched up, the person with the most cards wins.

WHOLE GROUPWhole Class Brainstorming* Ask students, "How can we create more congruent game pieces?"* Listen to all suggestions and then demonstrate how a student may use a geoboard by transferring to dotpaper (BLM 05.2 Square Dot Paper), cutting and matching, paper folding, transparent mirror (Miras), andcopying and pasting any computer draw program, if available. (See Notes to Teacher for an explanation ofeach method.)

COOPERATIVE GROUP WORKSmall Groups Working with Manipulatives* Set up one manipulative centre for each method of creating congruent shapes.* Tell students that they must create three pairs of congruent shapes and that each pair needs to be createdusing a different method.* Look for and assist students who are having difficulty with a given method.




* Advise students that when they are finished creating their congruent shapes, they should paste them ontothe blank concentration cards.* If time allows, have students play the game again in class with their new pieces; or alternatively havepartners take the cards home for practice on different nights.

CLOSUREWhole Class Discussion* Use the following prompts to ensure students have a common understanding.1. How can you tell if two figures are congruent, similar, or neither congruent nor similar?2. Describe the method you found easiest to create a congruent shape. (Teachers should accept allanswers and continue the discussion until all five methods have been discussed.)

* After this activity students should understand the following:1. "Congruent" means that a figure is the same shape and size as another figure.2. "Similarity" means that the figures are the same shape, but not necessarily the same size.3. How to construct congruent figures and demonstrate that two figures are congruent using a variety ofmethods. (See Notes to Teacher.)

COMMUNICATIONIndividual Journal Writing* After the brainstorming, ask students to apply what they have learned, by responding to the followingsituation in their math journal. (You may want students to copy the question into their math journals).* Another student has been asked to create congruent shapes but doesn't know how. Your job is to help thisstudent by explaining what congruency is and by giving them directions for one of the methods you haveused to create a congruent shape.* Ask students to use Puzzlemaker's Instruction Framework (BLM 04.2).* Remind students to use mathematical language (i.e., words from their dictionary).

Math Dictionary* Give students the following definitions to copy into their math dictionaries and ask them to draw an exampleand non-example of each of the following.- Congruent figures .- "Similar" figures .

APPLICATIONIndividual Homework* Students are asked to identify similar and congruent figures in their home. For each pair of figures theyshould draw a sketch and label the sketch as "congruent" or "similar." Students hand in completed sketchesthe following day.

AdaptationsEnrichment* Challenge students to discover another method for creating congruent shapes and write directions for howto use this method (i.e., measuring).

Consolidation* Ask students to choose a new partner and play the game again. They will also act as peer tutors,supporting students at the remediation stage.

Remediation* Pair students with a partner at the consolidation stage and have them play the game working as a team tomatch the cards. (Depending on level of remediation, students may want to practise playing the game with




Resources

cards face up.)

BLM 07.1 Congruent Figures Data Set BLM 07.1 Congruent.cwk

BLM 07.2 Similar Figures Data Set BLM 07.2 Similar.cwk

BLM 07.3 Congruency ConcentrationMaster

BLM 07.3 Congruency.cwk

ClarisWorks 5.0 (English)

chart paper 1

markers 1 set

blank paper 3

scissors 1

Transparent Mirrors (Mira) 10

geoboards 15

elastics for geoboards 1 box

Transparent Mirror (Miras) 10

polygon tiles 1 bucket




Notes to Teacher1. Creating Congruent ShapesAccording to the Ministry expectations, Grade 5 students should use paper folding, Miras, and computers;however, the Grade 4 students may also use any of the methods listed below:

* Geoboards and Isometric Dot Paper - Students create a shape by using elastics on a geoboard, thencopy the shape onto dot paper by counting the dots (where one dot is equal to one peg on the geoboard).Students then reproduce this shape again and cut both shapes out to stick onto their cards.* Cutting and Matching - Students choose a polygon to trace or draw their own shape. They then tracethe shape twice and cut it out .* Paper Folding - Students fold the paper in half and then draw a shape on one half. They cut throughboth pieces of paper, leaving them with two congruent shapes.* Transparent Mirror (Miras) - Students will draw a shape on one half of a page. They will place theMira in the centre of the page and looking through the transparent mirror (Mira), trace the reflection.* ClarisWorks - Using any computer draw program, students create a shape. They then click on theshape they have created, choose copy in the edit drop down menu. Place the curser on a blank area of thescreen and choose paste from the edit drop down menu.

2. Definitions for Congruent Figures and Similar Figures have been taken from the OntarioCurriculum Mathematics Document pages 78 and 83.

3. Concept Attainment/Concept Clarification: This instructional strategy can be used to teach or clarifyconcepts. In this subtask, it is used to teach the concept of congruent and similar shapes. See BeyondMonet: The Artful Science of Instructional Integration by Bennett and Rolheiser or Models of Teaching byJoyce and Weil for further information on this model of teaching.

4. BLMs 07.1 and 07.2 can be photocopied onto overheads and cut out so that the examples can beshown to the students one at a time.

Teacher Reflections


Polygon Puzzlers Subtask 8Puzzlemakers in Training 1 ... Simply Symmetrical







4m71 A – identify and sort quadrilaterals (e.g., square,trapezoid);

5m75 A – sort polygons according to the number of sides,angles, and vertices;

4m72 A – sort and classify two-dimensional figures accordingto shape;

4m84 A – draw lines of symmetry on two-dimensionalshapes;

5m89 A – construct two-dimensional shapes with one line ofsymmetry;



4m77 A – use mathematical language to describe geometricideas (e.g., line, angle);

5m82 A – use mathematical language to describe geometricideas (e.g., quadrilateral, scalene triangle);

DescriptionStudents use a variety of polygons to create a jigsaw puzzle design. The Grade 4 Puzzlemakers are asked toidentify lines of symmetry within their design, while the Grade 5 Puzzlemakers are asked to create a designwith one line of symmetry. This task allows students to demonstrate and assess their own understanding ofsymmetry as well as the attributes of polygons, including similar and congruent shapes.

GroupingsStudents Working As A Whole ClassStudents Working In PairsStudents Working Individually

Teaching / Learning StrategiesDemonstrationExperimentingModel Making

Assessment* Collect students' puzzle designs andassess and record on a checklist whetherthe Grade 4 students have accurately drawnthe lines of symmetry on all of the shapesincluded in their design and whether theGrade 5 students have constructed shapeswith one line of symmetry.

* Have students self assess theirunderstanding of the concepts covered sofar using BLM 8.1 Self AssessmentChecklist.* Collect and compare students' responseswith your teacher checklists and notes fromeach subtask.* Make note of any discrepancies on BLM02.6 Anecdotal Record so that they can bediscussed at the conference.

* Invite students to a conference in groupsof four or five.* Ask them to bring their journals, and youshould bring their self assessment checklists.* Have students select their best journalentry and share it with the group.* Discuss as a group what qualities make aneffective journal (i.e., clear explanations,using pictures, numbers and words, usingmathematical language).* Create an anecdotal record during theconference, of each student's strengths andweaknesses in understanding of concepts orin communication and indicate any need forremediation.* Give students feedback about theirstrengths and suggestions for review.




* Point out any discrepancies between yourchecklists and the students and allow themto show you new understanding.* Peers may also make positive commentsand suggestions during the conference(e.g., "I like the way you used pictures,numbers and words to explain your ideas."or "Using the proper mathematical wordswould make your journal better.").

Assessment StrategiesPerformance TaskSelf AssessmentConference

Assessment Recording DevicesChecklistAnecdotal Record

Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONWhole Class Demonstration* Draw an enlarged version of the red trapezoid, from the pattern block set, on chart paper.* Ask students, "How do you find a line of symmetry on a shape or a picture?"* Prompt students to identify paper folding, transparent mirror (Miras), and using measurement tools.* Demonstrate using all three methods on the trapezoid.* First cut the trapezoid shape out and fold it in half so that the uneven sides are touching.* Present the folded shape to the class and ask them why this is not a line of symmetry.* Prompt students to recognize that although the two sides match up, one is longer than the other and in orderfor it to be symmetrical it would have to line up exactly.* Fold the trapezoid in half so that the two even sides match up exactly and ask them "Is this a line ofsymmetry?" Prompt students to recognize it is a line of symmetry because the two sides overlap exactly.* Repeat this procedure with the transparent mirror (Mira), placing the transparent mirror (Mira) along each ofthe two fold lines you created, asking them, "Is this a line of symmetry? How do you know?"* Prompt students to recognize that it is the reflection of one side of the shape onto the other that has tomatch up in order for it to be symmetrical. If students have not used transparent mirrors (Miras) before, youmay want to show them that they have to look through the transparent mirror (Mira) to see the reflection, sothey may have to tilt their head and look through it on an angle.* Finally, use a metre stick to show that on either side of the first fold line, you have one side that is muchshorter than the other, where on the second fold line, the two sides are equal in length, therefore aresymmetrical.* Ask students, "If we wanted to draw a line of symmetry on the trapezoid, how would we know where toput it?" Accept all possible answers.* Go through each method and model how to draw the line of symmetry: Paper Folding, draw the line ofsymmetry on the fold with a ruler; transparent mirror (Mira), mark a point at the top and bottom of thetransparent mirror (Mira), then connect the points with a ruler; Ruler, measure the longest side and mark thehalfway point, then measure the opposite side marking the half way point. Connect the two points with aruler.* Explain that if you wanted to construct a shape with a line of symmetry, you would create one side of theshape and use the transparent mirror (Mira), paper folding, or measurement methods to create the other side.* Cut the trapezoid in half and demonstrate how to construct the other half.* Transparent Mirrors (Miras): draw one half and look at the reflection to draw the other half; Paper folding:




fold a piece of paper in half and draw half a trapezoid on the fold line, then cut it out so that when it isunfolded your fold line is the line of symmetry; Draw on graph or dot paper: draw one half and using the dotsor lines on the paper, draw the other side by counting the dots.

COOPERATIVE PARTNER WORKPartner Experimenting* Present students with a variety of polygon shapes.* Tell students that they will have 10 minutes to experiment, using paper folding, transparent mirrors (Miras),and measurement tools. Encourage students to try all three methods.* Have Grade 4 students make predictions about which shapes have lines of symmetry and which do nothave lines of symmetry on a variety of polygon shapes, by tracing the lines of symmetry with their finger.* Have students trace their shapes onto paper, cut them out, then test their predictions using the methodsoutlined in the whole class demonstration.* Ask students to draw any lines of symmetry found on the shapes.* Grade 5 students should attempt to construct shapes with one line of symmetry, using the three methodsdemonstrated in the whole class discussion. They can look at polygons to help them to construct shapes, butthey should not trace them.* Provide the Grade 5 students with transparent mirrors (Miras), blank paper, isometric dot paper, square dotpaper, and graph paper.* Monitor the classroom and assist any students who appear to be having difficulty.

WHOLE GROUPWhole Class Discussion* Have one person from each pair come to the chalk board and stick their shape to the board with a magnet ortape.* As a class, check that the Grade 4 students have labelled their lines of symmetry accurately. For any linesof symmetry that are not accurate or where multiple lines of symmetry have not been noticed, ask forvolunteers to come to the board to correct them.* Invite students to come and draw lines of symmetry on the Grade 5 shapes. If there are any shapes thatare not symmetrical, ask, "Why do you think this happened?"* Ask students "How do you think congruency is related to symmetry?" Accept students answers, thenprompt them to recognize that the figures on either side of the line of symmetry are congruent.

COOPERATIVE PARTNER WORKPairs Model Making* Tell students that in preparation for the culminating task, they will be practising making a jigsaw puzzledesign with geometric shapes.* Instruct the Grade 4 students that they may trace any shapes available to create their abstract design, butall shapes must have one line of symmetry.* Instruct the Grade 5 students that they will be creating an abstract design, but they must construct theirown shapes with one line of symmetry. They may look at polygon shapes for ideas.* Tell students to trace a minimum of five different polygon shapes onto construction paper which could beused multiple times. Students should make an additional copy of their shapes and put these aside for lateruse.* Inform students that when the shapes are cut out, students should arrange their designs on a piece ofpaper and glue them into place. This simulated puzzle design should cover most of the page.* Ask students to draw the lines of symmetry on all of their two dimensional shapes on the puzzle.* Remind students that they can use any of the methods for finding symmetry that were used above.* Students will share shapes and may brainstorm with a partner, but they will produce their own puzzledesign.* Observe students to ensure the Grade 4 students have chosen shapes with at least one line of symmetryand the Grade 5 students are constructing shapes with one line of symmetry. Provide assistance where




necessary.

CLOSURE Whole Class Discussion* Use the following prompt to ensure students have a common understanding: "What do we know aboutdrawing and constructing lines of symmetry?"

COMMUNICATIONIndividual Learning Log/Journal* Ask the Grade 4 students to write step-by-step directions for drawing a line of symmetry on a shape. Theyshould outline all three methods and should glue their extra shapes into their journals to assist with theirexplanation.* Ask the Grade 5 students to write step-by-step directions for constructing a shape with one line ofsymmetry. They should outline all three methods and should glue their extra shapes into their journals toassist with their explanations.* You may want the students to use Puzzlemaker's Instruction Framework (see BLM 04.2).* Remind students to use mathematical language (i.e., words from their dictionary).

Math Dictionary* Give students the following definition to copy into their math dictionaries and ask them to draw an example."Line of Symmetry" is a line that divides a shape into two congruent halves that fall on top of each otherwhen the shape is folded on the line.

APPLICATIONSelf Assessment* Distribute BLM 8.1 Self Assessment Checklist.* Tell students they are now going to be looking through all of the work they have completed so far: their mathjournal, math dictionary, and other activities.* Ask them to self assess the concepts that they have learned to this point, by checking off the appropriatebox on the checklist.* Tell students that when they finish the checklist, they should complete the sentence starters on the bottomof the sheet.* Students should hand in their self assessment when it is complete.

AdaptationsEnrichment* Challenge students to create a puzzle design that has many overlapping shapes. Students should label thelines of symmetry on the shape, but must recognize that a shape that is overlapped by another shape, maynot be symmetrical anymore.

Consolidation* Direct Grade 4 students to revisit BLM 01.2 Geometry in Games and identify lines of symmetry on the gameboard.* Direct Grade 5 students to revisit BLM 01.2 Geometry in Games and recreate shapes with one line ofsymmetry.

Remediation* Give small group mini-lessons, to review paper folding, using a Mira and measuring to determine orconstruct lines symmetry.

Cumulative Remediation




Resources

* Based on your anecdotal notes, determine if students need remediation on a particular concept.* Check the suggested adaptation in the subtask where that concept was first taught.

BLM 08.1 Self Assessment Checklist BLM 08.1 Self Assess.cwk

magnets or tape 1

isometric dot paper

square dot paper

blank paper

chart paper 1

Transparent Mirror (Miras) 1

rulers 1

polygon tiles 1set

Transparent Mirros (Mira) 1

Notes to Teacher1. Students should have previous knowledge of creating and identifying lines of symmetry from Grades 1, 2, and3.

2. If this is the first time that you have attempted conferencing as an assessment strategy, you need to beaware that some students find this intimidating the first time. Some suggestions for grouping students include:looking through prior assessment checklists and choosing students who are having difficulty in similar areastogether, grouping students based on ability level based on the diagnostic activity, and avoiding placingstudents who do not get along in the same group, as they may tend to be overly critical.* If you and the students are comfortable and familiar with this assessment strategy, feel free to use mixed abilityand/or random groupings.* Emphasize and model giving positive feedback.

Teacher Reflections


Polygon Puzzlers Subtask 9The Bermuda Rectangle ... Exploring Coordinate Systems


Expectations4m67 A • use language effectively to describe geometric



4m85 A – demonstrate an understanding of coordinatesystems and an ability to use them in simple games(e.g., battleship, bingo).

5m90 A – demonstrate an understanding of coordinatesystems on maps and grids.

DescriptionStudents relate plotting coordinates on a grid to the game of battleship. They then use their knowledge toplay a battleship-style coordinate game where students work in pairs to hide and locate a quadrilateral.


Teaching / Learning StrategiesDirect TeachingPeer PracticeDiscussion

Assessment* Observe students during the peer practiceBermuda Rectangle game. Record on achecklist whether students are able toindependently record their hits and misseson a coordinate grid. Use a highlighter toindicate those students who requireintervention, enrichment, consolidation, orremediation.

* Have students self assess their homework(BLM 9.4 Coordinate Systems), by using therating scale on the bottom of their sheet.Place Overhead of BLM 9.5 on theoverhead projector, so that they cancompare their work with the correctresponses.

* Teachers can collect the homework afterstudents have assessed their work andrecord any changes on the checklistpreviously used.

Assessment StrategiesObservationLearning LogSelf Assessment

Assessment Recording DevicesChecklistRating Scale

Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONWhole Class Brainstorming/Direct Teaching* Present BLM 9.1 Bingo Card on an overhead. Ask students, "How do we know where to put our markerwhen a number is called in Bingo?" Prompt students to recognize that they need to look at the letters on the




top and find the number in the appropriate column (i.e., if N16 is called, we would look in the N column andplace our marker on 16).* Randomly select three students and give them a location to mark on the Bingo Card, showing how they arelocating the numbers.* Distribute atlases to students. Have students all turn to the same page of the atlas (use a map with cities)and give them the name of a city.* Ask students, "How could I help you to find this city?" Prompt students to recognize that the letters andnumbers printed along the edges of the page, refer to a particular box.* Explain that the numbers and letters along the edge of the page, work like a Bingo card. Give them thecoordinates for the city you chose and have them place one finger on the letter and one finger on the numberthat you have given them and move their fingers in a straight line until they meet. Tell them the numbers andletters are called coordinates and they help us to find locations on maps and grids.* Give students a few more coordinates of particular cities, and ask them to find the cities on the map. (PairGrade 5 students with Grade 4 students wherever possible.)* After you give the coordinates, ask for thumbs up or thumbs down to determine how many students wereaccurate in determining the city.

COOPERATIVE PARTNER WORKPairs Peer Practice

* Tell students that we are going to use what we have learned about coordinate systems to play a gamecalled The Bermuda Rectangle.* Place an overhead of BLM 9.2 The Bermuda Rectangle Game Card on the overhead projector and gothrough the rules, while demonstrating on the overhead.* If possible pair Grade 4 students with Grade 5 students for the game.* Distribute a game card to each student.* Have students read the rules again, with their partner. Encourage students to select a square at randomand see if both students can find the coordinates. Allow time for students to seek clarification from theirpartner.* Have students place a divider between themselves and an opponent.* Instruct students to colour in three rectangles, one that is two squares, one that is three squares, and onethat is five squares.* Direct students to begin playing the game and remind them that it is important to record their guesses as an"H" if it is a hit and an "M" if it is a miss.

WHOLE GROUPWhole Class Discussion* Bring the class together to talk about successes and difficulties.* Ask students what strategies or tricks they may have found to help them win the game.* Ask students if they experienced any difficulties while playing the game.

COOPERATIVE PARTNER WORKPairs Peer Practice* Have students choose a different partner, from either grade to play the game again.* Based on your observations from the first game, you may want to implement adaptations at this point.

CLOSUREWhole Class Oral Explanation* Use the following prompt to ensure students have a common understanding: How did you use coordinatesto play Bermuda Rectangle?

* After this activity students should understand the following:




Resources

1) Coordinate systems have two sets of numbers or letters, which label a plane or a line on a grid.2) To find a location on a coordinate grid, you must find the spot where the two coordinates (letters ornumbers) meet in a box or on a vertex.

COMMUNICATIONIndividual Journal Writing/Math Dictionary* Use the Puzzlemaker's Journal Framework (BLM 01.1), to discuss what they did, what they thought, andwhat they learned.

* Give students the following two directions to record coordinate systems in their math dictionary.1. Draw a coordinate grid, labelling the spaces along the bottom with letters and the spaces up the side withnumbers.2. Colour in a square on the grid, then have them write brief directions for how to find that square.* Remind students to include the key concepts from the closure activity.

APPLICATIONHomework* Give students BLM 9.4 Coordinate Systems. Have students complete the assignment for the next day.

AdaptationsEnrichment* Challenge students to play a different version of The Bermuda Rectangle (BLM 9.3 The Bermuda VerticesEdition). Have students play the game, this time plotting coordinates by using the lines rather than the spaces.The goal of the game is find the four vertices (corners) of each rectangle.

Consolidation* Give students a new game card. Ask them to choose a new partner and play the game again. They willalso act as peer tutors, supporting students at the remediation stage.

Remediation* Pair students with a partner at the enrichment or consolidation stage and have them play the game again,this time with the divider down (like playing an open hand game of cards), until students get the idea.Depending on the level of remediation, you may need to do small group teaching, where students practisefinding both coordinates and moving their fingers to the appropriate square. This may be necessary for manyGrade 4 students as this is their first time they are expected to use a coordinate grid.

BLM 09.1 Bingo Card BLM 09.1 Bingo Card.cwk

BLM 09.2 Bermuda Rectangle Gameboard BLM 09.2 Bermuda.cwk

BLM 09.3 Bermuda Rectangle GameboardVertices Edition

BLM 09.3 Bermuda2.cwk

BLM 09.4 Coordinate Systems BLM 09.4 Coordinate Systems.cwk

BLM 09.5 Coordinate Systems Answers BLM 09.5 Coordinate.cwk

atlas




Notes to TeacherDirect teaching is used for the introduction of this activity because Grade 4 students will have no prior knowledgeof coordinates. In Grade 3, students only describe the movement on a grid (e.g., two squares right, followed byone square up). Grade 5 students should have prior knowledge of coordinate systems.

Teacher Reflections


Polygon Puzzlers Subtask 10Transformation Twister


Expectations4m65 A • understand key concepts in transformational

geometry using concrete materials and drawings;5m68 A • understand key concepts in transformational

geometry using concrete materials and drawings;4m81 A – demonstrate an understanding of translations,

reflections, and rotations (e.g., on a geoboard ordot paper);

5m86 A – describe the effect of a translation, reflection, androtation;

4m83 A – discover transformation patterns with and withoutthe use of computer applications;

4m82 A – apply translations, reflections, and rotations usingconcrete materials and drawings to pose and solveproblems;

5m87 A – apply translations, reflections, and rotations (e.g.,using concrete materials and grid paper or isometricdot paper) to pose and solve problems;



DescriptionStudents construct their own knowledge of transformations using their bodies to create translations,reflections, and rotations in a large open space such as a gym, hallway, or library resource centre. Onestudent spins a spinner labelled with each type of transformation while another student records the position ofeach player on chart paper using stick figure drawings. Students then work as a class to label the chart paperdrawings as "translations," "reflections," or "rotations." Students finally work in pairs to play a strategy-stylegame where the goal is to transform a polygon shape from start to home.


Teaching / Learning StrategiesThink / Pair / ShareDemonstrationPeer Practice

Assessment* Observe students during the Peer PracticeGame. Record on a checklist whetherstudents are able to independentlydemonstrate a translation, reflection, androtation to the game. Use a highlighter toindicate those students who requireintervention, enrichment, consolidation, orremediation.* Collect students' labelling homework andmake any further notes necessary on thechecklist.



Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONThink/Pair/Share - Activating Prior Knowledge* Ask students: "How can you move a polygon shape on a piece of paper without lifting it entirely off thepage?"* Give students 60 seconds to think about this problem. (You may want to use a 'Ready, Set, Think!' signal tomotivate them.)* Give students 90 seconds to share their ideas with a partner. (You may want to use a 'Ready, Set, Share!'signal.)* Bring students together as a class to share their ideas. If students do not generate the terms "translation"(slide), "reflection" (flip), and "rotation" (turn), then prompt them by showing a transformation on the board




and asking, "What do we call it when we move a shape like this?"

COOPERATIVE GROUP WORKWhole Class Demonstration* Invite students to a large open area to play a game of transformational twister.* Choose one student to be in charge of the spinner (BLM 10.1 Transformation Spinner) and show him/herhow to spin the spinner using a paper clip and a pencil.* Choose another student to record the information to keep track of the transformations on chart paper.* Inform the students that when it is their turn, they will be following directions on the spinner to create atransformation with their bodies from the last student's position. (See BLM 10.2 Transformation Stick Figures.)* As each student takes their turn, the recorder adds to the stick figure drawing on chart paper.* Encourage students to explore different flips (left, right, up, down), slides (left, right, up, down), and turns(1/4 turn, 1/2 turn, 3/4 turn).

WHOLE GROUPWhole Class Sketching to Learn* Take the chart paper back to class.* Have students take turns labelling a transformation.* Some students may notice that certain transformations could appear to be more than one transformation(i.e., sometimes a turn may look like a flip, depending on the shape). If this does not arise during the labelling,prompt students to notice where more than one type of transformation could have been used.

COOPERATIVE PARTNER WORKPairs Peer Practice* Explain to students that the purpose of the game is to use their knowledge of flips, slides, and turns totransform their polygon from the start position in the upper left hand corner of the game board to the homebox at the bottom right hand corner.* Have students choose a partner. (You may want to have students choose a partner who has a birthday inthe same month. Partner any remaining students according to closest birthdays.)* To each student, hand out a copy of BLM 10.1 Transformation Spinner, BLM 10.3 Transformation TwisterPattern Block Edition, a page of graph paper, and a paper clip.* Inform students that they will begin by choosing a blue rhombus, tan rhombus, or red trapezoid pattern blockand place it in the upper left hand corner of the graph paper.* Tell students that at their turn they will spin a spinner BLM 10.1 Transformation Spinner.* Demonstrate how to use the spinner, using a paper clip and a pencil (see Notes to Teacher).* Review the game rules BLM 10.3 and the options on the spinner with students before beginning the game,as indicated on BLM 10.1 Transformation Spinner.

CLOSUREWhole Class Discussion* Use the following prompts to ensure students have a common understanding.1) What is similar about the transformations?2) What is different about the transformations?

* After this activity students should understand the following:1) Three of the different ways to transform an object are: translation, reflection, and rotation.2) Each type of transformation can also be done in many different ways: Translate - up, down, left, right, any number of spaces; Reflect - left, right, up, down, on a side, on a vertex (point); Rotate - clockwise, counter-clockwise, any fractional amount, 1/4, 1/2, 3/4, and full turns.3) The effect of a translation is that the orientation of the shape is the same but is in a different location.4) The effect of a reflection or rotation is that the orientation can change or stay the same, depending on the




Resources

shape, i.e., if you flip an equilateral triangle up or down, it will appear to be upside down. If you flip it left orright the orientation will be the same.5) The effect of two consecutive transformations can appear the same, i.e., when you slide a trapezoid tothe right, or flip it to the right, it will be in the same position and orientation.6) You can move from one location to another in many different ways.

COMMUNICATIONIndividual Learning Log/Journal* Use the Puzzlemaker's Journal Framework (BLM 01.1), to discuss what they did, what they thought, andwhat they learned.* For a journal extension, have students look for transformations in the real world and write about what theyhave found in their journal.

Math Dictionary* See BLM 02.1 for definitions to add to their math dictionaries. Ask students to draw and label an example foreach definition.

APPLICATIONHomework* Collect the game cards from the Pairs Peer Practice activity and redistribute them randomly, ensuring no onehas their own game card.* Have students find the pattern block that the other student used and allow them to take it home, or trace andcut it out.* Inform students that for homework they will be labelling the types of transformations that the other studentused throughout the game. Remind students that there may be more than one option and they should label allpossible transformations.

AdaptationsInterventions

Enrichment* Explain to students that they will play a new version of the game in which the winner is to avoid getting intothe box first. No play can overlap a previous play. They must strategize to avoid blocking their next move.

Consolidation* Ask students to choose a different pattern block and practise the game with a partner.

Remediation* Pair students with a partner at the consolidation stage and have them play the game working as a team tomake decisions about moves.

BLM 10.1 Transformation Spinner BLM 10.1 Trans.cwk

BLM 10.2 Transformation Stick Figures BLM 10.2 Trans2.cwk

BLM 10.3 Transformation Twister PatternBlock Edition

BLM 10.3 Trans3.cwk




chart paper 2

markers 1 set

paper clips 1 box

pattern blocks 1

large open area

Notes to Teacher1. Although the formal terms for transformations are "reflections," "translations," and "rotations," they arecommonly referred to as "flips," "slides," and "turns." Students should be familiar with all terms.

2. The rhombus and trapezoid shapes were chosen, because it is easier to assess students' knowledgeof transformations using these shapes, than with regular polygons like a square or an equilateral triangle.

3. Spinning the Spinner* When using BLM 10.1 Transformation Spinner for the Cooperative Group Work activity, you may want toenlarge the spinner.* To use the spinner, simply place a paper clip in the centre of the spinner and place the point of a pencilthrough the paper clip. While holding the pencil with one hand, flick the paper clip with the other hand.

4. When giving students the definition for transformations, you may or may not want to include dilatation inyour definition, as the students are not working with this concept at this time.

Teacher Reflections


Polygon Puzzlers Subtask 11Pentomino Puzzlers


Expectations4m75 A – discover geometric patterns and solve geometric

puzzles with and without the use of computerapplications;

4m73 A – identify similar and congruent figures using avariety of media;

5m69 A • identify congruent and similar figures usingtransformations;

4m80 A – discuss ideas, make connections, and articulatehypotheses about geometric properties andrelationships;

5m85 A – discuss ideas, make conjectures, and articulatehypotheses about geometric properties andrelationships;

DescriptionStudents use their knowledge of congruent shapes and transformations to find all the possible combinationsof five squares to create pentominoes. They then work cooperatively to solve a variety of pentominochallenges.


Teaching / Learning StrategiesConcept ClarificationCollaborative/cooperative LearningDiscussion

Assessment* Observe students duringcollaborative/cooperative learning to see ifthey are able to independently find any ofthe 12 pentomino combinations. Listen forthe use of the terms "congruent,""reflection," "translation," and rotation aswell as evidence of a strategy for finding allthe possible combinations. Record on achecklist or anecdotal record. Use ahighlighter to indicate those students whorequire intervention, enrichment,consolidation, or remediation.

* Record evidence of 'making their thinkingvisible' - use of words to describe theirsolution: clarity, preciseness, use of themathematical terms "congruent," "similar,""reflection," "translation," and "rotation," useof drawings to show their solution: Can I seewhat the student did just by looking at thedrawing? Is there a strength/weakness ineither words or drawings?

* Provide specific feedback to each student:one positive comment and one suggestionfor improvement by using a different colourof sticky note or square of paper from thestudents' 'Noticeagrams.' Your response willhighlight an area of growth or strength aswell an area for intervention. These notescan be transferred to a central spot in theirfolder for storage and tracking or affixed tothe work.





Self Assessment

Assessment Recording DevicesAnecdotal RecordChecklist

Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONWhole Class Concept Clarification* Present "yes" and "no" examples (see BLM 11.1 for examples)* Ask students to turn to a partner and discuss what the two "yes" examples have in common.* Present test examples one at a time and ask students to indicate whether they think each is a "yes" or a"no."* Ask students to discuss with a partner a possible definition for a "pentomino."* Share ideas and construct a definition on chart paper of a pentomino.

COOPERATIVE GROUP/PARTNER WORKSmall Group Collaborative/Cooperative Learning* Challenge students to use the colour tiles to create as many pentominoes as they can.* Ask students to tape their tiles together as they go.

WHOLE GROUPWhole Class Discussion* Invite each group to bring one of their pentominoes to the meeting area.* Ask each group, in turn, to tape their pentomino onto a piece of chart paper.* Challenge each group to find any duplicate examples, "What do you notice?" Before removing a duplicatepentomino ask, "Tell me why you think this pentomino is a double" and "Tell me how we could check to see ifit is a match for another pentomino."* Model using the language of geometry by rewording the students response, e.g., "Do you think that thispentomino is a reflection (flip) of that pentomino? Let's check and see."* Count the number of different pentominoes so far. Ask students to predict how many different pentominoesthey think there might be in total.

COOPERATIVE GROUP/PARTNER WORKSmall Group Collaborative/Cooperative Learning* Challenge each group to check to see if all the pentominoes they created are different, before they continueto find more.* Continue to monitor the groups, prompting students to check for congruency.

CLOSUREWhole Class Discussion* Bring the students back together to share their findings. Ask each group, in turn, to add a pentomino to thecollection that is not already there. After each addition, ask the group whether they agree that it is differentfrom all those before. Continue until all possibilities are recorded.* Ask students to share their strategies for finding all possible combinations of five tiles linked edge to edge.* Explain that pentominoes are named by a letter of the alphabet so that specific pentominoes can be used insolving puzzles and communicating clearly about the solution.* Guide students to label each pentomino as F L I P N T U V W X Y Z. (See BLM 11.2 Naming Pentominoes.)* Add names of pentominoes to earlier definition.

COMMUNICATE




Resources

Individual/Math Dictionary* Ask students to record the class-created definition (with examples and non-examples) in their mathdictionary.Homework/Homelink day 1* Ask students to share their math dictionary entry with someone at home.* Ask students to create a set of pentominoes for use at home using 2.5 cm graph paper. Pentominoes shouldbe cut out, labelled front and back with the appropriate letter of the alphabet, and stored in the envelopeprovided. Envelope should be labelled with the student's name.

APPLICATIONIndividual Working with Manipulatives* Direct students to try the congruent shapes and similarity challenges (BLM 11.3). Describe or model thestrategies students might use to solve the challenge.* Explain that all solutions are to be recorded and labelled on grid paper.

Homework/Homelink day 2 * Direct students to select a congruency or similarity challenge to revisit or revise its solution, so that theirthinking is visible. (Students could be asked to use the Puzzlemaker's Instruction Framework, BLM 04.2.)Students should be prepared to present this solution and/or hand it in for feedback. Students could include a'Noticeagram' attached to the solution.* Ask students to share these challenges with someone at home and review the definitions of congruent andsimilar shapes from their math dictionary.

AdaptationsEnrichment* Explain to these students that you would like them to create and solve a congruency/similarity challengedifferent from any they have been given.

Consolidation* Ask students to continue to make congruent shapes using pairs of pentominoes. They could work alone,work with a partner of their choice, or with one assigned by the teacher.

Remediation* Model the solution of a congruency challenge such as, "Use I and L and W and N to create two congruentshapes." Think aloud the process you would use to solve the challenge.* Give students a similar but slightly different challenge such as, "Use Y and V and T and N to create twocongruent shapes to do together." Share the process, teacher and students thinking aloud.* Allow students to work together in twos or threes to solve another challenge. Guide students by promptingthem to use the strategies you developed together.* Ask students to try a further challenge independently.

BLM 11.1 What Is a Pentomino? BLM 11.1 pentomino.cwk

BLM 11.2 Naming Pentominoes BLM 11.2 Naming.cwk

BLM 11.3 Pentomino Challenges BLM 11.3 Challenges.cwk




BLM 11.4 2.5 cm grid paper BLM 11.4 grid paper.cwk

BLM 11.5 Please notice... BLM 11.5 Please notice....cwk

transparent tape 1

chart paper and markers 1

plastic bags of 60 colour tiles 1

Notes to Teacher1. Background Information - Martin Gardner first popularized pentominoes when he wrote about them in hisfamous column in Scientific American in November 1957. A collection of his columns is published inHexaflexagons and Other Mathematical Diversions: The First Scientific American Book of Puzzles andGames ISBN # 0226282546.

2. Groupings - Groups of two or three work well.

3. Students will need to have 60 squares in order to create the 12 pentomino combinations. It could besquares of paper that have been pre-cut and counted or a purchased manipulative such as Colour Tiles.

4. Noticeagram - Students write "PLEASE NOTICE" on the top of a square of paper or sticky note (see BLM11.4). They record something that they want you to notice when you read their work/solution. It could bemath vocabulary from their math dictionary or that they've labelled a drawing clearly. This strategy worksbest when a focus is provided by the teacher, e.g., 'On your Noticeagram, write me something about howyou made your thinking visible.'

Teacher Reflections


Polygon Puzzlers Subtask 12Puzzlemakers in Training 2 ... The Bermuda Triangle


Expectations4m64 A • explore transformations of geometric figures;4m65 A • understand key concepts in transformational

geometry using concrete materials and drawings;5m68 A • understand key concepts in transformational

geometry using concrete materials and drawings;4m66 A • describe location and movements on a grid;5m67 A • explore transformations of geometric figures;4m67 A • use language effectively to describe geometric



4m81 A – demonstrate an understanding of translations,reflections, and rotations (e.g., on a geoboard ordot paper);

5m86 A – describe the effect of a translation, reflection, androtation;

4m82 A – apply translations, reflections, and rotations usingconcrete materials and drawings to pose and solveproblems;

5m87 A – apply translations, reflections, and rotations (e.g.,using concrete materials and grid paper or isometricdot paper) to pose and solve problems;

4m85 A – demonstrate an understanding of coordinatesystems and an ability to use them in simple games(e.g., battleship, bingo).


DescriptionStudents apply their knowledge of coordinate systems and transformations from previous activities to create agameboard for the Bermuda Triangle Edition of Puzzlehedz Inc. Students create and follow directions fortransforming a variety of polygon tiles such as a tangram triangle and pattern block rhombus or trapezoid on acoordinate grid. This task allows students to demonstrate and assess their own understanding oftransformations and coordinates as well as their use and clarity of mathematical language.


Teaching / Learning StrategiesThink / Pair / SharePeer PracticeProblem Posing

Assessment* Observe students during The BermudaTriangle game. Record on a checklistwhether students are able to independentlywrite a set of directions and find theirpartner's Bermuda Triangle by followingdirections. Use a highlighter to indicatethose students who require intervention,enrichment, consolidation, or remediation.

* Review students' KWL charts and look attheir self assessments. Compare them toyour ongoing checklist of theirunderstanding of concepts.* Make an anecdotal record of eachstudent's areas of strength and areas thatstill requires more practice and refer back toadaptations for the relevant subtasks. Youcan use a new copy of BLM 02.6 AnecdotalRecord or update the record that wascompleted during Subtask 8.* Discuss any differences between thestudent's self assessment and your ongoingformative assessment.Record any decisions about further practicein the teacher comment section of theself-assessment.

Assessment StrategiesObservationSelf Assessment





Teaching / LearningTEACHER INPUT/CLASS DISCUSSIONWhole Class Think/Pair/Share* Present students with BLM 12.1 Mapping Out Routes on an overhead.* Ask students, "If you wanted to get from "Home" to the "Bermuda Triangle," how could you get there?" Tellstudents that they can not move diagonally.* Tell students that they will have one minute to think about the possibilities. You may want to give them a'Ready, Set, Think!' signal.* Have students join the person closest to them and give them one minute to share their ideas. You may wantto give them a 'Ready, Set, Share!' signal.* Bring students back together and randomly ask students to share their ideas with the class. Accept andencourage many suggestions.* If students do not suggest transformations, prompt them by asking, "How did we move ourselves acrossthe floor in the gym when we played Transformational Twister?"* Have one student give a suggestion of how to get from home to the Bermuda Triangle, using translations,reflections, and rotations.* Follow the student's directions, using a cut out triangle and moving it at each step.* Ask for a few more suggestions and model how the triangle could move.* Ask students, "If I wanted to let someone know how to find the Bermuda Triangle, how could I let themknow exactly where it is on the grid?" Prompt students to recognize that the vertices are on coordinates andrecord the coordinates at the vertices, e.g., (I, 15) (I, 18) (M, 18).

COOPERATIVE PARTNER WORKPairs Peer Practice* Explain to students that they will be creating a game board called "The Bermuda Triangle."* Have students get together with their partner from the think/pair share.* Distribute copies of BLM 12.2 The Bermuda Triangle Gameboard to each pair.* Have them cut out the triangle on the top right hand corner of the page.* Read together the sample instructions from BLM 12.3.* Have students follow the directions with their partner to transform their shape.* Instruct the students to trace the shape after each transformation, so that they can check their work later.

WHOLE GROUPWhole Class Demonstration* Put a copy of BLM 12.2 The Bermuda Triangle Game Board on an overhead.* Invite students up one by one to demonstrate each step of the transformation and trace the shape onto theoverhead.* Have students check their work against the sample on the overhead.* Invite any pairs of students who did not end up with their triangle at the right coordinate, to share wherethey think they made their mistake or ask for help from the class to determine where they might have erred.

COOPERATIVE PARTNER WORKIndividual/Pairs Problem Posing* Tell students that now they will be creating their own Bermuda Triangle Game using BLM 12.2 as thegameboard and by writing their own directions. (Use Puzzlemaker's Instruction Framework BLM 04.2.)* Inform them that when they are finished creating their instructions, they can exchange instructions with twoor three other people and attempt to solve their games.* Give each student a copy of BLM 12.2 The Bermuda Triangle Game Board.* Tell students that they should try moving the triangle at each step to ensure their directions are accurate.* Remind them to write the final coordinates for the triangle, so that the person playing the game can checkfor accuracy.* Check the students' process as they work and assist any students who have difficulty applying the




transformations or writing the directions.

CLOSUREWhole Class Discussion* Use the following prompts to ensure students have a common understanding.1) How is The Bermuda Triangle Game different from The Bermuda Rectangle?2) How is The Bermuda Triangle Game different from the Transformation Game?

* After this activity students should understand the following:1) When explaining how to move a shape or a point on a grid from one location to another, you can describethe transformation.2) When moving points on a grid, you can move it from one specific location to another specific location that isidentifiable by coordinates.3) You may want to go back and review the key learning in the closure section from Subtask 8 and 9.

COMMUNICATIONIndividual Learning Log/Journal* Tell students that this will be the final journal they write before the culminating task.* Tell students that the purpose of the journal is to help them review what they have learned throughout theunit and to help you to know which subtasks may require review.* Inform students that instead of writing about one task, they are going to summarize what they have learnedthroughout the unit.* Direct students to look at a collection of their work from the unit and read through all of their journal entriesto help them complete this journal entry.* Tell them to use the Puzzlemaker's Journal Framework (BLM 01.1), to discuss what they did, what theythought of it, and what they learned.* In addition they should add a section about what they think they still need to work on.* Remind students to use mathematical language to describe their ideas.

APPLICATIONIndividual* Have students revisit the KWL chart that they created in Subtask 2.* Tell students that they are now going to be filling in the final column of the KWL chart.* Explain that in order to complete this column they should think about the key things they have learned in thisunit and it will be a self assessment of their learning throughout the unit.* Provide students with the following headings on chart paper: "naming and sorting polygons," "angles,""congruent and similarity," "lines of symmetry," "coordinates," "transformations," and "mathematical language."* Tell students that they should not simply copy definitions or previous journals, but give a brief explanation ofwhat they know about a concept using pictures, numbers and/or words.* Ensure students work on this task independently and preferably in class.* Give students BLM 12.4 Target Self Assessment and ask them to assess themselves, by indicating wherethey think their learning is on the target. This should be handed in along with their KWL chart, when both arecomplete.

AdaptationsInterventions

Enrichment* Have students play a variation of The Bermuda Triangle game where one student draws a triangle at its endposition and explains (rather than writes) how their partner should transform the shape to the end location.This time they will tell their partner what type of transformation they should perform and what coordinatesthey should end up at (e.g., "slide the triangle so it ends up at A11, A7, D7," instead of saying "slide the




Resources

triangle up six squares." Their partner then has to calculate how many spaces to slide it or the direction andamount of a turn of the flip.

Consolidation/Remediation* Partner a student at the consolidation stage with a student at the remediation stage. Have them workthrough the process together, where the consolidation student verbally directs the remediation studentstep-by-step and the student at the remediation stage works through the process of creating the gameboard.* When they have created the game board, they can then switch game boards with another pairing and workthrough finding the end spot, again with the consolidation student leading the remediation student through theprocess.

BLM 12.1 Mapping Out Routes BLM 12.1 Mapping Out Routes.cwk

BLM 12.2 Bermuda Triangle Gameboard BLM 12.2 B Game.cwk

BLM 12.3 Bermuda Triangle SampleInstructions

BLM 12.3 B sample.cwk

BLM 12.4 Target Self Assessment BLM 12.4 Target.cwk

Notes to Teacher1. The rationale for using letters instead of numbers along the horizontal axis is that using ordered pairs ofnumbers is not dealt with until Grade 6 in the Mathematics Curriculum.

2. You may want to omit the journal entry and go directly to completing the third column of the KWL chart.

Teacher Reflections




Expectations4m61 A • solve problems using geometric models;4m65 A • understand key concepts in transformational

geometry using concrete materials and drawings;4m66 A • describe location and movements on a grid;4m67 A • use language effectively to describe geometric


4m72 A – sort and classify two-dimensional figures accordingto shape;

4m73 A – identify similar and congruent figures using avariety of media;

4m84 A – draw lines of symmetry on two-dimensionalshapes;



5m69 A • identify congruent and similar figures usingtransformations;


5m89 A – construct two-dimensional shapes with one line ofsymmetry;


DescriptionStudents apply their learning to the design and construction of a geometric puzzle. Students have access toany of the manipulatives they explored in Subtask 3 (pattern blocks, attribute blocks, tangrams, polygon tiles,colour tiles, and pentominoes) to help them create a puzzle design on coordinate grid paper. Students designa blueprint and a set of directions for the educational puzzle to meet certain design requirements which arespecific to their grade. In pairs, students test a draft version of their puzzle and directions. A partner asksquestions for clarification and the student Puzzlemaker records these clarifications for later revision. Thestudent Puzzlemaker also views and analyses the puzzle created by their partners. Finally, the students revisetheir products and written instructions to create their final product. Each student's prototype is then field testedby an adult at home and a student in class.


Teaching / Learning StrategiesBrainstormingCollaborative/cooperative LearningConferencing

AssessmentField Test Part 1 - Peer AssessmentHave students use BLM 13.3 for peerassessment of their partner's puzzle,design analysis, and written instructions.

Field Test Part 2 - Sharing withSomeone at HomeSend home BLM 13.4 . Photocopyfeedback form on the back of theexplanatory note.Depending on your community, you maywish to do this step after teacherassessment.

Field Test Part 3 - TeacherAssessment

Assessment StrategiesPerformance Task

Assessment Recording DevicesChecklistRubric

Teaching / LearningTEACHER INPUT/CLASS DISCUSSION




Whole Class Brainstorming* Tell students that they have finished their Puzzlemaker training and are now ready to create the final puzzledesign.* Revisit the design specifications and requirements together, (Grade 4 - BLM 13.1, Grade 5 - BLM 13.2) byreading them aloud step-by-step.* Ask students to share any ideas they have for the design of their puzzle.* Remind students that they need to create a design that is a recognizable object (e.g., robot, flower, fish,mask, etc.)* Record all brainstormed ideas on chart paper.* Discuss which design may be the most and least challenging. Emphasize choosing a design that is at anappropriate level of difficulty for them.

COOPERATIVE GROUP WORKSmall Group Collaborative/Cooperative Learning* Provide students with access to all of the manipulatives and tools that they have used during the unit.* Give students 15 minutes to explore shapes and discuss design ideas and strategies for incorporating andincluding the design specifications .

WHOLE GROUPWhole Class Discussion* Ask students to share any successes or challenges as well as respond to the challenges of others.

INDEPENDENT WORKIndividual Performance Task* Have students choose an idea for their design and record it on their assignment outline (BLM 13.1 or BLM13.2).* Check students' ideas for appropriateness of subject and level of difficulty.* Clarify for students that they may change their ideas as they go, justifying any changes they make.* Allow time for students to work independently to meet the design specifications and written requirements ofthe task: construction of the puzzle, tracing of their design on graph paper labelled with coordinates, labellingtheir design to show inclusion of the specifications, and writing step by step instructions for thereconstruction of their puzzle.* Ask students to store their polygon tiles in a plastic bag for later use.

COOPERATIVE PARTNER WORKPartner Peer Conferences* Pair students as they complete their independent work. Each student in turn will build a puzzle on graphpaper (labelled with coordinates) from the oral instructions given by their partner. The Puzzlebuilder may askfor clarifications, and the Puzzle designer should note these areas on the draft of their written instructions.The Puzzle designer and the Puzzlebuilder compare the finished puzzle with the original design, and discussthe design requirements and difficulties encountered during the building. They record areas for improvement.They switch roles and repeat the process.

INDEPENDENT WORKPerformance Task Continued* Encourage students to use the feedback they received during the peer conference to improve their puzzledesign and/or written instructions.

CLOSUREPuzzlehedz Inc. Field Test Part 1 - Peer Assessment* Pair students for peer assessment.* Instruct each student in turn to build the puzzle on coordinate graph paper from the written instructions of




Resources

their partner, compare their product to the Puzzlemaker's product and analyse it for its components. Findingswill be recorded using the peer assessment rubric (BLM 13. 3).Puzzlehedz Inc. Field Test Part 2 - Sharing Puzzle with Someone from Home* Instruct each student that they will need to take home several things: their plastic bag of shapes, a piece ofcoordinate graph paper, a copy of their labelled puzzle, written instructions, explanatory note, and feedbackform (BLM 13.4). See Note 4 in Notes to Teacher.Puzzlehedz Inc. Field Test Part 3-Teacher Assessment* Instruct students to organize their work in the following order: assignment page, home feedback, peerassessment, written instructions, labelled analysis of puzzle, KWL chart, and draft work including initial peerpractice.

COMMUNICATIONTeacher/Student Conferencing* Share your feedback with students and assist each student in setting a reasonable, measurable goal andstrategies for reaching that goal.* Send home a copy of the teacher rubric and goal setting for students to share with a parent/guardian (BLM13.7).* Monitor the return of the teacher rubric and goal setting including a parent signature. Provide dailyrecognition to the students as they return the forms.

CELEBRATION* Decide how you would like to celebrate the completion of the project, e.g., Puzzlehedz Inc. Grand Opening -invite parents/guardians to an open house where they can see a display of all the puzzle projects.

Adaptations

BLM 13.1 Calling All Grade 4Puzzlemakers!

BLM 13.1 Calling all4.cwk

BLM 13.2 Calling all Grade 5Puzzlemakers!

BLM 13.2 Calling all.cwk

BLM 13.3 Puzzlehedz Inc. Peer Rubric BLM 13.3 Puzzlehedz Inc.cwk

BLM 13.4 Sharing with Someone at Home BLM 13.4 Sharing.cwk

BLM 13.7 My Goals in Mathematics BLM 13.7 My Goals.cwk

coordinate grid paper 1

polygon tiles

pattern blocks

attribute blocks

tangrams 1 set




Notes to Teacher1. Part of the problem solving process is for students to decide which shapes they will use to meet the designrequirements. They may choose to mix and match different sets of polygon tiles (using pattern blocks andattribute blocks) or create their own.

2. Polygon tiles are available from a variety of educational suppliers.

3. Graph paper labelled with coordinates can be labelled with teacher assistance or created by the teacher, asthis is not an expectation for Grades 4 or 5.

4. Students should take home a copy rather than the original of their labelled puzzle design and writteninstructions for field test part 2. The purpose is for sharing/reflecting on the learning, rather than on revision.Depending on your community, you may wish to do this step after teacher assessment.

Teacher Reflections


Black Line Masters:


Appendices

Rubrics:

Resource List:

Unit Expectation List and Expectation Summary:



Resource List


Page 1

Blackline Master / File

BLM 01.1 Puzzlemaker's Journal FrameworkBLM 01.1 Journal.cwka framework for students to write about what they did,what they thought, and what they learned

ST 1

BLM 01.3 Diagnostic ChecklistBLM 01.3 Diagnostic.cwkchecklist for tracking concepts from previous grades

ST 1

BLM 02.1 KWL ChartBLM 02.1 KWL Chart.cwka graphic organizer for students to record what theyknow, want to know, and need to learn

ST 2

BLM 02.2 Polygon Data SetBLM 02.2 Polygon Data Set.cwkyes and no examples to be used during a conceptattainment lesson on polygons

ST 2

BLM 02.4 What's my Design?BLM 02.4 What's my Design.cwkgraphic organizer for recording and comparing results ofthe game of 'What's my Design'

ST 2

BLM 02.5 The FourFive Math CornerBLM 02.5 Math Corner.cwksample introductory letter to parents

ST 2

BLM 02.6 Anecdotal ObservationsBLM 02.6 Anecdotal.cwktemplate for recording anecdotal observations

ST 2

BLM 02.7 Polygon Puzzlers Tracking SheetBLM 02.7 Polygon.cwktracking sheets by grade for each subtask'sexpectations

ST 2

BLM 03.1 Tangram TemplateBLM 03.1 Tangram Template.cwktemplate for creating your own tangrams

ST 3

BLM 03.2 Tangram PaperBLM 03.2 Tangram Paper.cwktangram grid paper used for recording purposes

ST 3

BLM 04.1 HEX GameboardBLM 04.1 HEX Gameboard.cwkmaster of HEX gameboard

ST 4

BLM 04.2 Puzzlemaker's Instruction FrameworkBLM 04.2 Puzzlemaker.cwka framework for writing game/puzzle instructions

ST 4

BLM 04.3 HEX Rules and Strategy SummaryBLM 04.3 HEX Rules.cwka summary of the rules of the game, HEX, and a placeto record game strategies

ST 4

BLM 05.1 Model of a ClockBLM 05.1 Model of a Clock.cwk

ST 5

BLM 07.1 Congruent Figures Data SetBLM 07.1 Congruent.cwkyes and no examples to be used during a conceptattainment lesson on congruent figures

ST 7

BLM 07.2 Similar Figures Data SetBLM 07.2 Similar.cwkyes and no examples to be used during a conceptattainment lesson on similar figures

ST 7

BLM 07.3 Congruency Concentration MasterBLM 07.3 Congruency.cwkgame cards for Congruency Concentration

ST 7

BLM 08.1 Self Assessment ChecklistBLM 08.1 Self Assess.cwkself assessment template #1 - checkpoint subtask 8

ST 8

BLM 09.1 Bingo CardBLM 09.1 Bingo Card.cwk

ST 9

BLM 09.2 Bermuda Rectangle GameboardBLM 09.2 Bermuda.cwk

ST 9

BLM 09.3 Bermuda Rectangle GameboardVertices Edition

BLM 09.3 Bermuda2.cwk

ST 9

BLM 09.4 Coordinate SystemsBLM 09.4 Coordinate Systems.cwk

ST 9

BLM 09.5 Coordinate Systems AnswersBLM 09.5 Coordinate.cwk

ST 9

BLM 10.1 Transformation SpinnerBLM 10.1 Trans.cwkspinner labelled with translations, reflections androtations

ST 10

BLM 10.2 Transformation Stick FiguresBLM 10.2 Trans2.cwksample of stick figure drawings done while playingTransformation Twister

ST 10

BLM 10.3 Transformation Twister Pattern BlockEdition

BLM 10.3 Trans3.cwkrules for the game

ST 10

BLM 11.1 What Is a Pentomino?BLM 11.1 pentomino.cwkyes and no examples of a pentomino

ST 11

BLM 11.2 Naming PentominoesBLM 11.2 Naming.cwka master of all 12 pentominoes, each labelled with aletter of the alphabet for ease of identification

ST 11

BLM 11.3 Pentomino ChallengesBLM 11.3 Challenges.cwkchallenges with pentominoes related to congruency andsimilarity

ST 11

BLM 11.4 2.5 cm grid paperBLM 11.4 grid paper.cwk

ST 11

BLM 11.5 Please notice...BLM 11.5 Please notice....cwknote about something the student wants the teacher tonotice in their work

ST 11

BLM 12.1 Mapping Out RoutesBLM 12.1 Mapping Out Routes.cwk

ST 12

BLM 12.2 Bermuda Triangle GameboardBLM 12.2 B Game.cwk

ST 12

BLM 12.3 Bermuda Triangle Sample InstructionsBLM 12.3 B sample.cwk

ST 12

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Oct 26, 2001 at 11:08:06 AM Page D-1


Resource List


Page 2

BLM 12.4 Target Self AssessmentBLM 12.4 Target.cwkself assessment template #2 - checkpoint subtask 12

ST 12

BLM 13.1 Calling All Grade 4 Puzzlemakers!BLM 13.1 Calling all4.cwkgrade 4 culminating task outline

ST 13

BLM 13.2 Calling all Grade 5 Puzzlemakers!BLM 13.2 Calling all.cwkgrade 5 culminating task outline

ST 13

BLM 13.3 Puzzlehedz Inc. Peer RubricBLM 13.3 Puzzlehedz Inc.cwkpeer assessment rubric

ST 13

BLM 13.4 Sharing with Someone at HomeBLM 13.4 Sharing.cwksample explanatory letter to parents

ST 13

BLM 13.7 My Goals in MathematicsBLM 13.7 My Goals.cwkgoal setting template

ST 13

Licensed Software

ClarisWorks 5.0 (English) ST 4

ClarisWorks 5.0 (English) ST 7

Print

atlasclass set of atlases

ST 9

Beyond Monet: The Artful Science ofInstructional Integration

Barrie Bennett and Carol Rolheiser

integrating multiple instructional processes in the designof more powerful learning environments

0-9695388-3-9

Unit

Curriculum Ideas for Teachers: Geometry JuniorDivision 1987

Ontario Ministry of Education

This resource includes 2 books: Book 1 is Teachers'Notes. Book 2 contains learning activities withaccompanying black line masters.

0-7729-2112-1

Unit

Grandfather Tang's StoryAnn Tompert

a story told with tangrams - as new characters areintroduced, the tangram pieces are rearranged torepresent the new characters.

0-517-57487-X

ST 3

Helping Children Learn MathematicsRobert E. Reys et al

mathematics methodology0 - 205 - 27087 - 5

Unit

Math I Know - A Mathematics HandbookMary C. Cavanagh

A math resource book for when you're not sure about atopic, or need a place to look up definitions,expanations and rules. It also includes an almanac oftables and lists as well as a glossary of math terms.

0-669-47153-4

Unit

Mathematics A Good BeginningAndria P. Troutman and Betty K. Lichtenberg

mathematics methodology0-534-21948-9

Unit

Mathematics Every Elementary Teacher ShouldKnow

Derek Haylock and Douglas McDougall

explains basic mathematical concepts and procedures1-55244-012-5

Unit

Models of TeachingBruce Joyce, Marsha Weil and Emily Calhoun

a basic educational repertoire of instructional strategiesfor teachers

0-205-31038-9

Unit

Quest 2000 Professional HandbookRicki Wortzman et al

contains a glossary of terms simplified for use withstudents

0 - 201 - 69601 - 0

Unit



Resource List


Page 3

Quest 2000 Teacher Support Pkg Gr. 4Ricki Wortzman et al

See pages 30 & 31 for black line masters of a variety ofpolygons.

0-201-55271-X

Unit

Quest 2000 Teacher Support Pkg Gr. 5Ricki Wortzman et al

See pages 7 & 8 for black line masters of a variety ofpolygons.

0-201-55274

Unit

Three Pigs, One Wolf and Seven Magic ShapesGrace MacCarone and David Neuhaus

a familiar story, retold with tangrams.0590308572

ST 3

Website

Link to Learning

links to websites that support the Ontario curriculum K -8

http://www.linktolearning.comUnit

Material

blank paper3per person

ST 7

blank paper ST 8

card stock or bristol boardused for creating polygons other than provided as amanipulative

Unit

chart paper

as neededper group

Unit

chart paper5per class

ST 6


ST 7


ST 8

chart paper2

Tape two pieces of chart paper togetherper class

ST 10

chart paper and markers1

ST 11

chart paper strips10per group

ST 1

colour tilesbinper group

ST 3

coordinate grid paper1

This can be premade and copied.per person

ST 13

envelope1

letter or legal size envelope for storing cut out geoboardshapes

per person

ST 5

folder or envelope1

for storage of all work during the unitper person

ST 2

game pieces30

resusable game pieces such as bingo chips or buttonsper person

ST 4

geoboard dot paperapprox.per person

ST 5

geoboards1per pair

ST 3

isometric dot paper

See black line masters of your current math series.per person

ST 8

magnets or tape1per pair

ST 8

markers1 setper group

Unit

markers2

2 markers of different coloursper group

ST 1

markers1per group

ST 6

markers1 setper class

ST 7

markers1 setper class

ST 10

math dictionary1

Each student will create a personal glossary of terms.per person

Unit



Resource List


Page 4

math journal1

Each student will require a notebook/duotang forcommunication in mathematics.

per person

Unit

paper bags1

lunch size brown paper bagsper pair

ST 2

paper clips1 box

ST 10

pattern blocksbinper group

ST 3

pipe cleaners1per person

ST 5

polygon tilesbinper group

ST 3

rulers (30 cm)1per person

Unit

scissors1per person

ST 7

square dot paper

See black line masters of your current math series.per person

ST 8

string120 cmper pair

ST 6

tangrams1per person

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Transparent Mirrors (Mira)10per class

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transparent tape1

use dollar store variety - 10 rolls for $2per group

ST 11

Equipment / Manipulative

attribute blocks ST 13

elastics for geoboards1 boxper class

ST 7

gameboards1

Chinese Checkers, Checkers, Backgammon, Bingo,Monopoly etc.

per group

ST 1

geoboards1per person

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geoboards15per class

ST 7

pattern blocks1

Select from the blue or tan rhombus, or the redtrapezoid.

per person

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pattern blocks ST 13

plastic bags of 60 colour tiles1per group

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polygon tiles1

Each tile should be different.per pair

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polygon tiles1 bucketper group

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polygon tiles1setper pair

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polygon tiles

Power Polygons are available from a variety ofeducational suppliers.

per personST 13

rulers1per pair

ST 8

scissors1per person

ST 5

tangrams1 setper person

ST 13

Transparent Mirror (Miras)10per class

ST 7



Resource List


Page 5

Transparent Mirror (Miras)1per group

ST 8

Transparent Mirros (Mira)1per group

ST 8

variety of polygon shapesper pair

ST 6

Other

large open area ST 10

The Geometer's Sketchpadlicensed softwaredynamic geometry software

ST 5


Puzzlemaker’s Journal BLM 01.1

Your math journal is a record of what you have done and what you have learned in class. It has two main purposes:1. to help you think about your learning so that you can come to better understand the math we are studying; and 2. to give your teacher a chance to find out how you feel about the activities you are doing in class so he/she can see how you are doing.

Your journal must have at least the following 3 parts each time:

1) WHAT WE DID

Describe in detail what activity we did in math class that day.Use complete sentences.

2) WHAT YOU THOUGHT

Tell me what you thought of the activity. Was it too easy? Too hard? Boring? Interesting? Too noisy? Too quiet?

Did it remind you of other math that we have done? Use complete sentences.

3) WHAT YOU LEARNED

Think about what you learned from the activity - both about mathematics and about yourself. This is the most

important part of the journal. Use complete sentences.

Polygon Puzzlers Grade 4/5 Diagnostic Checklist BLM 01.3

Student Names

This diagnostic checklist focuses on the acquisition of concepts rather than specific expectations.

Interventions

Got it - Not Yet - X

PUZZLEHEDZ INC. KWL Chart

LearnWant to KnowKnow

BLM 02.1

Polygon Data Set - What is a polygon? BLM 02.2

This is a polygon. This is not a polygon.

This is a polygon.

Is this a polygon?

Tests Cases - Thumbs up. Thumbs down. Is this a polygon?

This is a polygon.

Is this a polygon?

This is a polygon.

This is a polygon. This is not a polygon.This is a polygon.

This is a polygon. This is not a polygon.

Is this a polygon?

This is a polygon.This is a polygon. This is not a polygon.

Bag # This is what the design looked like when I made it.

Comments and Suggestions

This is what the design should have looked like.

What’s My Design?Name

BLM 02.4

The FourFive Math Corner

Dear Parents and Guardians,

The focus of our studies for the next few weeks will be on geometry. During this time, students will be learning about two-dimensional, transformational, and coordinate geometry. All students will participate in the same activities, but the expectations for your child will be based on his/her grade level.

Students will use their math dictionaries to record definitions of new concepts as well as draw and label a picture to accompany each definition. I am recommending that students take their dictionary home, along with their assignments, so that they can share their understanding of new learning with you. This practice will also allow you to become familiar with the vocabulary of this unit.

Assignments during the unit will be varied. Students could be writing in their math journals, playing a geometric game or puzzle with someone from the family, solving geometric puzzles, creating a riddle, or investigating the use of geometry in the home. Please continue to check your child’s agenda each evening for specific details.

At the end of the unit, students will assume the role of a puzzlemaker from PUZZLEHEDZ INC. to design an educational puzzle for students in Grades 4 and 5. The puzzle must meet specific requirements depending on your child’s grade level. One evening, at home, you or your child’s older brother or sister will be asked to assume the role of someone who would like to buy the puzzle and try out it out. We will provide an organizer for you to use to record some positive comments as well as a positive suggestion about the puzzle.

Please call me if you have any questions or concerns.

Sincerely,

BLM 02.5

Puzzlemakers in Training Anecdotal Observations/Interventions

Name: Name: Name: Name:






BLM 02.6

Polygon Puzzlers Grade 4 Tracking Sheet BLM 02.7

Student Names

Subtask Number 2 5 4 8 6 73Use a highlighter to indicate those students who require interventions: enrichment, consolidation, or remediation.


Student Names

Subtask Number 9 12 1110

Summary of Interventions

*Note - Use rubric for Subtask 13

Use a highlighter to indicate those students who require interventions: enrichment, consolidation, or remediation.


Student Names

Subtask Number 2 5 4 8 6 73



Student Names

Subtask Number 9 12 1110

Summary of Interventions

*Note - Use rubric for Subtask 13


Tangram Template BLM 03.1

Tangram Paper BLM 03.2

HEXBLM 04.1 Hex Gameboard

CHALLENGE - ___________________________________________

_______________________________________________________

_______________________________________________________

MATERIALS -

______________________ ______________________

______________________ ______________________

HOW TO PLAY -

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

__________________________________________

REACHING YOUR GOAL -

_____________________________________________________________

_____________________________________________________________

_____________________________________________________________Puzzlemaker’s Instruction Framework BLM 04.2

Strategies We’ve Used to Play HEXHEX

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Players StrategiesCHALLENGE -Create an unbroken pathwaybetween the player’s two sides of the board.

MATERIALS -HEX gameboardsupply of counters in two colours

HOW TO PLAY - Decide who starts and which side of the board is yours.Take turns placing one of your markers in any empty hexagon cell.Build a pathway from your side of the board to the opposite side of the board. The corner hexagons belong to both sides.You may occupy any hexagon as long as it is not already occupied.The pathway can twist and turn but it must not be broken.

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REACHING YOUR GOAL - The first player to complete their pathway is the winner.

HEX Rules and Strategy Summary BLM 04.3

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Model of a Clock BLM 05.1

Congruent Figures Data Set

These are congruent.

BLM 07.1

These are congruent. These are not congruent.

These are congruent. These are congruent. These are not congruent.



Are these congruent? Are these congruent? Are these congruent?

Thumbs up or thumbs down?

Similar Figures Data Set BLM 07.2

These are similar. These are similar. These are not similar.




Are these similar? Are these similar? Are these similar?

Thumbs up or thumbs down?

Congruency Concentration Game Card Master * Note - Photocopy x3 for each pair of students.

*Note - Enlarge 200% if you would like the cards to be the size of a small file card.

BLM 07.3

BLM 08.1

Puzzlemakers in Training Part 1Self Assessment Checklist

Yes No1) I can identify, sort, and classify two-dimensional shapes.____________________________________________________2) I know what angles are.____________________________________________________3) I can identify congruent shapes.____________________________________________________4) I can identify lines of symmetry.____________________________________________________5) I can explain my ideas using geometric language.____________________________________________________

The activity I enjoyed the most was _________________________because______________________________________________________________________________________________________________________________________________________

The thing I understand the best is __________________________because______________________________________________________________________________________________________________________________________________________

Some things I need help on are _____________________________ ________________________________________________________________________________________________________

You can help me by ____________________________________________________________________________________________________________________________________________________________

B I N G O12 21 12 59 6541 27 2 16 4210 24 X 48 1671 20 16 87 1519 28 93 21 31

BLM 09.1 Bingo Card

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B E R M U D AO

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The Bermuda Rectangle Gameboard

Rules1. Colour in a 2 square, a 3 square, and a 5 square rectangle.2. Player 1 makes a guess about where the other person put their rectangle, e.g., (E, 5).3. If the guess is wrong, Player 2 says MISS. If the guess is correct, Player 2 says HIT and puts an X through that square.

4. The player who is guessing should record his/her guesses as H for hit and M for miss on the My Guesses side of his/her gameboard to avoid making the same guess twice.5. Game continues until one player sinks all of his/her opponent’s rectangles. Whenever your opponent hits all the squares on one of the rectangles, you must tell them.

My Bermuda Rectangles My Guesses

BLM 09.2

The Bermuda Rectangle Gameboard Vertices Edition

Rules1. Colour in a 2 square, a 3 square, and a 5 square rectangle.2. Player 1 makes a guess about where the other person put their rectangle, e.g., (E, 5).3. If the guess is wrong, Player 2 says MISS. If the guess is correct, Player 2 says HIT and puts an X through that vertex.

4. The player who is guessing should record his/her guesses as H for hit and M for miss on the My Guesses side of his/her gameboard to avoid making the same guess twice.5. Game continues until one player sinks all of his/her opponent’s retangles. Whenever your opponent hits all four vertices on one of the rectangles, you must tell them.

My Bermuda Rectangles My Guesses

B E R M U D A

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BLM 09.3

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A B C D E F G H I J K L M

BLM 09.4 Coordinate Systems

Follow the directions below to discover the mystery words.

Place the following letters at these coordinates: P at ( C, 11)

E at (I, 11)

D at (G, 7)

Z at (G, 9)

N at ( F, 3)

I at (E, 4)

U at (D, 10)

L at ( H, 10)

E at (E, 7)

H at (D, 6)

Z at (H, 6)

C at (G, 4)

Z at (E, 9)

Self Assessment

I got __________ of the letters in the correct boxes.4 3 2 1all most some a few

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A B C D E F G H I J K L M

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It spells Puzzlehedz Inc. !.

BLM 09.5 Coordinate Systems Answers

Choose oneRotation (turn)

1/4, 1/2, 3/4

Choose oneReflection (flip)

Up, Down, Left, Right

Choose oneTranslation (slide)

Up, Down,Left, Right

BLM 10.1 Transformation Spinner

Transformation Stick Figures

Flip Up or Down

Flip Left or Right

FLIPS

TURNS

1/4 Turn

1/2 Turn3/4 Turn

Start here

SLIDES

Slide Up or Down

Slide Leftor Right

Note: Flip could be done using top of head as a flip line instead of feet

BLM 10.2

1. Choose a blue rhombus, tan rhombus, or a red trapezoid as your game piece.2. Draw a box on the graph paper at the bottom right that is large enough for your

game piece or your partner’s game piece. This is HOME.3. Place your game piece in the upper left hand corner of the graph paper.

Trace your game piece.4. Spin the spinner and follow the outcome.5. Keep the following rules in mind as you play:

*Flips, slides, and turns are limited to the options on the spinner.* All flips, slides, and turns must be connected by at least one side or vertex (corner) to the previous transformation. * If the flip, slide, or turn will take you off the page, you must choose a

different direction to flip, slide or turn.* Transformations may not overlap, plan carefully!

6. Trace your polygon after each transformation.

CHALLENGE -Transform your pattern block from start to home before your opponent.

MATERIALS -* a blue rhombus, tan rhombus, or a red trapezoid pattern block* Transformation Spinner BLM 10.1* pencil* graph paper

REACHING YOUR GOAL -

HOW TO PLAY -

The winner is the person who uses the fewest moves to get all vertices of his/her polygon inside the finish box at the bottom right hand corner.

Transformation Twister - Pattern Block EditionBLM 10.3

This is a pentomino. This is not a pentomino.

What Is a Pentomino? BLM 11.1

(demonstrate using colour tiles or orange pattern block squares)

Yes Examples No Examples

This is not a pentomino.This is a pentomino.

Thumbs Up/Thumbs Down - Is this a pentomino?

(This is a no.) (This is a yes.)(This is a no.)

What is a pentomino?

Each pentomino piece represents one of 12 ways you can combine 5 squares of the same size, edge to edge. The letters F L I P N T U V W X Y Z are given to the shapes for ease of identification.

F L I P

N T U

V

W

X Y

Z

Naming Pentominoes BLM 11.2

Pentomino Challenges BLM 11.3

Congruency Challenge

This challenge requires 2 pentominoes to be put together to make 1 shape and then 2 different pentominoes to be put together to make the same or congruent shape.

How many different congruent shapes can you make?

Select 2 pentominoes and create one shape.Find 2 other pentominoes that can be put together to make the same or congruent shape.

Remember to -* Trace your shapes on 2.5 cm grid paper.* Colour each pentomino a different colour.* Label each pentomino with its alphabetical name.

2.1.

Similarity Challenge

This problem requires you to create a shape that looks the same but is triple or three times the size of the original pentomino.

1. Select ANY pentomino and set it aside.2. Draw a shape on 2.5 cm graph paper that is triple the size of the selected pentomino. (Length and width will be three times that of the original pentomino.)3. Use 9 of the remaining 11 pentominoes to create a shape 3 times the size of the selected pentomino.4. Colour each pentomino a different colour.5. Label each pentomino with its alphabetical name.

Steve Moretti

Steve Moretti

2.5 cm grid paperBLM 11.4

BLM 11.5 Noticeagram

Please notice... Please notice... Please notice...




BLM 12.1 Mapping Out RoutesBLM 12.1 Mapping Out RoutesBLM 12.1 Mapping Out RoutesBLM 12.1 Mapping Out RoutesBLM 12.1 Mapping Out RoutesBLM 12.1 Mapping Out RoutesBLM 12.1 Mapping Out Routes

Home

Bermuda Triangle

Cut out.

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A B C D E F G H I J K L M N O P Q

BLM 12.2 The Bermuda Triangle GameboardBLM 12.2 The Bermuda Triangle GameboardBLM 12.2 The Bermuda Triangle GameboardBLM 12.2 The Bermuda Triangle GameboardBLM 12.2 The Bermuda Triangle GameboardBLM 12.2 The Bermuda Triangle GameboardBLM 12.2 The Bermuda Triangle GameboardBLM 12.2 The Bermuda Triangle GameboardBLM 12.2 The Bermuda Triangle Gameboard

Cut out.

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A B C D E F G H I J K L M N O P Q

CHALLENGE -Find the Bermuda Triangle by transforming the triangle according to the instructions.

MATERIALS -Bermuda Triangle gameboardruler and pencilcut out triangle

Mark a point at A, l A, 5 and D, 1.Connect the points with a ruler to make a right angle triangle.Slide up 6 units.Flip to the right. Make a 1/4 turn counter-clockwise using the top point as your rotation point.

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3.4.5.

REACHING YOUR GOAL -If your triangle’s coordinates are at G, 11 K,11 K,8then you have found the Bermuda Triangle!

HOW TO PLAY -

Bermuda Triangle Sample Instructions BLM 12.3

Target Self-Assessment BLM 12.4

all

most

some

a few

Mark an X in the section that best describes your understanding of theconcepts in this unit.

Comments: ______________________________________________

_______________________________________________________

_______________________________________________________

_______________________________________________________

Teacher Comments: ______________________________________

_______________________________________________________

As an puzzlemaker for PUZZLEHEDZ INC., you specialize in creating educational puzzles based on real life objects such as birds, flowers, toys, or vehicles. Your current project requires you to create a model, including all the puzzle pieces, and a set of instructions for creating a geometric puzzle. Your work will be field tested by an adult who may wish to buy the product and by a student who is in Grade 4.

1. The puzzle must meet certain design specifications. Your model must include -

a variety of polygon shapes congruent shapessimilar shapessymmetryone of each type of transformation (slide, flip, and turn)use of coordinate grid paper as a base

2. In order to show that you have met all the design specifications, include a labelled blueprint of your model. Please label -

names of each of the polygon shapes in as many ways as possiblepairs of congruent shapespairs of similar shapesline of symmetry one of each type of transformationstart point on coordinate grid paper

3. Your puzzle must also include a set of step-by-step instructions for creating the puzzle. As this is an educational product, the use of correct mathematical language is important.

4. Please submit your concept for approval as soon as possible.

Name: __________________ Puzzle Design: _____________________

Design Approved by _____________ Date ____________

You will need to submit the model, analysis, and written instructions by _______.

CALLING ALL GRADE 4 PUZZLEMAKERS!

BLM 13.1

As a puzzlemaker for PUZZLEHEDZ INC., you specialize in creating educational puzzles based on real life objects such as birds, flowers, toys, or vehicles. Your current project requires you to create a model, including all the puzzle pieces, and a set of instructions for creating a geometric puzzle. Your work will be field tested by an adult who may wish to buy the product and by a student who is in Grade 5.

1. The puzzle must meet certain design specifications. Your model must include -

a variety of polygon shapes including a variety of trianglescongruent shapessimilar shapessymmetry (outline of whole puzzle must be a symmetrical shape)one of each type of transformation (slide, flip, and turn)use of coordinate grid paper as a base

2. In order to show that you have met all the design specifications, include a labelled blueprint of your model. Please label -

names of each of the polygon shapes including types of anglespairs of congruent shapespairs of similar shapesline of symmetry one of each type of transformationstart/end point on coordinate grid paper

3. Your puzzle must also include a set of step-by-step instructions for creating the puzzle. As this is an educational product, the use of correct mathematical language is important.

4. Please submit your concept for approval as soon as possible.

Name: __________________ Puzzle Design: _____________________

Design Approved by _____________ Date ____________

You will need to submit the model, analysis, and written instructions by _______.

CALLING ALL GRADE 5 PUZZLEMAKERS!

BLM 13.2

The puzzlemaker had a good strategy. They ‘made a diagram’ or ‘worked backwards’ from the specifications.

The puzzlemaker had more than one plan or had to change plans along the way.

For example, they may have begun with the hardest part first then ‘worked backwards’ from the specifications.

The puzzlemaker started to build without really making a plan.

The puzzlemaker used ‘guess and test’ as a strategy.

Level 2 Level 3 Level 4Level 1

Knowledge/Skills

Problem Solving

Tell me about your plan.

Understanding Concepts

Application of Required Procedures

Show me how you used the math ideas in your puzzle.

Tell me about the different math ideas in your puzzle.

Communication of Required Knowledge, Related Concepts, Procedures, and Problem Solving

Tell me how to make your puzzle.

The puzzlemaker could only explain a few of the math ideas to me.

The puzzlemaker showed me how they used a some of the math ideas in the puzzle.

It was somewhat difficult to create the puzzle design from the written instructions. Some of the math words were correct but the instructions were not really clear.

I could create most of the puzzle design from the written instructions. The instructions were clear and the math words were correct.

I could create the puzzle design from the written instructions. The steps were clear and easy to follow. The math words were correct and helped me a lot.

It was very difficult to create the puzzle design from the written instructions. The instructions were not clear and there weren’t many math words to help me.

The puzzlemaker showedme how they used a fewof the math ideas in thepuzzle.

The puzzlemaker showed me how they used all of the math ideas in the puzzle.

PUZZLEHEDZ INC. Name

peer assessment rubric BLM 13.3

The puzzlemaker could explain some of the math ideas to me.

The puzzlemaker could explain most of the math ideas to me.

The puzzlemaker explained almost all of the math ideas to me.

The puzzlemaker showed me how they used most of the math ideas in the puzzle.

Dear

Tonight I am bringing home my geometric puzzle to share with you. I would like you to see my finished product as well tell you about all the math that is in my puzzle.

Please give me some positive feedback as well as help me set a goal for the future.

I need to bring all the pieces of my project back tomorrow. Please help me remember.

love,

PUZZLEHEDZ INC.Request for Feedback

My child shared their geometric puzzle with

_________________________________.

We were very proud of ___________ because

__________________________________

__________________________________

__________________________________.

We feel that one way ______________ can

continue to improve his/her approach to

mathematics is to _____________________

__________________________________

__________________________________.

Sharing with Someone at Home BLM 13.4

Name: ________________ Date: ________________My Goals in Mathematics

My next goal in mathematics is

The strategies I will use to reach this goal are

I need my teacher to help me by

I need my family to help me by

Student’s Signature Parent/Guardian’s Signature Teacher’s Signature

BLM 13.7

Expectation List

Selected


Page 1

Assessed

Mathematics---Geometry and Spatial Sense• solve problems using geometric models; 24m61

• investigate the attributes of three-dimensional figures and two-dimensional shapes using concrete materials and drawings; 44m62

• explore transformations of geometric figures; 14m64

• understand key concepts in transformational geometry using concrete materials and drawings; 44m65

• describe location and movements on a grid; 34m66

• use language effectively to describe geometric concepts, reasoning, and investigations, and coordinate systems. 94m67

– identify and sort quadrilaterals (e.g., square, trapezoid); 34m71

– sort and classify two-dimensional figures according to shape; 44m72

– identify similar and congruent figures using a variety of media; 44m73

– construct congruent figures in a variety of ways (e.g., cutting and matching, using a geoboard); 14m74

– discover geometric patterns and solve geometric puzzles with and without the use of computer applications; 24m75

– use mathematical language to describe geometric ideas (e.g., line, angle); 34m77

– recognize and describe the occurrence and application of geometric properties and principles in the everyday world; 14m78

– discuss geometric concepts with peers and explain their understanding of the concepts; 34m79

– discuss ideas, make connections, and articulate hypotheses about geometric properties and relationships; 24m80

– demonstrate an understanding of translations, reflections, and rotations (e.g., on a geoboard or dot paper); 24m81

– apply translations, reflections, and rotations using concrete materials and drawings to pose and solve problems; 24m82

– discover transformation patterns with and without the use of computer applications; 14m83

– draw lines of symmetry on two-dimensional shapes; 34m84

– demonstrate an understanding of coordinate systems and an ability to use them in simple games (e.g., battleship, bingo). 24m85

Mathematics---Geometry and Spatial Sense• identify, describe, compare, and classify geometric figures; 55m65

• explore transformations of geometric figures; 15m67

• understand key concepts in transformational geometry using concrete materials and drawings; 45m68

• identify congruent and similar figures using transformations; 25m69

• use mathematical language effectively to describe geometric concepts, reasoning, and investigations, and coordinatesystems.

95m70

– sort polygons according to the number of sides, angles, and vertices; 35m75

– classify two-dimensional shapes according to angle and side properties (e.g., obtuse, scalene); 25m76

– demonstrate an understanding of congruent figures; 25m77

– demonstrate congruence of figures using paper folding, reflections in a transparent mirror (Mira), and various computerapplications;

15m80

– use a computer application to explore and extend geometric concepts; 15m81

– use mathematical language to describe geometric ideas (e.g., quadrilateral, scalene triangle); 35m82

– recognize and explain the occurrence and application of geometric properties and principles in the everyday world; 15m83

– discuss geometric concepts with peers and use mathematical language to explain their understanding of the concepts; 35m84

– discuss ideas, make conjectures, and articulate hypotheses about geometric properties and relationships; 25m85

– describe the effect of a translation, reflection, and rotation; 25m86

– apply translations, reflections, and rotations (e.g., using concrete materials and grid paper or isometric dot paper) to pose andsolve problems;

25m87

– explore tiling patterns that cover a plane; 25m88

– construct two-dimensional shapes with one line of symmetry; 35m89

– demonstrate an understanding of coordinate systems on maps and grids. 45m90

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Oct 26, 2001 at 11:08:10 AM Page F-1


Expectation Summary


Selected Assessed

English Language4e1 4e2 4e3 4e4 4e5 4e6 4e7 4e8 4e9 4e104e11 4e12 4e13 4e14 4e15 4e16 4e17 4e18 4e19 4e204e21 4e22 4e23 4e24 4e25 4e26 4e27 4e28 4e29 4e304e31 4e32 4e33 4e34 4e35 4e36 4e37 4e38 4e39 4e404e41 4e42 4e43 4e44 4e45 4e46 4e47 4e48 4e49 4e504e51 4e52 4e53 4e54 4e55 4e56 4e57 4e58 4e59 4e604e61 4e62 4e63 4e64 4e65 4e66 4e67 4e68 4e69 4e70

French as a Second Language4f1 4f2 4f3 4f4 4f5 4f6 4f7 4f8 4f9 4f104f11 4f12 4f13 4f14 4f15 4f16 4f17 4f18 4f19 4f20

Mathematics4m1 4m2 4m3 4m4 4m5 4m6 4m7 4m8 4m9 4m104m11 4m12 4m13 4m14 4m15 4m16 4m17 4m18 4m19 4m204m21 4m22 4m23 4m24 4m25 4m26 4m27 4m28 4m29 4m304m31 4m32 4m33 4m34 4m35 4m36 4m37 4m38 4m39 4m404m41 4m42 4m43 4m44 4m45 4m46 4m47 4m48 4m49 4m504m51 4m52 4m53 4m54 4m55 4m56 4m57 4m58 4m59 4m604m61 2 4m62 4 4m63 4m64 1 4m65 4 4m66 3 4m67 9 4m68 4m69 4m704m71 3 4m72 4 4m73 4 4m74 1 4m75 2 4m76 4m77 3 4m78 1 4m79 3 4m80 24m81 2 4m82 2 4m83 1 4m84 3 4m85 2 4m86 4m87 4m88 4m89 4m904m91 4m92 4m93 4m94 4m95 4m96 4m97 4m98 4m99 4m1004m101 4m102 4m103 4m104 4m105 4m106 4m107 4m108 4m109 4m1104m111 4m112 4m113 4m114 4m115 4m116 4m117 4m118 4m119

Science and Technology4s1 4s2 4s3 4s4 4s5 4s6 4s7 4s8 4s9 4s104s11 4s12 4s13 4s14 4s15 4s16 4s17 4s18 4s19 4s204s21 4s22 4s23 4s24 4s25 4s26 4s27 4s28 4s29 4s304s31 4s32 4s33 4s34 4s35 4s36 4s37 4s38 4s39 4s404s41 4s42 4s43 4s44 4s45 4s46 4s47 4s48 4s49 4s504s51 4s52 4s53 4s54 4s55 4s56 4s57 4s58 4s59 4s604s61 4s62 4s63 4s64 4s65 4s66 4s67 4s68 4s69 4s704s71 4s72 4s73 4s74 4s75 4s76 4s77 4s78 4s79 4s804s81 4s82 4s83 4s84 4s85 4s86 4s87 4s88 4s89 4s904s91 4s92 4s93 4s94 4s95 4s96 4s97 4s98 4s99 4s1004s101 4s102 4s103 4s104 4s105 4s106 4s107 4s108 4s109 4s1104s111 4s112 4s113 4s114 4s115 4s116 4s117 4s118 4s119 4s1204s121 4s122 4s123

Social Studies4z1 4z2 4z3 4z4 4z5 4z6 4z7 4z8 4z9 4z104z11 4z12 4z13 4z14 4z15 4z16 4z17 4z18 4z19 4z204z21 4z22 4z23 4z24 4z25 4z26 4z27 4z28 4z29 4z304z31 4z32 4z33 4z34 4z35 4z36 4z37 4z38 4z39 4z404z41 4z42 4z43 4z44 4z45 4z46 4z47 4z48 4z49 4z504z51 4z52 4z53 4z54 4z55 4z56 4z57 4z58 4z59 4z604z61 4z62

Health & Physical Education4p1 4p2 4p3 4p4 4p5 4p6 4p7 4p8 4p9 4p104p11 4p12 4p13 4p14 4p15 4p16 4p17 4p18 4p19 4p204p21 4p22 4p23 4p24 4p25 4p26 4p27 4p28 4p29 4p304p31 4p32 4p33 4p34 4p35 4p36

The Arts4a1 4a2 4a3 4a4 4a5 4a6 4a7 4a8 4a9 4a104a11 4a12 4a13 4a14 4a15 4a16 4a17 4a18 4a19 4a204a21 4a22 4a23 4a24 4a25 4a26 4a27 4a28 4a29 4a304a31 4a32 4a33 4a34 4a35 4a36 4a37 4a38 4a39 4a404a41 4a42 4a43 4a44 4a45 4a46 4a47 4a48 4a49 4a504a51 4a52 4a53 4a54 4a55 4a56 4a57 4a58 4a59 4a604a61 4a62 4a63 4a64 4a65 4a66 4a67 4a68 4a69 4a70

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Oct 26, 2001 at 11:08:15 AM Page G-1


Expectation Summary


Selected Assessed

English Language5e1 5e2 5e3 5e4 5e5 5e6 5e7 5e8 5e9 5e105e11 5e12 5e13 5e14 5e15 5e16 5e17 5e18 5e19 5e205e21 5e22 5e23 5e24 5e25 5e26 5e27 5e28 5e29 5e305e31 5e32 5e33 5e34 5e35 5e36 5e37 5e38 5e39 5e405e41 5e42 5e43 5e44 5e45 5e46 5e47 5e48 5e49 5e505e51 5e52 5e53 5e54 5e55 5e56 5e57 5e58 5e59 5e605e61 5e62 5e63 5e64 5e65 5e66

French as a Second Language5f1 5f2 5f3 5f4 5f5 5f6 5f7 5f8 5f9 5f105f11 5f12 5f13 5f14 5f15 5f16 5f17 5f18

Mathematics5m1 5m2 5m3 5m4 5m5 5m6 5m7 5m8 5m9 5m105m11 5m12 5m13 5m14 5m15 5m16 5m17 5m18 5m19 5m205m21 5m22 5m23 5m24 5m25 5m26 5m27 5m28 5m29 5m305m31 5m32 5m33 5m34 5m35 5m36 5m37 5m38 5m39 5m405m41 5m42 5m43 5m44 5m45 5m46 5m47 5m48 5m49 5m505m51 5m52 5m53 5m54 5m55 5m56 5m57 5m58 5m59 5m605m61 5m62 5m63 5m64 5m65 5 5m66 5m67 1 5m68 4 5m69 2 5m70 95m71 5m72 5m73 5m74 5m75 3 5m76 2 5m77 2 5m78 5m79 5m80 15m81 1 5m82 3 5m83 1 5m84 3 5m85 2 5m86 2 5m87 2 5m88 2 5m89 3 5m90 45m91 5m92 5m93 5m94 5m95 5m96 5m97 5m98 5m99 5m1005m101 5m102 5m103 5m104 5m105 5m106 5m107 5m108 5m109 5m1105m111 5m112 5m113 5m114 5m115 5m116 5m117 5m118 5m119 5m1205m121 5m122 5m123 5m124

Science and Technology5s1 5s2 5s3 5s4 5s5 5s6 5s7 5s8 5s9 5s105s11 5s12 5s13 5s14 5s15 5s16 5s17 5s18 5s19 5s205s21 5s22 5s23 5s24 5s25 5s26 5s27 5s28 5s29 5s305s31 5s32 5s33 5s34 5s35 5s36 5s37 5s38 5s39 5s405s41 5s42 5s43 5s44 5s45 5s46 5s47 5s48 5s49 5s505s51 5s52 5s53 5s54 5s55 5s56 5s57 5s58 5s59 5s605s61 5s62 5s63 5s64 5s65 5s66 5s67 5s68 5s69 5s705s71 5s72 5s73 5s74 5s75 5s76 5s77 5s78 5s79 5s805s81 5s82 5s83 5s84 5s85 5s86 5s87 5s88 5s89 5s905s91 5s92 5s93 5s94 5s95 5s96 5s97 5s98 5s99 5s1005s101 5s102 5s103 5s104 5s105 5s106 5s107 5s108 5s109 5s1105s111 5s112 5s113 5s114 5s115 5s116 5s117 5s118 5s119 5s1205s121 5s122 5s123 5s124 5s125 5s126 5s127 5s128

Social Studies5z1 5z2 5z3 5z4 5z5 5z6 5z7 5z8 5z9 5z105z11 5z12 5z13 5z14 5z15 5z16 5z17 5z18 5z19 5z205z21 5z22 5z23 5z24 5z25 5z26 5z27 5z28 5z29 5z305z31 5z32 5z33 5z34 5z35 5z36 5z37 5z38 5z39 5z405z41 5z42 5z43 5z44 5z45 5z46 5z47 5z48

Health & Physical Education5p1 5p2 5p3 5p4 5p5 5p6 5p7 5p8 5p9 5p105p11 5p12 5p13 5p14 5p15 5p16 5p17 5p18 5p19 5p205p21 5p22 5p23 5p24 5p25 5p26 5p27 5p28 5p29 5p305p31 5p32 5p33 5p34 5p35 5p36 5p37 5p38 5p39 5p40

The Arts5a1 5a2 5a3 5a4 5a5 5a6 5a7 5a8 5a9 5a105a11 5a12 5a13 5a14 5a15 5a16 5a17 5a18 5a19 5a205a21 5a22 5a23 5a24 5a25 5a26 5a27 5a28 5a29 5a305a31 5a32 5a33 5a34 5a35 5a36 5a37 5a38 5a39 5a405a41 5a42 5a43 5a44 5a45 5a46 5a47 5a48 5a49 5a505a51 5a52 5a53 5a54 5a55 5a56 5a57 5a58 5a59 5a605a61 5a62 5a63 5a64 5a65 5a66 5a67 5a68 5a69

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Oct 26, 2001 at 11:08:15 AM Page G-2


Page 1Unit Analysis

Assessment Recording Devices

6 Anecdotal Record10 Checklist1 Rating Scale1 Rubric

Assessment Strategies

1 Conference6 Learning Log9 Observation3 Performance Task4 Self Assessment

Groupings

13 Students Working As A Whole Class6 Students Working In Pairs8 Students Working In Small Groups12 Students Working Individually

Teaching / Learning Strategies

5 Brainstorming3 Classifying3 Collaborative/cooperative Learning3 Concept Clarification1 Conferencing2 Demonstration1 Direct Teaching6 Discussion1 Experimenting1 Learning Log/ Journal1 Model Making1 Numbered Heads3 Peer Practice1 Problem Posing1 Review1 Think Aloud3 Think / Pair / Share2 Working With Manipulatives

Analysis Of Unit Components

13 Subtasks108 Expectations115 Resources119 Strategies & Groupings

-- Unique Expectations -- 39 Mathematics Expectations

Resource Types

0 Rubrics 40 Blackline Masters 2 Licensed Software 13 Print Resources 0 Media Resources 1 Websites 38 Material Resources 19 Equipment / Manipulatives 0 Sample Graphics 2 Other Resources 0 Parent / Community 0 Companion Bookmarks

Written using the Ontario Curriculum Unit Planner 2.51 PLNR_01 March, 2001* Open Printed on Oct 26, 2001 at 11:08:24 AM Page H-1

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