Show Me Your Math – Connecting Math to Our Lives and ...



Birch Bark BitingGrade 6Integrated Inquiry ProjectGrade Six Mathematics will be the main focus of the Inquiry Project.Inquiry Project Focus: Historical Birch Bark bitings and the process of creating Birch Bark bitings.Essential Questions: Can Birch Bark biting be brought back into today’s culture and society or is it a lost cultural art form?Encompassing Essential Question:Mathematics Essential Question: What shapes are possible or impossible to bite into the birch bark?Social Studies Essential Question: Could Birch Bark bitings be used today as a source of economy?Science Essential Question: Do we have the natural resources today to support Birch Bark biting?Visual Arts Essential Question: Is there more than one way to create Birch Bark bitings?Inquiry Into: The mathematics within Birch Bark bitingAngles within 2-D shapes2-D shape transformationsThe history of Birch Bark biting and it’s connection to the economyThe process of creating Birch Bark biting and dyes for Birch Bark biting creations How Birch Bark biting influences/is influenced by Mi’kmaw cultureThe properties of the Birch trees and Birch barkIf the art of Birch Bark biting is relevant/present in today’s art culture or if it could be brought backThe geographic locations of Birch Bark bitings in Canada and why biting existed thereRationale for the Inquiry Project:While growing up, Josephine Peck’s mother would hand her a piece of birch bark and ask her what shapes she could bite into it. As a past time, Josephine would bite different shapes and designs into the bark and, when she could, would make dyes and use her birch bark bitings as stamps. To be able to bite shapes into the birch bark, Josephine was required to have an intrinsic understanding of the properties of shapes. For example, she knew that if the edges of the circle were not exactly equidistant from the centre, she would get a flower shape rather than a circle. With Birch Bark biting being a nearly lost art form, along with the Aboriginal cultural connections, learning about how to create Birch Bark bitings and the mathematical, scientific, social and artistic aspects behind these artworks may be very interesting and relevant to the students in your classroom. By addressing the essential questions (listed above) throughout the subjects, your students will be able to have a better understanding of the Mi’kmaw culture as well as the different cultural understandings and approaches to Science, Art and Mathematics.It is very important that this unit of study is completed with care and respect, drawing upon the knowledge of Elders who have completed Birch Bark bitings previously. Furthermore, the lessons should not be designed to implement Western European understandings on Aboriginal understandings, but should be focused on learning the understandings of the Aboriginal peoples through their culture and then find connections between the two cultural viewpoints. Students can also be required to research other cultural understandings as well. It is also highly suggested that students are required to look for bias in the texts that they read, so that misinformation does not lead to students having a skewed understanding of the Mi’kmaw culture and way of life. Each subject has its own individual essential question, which lead to the encompassing essential question, which will be answered through the completion of the RAFT Assessment Task. Within each subject, students can be required to complete mini projects to answer the question provided and show their understanding and engagement with the topic. The learning should be highly hands-on and student directed. There are times in which Teacher directed lessons (or follow up lessons) will be required, and some of these lessons are suggested later on in the Inquiry Unit Lesson Plan; however, students should be held responsible for the majority of the researching and finding answers to the questions posed throughout their study of Birch Bark biting.Below is a suggestion of the way to structure the subjects to answer the Essential Questions and support student learning.MathematicsBy having students participate in this tradition of birch bark biting, students will have the opportunity to engage with mathematics in a non-Western-European viewpoint. Students will be able to learn about shapes and the properties of shapes through discovering how to bite shapes into the bark, requiring them to not only create the shape but also imagine the shape and its features while biting the bark. The tactile properties of this activity may also prove beneficial for students. Students should be allowed to explore and experiment with different ways to bite shapes into the bark, allowing them to find what works, what does not work and why.By creating dyes, students can take their birch bark biting shapes and use them as stamps, allowing them to see how shapes are translated, rotated and/or reflected about a point. The students’ understandings of the properties of shapes can be further supported through teacher-directed lessons and other activities. Students should also be able to, after creating their birch bark biting, measure the angles and sides within their shapes and connect it to their understanding of how to bite the shapes into the birch bark (e.g., squares need to have four sides of equal lengths and equal internal angles). The sum of internal angles can also be seen and measured (either measuring each angle or by seeing the triangles created from the folds and finding the formula to measure the internal angles using the interior angles of the triangles).When creating their dyes, students can observe what the ratio is between the volume of water and plant matter to create the different colours. Students can record the ratios on a chart for the different colours and create a graph/table to represent these differences/similarities. Visual ArtsSince, traditionally, Birch Bark bitings were used like a stencil for the creation of designs on other items, these Birch Bark bitings lend themselves well to Visual Arts. Students should be given time to create designs through Birch Bark bitings and be allowed to use dyes (using the dyes created within the mathematics section) to make these designs into stamps. These can be extended into student-chosen artwork. Students should also research different cultural art forms (past and present) and find if there are other cultures that have art similar to Birch Bark biting. Students should also be allowed to spend time researching to see if there are other ways in which these Birch Bark biting designs could be created (different materials? different techniques?) Students can share their different techniques/styles with their class and discuss why they think it did or did not work.Within their research and experimentation with Birch Bark biting, students should also be required to research the history of Birch Bark biting within Canada or their region (in-person interviews, on-line research, books, etc.), who would be making these bitings, why and how they have evolved or if they have evolved.Students can present an artwork of their own that is based upon the Birch Bark bitings being discussed within the unit of study, showing their own techniques and use of the bitings. Social StudiesTo answer the Social Studies’ essential question, students should be required to research where Birch Bark biting existed, how Birch Bark biting has influenced the Mi’kmaw culture (or Aboriginal culture being studied) and Canadian culture. Students should be required to find out the purposes behind Birch Bark biting, whether it existed within only an artistic purpose, or if it also existed as an economic purpose as well. When students have an understanding of the value, purpose, and place of Birch Bark biting, students should be required to look at Birch Bark biting today, how it has been affected, and whether it still exists, or can exist again, as a cultural tradition and economic tool.ScienceStudents should be required to look at the Birch tree as well as the plants used for the dyes and analyze their features, determining why they exist within the areas they do, what features make them useful and how humans have affected (negatively or positively) the existence of plants in the specified area. Students should relate these plant features and availability to the requirements of Birch Bark biting to determine if Birch Bark biting is a sustainable activity. Students could also research to see if there are other plants in the region that have features that would be able to be used for Bark biting/dyes. Outcomes:MathematicsSP1: Create, label and interpret line graphs to draw conclusionsSP2: Select, justify and use appropriate methods of collecting data, includingQuestionnairesExperimentsDatabasesElectronic mediaSP3: Graph collected data and analyze the graph to solve problemsSS6: Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the imageSS7: Perform a combination of successive transformations of 2-D shapes to create a design and identify and describe the transformationsSS9: Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices)N5: Demonstrate an understanding of ratio, concretely, pictorially and symbolicallySS1: Demonstrate an understanding of angles by:Identifying examples of angles in the environmentClassifying angles according to their measureEstimating the measure of angles, using 450, 900, and 1800 as reference anglesDetermining angle measures in degreesSS2: Demonstrate that the sum of interior angles is:1800 in a triangle3600 in a quadrilateralSS4: Construct and compare triangles, including ScaleneIsoscelesEquilateralRightObtuseAcutein different orientationsSS5: Describe and compare the sides and angles of regular and irregular polygonsEnglish Language Arts1.1: Contribute thoughts, ideas and questions to discussions and compare their own ideas with those of peers and others1.3: Defend and/or support their opinions with evidence2.1: Contribute to and respond constructively in conversation, small-group and whole-group discussions3.2: Detect examples of prejudice, stereotyping or bias in oral language; recognize their negative effect on individuals and cultures; and attempt to use bias-free language5.1: Answer, with increasing independence, their own questions and those of others by selecting relevant information from a variety of textsDemonstrate understanding of the purpose of classification systems and basic reference materialsUse a range of reference texts and a database or an electronic search to facilitate the selection process7.4: Respond critically to texts by:Applying a growing range of strategies to analyze and evaluate a textDemonstrate growing awareness that all texts reflect a purpose and a perspectiveRecognizing when language is being used to manipulate, persuade or control themDetecting prejudice, stereotyping and bias Visual Arts1.2: Demonstrate ability and initiative in the use of techniques, technologies, materials and equipment3.1: Compare works of art across time and culture3.3: Use technology to locate and explore works of art4.1: Discuss ideas and approaches with sensitivity and respect4.4: Discover art as a way of expressing ideas5.3: Demonstrate an understanding of the lives of artists within cultural/historical/social contextsSocial Studies6.1.1: Explore the concept of culture and demonstrate an understanding of its role in their livesClassify elements of culture as material or non-materialInvestigate how cultures are transmitted from generation to generationIdentify factors that shape culture6.1.2: Identify, locate and map major cultural regions of the worldRecognize that there are various criteria for defining a cultural region, such as language, religion, location and place, shared traditions and history6.3.1: Examine how traditions relate to culture in a selected cultural regionDescribe how customs and rituals are reflected in the region’s cultureAnalyze how change factors affect cultural traditions6.3.3: Explain how economic systems relate to culturesIdentify different economic systemsExamine the differences among different economic systemsExplain how the economic programs and services of a country influence its cultureIdentify current economic trends that are influencing culture6.4.1: Analyze how the arts reflect beliefs and values in a selected cultural regionIdentify visual arts, crafts, dance and music practiced in the regionAnalyze how crafts and visual art reflect the beliefs and values of the culture6.6.1: Illustrate an understanding of how cultures from around the world have contributed to the development of Canada’s multicultural mosaicSciencePropose questions and gather information about the relationship among the structural features of plants and animals in their environments and identify the positive and negative impacts of humans on these resources (204-1, 108-8)Teacher-Directed / Follow-Up Lessons:MathematicsReview bar and double bar graphs and introduce the line graph and their attributesPurposes of different types of graphs and how to choose the appropriate graph for your dataHow to formulate a good question when collecting dataDiscrete vs. Continuous dataDifferent ways to collect dataHow to use databases to collect dataHow to read and understand different graphsCombining transformations (reflection followed by a translation, two translations, two reflections, a translation followed by a rotation, two rotations)How to plot points and perform transformations in a Cartesian planeRotations of shapes about a centre of rotation on a vertex, outside the shape and within the shapeHow ratios and percents can be represented by decimals and fractionsRatios as a comparison between two numbersEquivalent ratios and Equivalent fractionsMeasuring angles in degrees and using a protractor to measure anglesAngle names (right, straight, acute, obtuse, reflex)Benchmarks of 1800, 900 and 450Naming and identifying properties of different triangles (scalene, isosceles, equilateral, right, acute, obtuse)Review of polygons (regular, irregular)English Language ArtsHow to use sources within your writing/presentations (citations, using quotations to defend and support the opinion) How to read for bias/stereotyping/racismHow to use databases for researchHow to generate good questionsHow to respond to peers’ statements in a positively constructive mannerVisual ArtsHow to find works of art (databases, books, on-line museums)How to use techniques/technologies/toolsHow to agree/disagree with ideas appropriately and constructivelyHow to respond to and analyze artwork with respect to the artist and othersSocial StudiesWhat culture isDifference between material/non-material cultureHow to create maps, different types of maps (geographic, cultural, environmental, traditions, etc.)Different kinds of economy in existence; what is economy? Today’s Canadian Identity (multiculturalism—who is involved in this multicultural identity and why)ScienceHow to gather information to answer questions (research, experiments, etc.)How to create good questions, hypothesesHuman impacts on the earthHow plants/animals adapt to their environment (features of plants/animals)Skill Development:Organizational and Self-ManagementStudents will be expected to complete research tasks, research, the RAFT, and other tasks independently Students will be expected to complete activities by a pre-determined time and have check-up interviews with the teacherStudents will be required to do individual/small group research with minimal teacher supportStudents will need to create, organize, invite and run the RAFT Part 1 task as a class (can be broken into smaller presentation groups), with teacher support.Use competencies expected in high performance work organizations (e.g. Team work, problem solving, communications, decision making, project management)Students should be allowed time to discuss ideas and findings with each other in classStudents should be required to have their RAFT completed in stages with multiple due dates to keep them on track and provide feedback/support for problemsStudents will be required to complete the RAFT Part 2 individually and complete the research required to support their argumentSmaller projects can be completed in pairs/small groups or independentlyStudents should try to use different tactics for creating the birch bark biting in mathematics and artStudents should be allowed to explore different ways to mix water and plant matter for creating dyes without large teacher supportWhen completing RAFT part 1, students should be required to designate roles and responsibilities, keep notes as to what their plan will be, work as a group to solve problems, and keep a set of due dates to prepare and complete the task in stepsStudents should create and send invitations to the community to attend the Birch Bark biting workshopConduct research, share information, make decisions, solve problemsStudents should have experience in folding and biting Birch BarkStudents can brainstorm areas of interest in Birch Bark biting to research more in-depthStudents will choose their own method of presenting their RAFT part 2Students will answer their RAFT using research they have collected from books, interviews, online articles and their own personal opinions created through their learningUse technology in a purposeful mannerStudents can photograph their Birch Bark bitings to record the process of how to create a Birch Bark bitingStudents can use cameras/video cameras to film the process of making Birch Bark bitingsStudents can (with permission) record interviews with elders/expertsStudents can use technology in the production and/or presentation of their RAFTStudents can use the internet as a source of informationEngage in authentic investigations using a variety of media, methods and sourcesStudents will complete in-person interviews with individuals who have made Birch Bark bitingsStudents can research different individuals who make Birch Bark bitings and different folding techniquesStudents can search for videos (interviews) of elders who do Birch Bark bitingsStudents can write letters to elders regarding Birch Bark bitingsStudents can visit museums that have Birch Bark bitings in them and/or speak to archaeologists or experts on Birch Bark bitingsBe required to communicate what they are learning with a variety of audiencesStudents will be required to invite and teach members of their community how to create Birch Bark bitings.Students will be required to prepare a persuasive argument (written, oral, visual) and present it to their classPossible Areas or Questions:Where are there Birch trees in the area?How do you collect the birch bark?What designs/shapes are possible?How do you prepare the bark?When did Birch Bark biting start?Why were Birch Bark bitings made?Are there other art forms today that are like Birch Bark bitings?Is it possible to bring Birch Bark biting back?Are there other types of bark that you could use to create the bitings?How is Birch Bark biting a source of economy?Are there other cultures that do Birch Bark bitings?Is it environmentally possible to sustain/maintain Birch Bark biting?Possible Resources (people, web-based, books, other)An Elder within the community who has created or does create Birch Bark biting and/or dyesBirch Bark biting examples Videos of Birch Bark biting / Interviews about Birch Bark biting Mi’kmaq Culture and History links: Directions Teachings: (Canadian Museum of Civilization)Information on dyes and how dyes were made:Wallis, Wilson D., and Ruth Sawtell Wallis. “Shelter, Food, Clothing, Crafts.” The Micmac Indians of Eastern Canada. Minnesota, Minneapolis: University of Minnesota Press, 1955. 57-97. rmational on Birch Bark Biting:“Wigwas: Bark Biting.” Our Legacy: ka-ka-pe-isi-nakatamakawiyahk T’a bet’ a dene dahidli. Thunder Bay National Exhibition Centre, 1983. 1-21. Outcomes Possibly Achieved:Mathematics6N6: Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially and symbolically6N8: Demonstrate an understanding of multiplication and division of decimals (1-digit whole number multipliers and 1-digit natural divisor)6PR3: Represent generalizations arising from number relationships, using equations with letter variablesInformation and Communication Technology Integration 4-6BOC 6.2: Use and create information texts in a range of media, using specialized text features of those media to support the communication, with teacher assistanceSEHI 6.1: Share information resources, media equipment and computer equipmentSEHI 6.3: Begin to identify social and ethical issues associated with the global access and distribution of information; and to develop concern for the accuracy of information, personal privacy and safety when in electronic environments such as Internet, with the assistance of the teacherSEHI 6.4: Identify changes in the ways that information is collected, represented and transmitted and the impacts such changes have on individuals, communities and culturesSEHI 6.6: Identify and give specific examples where cultural values and experiences influence the information and entertainment products they usePTS 6.4: Conduct simple research, then plan and create a representation of their learning, such as a storyboard, a multimedia presentation, an audio recording, a web page or a print publication independently and in collaboration with othersRPSD 6.1: Locate relevant information by using the appropriate organizational features of and search strategies applicable to books, other print, audio CDs, videos, computer software, multimedia, online periodicals and the Internet, with some teacher assistanceRPSD 6.2: Use appropriate technological tools for concept mapping, problem solving, observation, measurement, calculation, graphing and charting to explore concepts under studyRPSD 6.3: Use research information to support arguments, with teacher supportRPSD 6.5: Acknowledge the sources of their information using simple citation formats, with independenceEnglish Language Arts1.2: Ask and respond to questions to seek clarification or explanation of ideas and concepts2.4: Engage in, respond to and evaluate a variety of oral presentations and other texts3.3: Make a conscious attempt to consider the needs and expectations of their audience4.1: Select, independently, texts appropriate to their range of interests and learning needs9.1: Create written and media texts using an increasing variety of formsDemonstrate understanding that particular forms require the use of specific features, structures and patterns9.2: Address the demands of an increasing variety of purposes and audiencesMake informed choices of form, style and content for specific audiences and purposes9.3: Invite responses to early drafts of their writing/media productionsUse audience reaction to help shape subsequent draftsReflect on their final drafts from a reader’s/viewer’s/listener’s point of view10.1: Select from a range of prewriting, drafting, revising, editing, proofreading and presentation strategies to develop effective pieces of writing and other representations10.2: Use the convention of written language in final products10.3: Use technology with increasing proficiency to create, revise, edit and publish texts10.5: Select, organize and combine relevant information, from three to five sourcesVisual Arts1.1: Express through art making an awareness of the complexities of the world and their role in it1.3: Use a combination of visual elements and principles of art and design in art making2.1: Work independently and collaboratively to apply learned skills, solve problems, and respond to experiences and ideas3.2: Demonstrate an awareness of artists’ styles, intentions and approaches4.2: Show appreciation of individual differences in artwork6.2: Examine the role of the media and discuss their effects on their lives and the lives of othersUnits Included:Mathematics:Unit 4: Data RelationshipsUnit 5: Motion GeometryUnit 6: Ratio and PercentUnit 9: MeasurementUnit 10: 2-D GeometryScience:Life Science: Diversity of LifeAdaptations and Natural SelectionSocial Studies:Unit 1: An Introduction to CultureUnit 3: Some Elements of CultureUnit 4: Expressions of CultureUnit 6: Canada: Reflections on a Multicultural MosaicRAFT Assessment TaskPart 1:Your community has decided that Birch Bark biting will be a good way of bringing tourists to the community, as it is culturally and historically unique. However, the community members do not know how to create these Birch Bark bitings. You have been asked to design and run a workshop to teach the community how to make Birch Bark bitings.Part 2:The Community Chief and Council are still unsure of using Birch Bark biting as a tourist attraction. You have been asked to create a persuasive argument explaining to the Chief and Council why Birch Bark biting is a viable tourist attraction, why it will be beneficial to the economy and how it can be sustained by the local environment.Birch Bark Biting Grade 6Mathematics Teacher-Directed LessonsWhich Month to Ski?Grade 6Teacher’s NotesLesson SummaryIn this activity, students will summarize data information and create and describe a double bar graph depicting the data they were given/researched. This activity comes from National Council of Teachers of Mathematics’ (2007) Navigating through Problem Solving and Reasoning in Grade 5. This activity can be used as a refresher activity to double bar graphs, which were discussed in Grade 5.Connection to the Inquiry ProjectWithin the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students will also be responsible for recording and making a chart/graph depicting the different ratios of plant materials to volume of water that create the different colours of dye. By engaging in activities that promote students’ understandings of how to create and read graphs, students will be able to create, read and understand graphs depicting the similarities and differences between traditional dyes.Outcomes AddressedPR1: Demonstrate an understanding of the relationships within tables of values to solve problemsSP3: Graph collected data and analyze the graph to solve problemsCan students describe, using everyday language, orally or in writing, the relationship shown on a graphLessonTeachers can use the activity “Which Month to Ski?” from National Council of Teachers of Mathematics’ Navigating through Problem Solving in Grades 5 to support students’ learning and understanding of creating and interpreting double bar graphs and the data used to create double bar graphs.Students can be given the resources within the Blackline Masters in the Navigating through Problem Solving and Reasoning in Grade 5, or students can be given/research an area of interest that has data that can be translated into a double bar graph. Students, in small groups and with large group support, will read and analyze the information and find ways to represent the information in double bar graphs.Throughout this activity, students will need to have discussions as a whole group and with teacher support as to how to interpret and organize data to form a double bar graph.Following the students’ creation of the double bar graphs, they can then use the information to answer the given question (either created or taken from Navigating through Problem Solving and Reasoning in Grade 5). This activity can be completed prior to learning about line graphs, to ensure that students understand the other graphs and their meanings from the previous grades before moving on to more types of graphs.AssessmentCan students determine an appropriate type of graph for displaying a set of collected data and justify the choice of the graph?Can students describe, using everyday language, orally or in writing, the relationship shown on a graph?Can students interpret a given graph to draw conclusions?Can students state, using mathematical language, the relationship in a given table of values?UnitsThis activity can be used in the following unit:Unit 3: Patterns in MathematicsUnit 4: Data RelationshipsCarina’s Pet ShopGrade 6Teacher’s NotesLesson SummaryThis activity is from National Council of Teachers Mathematics’ (2007) Navigating through Problem Solving and Reasoning in Grade 5.Connection to the Inquiry ProjectWithin the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students will also be responsible for recording and making a chart/graph depicting the different ratios of plant materials to volume of water that create the different colours of dye. By engaging in activities that promote students’ understandings of how to create and read graphs, students will be able to create, read and understand graphs depicting the similarities and differences between traditional dyes.Outcomes AddressedN2: Solve problems involving whole numbers and decimal numbersPR1: Demonstrate an understanding of the relationships within tables of values to solve problemsPR3: Represent generalizations arising from number relationships, using equations with letter variablesSP1: Create, label and interpret line graphs to draw conclusionsSP3: Graph collected data and analyze the graph to solve problemsSS8: Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairsPR2: Represent and describe patterns and relationships using graphs and tablesLessonTeachers can use the activity “Carina’s Pet Shop” from National Council of Teachers of Mathematics’ (2007) Navigating through Problem Solving and Reasoning in Grade 5 to support students’ learning and understanding of representing data and understanding how to construct and understand graphs as well as rate of change.In this activity, the students are given a situation in which Carina has a projected and actual sales outcome from her pet store. This activity is designed for students to discuss the rate of change of the data (however this can be removed from the activity), as well as for the students to take the data from the story and create graphs to determine what Carina’s projected animal sales will be.This activity can be a starting point to discussing which type of graph Carina should be using—bar graph or line graph or another graph and why. Students can also discuss whether the data is continuous or discrete and how they know. Students can then work in small groups to create the graphs representing Carina’s actual sales and then work together to determine her projected sales. Students should have the opportunity to share their graphs and determined projected sales with the class as well as explain how they came to their findings. This activity also offers some extension questions based upon hypothetical sales with new animals and answer simple algebraic questions based upon the sale number relationships.AssessmentCan students identify which operation is necessary to solve a given problem and solve it?Can students state, using mathematical language, the relationship in a given table of values?Can students predict the value of an unknown term, using the relationship in a table of values, and verify the prediction?Can students represent a pattern rule using a simple mathematical expression, such as 4d or 2n + 1?Can students determine the common attributes (title, axes and intervals) of a line graph?Can students determine whether a given set of data can be represented by a line graph (continuous data) or a series of points (discrete data) and explain why?Can students create a line graph from a given table of values or a given set of data?Can students interpret a given line graph to draw conclusions?Can students determine an appropriate type of graph for displaying a set of collected data and justify the choice of the graph?Can students label the axes of the first quadrants of a Cartesian plane and identify the origin?Can students plot a point in the first quadrant of a Cartesian plane, given its ordered pair?Can students describe, using everyday language, orally or in writing, the relationship shown on a graphUnitsThis activity can be used in the following unit:Unit 3: Patterns in MathematicsUnit 4: Data RelationshipsFractions with a PointGrade 6Teacher’s NotesLesson SummaryStudents will be introduced to writing fractions in decimal form through the use of Decimal Grids-Tenths, Parallel Number Lines, and Decimal Grids-Hundredths. Students will also learn how to write fractions and decimals as percents. This activity may be best used over multiple lessons. This lesson is from National Council of Teachers of Mathematics’ (2007) Navigating through Number and Operations in Grades 3-5. Connection to the Inquiry ProjectThe understanding of decimals and fractions, as well as how to perform operations on decimals and fractions, will assist students in the Science component of the Inquiry project. When creating dyes, students will be using their understanding of fractions and decimals to indicate the amount of water/plant material used to create the dye colour. Their understanding of fractions and decimals will also assist students when they begin working with ratios and comparing the ratio of water to plant material when making dyes.Outcomes AddressedN6: Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially and symbolicallyN4: Relate improper fractions to mixed numbers and mixed numbers to fractionsLessonTeachers can use the activity “Fractions with a Point” from National Council of Teachers of Mathematics’ Navigating through Number and Operations in Grades 3-5 to support students’ learning of converting fractions to decimals and decimals to fractions. Students can also be required to convert improper fractions to mixed fractions and vice versa in this activity, as the activity only requires students to change fractions to decimals and percents and vice versa.This lesson is one that should be completed as a whole class activity. Students will use the decimal grids-tenths, parallel number lines, decimal grids-hundredths, and charts to find the value of fractions, decimals and percents as well as understand the relationship between fractions, decimals and percents. Students can complete sections individually or in small groups, however a discussion with the whole class should be had to address any misunderstandings or questions and to extend the class’ understanding of fractions and decimals.Students should be given plenty of opportunity to practice converting decimals to fractions and/or percents and vice versa. It would also be beneficial for students to be able to practice converting these fractions/decimals/percents using a real-life problem. Students can also be given manipulatives, such as base ten blocks, to support their understanding of decimals, fractions and percents and how they are related to each other.AssessmentCan students explain that “percent” means “out of 100”?Can students use concrete materials and pictorial representations to illustrate a given percent?Can students express a given percent as a fraction and a decimal?Can students demonstrate, using models, that a given improper fraction represents a number greater than 1?Can students translate a given improper fraction or mixed number between concrete, pictorial and symbolic forms?Can students express improper fractions as mixed numbers and mixed numbers as improper fractions?Can students place a given set of fractions, including mixed numbers and improper fractions, on a number line and explain strategies used to determine position?UnitsThis activity can be used in the following unit:Unit 6: Ratio and PercentUnit 7: FractionsGoing for GoldGrade 6Teacher’s NotesLesson SummaryIn this activity, students will look at a set of data given in a table and see if there are other ways the data can be organized. Students can use different types of graphs to graph the data as well and discuss the effects of the graphs on the data. This activity is from nrich..Connection to the Inquiry ProjectWithin the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students will also be responsible for recording and making a chart/graph depicting the different ratios of plant materials to volume of water that create the different colours of dye. By engaging in activities that promote students’ understandings of how to create and read graphs, students will be able to create, read and understand graphs depicting the similarities and differences between traditional dyes.Outcomes AddressedSP3: Graph collected data and analyze the graph to solve problemsPR2: Represent and describe the relationships using graphs and tablesSP1: Create, label and interpret line graphs to draw conclusionsLessonThis activity can be accessed from . The Nrich teacher notes can be accessed from and a printable worksheet can be accessed from . An article on the math of medals in the Olympics can be found at: . The teacher can use this activity to support students’ understanding of how to create graphs, read data, and determine which graph accurately portrays the information in the table. Student discussion and involvement (either whole group and/or small group work can be used) should be included throughout the activity.Students can look at the data and arrange the data in different types of graphs and discuss the ways that the different types of graphs affect the data and how we would read the data. Students can also find the value of the medals (51 gold medals x 3 points/medal + 21 medals x 2 points/medal + 28 medals x 1 point/medal = 153 + 42 + 28 = 223 points, etc.) and then graph the results and see if there is a difference between the ranking of the countries.If desired, students can extend their understanding of graphs, using the medals from Olympics, and be required to compare the countries’ rankings over a given number of years and then explain the graph they chose to represent this data and why and explain what the graphs are saying.AssessmentCan students determine an appropriate type of graph for displaying a set of collected data and justify the choice of graph?Can students solve a given problem by graphing data and interpreting the resulting graph?Can students describe, using everyday language, orally or in writing, the relationship shown on a graph?Can students determine whether a given set of data can be represented by a line graph (continuous data) or a series of points (discrete data) and explain why?UnitsThis activity can be used in the following unit:Unit 4: Data RelationshipsReal StatisticsGrade 6Teacher’s NotesLesson SummaryStudents will compare a given data set with their own data set collected through a school questionnaire. Students will also be required to use their understanding of percents to read the data and the subsequent graphs that they make. This activity is from nrich..Connection to the Inquiry ProjectWithin the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students will also be responsible for recording and making a chart/graph depicting the different ratios of plant materials to volume of water that create the different colours of dye. By engaging in activities that promote students’ understandings of how to create and read graphs, students will be able to create, read and understand graphs depicting the similarities and differences between traditional dyes. Students’ understandings of ratios, percents, decimals and fractions will be helpful in determining the quantity of water/plant materials as well as determining the ratio between plant material and water.Outcomes AddressedSP2: Select, justify and use appropriate methods of collecting data, including:QuestionnairesSP3: Graph collected data and analyze the graph to solve problemsPR2: Represent and describe patterns and relationships, using graphs and tablesN6: Demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially and symbolicallyLessonThis activity can be accessed from . The Nrich teacher notes can be accessed from and a printable worksheet can be accessed from . *Note: Students in Grade 6 are limited to working with whole number percents, therefore the graph on Nrich should be altered so that the percents are whole numbers or, in the least, easily translated into a proper fraction.If you would like your students to conduct research on different types of questions and/or would like to draw some data from to analyze and/or compare, you can visit: (United Kingdom) or (Canada)Students, in this activity, can look at the data presented on the Nrich site and gather the same data from their own school and graph and compare the data. Students should be sure to create their data based upon percentages (but can also change the percentages into decimals and/or fractions). Students can then present their graphs to the class and discuss their findings and/or can be put up for the school to see.Students can also be required to look at the data and graph the data in multiple ways (e.g., numbers of boys vs. girls, ways students get to school in different seasons, ages/grades of the students etc.) and then the students can present the different graphs to the class and can discuss them, including the differences and similarities and what the graphs are representing.AssessmentCan students design and administer a questionnaire for collecting data to answer a given question and record the results?Can students determine an appropriate type of graph for displaying a set of collected data and justify the choice of graph?Can students solve a given problem by graphing data and interpreting the resulting graph?Can students describe, using everyday language, orally or in writing, the relationship shown on a graph?Can students explain that “percent” means “out of 100”?Can students explain that a percent is a ratio out of 100?Can students express a given percent as a fraction and a decimal?UnitsThis activity can be used in the following unit:Unit 4: Data RelationshipsUnit 6: Ratio and PercentWhat Are You Plotting? / Two Number LinesGrade 6Teacher’s NotesLesson SummaryStudents will be introduced to plotting points on the first quadrant of a Cartesian plane. This activity is from nrich..Connections to the Inquiry ProjectThis activity introduces students to the beginning processes of learning how to plot shapes onto Cartesian planes, so as to support students’ abilities to work with 2-D shapes. When students plot and transform 2-D shapes on a Cartesian plane, students can see the distance and change of the shape. This is connected to the transformations that occur when students bite shapes/patterns into birch bark. When creating birch bark bitings, students must visualize the shapes that they are biting and understand the types of lines that they want to bite, as well as the end shape they desire to have. Understanding the properties of shapes, the ways that shapes transform, as well as the sides of 2-D shapes, will assist them in visualizing how to bite the shapes.Outcomes AddressedSS8: Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairsLessonThe “What Are You Plotting?” activity can be accessed from . The Nrich printable sheet can be accessed from “Two Number Lines” activity can be accessed from . The Nrich teacher notes can be accessed from and a printable page can be accessed from . These activities should not take too much time and can be used as mini lessons/introduction to plotting ordered pairs on a Cartesian plane.The students and teacher should have a copy of either the grid on the Nrich site or a basic copy of the first quadrant of a Cartesian plane. The teacher’s copy should be shown/projected so that all the students can see the plane and follow along from their seats. As a whole class, the different coordinates can be found and discussed. It should be made clear that when graphing points on a Cartesian plane, the coordinates are listed (x, y) axes rather than (y, x). The class can then discuss their findings.Following this activity, “The Two Number Lines” activity can be introduced, in which students must identify what the coordinates are of the plotted dots and then answer the question of what the coordinates would be if Max and Mandy moved the same distance. Students can be given time to do this individually and then should return to the whole class to discuss their findings.AssessmentCan students label the axes of the first quadrants of a Cartesian plane and identify the origin?Can students plot a point in the first quadrant of a Cartesian plane, given its ordered pair?Can students match points in the first quadrant of a Cartesian plane with their corresponding ordered pair?UnitsThis activity can be used in the following unit:Unit 4: Data RelationshipsPatterns ActivityGrade 6Teacher’s NotesLesson SummaryStudents will solve problems from tables, solve word sketch problems, extend a pattern, and complete a table and graph of their data.Connection to the Inquiry ProjectWithin the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students will also be responsible for recording and making a chart/graph depicting the different ratios of plant materials to volume of water that create the different colours of dye. By engaging in activities that promote students’ understandings of how to create and read graphs, students will be able to create, read and understand graphs depicting the similarities and differences between traditional dyes.Outcomes Addressed6PR1 demonstrate an understanding of the relationships within tables of values to solve problems6PR2 represent and describe patterns and relationships using graphs and tablesLessonThere are three parts to this lesson. The lesson can be done as a learning stations activity or can be worked on one activity at a time. The three parts to the activity will be described separately so as to be used as individual tasks or learning stations.Problems From TablesStudents will need graph paper, loose leaf, and a box of problem cards for this activity/station. Each problem card will have a picture, a table of values, and a question. Students will choose a card from the box and answer the question on the loose leaf and graph paper provided. They must include a graph and show all their work. If this is a learning station, students should do at least three of these questions before moving on to another station. If this activity is being used as an independent lesson, students can work on more than just three problems. If an overhead projector and/or Mimio or Smart Board technology is available (or even just a regular white board), some students could be the teacher and work through their problem on the board, explaining their steps as they go along. This can be beneficial for many reasons (students are excited to write on the board, they gain confidence from being at the head of the class – even if they are not the smartest student there, the other students get to hear the explanations from a students’ perspectives, etc.). Pattern Block Puzzles!For this activity, students will require pattern blocks (in a box) and the Pattern Block Puzzles! worksheet to record their data.Students will choose any pattern block out of the box and gather several of the same shape (and colour) blocks. With these pattern blocks, students will create a train by connecting the pattern blocks together, aligning them like a train with only one side touching (see the example below). Each student’s train is expected to be at least 6 units (or shapes) long.171450012763500Ex.Once the train is assembled, students will complete the table on their worksheet that compares the number of units to the perimeter of the whole train. Then, they will sketch a graph of their data from the table of values. Students will also write an equation to describe the data they have graphed.[Students should be encouraged to answer the bubble questions on the worksheet. They can either provide a written answer on their sheet or discuss verbally their answers with a neighbor.]Where Do We Meet?A box containing a series of cards with questions (included with the student worksheet) and graph paper are needed for this lesson.Students choose a card out of the box and create a table of values to go with each option the problem on the card (i.e. each cell phone company, each person, each of the two things being compared). They will graph the data from their table of values on one grid (they’ll have two lines) and completely label their graph. Students are also asked to explain how they went about solving the problem. They can write these explanations to be submitted to the teacher for assessment or discuss their strategies with their group members (depends on the desires of the teacher).AssessmentStudents should be able to:generate values in one column of a table of values if given values in the other column and a pattern ruleFormulate a rule to describe the relationship between two columns of numbers in a table of valuesstate, using mathematical language, the relationship in a given table of valuescreate a concrete or pictorial representation of the relationship shown in a table of valuespredict the value of an unknown term using the relationship in a table of values and verify the predictiondescribe the pattern within each column of a given table of valuescreate a table of values to record and reveal a pattern to solve a given problemtranslate a pattern to a table of values and graph the table of values strictly linear graphs with discrete elementsdescribe, using everyday language, orally or in writing, the relationship shown on a graphUnitsThis lesson could be used in: Unit 3: Patterns in MathematicsUnit 4: Data Relationships in grade 4.422910071882000Choose a card from the box. Solve the problem on the card on a sheet of loose leaf or graph paper. Show all work. Repeat the activity with at least two other cards.Time in minutesNumber of stairs climbed00515103015452060388620091440000How many stairs can you climb in 60 minutes?How much will it cost for 125 hats?320040027368500Number of Hats OrderedCost015.001035.002055.003075.004095.00How much will it cost to travel 65 km by taxi?-22860080835500Distance traveled (km)Cost02.50105.50208.503011.504014.50How far will she run in 30 seconds?400050022987000Time in secondsDistance run in meters0013.226.439.6412.8How much will it cost for 70 minutes of long distance calling?Time calling long distance in minutesCost05.0056.25107.50158.752010.00491490084518500468630012954000How much will it cost for a 7 hour job?Time in hoursCost for the electrician025.00157.50290.003122.504155.00How much will it cost to have a party for 150 people?400050015938500Number of guests at the partyCost for Catering0125.0020275.0040425.0060575.0080725.00Pattern Block Puzzles!Choose a pattern block from the box. Use the pattern block to make a train by connecting them together touching one side only. Find the perimeter of each train. Make a sketch of your pattern below to show which pattern you used. Extend it for at least 6 units.22860015240000377190048895What is the difference between each y value?00What is the difference between each y value?plete the table of values below.Number of UnitsxPerimetery123456789104572000-114300Do you see the difference from the table in the graph? Where is it?00Do you see the difference from the table in the graph? Where is it?Sketch a graph of your data.Write an equation to describe your pattern.For each of the problems in the box you will need to create a table of values for each option. You will then need to sketch a graph of each line and determine where the two lines intersect to solve the problems.Be sure to show both graphs on the same grid. 480060011684000Accurately label your graphs.Give clear explanations as to how you solved the plete at least three of the problems from the box on graph paper.-19050-5715000Katie can run 8 m/s and Kelli can run 5 m/s. They are competing in a 500 m race so Katie tells Kelli she can have a 50 m head start. When will Katie pass Kelli? How do you know?5143500110744000One cell phone company charges a $10 base fee plus $0.15 per minute. Another company charges no base fee and $0.25 per minute. For what number of minutes will these plans give the same cost? Explain how you know.3429000102870000A new gym opens up and offers two different membership options. One option is to pay a $20 base fee plus $2 per visit. The other option is to pay no base fee, and $3 per visit. For what number of visits would both options cost the same?Kate and Tim have a small business building decorative clocks. Tim can build 3 clocks in an hour. He already has 5 built. Kate can build 4 clocks in an hour. She already has 3 built. How long will it be before they have both built the same number of clocks?5257800-352425004800600101663500One phone company charges a $15 base fee plus $0.10 per minute for long distance. Another company charges no base fee and $0.35 per minute for long distance. For what number of minutes will these plans give the same cost? Explain how you know.3543300151955500A Video store offers two membership options. The first membership offer charges a base fee of $25.00 and only $1.50 for each movie rental. The second option charges a base fee of $10.00 and $3.50 for each movie rental. For what number of movie rentals will both plans cost the same?Exploring Lines, Midpoints and Triangles Using Coordinate GeometryGrades 6Teacher’s NotesLesson SummaryThis activity is from National Council of Teachers of Mathematics’ (2002) Navigating through Geometry in Grades 6-8. In this activity, students will explore lines, midpoints and triangles on the first quadrant of a Cartesian plane.Connections to the Inquiry ProjectWhen students plot and transform 2-D shapes on a Cartesian plane, students can see the distance and change of the shape. This is connected to the transformations that occur when students bite shapes/patterns into birch bark. When creating birch bark bitings, students must visualize the shapes that they are biting and understand the types of lines that they want to bite, as well as the end shape they desire to have. Understanding the properties of shapes, the ways that shapes transform, as well as the sides of 2-D shapes, will assist them in visualizing how to bite the shapes.Outcomes AddressedSS8: Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairsSS4: Construct and compare triangles, includingScaleneIsoscelesEquilateralRightObtuseAcutein different orientations LessonIn this activity, from National Council of Teachers of Mathematics’ (2002) Navigating through Geometry in Grades 6-8, students will be able to become better familiar with plotting points on a Cartesian grid as well as determine the distance between two points vertically and horizontally. Furthermore, students will be able to compare and contrast triangles with the aid of the Cartesian plane.This activity can be used multiple times throughout the year, having students focus on plotting points and determining distance between the points first and then, later, using these skills to plot and draw different triangles and compare and contrast them to further understand the properties of the triangles.The activities that can be done with this lesson can be whole group activities, having the teacher present one quarter of the Cartesian grid to the students and draw a line segment on the grid and have the students (with help if required) to determine what the coordinates are, as well as what the distance is between the two points. The teacher can also give students the coordinates of the line segments and have them draw the line segments and determine the distance between the two points. When looking at triangles, the teacher can give the students the coordinates of the vertices of the triangle and then have students draw the triangles using these coordinates. Students can look at multiple triangles on the same grid and make observations about the similarities and differences between the triangles.The National Council of Teachers of Mathematics’ (2002) Navigating through Geometry in Grades 6-8 provides other ways of using and presenting this activity to students as well.AssessmentCan students label the axes of the first quadrant of a Cartesian plane and identify the origin?Can students plot a point in the first quadrant of a Cartesian plane, given its ordered pair?Can students match points in the first quadrant of a Cartesian plane with their corresponding ordered pair?Can students draw shapes or designs, given ordered pairs, in the first quadrant of a Cartesian plane?Can students determine the distance between points along horizontal and vertical lines in the first quadrant of a Cartesian plane?Can students draw shapes or designs in the first quadrant of a Cartesian plane and identify the points used to produce them?Can students identify the characteristics of a given set of triangles according to their sides and/or their interior angles?Can students draw a specified triangle, e.g., scalene?Can students replicate a given triangle in a different orientation and show that the two are congruent?UnitsThis activity can be used in the following units: Unit 4: Data RelationshipsUnit 10: 2-D GeometryDoughnut PercentsGrade 6Teacher’s NotesLesson SummaryStudents will practice changing fractions to decimals/percentages, decimals to fractions/percents and/or percents to decimals/fractions by playing a game involving dominoes with percents, decimals or fractions written on them. Students must have the ends of the dominoes touching another domino piece with an equivalent number value. This activity is from nrich..Connection to the Inquiry ProjectWithin the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students’ understandings of ratios, percents, decimals and fractions will be helpful in determining the quantity of water/plant materials as well as determining the ratio between plant material and water.Outcomes AddressedN6: Demonstrate an understanding of percent (limited to whole numbers) symbolicallyN4: Relate improper fractions to mixed numbersLessonThis activity can be accessed from . The Nrich teacher notes can be accessed from and the printable sheet can be accessed from . The printable (and editable) domino cards can be found on the activity site.*Note: The Nrich site’s domino cards have percents and fractions that are explored in Grades above Grade 6. Ensure that the percents, fractions and decimals used in this game are appropriate for the developmental level of your class.Students will practice changing fractions to decimals/percentages, decimals to fractions/percents and/or percents to decimals/fractions by playing a game involving dominoes with percents, decimals or fractions written on them. Students must have the ends of the dominoes touching another domino piece with an equivalent number value. The Nrich activity says that students should complete this activity in silence, however students (especially when beginning understanding percents and their relationship to decimals and fractions) can be encouraged to discuss how to solve the problem. This activity can also be done as a whole group/small group activity, in which the teacher can review with the students how to determine the percent from a fraction/decimal (and so on) and then work with the students to solve one of the games together. Students can also work in small groups to solve the problem and then return to the whole class to discuss the answer.Students can also be required, following playing and understanding the game, to create their own domino pieces and play them with their peers. AssessmentCan students explain that “percent” means “out of 100?”Can students identify a given percent as a fraction and a decimal?Can students translate a given improper fraction between symbolic forms?Can students identify improper fractions as mixed numbers and mixed numbers as improper fractions?Can students translate a given mixed number between symbolic forms?UnitsThis activity can be used in the following unit:Unit 6: Ratio and PercentUnit 7: FractionsNutty MixtureGrades 6Teacher’s NotesLesson SummaryThis activity is from nrich.. Students are given a word problem and are required to define the different ratios of nuts in a bag.Connection to the Inquiry ProjectWithin the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students’ understandings of ratios, percents, decimals and fractions will be helpful in determining the quantity of water/plant materials as well as determining the ratio between plant material and water.Outcomes Addressed6N5: Demonstrate an understanding of ratio, concretely, pictorially and symbolicallyLessonFind the teacher notes for this activity at can complete this activity individually or in small groups. Students may be allowed to use manipulatives or drawings to determine the ratio of the nuts. Each student should receive the worksheet or the worksheet can be displayed to the entire class.This activity can also be designed as a centre. The centre should have at least one copy of the worksheet available, as well as manipulatives and paper available for students to build or draw models. AssessmentCan students write a ratio from a given concrete or pictorial representation?Can students express a given ratio in multiple forms, such as 3:5 or 3 to 5?Can students explain the part/whole and part/part ratios of a set?Can students solve a given problem involving ratios?UnitsThis activity can be used in the following unit: Unit 6: Ratio and PercentRod RatiosGrades 6Teacher’s NotesLesson SummaryThis activity is from nrich.. Students use Cuisenaire rods to determine different ratios between the rods.Connection to the Inquiry ProjectWithin the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students’ understandings of ratios, percents, decimals and fractions will be helpful in determining the quantity of water/plant materials as well as determining the ratio between plant material and water.Outcomes Addressed6N5: Demonstrate an understanding of ratio, concretely, pictorially and symbolicallyLessonFind the teacher notes for this activity at activity on the website above provides a good interactive tool for completing this activity as a whole class. It would be beneficial to provide the students with Cuisenaire rods to perform this activity with. If you do not have Cuisenaire rods, or enough Cuisenaire rods, you can print them off here: for the .doc file, go to “Make Your Own Cuisenaire Rods” at this site: can complete the different questions individually or in small groups and then return to the class to discuss their findings.AssessmentCan students write a ratio from a given concrete or pictorial representation?Can students express a given ratio in multiple forms, such as 3:5 or 3 to 5?Can students explain the part/whole and part/part ratios of a set?Can students solve a given problem involving ratios?UnitsThis activity can be used in the following units: Unit 6: Ratio and PercentAm I Unique?Grade 6Teacher’s NotesLesson SummaryStudents will complete this activity in pairs or small groups. Each student will draw a triangle and measure the sides and angles of the triangle. The partner, using three hints about the angles/sides, will try to draw the same triangle. Students will then decide if the triangle is unique or not.Connection to the Inquiry ProjectBirch bark biting, and having students bite shapes into the material, requires students to use their intrinsic understanding of the shapes. However, students, through learning about measurement and triangle geometry will strengthen their understandings of the properties of triangles and be able to prove that the shapes that they are biting, and that other artists have bitten, are triangles. Understanding the mathematical components of shapes through these more direct instructions may also prove helpful for students when they are visualizing the shapes that they bite.Outcomes Addressed6SS1: Demonstrate an understanding of angles by:Identifying examples of angles in the environmentClassifying angles according to their measureEstimating the measure of angles, using 450, 900 and 1800 as reference anglesDetermining angle measures in degreesDrawing and labeling angles when the measure is specified 6SS2: Demonstrate that the sum of interior angles is:1800 in a triangle3600 in a quadrilateral6SS3: Develop and apply a formula for determining the:Perimeter of polygonsArea of rectanglesVolume of right rectangular prisms6SS4: Construct and compare triangles, including:ScaleneIsoscelesEquilateralRightObtuseAcutein different orientations.6SS5: Describe and compare the sides and angles of regular and irregular polygonsLessonThis activity can be completed at the beginning and/or during the unit. If being completed at the beginning of the unit, students can begin to notice different types of triangles and then, throughout the unit, be able to put names to these triangles they created. This activity can be completed again later on to see if students are able to better understand how to find unique triangles and/or to further compare different triangles.Small Group Activity:Divide students into groups and give each student or each group the Am I Unique? sheet. Each student should also have a blank piece of paper as well as a ruler and a protractor. Each student will draw a triangle on the paper and measure the sides and angles. The partners will ask each other for three pieces of information only and then will try to draw each others’ triangle. If the student draws a congruent triangle, then they should consider whether this was the only possible triangle that could have been created. If so we will say this information generated a unique triangle. If the student does not draw a congruent triangle to their partner’s, discuss why.Once students have completed a few different triangles and have found some unique and not unique triangles, students should determine which three pieces of information will result in a unique triangle. Students can explain their findings in writing or the class can gather together to discuss the different findings in the different groups.Centre Activity:Place a copy of the Am I Unique? sheets at the table or centre area (enough for each group). Have students complete the activity and see if they can find the three pieces of information that will result in a unique triangle. AssessmentsCan students explain, using models, that the sum of the interior angles of a triangle is the same for all triangles?Can students explain, using models, how the perimeter of any polygon can be determined?Can students generalize a rule (formula) for determining the perimeter of polygons?Can students solve a given problem involving the perimeter of polygons?Can students identify the characteristics of a given set of triangles according to their sides and/or their interior angles?Can students estimate the measure of an angle, using 450, 900 and 1800 as reference angles?Can students measure, using a protractor, given angles in various orientations?Can students draw and label a specified angle in various orientations, using a protractor?Can students draw and label a specified angle in various orientations, using a protractor?Can students draw a specified triangle, e.g., scalene?Can students replicate a given triangle in a different orientation and show that the two are congruent?Can students demonstrate that the sides of a given regular polygon are of the same length and that the angles of a regular polygon are of the same measure?Can students demonstrate congruence (sides to sides and angles to angles) in a regular polygon by superimposing?UnitsThis activity can be used in the following units:Unit 9: MeasurementUnit 10: 2D GeometryAm I Unique?In any triangle we can measure 3 sides (a, b, c) and 3 angles (∠A, ∠B, ∠C). For this task you will need a partner. Both you and your partner will draw a triangle and measure all 6 components without showing the other person. Your partner may now ask you for three pieces of information only and try to draw your triangle. You should also ask for three pieces of information about your partner’s triangle and see if you can draw that triangle. If using only these pieces of information, you made a congruent triangle then you will consider whether this was the only possible triangle you could have created. If so we will say this information generated a unique triangle. If you did not draw a congruent triangle to your partner’s, discuss why. We will say these pieces of information did not generate a unique triangle. Record your discoveries in the table below.Side aSide bSide c∠A∠B∠CUniqueNot UniqueWhich 3 pieces of information will result in a unique triangle? Explain your discoveries.Using Venn Diagrams to Reason about ShapesGrade 6Teacher NotesLesson SummaryIn this activity, students will organize different types of triangles using a Venn diagram. Students will be required to look at the properties of the different triangles to justify where they place them. This activity comes from National Council of Teachers of Mathematics’ (2002) Navigating through Geometry in Grades 6-8.Connection to the Inquiry ProjectWhen creating birch bark bitings, students must visualize the shapes that they are biting and understand the types of lines and angles that they want to bite, as well as the end shape they desire to have. Understanding the properties of shapes will assist them in visualizing how to bite the shapes.Students can also be required to bite their shapes (students can be posed the question “Can you bite a shape? Now bite a shape that is completely different”) and can organize their bitten shapes, looking at the results of their biting. Students will gain an understanding of the angles and differences of shapes visually and tactilely, which will support their understandings of geometry and measurement.Outcomes AddressedSS1: Demonstrate an understanding of angles by:Classifying angles according to their measureDetermining angle measures in degreesSS4: Construct and compare triangles, including:ScaleneIsoscelesEquilateralRightObtuseAcutein different orientations.Lesson“Using Venn Diagrams to Reason about Shapes” is taken from National Council of Teachers of Mathematics’ Navigating through Geometry in Grades 6-8. In this activity, students will sort triangles into different categories, taking into account the properties of the different triangles. Students should be able to justify their reasons for sorting the triangles in the ways they do. This activity can be completed as a whole group / small group activity when comparing the different triangles. Students can measure the sides and angles of the triangles and organize them into different groupings. Students can present their groupings to their class and discuss why these groupings may or may not work. Students can also be required to sort as a whole class with the teacher supporting and/or initiating questions for students to consider. Student volunteers can suggest where to categorize the triangles and give a supporting reason why (students can be in small groups).AssessmentsCan students identify the characteristics of a given set of triangles according to their sides and/or their interior angles?Can students sort a given set of triangles and explain the sorting rules?Can students measure, using a protractor, given angles in various orientations?Can students classify a given set of angles according to their measure; e.g., acute, right, obtuse, straight, reflex?UnitsThis activity can be used in the following units:Unit 9: MeasurementUnit 10: 2-D GeometryDiscovering Angle TheoremsGrade 6Teacher’s NotesLesson SummaryStudents will draw two parallel lines and a transversal line and measure the eight angles created. Students will observe any patterns and share their findings with the class.Connection to the Inquiry ProjectWhen creating birch bark bitings, students must visualize the angles that they are biting and understand the types of angles that they want to bite, as well as the end shape they desire to have. Understanding the properties of shapes and the degrees of angles will assist them in visualizing how to bite the shapes.Students can also be required to bite their shapes (students can be posed the question “Can you bite a shape with an “n” degree angle?) and can look at the results of their biting. Students will gain an understanding of the angles visually and tactilely, which will support their understandings of measurement.Outcomes AddressedSS1: Demonstrate an understanding of angles by:Identifying examples of angles in the environmentClassifying angles according to their measureEstimating the measure of angles, using 450, 900 and 1800 as reference anglesDetermining angle measures in degreesDrawing and labeling angles when the measure is specified LessonThis activity is designed to use the computer program Geometer’s Sketchpad. If this resource is unavailable in your school or classroom, the activity can be altered to students drawing the transversals on paper/graph paper.Prior to students using the Geometer’s Sketchpad to draw the transversals, a demonstration may prove worthwhile.Activity:Students can be given a copy of Discovering Angle Theorems worksheet, which contains student instructions for the activity. Students should use the Geometer’s Sketchpad (or paper) to create two parallel lines and a transversal line. You may want students to measure the angles on the computer or print out their creations and measure them in their own area. Students will then measure each angle created, eight angles in total, and document this information on paper or on their diagram. A new angle should then be created and re-measured. Students should compare their data and see if they find any patterns. Following the activity, students should be brought back into a whole class group and a discussion should follow on the findings.Extension:Students can search for transversals existing in the environment (created or natural) and be required to measure the angles. Students could also create their own designs, which involve transversals, and then measure the angles within their design, noting any patterns they find.AssessmentsCan students classify a given set of angles according to their measure; e.g., acute, right, obtuse, straight, reflex?Can students estimate the measure of an angle, using 450, 900 and 1800 as reference angles?Can students sketch 450, 900 and 1800 angles without the use of a protractor and describe the relationship among them?Can students measure, using a protractor, given angles in various orientations?Can students draw and label a specified angle in various orientations, using a protractor?Can students identify line segments on given diagrams that are either parallel or perpendicular?Can students draw a line segment parallel to another line segment and explain why they are parallel?Can students draw a line segment perpendicular to another line segment and explain why they are perpendicular?Can students draw the perpendicular bisector of a line segment, using more than one method, and verify the construction?Can students draw the bisector of a given angle, using more than one method, and verify that the resulting angles are equal?UnitsThis activity can be used in the following units:Unit 9: MeasurementDiscovering Angle TheoremsUsing Geometer’s Sketchpad draw two parallel lines and a line that cuts across both of them, also called a transversal. Here’s how to do it:Place two points anywhere on the screen, preferably somewhat close together.Select both points. Choose > Construct > Line.Somewhere off this line place another point.Select the line and the new point and choose > Construct > Parallel line.Now place a point on each line, select these two points and choose > Construct > Line. You should have a diagram that looks like the one below. Now that you have your model, your task is to explore the angles you have created and see if you can make any generalizations about the relationships among the angles. Measure each of the 8 angles you have created and describe any patterns you notice. Adjust your diagram by dragging one of the points used to create the transversal and see if the patterns still hold true. Write about your discoveries and be prepared to share.Exploring TrianglesGrade 6Teacher’s NotesLesson SummaryStudents will measure and draw different triangles, using pre-determined lengths and explore the possible and impossible sizes of triangles.Connection to the Inquiry ProjectBirch bark biting, and having students bite shapes into the material, requires students to use their intrinsic understanding of the shapes. However, students, through learning about measurement and triangle geometry will strengthen their understandings of the properties of triangles and be able to prove that the shapes that they are biting, and that other artists have bitten, are triangles. Understanding the mathematical components of shapes through these more direct instructions may also prove helpful for students when they are visualizing the shapes that they bite.Outcomes AddressedSS1: Demonstrate an understanding of angles by:Identifying examples of angles in the environmentClassifying angles according to their measureEstimating the measure of angles, using 450, 900 and 1800 as reference anglesDetermining angle measures in degreesDrawing and labeling angles when the measure is specifiedSS2: Demonstrate that the sum of interior angles is:1800 in a triangle3600 in a quadrilateralSS4: Construct and compare triangles, including:ScaleneIsoscelesEquilateralRight ObtuseAcutein different orientationsLessonEach student should receive the Exploring Triangles worksheet, or the worksheet should be displayed for all students to see. Each student should also receive or have the 24cm long string, a ruler, protractor, graph paper, writing utensils, and paper for the response/reflect component of the activity.Each student should measure out the triangles that are described in the activity, draw the triangles and measure the angles and sides. Students should create multiple triangles to see if certain triangles can or cannot be made. Discoveries about the different triangles should be noted either on the paper or on the graph paper with the triangles.Alternatively, students can draw, measure and analyze the triangles alone or in a small group and then, as a large class, discuss the specific questions posed.If this activity is being completed at the beginning of the 2-D Geometry unit, students may explore different triangular shapes without directly connecting the names of the triangles; likewise, this can act as an introductory activity to the different types of triangles.If this activity is being completed during the unit, students can continue to extend their understanding of the different triangles and can be asked to create specific types of triangles. AssessmentsCan students classify a given set of angles according to their measure; e.g., acute, right, obtuse, straight, reflex?Can students estimate the measure of an angle, using 450, 900 and 1800?Can students measure, using a protractor, the angles of the triangle?Can students explain, using models, that the sum of the interior angles of a triangle is the same for all triangles?Can students identify the characteristics of a given set of triangles according to their sides and/or their interior angles?Can students draw a specified triangle?UnitsThis activity can be used in the following units:Unit 9: MeasurementUnit 10: 2-D GeometryExploring TrianglesCut a piece of string that is 24 cm long. This is the perimeter of your triangle. Your task is to find what triangles are possible and which are impossible. Draw at least 5 different triangles that you can make that have a perimeter of 12cm. Use rulers and measure precisely. Measure the angles in each triangle. Record these on blank paper.Here are some questions to think about:What is the sum of the angles in each triangle? Why do you suppose this is the case? Explain.Can you make a triangle where the longest side is 6cm? Why or why not? What about 7 or 8 cm? Make some generalizations about side lengths that create triangles and side lengths that are impossible, given a specific perimeter.Make at least 3 triangles where two sides are equal in length. Sketch them on your paper. Be precise. Measure the angles and record the measurements. Triangles with two equal sides are called isosceles triangles. What else is true about isosceles triangles?Is it possible to make a triangle with three equal sides and a perimeter of 12cm? If so sketch it on your paper and measure the angles. Triangles with three equal sides are called equilateral triangles. What else is true about equilateral triangles?Reflect: Suppose you had a string that was length n units as the perimeter of your triangle. What can you say about the possible side lengths of triangles?Number the SidesGrades 6Teacher’s NotesLesson SummaryThis activity is from nrich.. Students will determine the length of the sides of similar triangles. Students will be required to use ratio to solve the problems.Connection to the Inquiry ProjectBirch bark biting, and having students bite shapes into the material, requires students to use their intrinsic understanding of the shapes. However, students, through learning about measurement and triangle geometry will strengthen their understandings of the properties of triangles and be able to prove that the shapes that they are biting, and that other artists have bitten, are triangles. Understanding the mathematical components of shapes through these more direct instructions may also prove helpful for students when they are visualizing the shapes that they bite.Within the Science component, students will be making traditional dyes, looking at the ratio of water to plant product. Students’ understandings of ratios, percents, decimals and fractions will be helpful in determining the quantity of water/plant materials as well as determining the ratio between plant material and water.Outcomes AddressedN5: Demonstrate an understanding of ratio, concretely, pictorially and symbolicallySS5: Describe and compare the sides and angles of regular and irregular polygonsLessonFind the teacher notes for this activity at finding the length of the sides, students can also be required to write down the ratio of the sides of the different triangles.Different triangles can also be given to students if the ones given are too simple. Students can also be required to create triangles that have the length of the sides increase by a chosen ratio and have their peers attempt to discover this ratio.AssessmentCan students write a ratio from a given concrete or pictorial representation?Can students express a given ratio in multiple forms, such as 3:5 or 3 to 5?Can students explain the part/whole and part/part ratios of a set?Can students solve a given problem involving ratios?Can students demonstrate congruence (sides to sides and angles to angles)?UnitsThis activity can be used in the following units: Unit 6: Ratio and PercentUnit 10: 2-D GeometryMeasurementGrades 6Teacher’s NotesLesson SummaryStudents will use shapes to perform different geometric activities. This activity can be used for multiple grades. There is a SmartBoard document that accompanies this activity at to the Inquiry ProjectWhen creating birch bark bitings, students must visualize the angles that they are biting and understand the types of angles that they want to bite, as well as the end shape they desire to have. Understanding the properties of shapes and the degrees of angles will assist them in visualizing how to bite the shapes.Outcomes Addressed6SS1: Demonstrate an understanding of angles by:Estimating the measure of angles, using 450, 900 and 1890 as reference anglesDetermining angle measures in degrees6SS2: Demonstrate that the sum of interior angles is:1800 in a triangle3600 in a quadrilateral 6SS3: Develop and apply a formula for determining the:Perimeter of polygonsArea of rectangles6SS5: Describe and compare the sides and angles of regular and irregular polygonsLessonClass ActivityUsing the SmartBoard document (if the technology is available), allow students to perform geometric measurements and/or transformations to the shapes given in the activity. You can provide students with the PDF or Document file as well so students are able to complete the activities at their desk. Students can discuss what they notice about the angles, the shapes following transformation(s) or other observations or questions. This activity would lend itself well to supporting understanding of geometric measurements or transformations prior to having students complete small group or independent work. Other 2-D geometric shapes (or 3-D, if applicable) can be created and measured as well.Small Group / Independent ActivityStudents can each be given the PDF or Document file of the worksheet and students can complete geometric measurements or transformations on the shapes. Students can make observations about what they see from their work on the 2-D shapes. Students can return to the class to discuss their observations or students can be given questions to answer regarding measurement and/or transformations.For students who have difficulty with measurement or transformations, students can use cut-outs or 2-D shape tiles to support their work with transformations, protractors can be provided and/or pair work can be used to support learning.For students who easily understand measurement and/or transformations can be required to create more complex 2-D shapes (or 3-D shapes) and perform measurements or transformations. Students should be required to make any observations or generalizations that they notice. Students who easily understand geometry may be able to support those students who are struggling, as well.AssessmentCan students estimate the measure of an angle, using 450, 900 and 1800 as reference angles?Can students measure, using a protractor, given angles in various orientations?Can students explain, using models, that the sum of the interior angles of a triangle is the same for all triangles?Can students explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals?Can students explain, using models, how the area of any rectangle can be determined?Can students generalize a rule (formula) for determining the area of rectangles?Can students explain, using models, how the perimeter of any polygon can be determined?Can students generalize a rule (formula) for determining the perimeter of polygons, including rectangles and squares?Can students demonstrate that the sides of a given regular polygon are of the same length and that the angles of a regular polygon are of the same measure?UnitsThis activity can be used in the following units: Unit 9: MeasurementUnit 10: 2-D GeometryFoldingGrade 6Teacher’s NotesLesson SummaryIn this activity, students will attempt to fold different shapes (triangles and quadrilaterals) from a piece of paper. Students can look at the attributes of these shapes through the lines made from folding, the shape made and/or other attributes formed. This activity is from nrich..Connection to the Inquiry ProjectMuch like biting, folding paper is another way to support students understanding of geometry through a tactile medium. Students are required to understand the properties of shapes by folding the paper to create the sides of the 2-D shapes, quadrilaterals in this activity. Folding (or cutting) may be an easier method to start with, compared to biting. With folding, students are able to see what they are doing, unlike in birch bark biting where the bark is in their mouth and their eyes become visualizations of their actions. Folding can also give students time to practice their folding techniques prior to using the “final product” birch bark, something that may relieve much stress in some students. This is also a good option if there is a limited amount of birch bark available for use. When students bite shapes into the birch bark, these shapes can be turned into stamps, using the dyes created within the science component. By taking the dye, biting and a piece of paper, students can stamp the biting, rotation/translate their biting and stamp again. In this way, students will be able to see the transformation in process. For a reflection, students can stamp their biting, fold the paper in half (over the just stamped area) and press down. When the paper is opened again, the reflection of the original stamp should show.Outcomes AddressedSS6: Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the imageSS7: Perform a combination of successive transformations of 2-D shapes to create a design and identify and describe the transformationsSS1: Demonstrate an understanding of angles by:Estimating the measure of angles, using 450, 900 and 1800 as reference anglesDetermining angle measures in degreesSS2: Demonstrate that the sum of the interior angles is:1800 in a triangle3600 in a quadrilateralSS4: Construct and compare triangles, includingScaleneIsoscelesEquilateralRightObtuseAcutein different orientationsSS5: Describe and compare the sides and angles of regular and irregular polygonsLessonThis activity can be accessed from . The nrich teacher notes can be accessed from and a printable worksheet can be accessed from paper folding activity can be used multiple times throughout the units and can be made to focus on one or two learning outcomes at a time.Using a piece of paper, students can fold the paper and try to make different types of triangles and/or regular or irregular polygons. Students can be required to measure the angles of these shapes that they have folded to see if they are, in fact, a regular/irregular polygon or the specified triangle they were attempting to fold.If, instead, students fold and cut the shapes, these shapes can be used to support transformations of shapes by tracing the edge of the cut area and then moving the paper (translation, rotation, reflection) and re-trace the shape. Students can perform multiple transformations and then see what the effects of these transformations are on the shape they cut out.Folding paper is also helpful in having students see the triangles that can be found within other shapes as well as proving that the sum of the interior angles of triangles is 1800 and the sum of the interior angles of a quadrilateral is 3600.AssessmentCan students model a given set of successive translations, successive rotations or successive reflections of a 2-D shape?Can students describe the transformations performed on a 2-D shape to produce a given image?Can students model a given combination of two different types of transformations of a 2-D shape?Can students model a given set of successive transformations (translations, rotations and/or reflections) of a 2-D shape?Can students create a design using one or more 2-D shapes and describe the transformations used?Can students estimate the measure of an angle using 450, 900 and 1800 as reference angles?Can students measure, using a protractor, given angles in various orientations?Can students identify the characteristics of a given set of triangles according to their sides and/or their interior angles?Can students sort a given set of triangles and explain the sorting rule?Can students sort a given set of 2-D shapes into polygons and non-polygons and explain the sorting rule?Can students demonstrate that the sides of a given regular polygon are of the same length and the angles of a regular polygon are of the same measure?Can students sort a given set of polygons as regular or irregular and justify the sorting?Can students demonstrate congruence (sides to sides and angles to angles) in a regular polygon by superimposing?Can students explain, using models, that the sum of the interior angles of a triangle is the same for all triangles?Can students explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals?UnitsThis activity can be used in the following unit:Unit 5: Motion GeometryUnit 9: MeasurementUnit 10: 2-D GeometryExploring Regular PolygonsGrade 6Teacher’s NotesLesson SummaryStudents will examine regular polygons and discover their reflective symmetry, rotational symmetry, tiling capabilities and interior angles. A SmartBoard document is available for this activity at to the Inquiry ProjectBirch bark biting, and having students bite shapes into the material, requires students to use their intrinsic understanding of the shapes. However, students, through learning about measurement and geometry will strengthen their understandings of the properties of regular polygons and be able to prove that the shapes that they are biting, and that other artists have bitten, are regular polygons. Understanding the mathematical components of shapes through these more direct instructions may also prove helpful for students when they are visualizing the shapes that they bite.When students bite shapes into the birch bark, these shapes can be turned into stamps, using the dyes created within the science component. By taking the dye, biting and a piece of paper, students can stamp the biting, rotation/translate their biting and stamp again. In this way, students will be able to see the transformation in process. For a reflection, students can stamp their biting, fold the paper in half (over the just stamped area) and press down. When the paper is opened again, the reflection of the original stamp should show.Outcomes Addressed6SS1: Demonstrate an understanding of angles by:Identifying examples of angles in the environmentClassifying angles according to their measureEstimating the measure of angles, using 450, 900 and 1800 as reference anglesDetermining angle measures in degreesDrawing and labeling angles when the measure is specified6SS2: Demonstrate that the sum of interior angles is:1800 in a triangle3600 in a quadrilateral6SS5: Describe and compare the sides and angles of regular and irregular polygons6SS6: Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology and draw and describe the image6SS7: Perform a combination of successive transformations of 2-D shapes to create a design and identify and describe the transformationsLessonItems needed or beneficial for the activity: Geoboards and elastics, polygon tiles, paper polygonal shapes, graph paper/paper, protractors, ruler, scissors, SmartBoardIndividual / Small Group ActivityEach student can be given a copy of Exploring Regular Polygons worksheet, or a copy can be displayed for the class to see. The students will measure, analyze, and transform regular polygons. Students will note which polygons have reflective symmetry and how many lines of symmetry for each, if the polygon has rotational symmetry and to what degree they have rotational symmetry, which polygons can be tiled, and students will measure the internal angles of polygons and connect these polygonal angles to triangles. Students should record their findings and, when appropriate, draw their transformations of polygons. Students should be prepared to discuss their findings with their class. Students’ work can also be handed in for formative assessment.If this activity is done in small groups, each member of the group should be required to complete the work. Students should be encouraged to discuss each section with each other thoroughly and to use the resources available to them. Students can also create a poster showing what they have discovered about regular polygons. These posters can be presented and/or displayed in the class.Large Group / Class ActivityThe Exploring Regular Polygons is available as a SmartBoard. As a large group or a class, using this may be beneficial. The group/class can use the SmartBoard to learn about regular polygons together. Students should be required to complete the work at their desk/space along with the teacher/student at the SmartBoard. If this activity is being completed as a class, ensure that there is enough time provided for discussions and questions regarding regular polygons. Along with the SmartBoard, students should still have access to manipulatives and other resources to aid them in transforming and understanding regular polygons.Centre ActivityAt the centre, provide one or two copies of the Exploring Regular Polygons worksheet, as well as geoboards, graph paper/paper, rulers, protractors, polygon tiles, and scissors, paper polygonal shapes (for folding to find reflective symmetry). Students can work through the different sections as they choose. Students should be required to write down their findings and pass them in for formative assessment. ExtensionStudents can use their understanding of regular polygons by creating their own design or creation utilizing patterns formed by regular polygons (e.g. images, quilts, pillow covers, sculptures). Students should be required to write an explanatory piece about their completed creation, describing the ways that they transformed regular polygons and, if deemed appropriate, their method of creating the piece. AssessmentsCan students measure, using a protractor, given angles in various orientations?Can students explain, using models, that the sum of the interior angles of a triangle is the same for all triangles?Can students explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals?Can students demonstrate that the sides of a given regular polygon are of the same length and that the angles of a regular polygon are of the same measure?Can students demonstrate congruence (sides to sides and angles to angles) in a regular polygon by superimposing?Can students model a given set of successive translations, successive rotations or successive reflections?Can students describe the transformations performed on a 2-D shape to produce a given image?Can students demonstrate that a 2-D shape and its transformation image are congruent?Can students model a combination of two different types of transformations of a 2-D shape?Can students draw and describe a 2-D shape and its image, given a combination of transformations?Can students create a design using one or more 2-D shapes and describe the transformations used?UnitsThis activity can be used in the following units:Unit 5: Motion Geometry; Unit 9: Measurement; Unit 10: 2-D GeometryRegular?Examine the regular polygons. What makes them "regular"? Make as many general statements as you can that you believe is true of all regular polygons.Reflective SymmetryExplore regular polygons to determine which have reflective symmetry and how many lines of reflective symmetry they have. Record your findings. Can you find any patterns or make any generalizations?Rotational SymmetryExplore regular polygons to determine which have rotational symmetry and what degree of rotational symmetry they have. Record your findings. Can you find any patterns or make any generalizations?Tiling the PlaneExplore regular polygons to determine which can be used to tile the plane and which cannot. Record your findings. Can you find any patterns or make any generalizations?What's your angle?Measure the interior angles in the regular polygons. Also examine the sum of the interior angles in each regular polygon. Record your findings. Can you find any patterns or make any generalizations?Let's make triangles?Try cutting each polygon into triangles. How many different ways can you do this? Record your findings. How can this help you to prove your conjecture in the last question? Explain.Regular Polygons Transformation TeaseGrade 6Teacher’s NotesLesson SummaryStudents will perform transformations on a Cartesian plane and identify the coordinates of the shape following the transformation. This activity is from nrich..Connections to the Inquiry ProjectWhen students plot and transform 2-D shapes on a Cartesian plane, students can see the distance and change of the shape. This is connected to the transformations that occur when students bite shapes/patterns into birch bark. When creating birch bark bitings, students must visualize the shapes that they are biting and understand the types of lines that they want to bite, as well as the end shape they desire to have. Understanding the properties of shapes, the ways that shapes transform, as well as the sides of 2-D shapes, will assist them in visualizing how to bite the shapes.When students bite shapes into the birch bark, these shapes can be turned into stamps, using the dyes created within the science component. By taking the dye, biting and a piece of paper, students can stamp the biting, rotation/translate their biting and stamp again. In this way, students will be able to see the transformation in process. For a reflection, students can stamp their biting, fold the paper in half (over the just stamped area) and press down. When the paper is opened again, the reflection of the original stamp should show.Outcomes Addressed6SS8: Identify and plot points in the first quadrant of a Cartesian plane using whole number ordered pairs6SS9: Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices)LessonThis activity can be accessed from . The nrich teacher notes can be accessed from and a printable page can be accessed from . *Note: In the Nrich activity, the transformations take place over all four quadrants of a Cartesian plane. For a Grade 6 activity, this should be limited to only the first quadrant of the Cartesian plane and each shape should be translated only once. This can be adapted as needed to support the developmental level of your students, however. This activity should be introduced as a whole group activity. Using a Smartboard application, overhead projector or other type of technology, the first quadrant of a Cartesian plane should be shown to the whole class. Each student should also have their own copy of the Cartesian plane. Alternatively, small groups can be made and given a laminated quadrant or a paper quadrant placed in a sheet protector and a white board marker. If required, students can also be given shapes to support their learning of transformations on a Cartesian plane (however, students should be encouraged to visualize the transformation first). Prior to beginning the transformations, students should show that they know the vertices names as well as where the origin is on the Cartesian plane. If required, a quick refresher on how to plot points using coordinate pairs/identify the coordinates of a point can be done. The teacher can draw a shape on the board and have students copy this shape down. Students can be required to identify the coordinates of the vertices of the shape and then asked where they think the shape will be following the specified transformation (translation, rotation, reflection). Students can complete the transformation at their desks (individually or in small groups/pairs) and then a volunteer can draw the resultant shape on the projected version. A discussion can be then had about what happened to the shape, the distance of the transformed shape to the original shape, the coordinates of the original shape, etc. Different shapes and transformations can be completed in a similar manner. Students can then be allowed to complete their own transformations using their own shapes individually or in small groups/pairs. If using groups, ensure that the group sizes are small so that each student has access to the Cartesian plane sheet or ensure that each student has their own page.A follow up assessment activity can be completed or observations can be made during the whole group activity and the subsequent individual/small group activity time.AssessmentCan students label the axes of the first quadrant of a Cartesian plane and identify the origin?Can students plot a point in the first quadrant of a Cartesian plane?Can students draw shapes or designs, given ordered pairs, in the first quadrant of a Cartesian plane?Can students determine the distance between points along horizontal and vertical lines in the first quadrant of a Cartesian plane?Can students draw shapes or designs in the first quadrant of a Cartesian plane and identify the points used to produce them?Can students identify the coordinates of the vertices of a given 2-D shape in the first quadrant of a Cartesian plane?Can students perform a transformation on a given 2-D shape and identify the coordinates of the vertices of the image in the first quadrant of a Cartesian plane?Can students describe the positional change of the vertices of a given 2-D shape to the corresponding vertices of its image as a result of a transformation within the first quadrant of a Cartesian plane?UnitsThis activity can be used in the following unit:Unit 4: Data RelationshipsUnit 5: Motion Geometry ................
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