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DRAFT Birch Bark Biting 6 1

Birch Bark Biting

Grade 6

Integrated Inquiry Project

Grade 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 bitingo Angles within 2-D shapes

o 2-D shape transformations

The history of Birch Bark biting and it’s connection to the economy The process of creating Birch Bark biting and dyes for Birch Bark biting creations How Birch Bark biting influences/is influenced by Mi’kmaw culture The properties of the Birch trees and Birch bark If the art of Birch Bark biting is relevant/present in today’s art culture or if it

could be brought back The geographic locations of Birch Bark bitings in Canada and why biting

existed there

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Rationale 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.

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Mathematics

By 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 Arts

Since, 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.

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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 Studies

To 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.

Science

Students 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:

Mathematics

SP1: Create, label and interpret line graphs to draw conclusions SP2: Select, justify and use appropriate methods of collecting data, including

o Questionnaireso Experimentso Databaseso Electronic media

SP3: Graph collected data and analyze the graph to solve problems

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SS6: Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image

SS7: Perform a combination of successive transformations of 2-D shapes to create a design and identify and describe the transformations

SS9: 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 symbolically SS1: Demonstrate an understanding of angles by:

o Identifying examples of angles in the environmento Classifying angles according to their measureo Estimating the measure of angles, using 450, 900, and 1800 as reference angleso Determining angle measures in degrees

SS2: Demonstrate that the sum of interior angles is:o 1800 in a triangleo 3600 in a quadrilateral

SS4: Construct and compare triangles, including o Scaleneo Isosceleso Equilateralo Righto Obtuseo Acute

in different orientations SS5: Describe and compare the sides and angles of regular and irregular polygons

English Language Arts

1.1: Contribute thoughts, ideas and questions to discussions and compare their own ideas with those of peers and others

1.3: Defend and/or support their opinions with evidence 2.1: Contribute to and respond constructively in conversation, small-group and

whole-group discussions 3.2: Detect examples of prejudice, stereotyping or bias in oral language; recognize

their negative effect on individuals and cultures; and attempt to use bias-free language

5.1: Answer, with increasing independence, their own questions and those of others by selecting relevant information from a variety of texts

o Demonstrate understanding of the purpose of classification systems and basic reference materials

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o Use a range of reference texts and a database or an electronic search to facilitate the selection process

7.4: Respond critically to texts by:o Applying a growing range of strategies to analyze and evaluate a texto Demonstrate growing awareness that all texts reflect a purpose and a

perspectiveo Recognizing when language is being used to manipulate, persuade or control

themo Detecting prejudice, stereotyping and bias

Visual Arts

1.2: Demonstrate ability and initiative in the use of techniques, technologies, materials and equipment

3.1: Compare works of art across time and culture 3.3: Use technology to locate and explore works of art 4.1: Discuss ideas and approaches with sensitivity and respect 4.4: Discover art as a way of expressing ideas 5.3: Demonstrate an understanding of the lives of artists within

cultural/historical/social contexts

Social Studies

6.1.1: Explore the concept of culture and demonstrate an understanding of its role in their lives

o Classify elements of culture as material or non-materialo Investigate how cultures are transmitted from generation to generationo Identify factors that shape culture

6.1.2: Identify, locate and map major cultural regions of the worldo Recognize that there are various criteria for defining a cultural region, such

as language, religion, location and place, shared traditions and history 6.3.1: Examine how traditions relate to culture in a selected cultural region

o Describe how customs and rituals are reflected in the region’s cultureo Analyze how change factors affect cultural traditions

6.3.3: Explain how economic systems relate to cultureso Identify different economic systemso Examine the differences among different economic systemso Explain how the economic programs and services of a country influence its

cultureo Identify current economic trends that are influencing culture

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6.4.1: Analyze how the arts reflect beliefs and values in a selected cultural regiono Identify visual arts, crafts, dance and music practiced in the regiono Analyze how crafts and visual art reflect the beliefs and values of the culture

6.6.1: Illustrate an understanding of how cultures from around the world have contributed to the development of Canada’s multicultural mosaic

Science

Propose 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:

Mathematics

Review bar and double bar graphs and introduce the line graph and their attributes Purposes of different types of graphs and how to choose the appropriate graph for

your data How to formulate a good question when collecting data Discrete vs. Continuous data Different ways to collect data How to use databases to collect data How to read and understand different graphs Combining 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 plane Rotations of shapes about a centre of rotation on a vertex, outside the shape and

within the shape How ratios and percents can be represented by decimals and fractions Ratios as a comparison between two numbers Equivalent ratios and Equivalent fractions Measuring angles in degrees and using a protractor to measure angles Angle names (right, straight, acute, obtuse, reflex) Benchmarks of 1800, 900 and 450

Naming and identifying properties of different triangles (scalene, isosceles, equilateral, right, acute, obtuse)

Review of polygons (regular, irregular)

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How to use sources within your writing/presentations (citations, using quotations to defend and support the opinion)

How to read for bias/stereotyping/racism How to use databases for research How to generate good questions How to respond to peers’ statements in a positively constructive manner

Visual Arts

How to find works of art (databases, books, on-line museums) How to use techniques/technologies/tools How to agree/disagree with ideas appropriately and constructively How to respond to and analyze artwork with respect to the artist and others

Social Studies

What culture is Difference between material/non-material culture How 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)

Science

How to gather information to answer questions (research, experiments, etc.) How to create good questions, hypotheses Human impacts on the earth How plants/animals adapt to their environment (features of plants/animals)

Skill Development:

Organizational and Self-Management

Students 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 teacher

Students will be required to do individual/small group research with minimal teacher support

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Students 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 class

Students should be required to have their RAFT completed in stages with multiple due dates to keep them on track and provide feedback/support for problems

Students will be required to complete the RAFT Part 2 individually and complete the research required to support their argument

Smaller projects can be completed in pairs/small groups or independently Students should try to use different tactics for creating the birch bark biting in

mathematics and art Students should be allowed to explore different ways to mix water and plant matter

for creating dyes without large teacher support When 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 steps

Students should create and send invitations to the community to attend the Birch Bark biting workshop

Conduct research, share information, make decisions, solve problems

Students should have experience in folding and biting Birch Bark Students can brainstorm areas of interest in Birch Bark biting to research more in-

depth Students will choose their own method of presenting their RAFT part 2 Students will answer their RAFT using research they have collected from books,

interviews, online articles and their own personal opinions created through their learning

Use technology in a purposeful manner

Students can photograph their Birch Bark bitings to record the process of how to create a Birch Bark biting

Students can use cameras/video cameras to film the process of making Birch Bark bitings

Students can (with permission) record interviews with elders/experts Students can use technology in the production and/or presentation of their RAFT Students can use the internet as a source of information

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Engage in authentic investigations using a variety of media, methods and sources

Students will complete in-person interviews with individuals who have made Birch Bark bitings

Students can research different individuals who make Birch Bark bitings and different folding techniques

Students can search for videos (interviews) of elders who do Birch Bark bitings Students can write letters to elders regarding Birch Bark bitings Students can visit museums that have Birch Bark bitings in them and/or speak to

archaeologists or experts on Birch Bark bitings

Be required to communicate what they are learning with a variety of audiences

Students 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 class

Possible 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 dyes

Birch Bark biting exampleso http://aboriginalperspectives.uregina.ca/rosella/lessons/math/

examples.shtmlo http://www.lttacollection.ca/content/lesson-plan.asp?

SessionId=3543454&ItemId=273&ProvinceId=2

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http://www.lttacollection.ca/content/lesson-plan.asp?SessionId=3543454&ItemId=273&ProvinceId=2

http://www.lttacollection.ca/content/lesson-plan.asp?SessionId=3543454&ItemId=273&ProvinceId=2

http://aboriginalperspectives.uregina.ca/rosella/lessons/math/examples.shtml

http://aboriginalperspectives.uregina.ca/rosella/lessons/math/examples.shtml


o www.canadiannorthernart.com/SallyBirchbark.shtml o http://visionquest.pagc.sk.ca/index.asp?page=4&m=1&ln=1

Videos of Birch Bark biting / Interviews about Birch Bark bitingo http://aboriginalperspectives.uregina.ca/rosella/index.shtml o www.youtube.com/watch?v=bFJaa9ndAts o http://www.isuma.tv/hi/en/birch-bark-biting-with-rosella-carney o http://visionquest.pagc.sk.ca/media.asp?mediafile=movies/

bbarkmedium.flv o http://www3.edu.gov.mb.ca/cn/support/aboriginal/birchbarkbiting.html

Mi’kmaq Culture and History links: o http://www.native-languages.org/mikmaq_culture.htm o Four Directions Teachings:

http://www.fourdirectionsteachings.com/main.htmlo Museums (Canadian Museum of Civilization)

Information on dyes and how dyes were made:o 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. Print.

Informational on Birch Bark Biting:o “Wigwas: Bark Biting.” Our Legacy: ka-ka-pe-isi-nakatamakawiyahk T’a bet’ a

dene dahidli. Thunder Bay National Exhibition Centre, 1983. 1-21. http://scaa.sk.ca/ourlegacy/solr?query=ID:25614&start=0&rows=10&mode=results

o http://brucebyfield.com/2009/07/31/the-first-nations-art-of-birch-bark- biting/

o http://www.baribal.nl/educatief/spreekbeurt/birchbarkbiting_en.html o http://www.artsask.ca/en/collections/themes/commonplace/

angelique_merasty/untitled_birch_bark_biting o http://www.nativerenaissance.com/AngeliqueLevac.html o http://resources.curriculum.org/secretariat/figures/index.html o http://elephantaday.blogspot.ca/2012/03/elephant-no-177-birchbark-

biting.html o http://www.myiaiaonline.com/kgreendeer/wp-content/uploads/

2012/03/Art-History-Research-Paper-enhanced1.pdf o http://www.thecanadianencyclopedia.com/articles/birchbark-biting o http://www.cmmns.com/KekinamuekPdfs/Ch8screen.pdf

Other Outcomes Possibly Achieved:

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http://www.cmmns.com/KekinamuekPdfs/Ch8screen.pdf

http://www.thecanadianencyclopedia.com/articles/birchbark-biting

http://www.myiaiaonline.com/kgreendeer/wp-content/uploads/2012/03/Art-History-Research-Paper-enhanced1.pdf

http://www.myiaiaonline.com/kgreendeer/wp-content/uploads/2012/03/Art-History-Research-Paper-enhanced1.pdf

http://elephantaday.blogspot.ca/2012/03/elephant-no-177-birchbark-biting.html

http://elephantaday.blogspot.ca/2012/03/elephant-no-177-birchbark-biting.html

http://resources.curriculum.org/secretariat/figures/index.html

http://www.nativerenaissance.com/AngeliqueLevac.html

http://www.artsask.ca/en/collections/themes/commonplace/angelique_merasty/untitled_birch_bark_biting

http://www.artsask.ca/en/collections/themes/commonplace/angelique_merasty/untitled_birch_bark_biting

http://www.baribal.nl/educatief/spreekbeurt/birchbarkbiting_en.html

http://brucebyfield.com/2009/07/31/the-first-nations-art-of-birch-bark-biting/

http://brucebyfield.com/2009/07/31/the-first-nations-art-of-birch-bark-biting/

http://scaa.sk.ca/ourlegacy/solr?query=ID:25614&start=0&rows=10&mode=results

http://scaa.sk.ca/ourlegacy/solr?query=ID:25614&start=0&rows=10&mode=results

http://www.civilization.ca/home

http://www.fourdirectionsteachings.com/main.html

http://www.native-languages.org/mikmaq_culture.htm

http://www3.edu.gov.mb.ca/cn/support/aboriginal/birchbarkbiting.html

http://visionquest.pagc.sk.ca/media.asp?mediafile=movies/bbarkmedium.flv

http://visionquest.pagc.sk.ca/media.asp?mediafile=movies/bbarkmedium.flv

http://www.isuma.tv/hi/en/birch-bark-biting-with-rosella-carney

http://www.youtube.com/watch?v=bFJaa9ndAts

http://aboriginalperspectives.uregina.ca/rosella/index.shtml

http://visionquest.pagc.sk.ca/index.asp?page=4&m=1&ln=1

http://www.canadiannorthernart.com/SallyBirchbark.shtml


Mathematics

6N6: Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially and symbolically

6N8: 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 variables

Information and Communication Technology Integration 4-6

BOC 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 assistance

SEHI 6.1: Share information resources, media equipment and computer equipment SEHI 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 teacher

SEHI 6.4: Identify changes in the ways that information is collected, represented and transmitted and the impacts such changes have on individuals, communities and cultures

SEHI 6.6: Identify and give specific examples where cultural values and experiences influence the information and entertainment products they use

PTS 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 others

RPSD 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 assistance

RPSD 6.2: Use appropriate technological tools for concept mapping, problem solving, observation, measurement, calculation, graphing and charting to explore concepts under study

RPSD 6.3: Use research information to support arguments, with teacher support RPSD 6.5: Acknowledge the sources of their information using simple citation

formats, with independence


1.2: Ask and respond to questions to seek clarification or explanation of ideas and concepts

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2.4: Engage in, respond to and evaluate a variety of oral presentations and other texts

3.3: Make a conscious attempt to consider the needs and expectations of their audience

4.1: Select, independently, texts appropriate to their range of interests and learning needs

9.1: Create written and media texts using an increasing variety of formso Demonstrate understanding that particular forms require the use of specific

features, structures and patterns 9.2: Address the demands of an increasing variety of purposes and audiences

o Make informed choices of form, style and content for specific audiences and purposes

9.3: Invite responses to early drafts of their writing/media productionso Use audience reaction to help shape subsequent draftso Reflect on their final drafts from a reader’s/viewer’s/listener’s point of view

10.1: Select from a range of prewriting, drafting, revising, editing, proofreading and presentation strategies to develop effective pieces of writing and other representations

10.2: Use the convention of written language in final products 10.3: Use technology with increasing proficiency to create, revise, edit and publish

texts 10.5: Select, organize and combine relevant information, from three to five sources

Visual Arts

1.1: Express through art making an awareness of the complexities of the world and their role in it

1.3: Use a combination of visual elements and principles of art and design in art making

2.1: Work independently and collaboratively to apply learned skills, solve problems, and respond to experiences and ideas

3.2: Demonstrate an awareness of artists’ styles, intentions and approaches 4.2: Show appreciation of individual differences in artwork 6.2: Examine the role of the media and discuss their effects on their lives and the

lives of others

Units Included:

Mathematics:

Unit 4: Data Relationships

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Unit 5: Motion Geometry Unit 6: Ratio and Percent Unit 9: Measurement Unit 10: 2-D Geometry

Science:

Life Science: Diversity of Lifeo Adaptations and Natural Selection

Social Studies:

Unit 1: An Introduction to Culture Unit 3: Some Elements of Culture Unit 4: Expressions of Culture Unit 6: Canada: Reflections on a Multicultural Mosaic

RAFT Assessment Task

Part 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

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Grade 6

Mathematics Teacher-Directed Lessons

Which Month to Ski?

Grade 6

Teacher’s Notes

Lesson Summary

In 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 Project

Within 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 Addressed

PR1: Demonstrate an understanding of the relationships within tables of values to solve problems

SP3: Graph collected data and analyze the graph to solve problems Can students describe, using everyday language, orally or in writing, the relationship shown

on a graph

Lesson

Teachers 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.

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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.

Assessment

Can 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?

Units

This activity can be used in the following unit:

Unit 3: Patterns in MathematicsUnit 4: Data Relationships

Carina’s Pet Shop

Grade 6

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Teacher’s Notes

Lesson Summary

This activity is from National Council of Teachers Mathematics’ (2007) Navigating through Problem Solving and Reasoning in Grade 5.



Outcomes Addressed

N2: Solve problems involving whole numbers and decimal numbers PR1: Demonstrate an understanding of the relationships within tables of values to solve

problems PR3: Represent generalizations arising from number relationships, using equations with

letter variables SP1: Create, label and interpret line graphs to draw conclusions SP3: Graph collected data and analyze the graph to solve problems SS8: Identify and plot points in the first quadrant of a Cartesian plane, using whole number

ordered pairs PR2: Represent and describe patterns and relationships using graphs and tables

Lesson

Teachers 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

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questions based upon hypothetical sales with new animals and answer simple algebraic questions based upon the sale number relationships.

Assessment

Can 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 graph

Units

This activity can be used in the following unit:Unit 3: Patterns in MathematicsUnit 4: Data Relationships

Fractions with a Point

Grade 6

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Teacher’s Notes

Lesson Summary

Students 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.


The 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 Addressed

N6: Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially and symbolically

N4: Relate improper fractions to mixed numbers and mixed numbers to fractions

Lesson

Teachers 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.

Assessment

Can students explain that “percent” means “out of 100”?

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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?

Units

This activity can be used in the following unit:Unit 6: Ratio and PercentUnit 7: Fractions

Going for Gold

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Grade 6

Teacher’s Notes

Lesson Summary

In 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.maths.org.



Outcomes Addressed

SP3: Graph collected data and analyze the graph to solve problems PR2: Represent and describe the relationships using graphs and tables SP1: Create, label and interpret line graphs to draw conclusions

Lesson

This activity can be accessed from http://nrich.maths.org/7800. The Nrich teacher notes can be accessed from http://nrich.maths.org/7800/note and a printable worksheet can be accessed from http://nrich.maths.org/7800/note?nomenu=1. An article on the math of medals in the Olympics can be found at: http://plus.maths.org/content/maths-gold-medals-four-olympic-thoughts.

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.

Assessment

Can students determine an appropriate type of graph for displaying a set of collected data and justify the choice of graph?

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http://plus.maths.org/content/maths-gold-medals-four-olympic-thoughts

http://nrich.maths.org/7800/note?nomenu=1

http://nrich.maths.org/7800/note

http://nrich.maths.org/7800


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?

Units

This activity can be used in the following unit:Unit 4: Data Relationships

Real Statistics

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Grade 6

Teacher’s Notes

Lesson Summary

Students 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.maths.org.


Within 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 Addressed

SP2: Select, justify and use appropriate methods of collecting data, including:o Questionnaires

SP3: Graph collected data and analyze the graph to solve problems PR2: Represent and describe patterns and relationships, using graphs and tables N6: Demonstrate an understanding of percent (limited to whole numbers) concretely,

pictorially and symbolically

Lesson

This activity can be accessed from http://nrich.maths.org/4938. The Nrich teacher notes can be accessed from http://nrich.maths.org/4938/note and a printable worksheet can be accessed from http://nrich.maths.org/4938/note?nomenu=1.

*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: http://www.censusatschool.org.uk/get-data/results/phase10/phase10 (United Kingdom) or http://www19.statcan.gc.ca/04/04_000-eng.htm (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.

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http://www19.statcan.gc.ca/04/04_000-eng.htm

http://www.censusatschool.org.uk/get-data/results/phase10/phase10





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.

Assessment

Can 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?

Units

This activity can be used in the following unit:Unit 4: Data RelationshipsUnit 6: Ratio and Percent

What Are You Plotting? / Two Number Lines

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Grade 6

Teacher’s Notes

Lesson Summary

Students will be introduced to plotting points on the first quadrant of a Cartesian plane. This activity is from nrich.maths.org.

Connections to the Inquiry Project

This 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 Addressed

SS8: Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs

Lesson

The “What Are You Plotting?” activity can be accessed from http://nrich.maths.org/1113. The Nrich printable sheet can be accessed from http://nrich.maths.org/1113/index?nomenu=1.

The “Two Number Lines” activity can be accessed from http://nrich.maths.org/5653. The Nrich teacher notes can be accessed from http://nrich.maths.org/5653/note and a printable page can be accessed from http://nrich.maths.org/5653/note?nomenu=1.

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.

Assessment

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http://nrich.maths.org/1113/index?nomenu=1



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 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 Relationships

Patterns Activity

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Grade 6

Teacher’s Notes

Lesson Summary

Students will solve problems from tables, solve word sketch problems, extend a pattern, and complete a table and graph of their data.



Outcomes Addressed

6PR1 demonstrate an understanding of the relationships within tables of values to solve problems

6PR2 represent and describe patterns and relationships using graphs and tables

Lesson

There 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 Tables

Students 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!

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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.

Ex.

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).

Assessment

Students should be able to:

- generate values in one column of a table of values if given values in the other column and a pattern rule

o Formulate a rule to describe the relationship between two columns of numbers in a table of values

- state, using mathematical language, the relationship in a given table of values- create a concrete or pictorial representation of the relationship shown in a table of values- predict the value of an unknown term using the relationship in a table of values and verify

the prediction- describe the pattern within each column of a given table of values- create a table of values to record and reveal a pattern to solve a given problem- translate a pattern to a table of values and graph the table of values

o strictly linear graphs with discrete elements- describe, using everyday language, orally or in writing, the relationship shown on a graph

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Units

This lesson could be used in: Unit 3: Patterns in MathematicsUnit 4: Data Relationships in grade 4.

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Choose 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.

How many stairs can you climb in 60 minutes?

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Time in minutes

Number of stairs

climbed0 05 1510 3015 4520 60


How much will it cost for 125 hats?

How much will it cost to travel 65 km by taxi?

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Number of Hats Ordered

Cost

0 15.0010 35.0020 55.0030 75.0040 95.00


How far will she run in 30 seconds?

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Distance traveled (km)

Cost

0 2.5010 5.5020 8.5030 11.5040 14.50


How much will it cost for 70 minutes of long distance calling?

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Time in

seconds

Distance run in meters

0 01 3.22 6.43 9.64 12.8

Time calling long distance in minutes Cost0 5.005 6.2510 7.5015 8.7520 10.0

0


How much will it cost for a 7 hour job?

How much will it cost to have a party for 150 people?

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Time in hours

Cost for the electrician

0 25.001 57.502 90.003 122.504 155.00


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Pattern 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.

Ex.

Complete the table of values below.

Number of Units

x

Perimeter

y

1

2

3

4

5

6

7

8

9

10

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Number of guests at the party

Cost for Caterin

g0 125.0020 275.0040 425.0060 575.0080 725.00


Sketch a graph of your data.

Write an equation to describe your pattern.

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Do you see the difference from the table in the graph? Where is it?


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.

Accurately label your graphs.

Give clear explanations as to how you solved the problem.

Complete at least three of the problems from the box on graph paper.

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Katie 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?

One 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.

A 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

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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?

One 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

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for long distance. For what number of minutes will these plans give the same cost? Explain how you know.

A 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 Geometry

Grades 6

Teacher’s Notes

Lesson Summary

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This 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.


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 Addressed

SS8: Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs

SS4: Construct and compare triangles, includingo Scaleneo Isosceleso Equilateralo Righto Obtuseo Acute

in different orientations

Lesson

In 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.

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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.

Assessment

Can 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?

Units

This activity can be used in the following units: Unit 4: Data RelationshipsUnit 10: 2-D Geometry

Doughnut Percents

Grade 6

Teacher’s Notes

Lesson Summary

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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. This activity is from nrich.maths.org.


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 Addressed

N6: Demonstrate an understanding of percent (limited to whole numbers) symbolically N4: Relate improper fractions to mixed numbers

Lesson

This activity can be accessed from http://nrich.maths.org/6945. The Nrich teacher notes can be accessed from http://nrich.maths.org/6945/note and the printable sheet can be accessed from http://nrich.maths.org/6945/note?nomenu=1. 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.

Assessment

Can 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?

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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: Fractions

Nutty Mixture

Grades 6

Teacher’s Notes

Lesson Summary

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This activity is from nrich.maths.org. Students are given a word problem and are required to define the different ratios of nuts in a bag.



Outcomes Addressed

6N5: Demonstrate an understanding of ratio, concretely, pictorially and symbolically

Lesson

Find the teacher notes for this activity at http://nrich.maths.org/4788/note.

Students 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.

Assessment

Can 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?

Units

This activity can be used in the following unit: Unit 6: Ratio and Percent

Rod Ratios

Grades 6

Teacher’s Notes

Lesson Summary

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This activity is from nrich.maths.org. Students use Cuisenaire rods to determine different ratios between the rods.



Outcomes Addressed

6N5: Demonstrate an understanding of ratio, concretely, pictorially and symbolically

Lesson

Find the teacher notes for this activity at http://nrich.maths.org/4782

The 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:

http://showmeyourmath.ca/sites/default/files/resources/5-6/student_worksheets/Make_Your_Own_Cuisenaire_Rods.pdf

Or for the .doc file, go to “Make Your Own Cuisenaire Rods” at this site:

http://showmeyourmath.ca/Teacher_Notes_5-6/grade_six

Students can complete the different questions individually or in small groups and then return to the class to discuss their findings.

Assessment

Can 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?

Units

This activity can be used in the following units: Unit 6: Ratio and Percent

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Am I Unique?

Grade 6

Teacher’s Notes

Lesson Summary

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Students 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.


Birch 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 Addressed

6SS1: Demonstrate an understanding of angles by:o Identifying examples of angles in the environmento Classifying angles according to their measureo Estimating the measure of angles, using 450, 900 and 1800 as reference angleso Determining angle measures in degreeso Drawing and labeling angles when the measure is specified

6SS2: Demonstrate that the sum of interior angles is:o 1800 in a triangleo 3600 in a quadrilateral

6SS3: Develop and apply a formula for determining the:o Perimeter of polygonso Area of rectangleso Volume of right rectangular prisms

6SS4: Construct and compare triangles, including:o Scaleneo Isosceleso Equilateralo Righto Obtuseo Acute

in different orientations. 6SS5: Describe and compare the sides and angles of regular and irregular polygons

Lesson

This 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:

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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.

Assessments

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, 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?Units

This activity can be used in the following units:Unit 9: MeasurementUnit 10: 2D Geometry

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Am I Unique?

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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 a Side b Side c A∠ B∠ C∠ Unique Not Unique

Which 3 pieces of information will result in a unique triangle? Explain your discoveries.

Using Venn Diagrams to Reason about Shapes

Grade 6

Teacher Notes

Lesson Summary

In 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.

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This activity comes from National Council of Teachers of Mathematics’ (2002) Navigating through Geometry in Grades 6-8.


When 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 Addressed

SS1: Demonstrate an understanding of angles by:o Classifying angles according to their measureo Determining angle measures in degrees

SS4: Construct and compare triangles, including:o Scaleneo Isosceleso Equilateralo Righto Obtuseo Acute

in 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).

Assessments

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 rules? Can students measure, using a protractor, given angles in various orientations?

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Can students classify a given set of angles according to their measure; e.g., acute, right, obtuse, straight, reflex?

Units

This activity can be used in the following units:Unit 9: MeasurementUnit 10: 2-D Geometry

Discovering Angle Theorems

Grade 6

Teacher’s Notes

Lesson Summary

Students 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.

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When 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 Addressed

SS1: Demonstrate an understanding of angles by:o Identifying examples of angles in the environmento Classifying angles according to their measureo Estimating the measure of angles, using 450, 900 and 1800 as reference angleso Determining angle measures in degreeso Drawing and labeling angles when the measure is specified

Lesson

This 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.

Assessments


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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?

Units

This activity can be used in the following units:Unit 9: Measurement

Discovering Angle Theorems

Using 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:

1. Place two points anywhere on the screen, preferably somewhat close together.

2. Select both points. Choose > Construct > Line.

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3. Somewhere off this line place another point.4. Select the line and the new point and choose > Construct > Parallel line.5. 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 Triangles

Grade 6

Teacher’s Notes

Lesson Summary

Students will measure and draw different triangles, using pre-determined lengths and explore the possible and impossible sizes of triangles.

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Outcomes Addressed

SS1: Demonstrate an understanding of angles by:o Identifying examples of angles in the environmento Classifying angles according to their measureo Estimating the measure of angles, using 450, 900 and 1800 as reference angleso Determining angle measures in degreeso Drawing and labeling angles when the measure is specified

SS2: Demonstrate that the sum of interior angles is:o 1800 in a triangleo 3600 in a quadrilateral

SS4: Construct and compare triangles, including:o Scaleneo Isosceleso Equilateralo Right o Obtuseo Acute

in different orientations

Lesson

Each 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.

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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.

Assessments


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?

Units

This activity can be used in the following units:Unit 9: MeasurementUnit 10: 2-D Geometry

Exploring Triangles

Cut 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:

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1. What is the sum of the angles in each triangle? Why do you suppose this is the case? Explain.

2. 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.

3. 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?

4. 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 Sides

Grades 6

Teacher’s Notes

Lesson Summary

This activity is from nrich.maths.org. Students will determine the length of the sides of similar triangles. Students will be required to use ratio to solve the problems.

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Outcomes Addressed

N5: Demonstrate an understanding of ratio, concretely, pictorially and symbolically SS5: Describe and compare the sides and angles of regular and irregular polygons

Lesson

Find the teacher notes for this activity at http://nrich.maths.org/5639/note

When 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.

Assessment

Can 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)?

Units

This activity can be used in the following units: Unit 6: Ratio and PercentUnit 10: 2-D Geometry

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Measurement

Grades 6

Teacher’s Notes

Lesson Summary

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Students 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 http://showmeyourmath.ca/Teacher_Notes_5-6/grade_six.


When 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 Addressed

6SS1: Demonstrate an understanding of angles by:o Estimating the measure of angles, using 450, 900 and 1890 as reference angleso Determining angle measures in degrees


6SS3: Develop and apply a formula for determining the:o Perimeter of polygonso Area of rectangles

6SS5: Describe and compare the sides and angles of regular and irregular polygons

Lesson

Class Activity

Using 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 Activity

Students 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.

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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.

Assessment

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 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?

Units

This activity can be used in the following units: Unit 9: MeasurementUnit 10: 2-D Geometry

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Folding

Grade 6

Teacher’s Notes

Lesson Summary

In 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.maths.org.


Much 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

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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 Addressed

SS6: Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image

SS7: Perform a combination of successive transformations of 2-D shapes to create a design and identify and describe the transformations

SS1: Demonstrate an understanding of angles by:o Estimating the measure of angles, using 450, 900 and 1800 as reference angleso Determining angle measures in degrees

SS2: Demonstrate that the sum of the interior angles is:o 1800 in a triangleo 3600 in a quadrilateral

SS4: Construct and compare triangles, includingo Scaleneo Isosceleso Equilateralo Righto Obtuseo Acute

in different orientations SS5: Describe and compare the sides and angles of regular and irregular polygons

Lesson

This activity can be accessed from http://nrich.maths.org/1797. The nrich teacher notes can be accessed from http://nrich.maths.org/1797/note and a printable worksheet can be accessed from http://nrich.maths.org/1797/note?nomenu=1

This 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.

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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.

Assessment

Can 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?

Units

This activity can be used in the following unit:Unit 5: Motion GeometryUnit 9: MeasurementUnit 10: 2-D Geometry

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Exploring Regular Polygons

Grade 6

Teacher’s Notes

Lesson Summary

Students 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 http://showmeyourmath.ca/Teacher_Notes_5-6/grade_six.


Birch 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.

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Outcomes Addressed

6SS1: Demonstrate an understanding of angles by:o Identifying examples of angles in the environmento Classifying angles according to their measureo Estimating the measure of angles, using 450, 900 and 1800 as reference angleso Determining angle measures in degreeso Drawing and labeling angles when the measure is specified


6SS5: Describe and compare the sides and angles of regular and irregular polygons 6SS6: Perform a combination of translations, rotations and/or reflections on a single 2-D shape,

with and without technology and draw and describe the image 6SS7: Perform a combination of successive transformations of 2-D shapes to create a design and

identify and describe the transformations

Lesson

Items needed or beneficial for the activity: Geoboards and elastics, polygon tiles, paper polygonal shapes, graph paper/paper, protractors, ruler, scissors, SmartBoard

Individual / Small Group Activity

Each 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 Activity

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The 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 Activity

At 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.

Extension

Students 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.

Assessments

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 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 Geometry

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Regular?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.

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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?

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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?

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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?

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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?

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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

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Transformation Tease

Grade 6

Teacher’s Notes

Lesson Summary

Students will perform transformations on a Cartesian plane and identify the coordinates of the shape following the transformation. This activity is from nrich.maths.org.


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 Addressed

6SS8: Identify and plot points in the first quadrant of a Cartesian plane using whole number ordered pairs

6SS9: Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices)

Lesson

This activity can be accessed from http://nrich.maths.org/1111. The nrich teacher notes can be accessed from http://nrich.maths.org/1111/note and a printable page can be accessed from http://nrich.maths.org/1111/note?nomenu=1.

*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

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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.

Assessment

Can 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?

Units

This activity can be used in the following unit:Unit 4: Data RelationshipsUnit 5: Motion Geometry

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