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Mathematics 9 Learn EveryWare
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Mathematics 9: Unit 1 19 Teacher’s Guide
mathematics 9 learn everyware: Teacher’s guide
Unit 1: Geometry of Polygons and 3-D Objects
Unit 1 Introduction
Unit 1 centres on the theme of visually appealing design. The student will look at how visually stimulating logos and packages are created. The concepts of symmetry, transformations, and similar polygons will be applied to visually appealing designs. The student will also look at the use of scale factor in enlargements and reductions of logos that are used in advertising. Surface area will be discussed through analysis of packaging materials and marketing displays.
The following blueprint identifies the critical questions that will be addressed in each lesson of Unit 1. It also identifies specific areas where the student may need additional support with concepts as well as potential misconceptions.Unit 1: Geometry of Polygons and 3-D Objects / MathLinks 9
Chapters 1 and 4
of the course
20 h / Unit Overarching Inquiry/Issue and Unit Problem
Unit inquiry/ Critical Questions
1. How can concepts of symmetry, transformations, similar triangles, and similar polygons be used to make appealing designs?
2. How is reduction or enlargement used to effectively place logos on packaging?
3. How can scale diagrams and scale factors be used to enlarge a logo or product for magazine or billboard advertising?
4. What role does surface area play in determining package size and material requirements?
5. How can surface area be used to effectively market a product?
Unit 1 Project
1. The student pretends to work for a design company that has been asked to create product packaging and branding for a new product. The student creates a logo for a product that incorporates line and rotation symmetry. (This task is based on “Math Links” on pages 5, 15, 25, and 35 of the textbook.)
2. The student enlarges or reduces the logo to fit on the front and side of the product package.
3. The student uses scale diagrams and scale factors to enlarge the logo for a billboard or magazine advertising campaign. (This task is based on “Math Links” on page 145 of the textbook.)
4. The student creates a signature logo for the design company that incorporates similar polygons. (This task is based on “Math Links” on pages 153 and 159 of the textbook.)
5. The student determines the surface area of the individual product package. (This task is based on “Math Links” on pages 35 and 39 of the textbook.)
6. The student designs shipping packaging for holding multiple boxes of the product that ensures minimal material use and maximum use of space. The student will then determine the surface area of the shipment package. (This task is based on “Math Links” on page 39 of the textbook.)
7. The student creates a composite 3-D package sample for the product and determines its surface area. (This task is based on “Math Links” on pages 35 and 39 of the textbook.)
8. The student creates a display unit to showcase the product. / Strand and Specific Outcomes (SOs) of Unit
Strand 3 Shape and Space:
SO 3.2 Determine the surface area of composite 3-D objects to solve problems.
[C, CN, PS, R, V]
SO 3.3 Demonstrate an understanding of similarity of polygons.
[C, CN, PS, R, V]
SO 3.4 Draw and interpret scale diagrams of 2-D shapes.
[CN, R, T, V]
SO 3.5 Demonstrate an understanding of line and rotation symmetry.
[C, CN, PS, V / Unit Assessment
· Lesson Question Sets
· Unit Project
· Unit Test (optional)
P of S / Lesson Inquiry/Essential Questions / Get Focused / Lesson Lab/Assessment Action Learning / Reflections
/Connections / Identify Misconceptions, Difficulties, and Strategies
Unit 1 Introduction
[as shown above] / advertising
SO 3.5 / Lesson 1: Line Symmetry
What role does line symmetry play in creating a visually appealing design? / Introduce examples and non-examples of symmetry. / Identify whether a figure has one or more lines of symmetry (and where they are located) or no lines of symmetry. / Have the student find examples of symmetry in daily life (e.g., advertising, signage, logos). / Identifying location and type of line symmetry.
SO 3.5 / Lesson 2: Rotation Symmetry
What role does rotation symmetry play in creating a visually appealing design? / Introduce examples and non-examples of rotation symmetry. Have the student find examples in daily life (e.g., signage and logos). / Identify the order and angle of rotation for a figure. Determine the direct relationship between order and angle of rotation. / Have the student create a logo for the product packaging that incorporates line and rotation symmetry. Identify the line(s) of symmetry and the order and angle of rotation. / Identifying region of repeating design and calculating angle of rotation. The student may need a reminder of angles on a Cartesian plane.
SO 3.5 / Lesson 3: Transformations
How can transformations yield designs having symmetry and visual appeal? / Introduce examples and non-examples of transformation. Have students find examples in daily life (e.g. signage, logos). / Watch Exploring Tessellations and Transformations (Object Interactive). / Have the student find examples of transformations in daily life (e.g., advertising, signage, logos). / Extension of transformations covered in Grades 6 and 7 Shape and Space outcome. Review Cartesian plane and coordinates. A student who needs more review of previously learned concepts may need more time to complete this lesson.
· understanding that a tessellation has no gaps or overlaps
· understanding that a figure can be transformed in more than one way
· being able to distinguish between the transformations
1 class (may need 2 classes)
SO 3.4 / Lesson 4: Enlargements and Reductions
How can an enlargement or reduction be drawn for two-dimensional (2-D) shapes to produce proportional and visibly identifiable designs? / Identify examples where existing logos have been enlarged or reduced. / The student will analyze an existing product package to determine if all the versions of its logo on the package are proportional. / Have the student determine the dimensions of the product package. Then identify the minimum dimensions of the logo so that it can be visible on the front and side of the product packaging. Using the dimensions of the product packaging, the student should determine the scale factor that needs to be applied to the logo to create proportional logos on the packaging. / Scale factor. Some students may not enlarge or reduce all the dimensions of the new figure.
SO 3.4 / Lesson 5: Scale Diagrams
How can scale be used to create proportionally accurate diagrams? / Find examples in magazines, billboards, etc., where a product’s size has been manipulated to meet specific requirements. / The student will analyze an existing item drawn to scale. He or she will then determine the scale factor. / Enlarge a logo for a magazine or billboard advertising campaign.
SO 3.3, 3.4 / Lesson 6: Similar Triangles
How can similar triangles be used to create visually appealing designs? / Identify logos or products that have similar triangles. / Analyze the use of similar triangles in quilts and architecture.
SO 3.3 / Lesson 7: Similar Polygons
How can similar polygons be used to create visually appealing designs? / Analyze similar polygons used to create
rep-tiles. / Watch Exploring Similarity and Congruence (Video Interactive). / Create a logo for the design company that incorporates similar polygons.
SO 3.2 / Lesson 8: Surface Area
How can symmetry be used to determine the surface area of objects? / Identify products with excessive packaging. Identify products with effective packaging. What makes the packaging effective? / Determine surface area of example product packages used in Lesson 4. / Determine the surface area of the student’s product package based on the optimal logo size determined in
Lesson 4. Design packaging for holding multiple boxes of the product for bulk packaging and shipping that ensures minimal material use and maximum use of space. / SA calculations were part of the Grade 8 Shape and Space curriculum. This lesson will focus more on using symmetry to simplify the SA formulas.
· recognizing which SA formula to use for prisms vs. cylinders
· understanding difference between SA and volume
· recognizing difference between surface area and volume (space utilization) in bulk shipment packaging
· applying concepts of enlargement, reduction, and scale factor to 3-D shapes
SO 3.2 / Lesson 9: Surface Area of Composite 3-D Objects
How can composite 3-D objects be used to maximize surface area to produce visually appealing packaging and displays? / Have the student find examples of different types of composite product packaging. Discuss use of displays in stores. / Determine surface area of example composite packages. One teaching tool could be to have the student break packages apart into nets. / Create a composite
3-D package sample for an individual product based on the optimal logo size that was determined in
Lesson 4. / · recognizing that the composite is made up of two or more objects and determining which SA formula(s) to use for each part of the object
· identifying areas of overlap and subtracting them from the total surface area calculation
1–2 classes / Unit 1 Summary / Project wrap up. Presentation of design portfolio and unit exam.
Unit 1 Project
This project can be completed individually or in a group setting. Throughout this unit, the student is asked to complete certain components of the project. The student is asked to keep track of his or her project work in a portfolio. You may choose to have the student hand in the portfolio at the end of each component or wait and have the completed portfolio submitted at the end of the unit. The student’s designs will be used for the Unit 2 and Unit 3 projects, so it is crucial that the portfolios are kept until that time.
The student will pretend to be working as part of a design company that designs logos, packaging, advertisements, and displays for consumer products. The student will create a logo, packaging, advertisements, and displays for a product of his or her choice. Alternatively, the student can analyze the logo and packaging of a current consumer product.
As the student progresses through each unit, he or she is asked to complete a specific component of the project. The student is advised to refer to the Unit 1 Project Self-Assessment Rubric at the completion of each project component to ensure that the project standards are met.
Unit 1 Project Self-Assessment Rubric4 / 3 / 2 / 1
(How well did I create a plan to accomplish the project tasks?) / · I identified all the important parts of the project and clearly showed how the parts worked together.
· I was able to always show pictures, diagrams, models, or computation to support my plan. / · I identified most of the important parts of the project and generally showed how the parts worked together.
· I was usually able to show pictures, diagrams, models, or computation to support my plan. / · I identified some of the important parts of the project and sometimes showed how the parts worked together.
· I was occasionally able to show pictures, diagrams, models, or computation to support my plan. I show some of the steps, but my plan is not clear. / · I identified almost no important parts of the project.
· My plan is not practical. I show almost none of the steps I use to solve the project components.
(Was I able to communicate how to solve the project components, and were my solutions accurate?) / · I use math terms precisely and appropriately to show I understand how the math is used to solve the project components.
· I correctly solved all of the essential steps in each project component. / · I use math terms accurately and correctly to show I understand how the math is used to solve the project components.
· I correctly solved most of the essential steps in each project component. My errors are minor. / · I use some math terms inappropriately. This makes it difficult to understand how the math is used to solve the project components.
· I correctly solved some of the essential steps in each project component. My errors create confusion in the project components. / · I use a lot of math terms inappropriately. This makes it very difficult to understand how the math is used to solve the project components.
· It is difficult to see if I solved the project component. My errors are distracting.
Diagrams and Sketches
(Was I able to support my thinking with diagrams and sketches?) / · My diagrams and/or sketches effectively convey concepts.
· My diagrams and/or sketches provide meaningful description or explanation of concepts. / · My diagrams and/or sketches are clear and easy to understand.
· My diagrams and/or sketches ensure the concept is easy to understand. / · My diagrams and/or sketches are somewhat difficult to understand.
· My diagrams and/or sketches make it difficult to understand the concept. / · My diagrams and/or sketches are difficult to understand or I did not use any diagrams and/or sketches.
(Did I contribute to my team?) / · I show thorough and detailed evidence of my collaboration.
· I listen to other’s suggestions and work cooperatively on the project. / · I show some evidence of my collaboration.
· I usually listen to other’s suggestions and work cooperatively on the project. / · I present little evidence of my collaboration.
· I rarely listen to other’s suggestions and struggle with working cooperatively on the project. / · I present no evidence of collaboration.
Some components of the project align with “Math Link” activities from the textbook. Various blackline masters are also available on the MathLinks 9 Teacher’s Resource CD-ROM for the corresponding “Math Link” activities. You may find that these are useful scaffolding tools for the student as he or she completes the different project components. The answers to the “Math Link” activities can be found in the MathLinks 9 Teacher’s Resource in the “Chapter 1” section.