Math Menu - Transformational Geometry

How We Express Ourselves OCTOBER 2011

LEARNING ABOUT OUR WORLD THROUGH MATHEMATICS

MATH MENU

Each activity in this menu will help you explore the concepts we are investigating with a small group, a partner, or individually.

Conceptual Understandings:

T

hrough the investigations in this unit you will explore and develop your understanding of the following concepts: •

•

•

Manipulation of shape and space takes place for a particular purpose.

Consolidating what we know of geometric concepts allows us to make sense of and interact with our world.

Geometric tools and methods can be used to solve problems relating to shape and space.

WHO WA S M. C. E S CHE R? Click here to learn more about this amazing mathematical artist.

How will the Math Menu work?

After the pre-assessment, we will have whole class lessons depending on the needs of the class. The remainder of the time will be devoted to guided practice groups and Math Menu time.

•You must stay on task and allow others to complete their work.

Understand these concep ts?

Challenge yourself and complete the project on page 2!

Guidelines •Read the descriptions of the activities before you select.

•Once you choose an activity, you must try to complete it.

•You must record how you spent your time on the Google Form.

•You do not need to complete all of the menu options.

What is the

Golden Ratio?

Learn more at Math Is Fun and Mr. Narain’s website.

Discover The Alhambra Great Buildings on Line The symmetrical patterns

Math Menu

Choose at least 6 activities - you must include 1 from each column and row.

Learning Intentions:

Visual Learners

Auditory Learners

Kinesthetic Learners

Make a glossary of key terms to help someone use the language of mathematics to describe 2D and 3D shapes.

Need help? Go to BBC Bitesize.

Make a podcast to describe the qualities of 2D and 3D shapes using appropriate mathematical language.

Understand the properties of circles

Explore the relationship of a circle’s circumference to its area. After investigating with this tool, do the problems.

Create a chart to record your findings.

Write an instruction book on how to find the circumference and area of a circle.

Listen to the song, Circles.

Complete the online circle problems and check you answers with the key. If you understand how to calculate the diameter, radius, circumference and area of a circle, create a poem that explains the formulae. Recite this poem to a friend or record it and send to Ms Fenton’s dropbox.

Make a circle mobile consisting of at least 5 circles. Each circle should be labelled with the radius, diameter, circumference and area. Write the formula for finding the circumference and the area on separate circles.

Understand the relationships between area and perimeter, between area.

View the interactive video on perimeter and area. Click on the activity button (download the pdf and print) then complete. Create a slide show to explain how to find the area and perimeter of different shapes.

Watch the video and listen to the song, ‘Perimeter’. Explore how you would find the area to shapes in the video (use the information here to help you - perimeter & area) and then create a rap or chant (like the Perimeter song) to teach others how to find the area of the different shapes.

Practice finding the perimeter and area of rectangles. How would you find the perimeter and area of different pattern blocks? Create a picture using the pattern blocks and take a photo of it. Embed the photo on your blog and write a post explaining how you would find the perimeter of your picture and how you would calculate different parts of your picture.

(Provide the answers either in your post or as an embedded file)

Understand the application of flips (reflections), slides (translations) and turns (rotations) will result in a transformation of a plane figure.

Explore tessellations and transformations at Math Interactives. Download the activity, print and complete it while exploring this site. When finished click on the ‘Use It’ tab and play the decorating game, The Flip.

Watch and listen to the lesson on transformations at BrainPop ( you will need to log in). Create a song or chant that explains the key ideas from this presentation.

Trace a pattern block on a piece of grid paper and then conduct a series of slides, flips and rotations, tracing how each move changes the position of the block. Describe the transformation to a friend and record your conversation.

Understand that 2D representations of 3D objects can be used to visualize and solve problems

Use this interactive tool to create a floor plan for our classroom. Experiment with the space until you find a design that you think will work for our class - meeting our needs.

Design a survey for the students in our class to find out their preferences for the layout of our classroom. Based on your results, prepare a floorplan using this interactive tool that will meet our needs.

1. Complete The Castle activity using blocks. For each design you build, take a photo and record your answers to the questions below the photo.

2. Complete Castles on the Ground.

Understand the common language used to describe shapes

2D Shapes Song 3D Shapes Song

Use the nets to build a set of 3D shapes. Show them to a friend and describe their properties. Record your description using GarageBand or Photo Booth.

Just for fun!

Ms Fenton’s Challenge Project

Play MATHO Want to test your geometric vocabulary knowledge? Play MATHO - a bingo type game with geometry.

Quilting Race In this game you try to beat the clock as you complete a symmetrical quilt design.

Tessellation Artist Explore how to create tessellations with this online tool. Scroll down at the site to see the instructions.

Create a design to satisfy Ms Tessell and you will will the contract.

Tessellations in Nature View the film, Mathematics in the Honeycomb (part 1 & part 2). Where else can you find examples?

Geometry Games Visit MathPlay.com to select from a variety of geometry games.

Explore Art & Math View the animated film, Sky and Water and explore the work of mathematical artists. Is there anyone here you would like to learn more about?

Golf Transformations Explore transfor mational geometry with this golf game

by Math Frog.

Looking for a creative designer who understands the Golden Ratio and the beauty of M.C. Escher’s work.

Ms Tessell wants to hire a designer to create a new room in her home. She wants this room to reflect the principles of the Golden Ratio and her love of geometric design. Her favourite building is The Alhambra and she adores the work of M.C. Escher.

She will award the contract to the designer who best brings these ideas together in their proposal.

Guidelines The room has not yet been built - you may determine the dimensions.

Your proposal must include a diagram, indicating windows and doors, with measurements of all elements You must include drawings to illustrate your design proposals for the walls and floor Explanations for the choices you made in your design

Remember...

You must follow the design process. When you submit your proposal to Ms Tessell she will want to see the following: •Research notes •Plans (mock-ups) •Revisions •Final proposal