Linear+and+Quadratic+Functions+10

=Beauty is in the Phi of the Beholder=

Grade 7 Number AOI Link: Human Ingenuity //The emphasis in this unit is on ideal proportions and how these are found in nature and used in architecture.//

Textbook reference: MYP Book 2 Chapters 12, 22

Guiding Questions

 * 1) How can beauty be defined? Are these definitions reasonable?
 * 2) How can you use ratio and proportion to connect real world and mathematical ideas?

Benchmarks

 * 1) Master understanding of ratio of a comparison of quantities of the same kind, rates as a comparison of quantities of a different kind, proportions as statements of equivalent ratios and percent as a comparison of the whole amount which is 100%.
 * 2) Find the ratio of two or more quantities
 * 3) Recognize and use common measures of rate
 * 4) Develop, analyze and explain methods for solving proportions such as equivalent ratios, cross multiplication, scaling, etc.
 * 5) Use ratio and proportionality to solve a wide variety of problems.
 * 6) Apply rates to solving problems including speed and density problems.

Unit Assessment Tasks
[|Math 07 - Ratio and Proportion - The Phi Task.docx] ||  || x || x || x ||
 * **Task/Criteria** || **A** || **B** || **C** || **D** ||
 * Investigating Phi
 * Test || x ||  ||   ||   ||

**Knowledge and Understanding**
 * **Content:** || **Extension** ||
 * * ratio
 * proportion
 * rates
 * scale drawing ||  ||
 * **Skills**: ||  ||
 * # demonstrate and understanding of the ideas and notation of ratio
 * 1) provide a definition for the ratio of two or more quantities
 * 2) write a ratio in lowest terms
 * 3) write equivalent ratios
 * 4) divide a quantity into a given ratio
 * 5) solve problems involving ratios and proportions
 * 6) Describe how to use a scale factor to enlarge or reduce a diagram
 * 7) Use scale factors to write proportions to solve problems
 * 8) explain the difference between a ratio and a rate
 * 9) understand the concept, and calculate a unit rate
 * 10) solve problems involving rate ||   ||

Links and Resources
[|Math 07 - Ratio and Proportion - Word Problems involving Ratio.pdf] || Worksheet on ratios and solving problems involving ratio || [|Math 07 - Ratio and Proportion - Rates Homework.pdf] || Worksheet on rates || [|Math 07 - Ratio and Proportion - Ratio and Proportion Check.pdf] || Worksheet and review practice || [|Math 09 - Ratio and Proportion - Ratios and Rates Check.pdf] || Worksheet and review practice ||
 * Ratio practice
 * Rate practice
 * Simplifying ratios || interactive applets ||
 * Equivalent ratios || interactive applets ||
 * The Golden section || Website describing the golden number ||
 * The Phi matrix || Website describing the Phi matrix and how it can be used ||
 * Ratio and proportion check
 * Ratio and rates check
 * [|Math 07 - Ratio and Proportion Challenging Questions.doc] || Challenging ratio and rate questions to differentiate for advanced learners ||

Lesson Sequence
The Divine Proportion


 * investigate ideal proportions using the Vitruvian man concept - "is the ratio of our armspan to our height really equal to 1 as suggested by Vitruvian man?
 * Lesson reference
 * [|Math 07 - Ratio and Proportion - Ideal Proportions]

Ratio and proportion
 * investigate and explore concepts of ratio and proportion. Use the "capture-recapture" activity to consolidate understanding
 * [|Math 07 - Ratio and Proportion - Ratio and Proportion.docx]
 * [|Math 07 - Ratio and Proportion - Solving Proportions Worksheet.pdf]
 * [|Math 07 - Ratio and Proportion - Word Problems involving Proportion.pdf]
 * [|Math 07 - Ratio and Proportion - Ratios Homework.pdf]
 * [|Math 07 - Ratio and Proportion - Word Problems involving Ratio.pdf]

Scale drawings
 * lots of different activities here. See some examples on page 252

Constructing Phi grids
 * students learn to construct a grid in the Geometer's Sketchpad based on proportions of Phi apply it to nature, themselves and other elements of design.
 * [|Math 07 - Ratio and Proportion - The Golden Rectangle and Ratio Activity.pdf]
 * [|Math 07 - Ratio and Proportion - Phi Grids.gsp]

Rates
 * Good opportunity to differentiate for stronger students. See examples in lesson.
 * [|Math 07 - Ratio and Proportion - Rates Worksheet.pdf]