# Creating a Proportional Replica of Aileron for a Display

Length:  Two 90-minute class periods

In the spring of 2012, the Aileron sculpture was installed in McCabe Park. This is the former location of the McConnell airfield. The sculpture represents the biplane of the early 20th century. It was fabricated by artist Michael Dillon using traditional blacksmithing techniques and tools that were used in the manufacturing of railroad equipment—another historic reference to Sylvan Park.

In this Mathematics Lesson, students will:

• The students will compae ratios of fractions to help create a proportion
• The students will use be able to recognize and represent proportional relationships.
• The students will demonstratw their understanding of proportional relationships by creating a table and/or graph and exlaning their rationale for proportinality based on evidence from the table and/or graph. The students will be able to discuss directly proportional relationships.
• The students will demonstrate their understanding of proportional relationships by identifying the constant of proportionality (unit rate).
• The students will e able to explain the proportional relationships of the pictures in Task 1 based on their graphs.
• The students will be able to explain the proprotional relationship of the sculptures in Task 2 based on their graphs.
• The students will create a scale drawing of a created artwork. The students will use the drawings to create a sculpture that has proportional dimensions.

### Standards & Objectives

Learning objectives:

Clear Learning Targets:

• I can solve real-world problems using ratio, rates, and proportions.
• I can create a table, graph, and/or equation to epresent the relationship between two or more quantities.
• I can recognise and represent proportional relationships.

• Solve real-world problems using ratios, rates, and proportions.
• create a table, graph, and/or equation.
• Recognize the pattern in a table by comparaing two quantities.
• Graph the quantities to show the relationship.
• Recognize the relationship between two or more quantities as proportional.
Essential and guiding questions:

Assessing Questions:

• What patterns do you notice in the table that you created?
• What relationship fo you notice between the quantities?

• How might you use previous learning to help solve the task?
• What is another way/model you coulf illustrate your thinking?
• What is another tool you could use to solve the problem?
• If you change the dimensions to __, how would that change your answer?
• How can you determin if there is a directly proportional relationship?

### Lesson Variations

Blooms taxonomy level:
Analyzing
Differentiation suggestions:

• The teacher will review the concept of ratios, rates, and unit rates.
• The teacher will review how to set-up and solve a proportion.
• The teacher will monitor students in small groups and use questioning to guide student learning.
• The teacher will demonstrate how to recognize proportional relationships.

Opportunities to differentiate learning: (explain how you address particular student needs by differentiating process, content, or product)

• The teacher will group students  strategically.
• The teacher will use private think time, small group think time, and whole group think time to help students clarify mathematical thinking.
• The teacher will use  intervention/enrichment strategies to meet the diverse needs of learners.
• The students will complete an individual differentiated assignment