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

Academic standards
CCSS.Math.Content.6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all...
CCSS.Math.Content.6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same...
CCSS.Math.Content.6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to...
CCSS.Math.Content.6.NS.C.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and...
CCSS.Math.Content.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings...
CCSS.Math.Content.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0, and use rate language in the context of a ratio relationship....
CCSS.Math.Content.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,...
CCSS.Math.Content.7.RP.A.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different...
CCSS.Math.Content.7.RP.A.2
Recognize and represent proportional relationships between quantities.
CCSS.Math.Content.7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and...
CCSS.Math.Content.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships...
CCSS.Math.Content.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive...
CCSS.Math.Content.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal...
CCSS.Math.Content.8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For...
CCSS.Math.Content.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a...
CCSS.Math.Content.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or...
CCSS.Math.Content.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For...
GLE 0606.2.3
Understand and use ratios, rates and percents.
GLE 0606.3.5
Use multiple representations including symbolic algebra to model and/or solve contextual problems that involve linear relationships.
GLE 0606.3.6
Understand and use the Cartesian coordinate system.
GLE 0706.2.3
Develop an understanding of and apply proportionality.
GLE 0706.3.5
Understand and graph proportional relationships.
GLE 0706.3.6
Conceptualize the meanings of slope using various interpretations, representations, and contexts.
GLE 0706.4.2
Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed.
GLE 0706.4.4
Understand and use ratios, derived quantities, and indirect measurements.
GLE 0806.3.4
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
SPI 0606.2.6
Solve problems involving ratios, rates and percents.
SPI 0606.3.9
Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.
SPI 0706.1.3
Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.
SPI 0706.2.6
Express the ratio between two quantities as a percent, and a percent as a ratio or fraction.
SPI 0706.3.4
Interpret the slope of a line as a unit rate given the graph of a proportional relationship.
SPI 0706.3.5
Represent proportional relationships with equations, tables and graphs.
SPI 0806.1.1
Solve problems involving rate/time/distance (i.e., d = rt).
SPI 0806.1.3
Calculates rates involving cost per unit to determine the best buy.
SPI 0806.3.4
Translate between various representations of a linear function.
SPI 0806.3.7
Identify, compare and contrast functions as linear or nonlinear.
SPI 0806.4.4
Convert between and within the U.S. Customary System and the metric system.
TSS.Math.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0. Use rate language in the context of a ratio relationship.
TSS.Math.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems.
TSS.Math.7.RP.A.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For...
TSS.Math.7.RP.A.2
Recognize and represent proportional relationships between quantities.
TSS.Math.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in...
TSS.Math.8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and derive...
TSS.Math.8.F.A.3
Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
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.

Task Objectives:

  • 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?

Advancing Questions:

  • 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: 

Scaffolding (to address learning difficulties):

  • 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

Helpful Hints

Materials and Resources: