The Road to Success


Author:

Jamie Dicks

Unit Title:

The Road to Success

Grade:

7

Subject:

Mathematics

Unit Activities:

Background Knowledge: 

Students will need to have basic knowledge of circles and 2D shapes. Students will also be expected to have knowledge of basic computation.

Date:

July 2013

The Big Idea (including global relevance)

Big Idea: City Planning and Safety

Global Relevance:

Every day, people use different forms of transportation to get from one place to another.  This transportation is planned out carefully by different individuals, especially civil engineers.  The way that the roads are planned out affects everyone because it allows traffic to flow smoothly.  It also creates a safe way to get from one place to another.  By using mathematics and careful planning, many lives are affected by this process.

Through this unit, students will develop knowledge of road maps and find that mathematics is closely related to the planning of transportation routes.  This affects individual students because they are able to see that math is directly related to an aspect of their lives that they experience each and every day. They are also able to take this relevance and apply it to a project of redesigning an intersection.

In addition, if students become involved in designing road maps and city planning, this opens up opportunities for students to develop interest in becoming a civil engineer.  This will affect the community because these students could eventually have a career in engineering in which they will design roadways that will reduce traffic and car crashes in the future.  

The Essential Question
How can we change the most dangerous intersections to make them safer?
Justification for Selection of Content

The 7th grade common core standards cover 2D geometry, such as circumference, area of circles, and area/circumference circle relationships.

The Challenge

Students will choose a known dangerous intersection and redesign it so that it has a roundabout instead of a traditional intersection.

The Hook

Students will watch videos of car crashes at traditional intersections and use previous mathematical knowledge to analyze car crash statistics.  

Teacher's Guiding Questions
  • What is a roundabout?
  • How big does a roundabout need to be?
  • How can you find the circumference of a roundabout if you know how much area it takes up?
  • How do you find circumference?
  • How do you find the area of a circle?
  • How do you find the circumference of a circle?
  • How can we make intersections safer?

ACS (Real world applications; career connections; societal impact)

Applications – This challenge will allow students to see the mathematics involved in designing roadways, which they experience every day in their lives.

Career – This unit has a direct relationship with civil engineering.

Societal – This challenge will allow students to connect with the community by becoming more aware of traffic patterns and ways to make transportation safer.

Engineering Design Process (EDP)

Students will go through the Engineering Design Process as they complete the challenge of creating a road map.  They will have to do research on roundabouts and how they work.  They will come up with a design for a new intersection and present it to their peers by using schoology.  They will reflect on their design and come up with possible revisions after considering several different designs.  

Unit Academic Standard

7.G.4 – Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Unit Activities

Activity 1 (1 Day): The Hook

Day 1: Hook, Essential Questions, Guiding Questions

Activity 2 (1 Day): Pre-Assessment

Day 2 : Pre-Assessment and Survey

Activity 3 (7 Days): Background information on Circles

Day 3: Digits (copyright Pearson) Lesson 11-2 on Center, Radius, and Diameter – assign homework online

Day 4: Digits (copyright Pearson) Lesson 11-2 on Circumference – assign homework online

Day 5: Digits (copyright Pearson) Lesson 11-3 on Area – assign homework online

Day 6: Circle parts, area, and circumference practice in class (differentiated)

Day 7: Digits (copyright Pearson) Lesson 11-4 on Relating Area and Circumference

Day 8: Practice on Relating Area and Circumference (differentiated)

Day 9: Digits (copyright Pearson) Lesson 11-5 on Problem Solving

(Worksheet c: Digits Topic 11 Notes)

Activity 4: Civil Engineer Visit

Day 10: Civil Engineer comes in to talk about creating safe intersections and roundabouts

Activity 5: Roundabouts Lab

Day 11: Roundabouts lab

Day 12: Anderson Ferry/Foley Intersection problem

Activity 6: The Challenge: Designing a Safer Intersection

Day 13: Challenge: teams research intersection (give list if students cannot find out) and redesign it so that it has a roundabout

Day 14:  Finish challenge

Activity 7: Review Post-Assessment

Day 15: Review of Topic 11

Day 16: Post-Assessment and Survey

Where the CBL and EDP appear in the Unit

Activity 1: The Hook

Activity 5: Roundabouts Lab

Activity 6: The Challenge: Designing a Safer Intersection

Misconceptions

A square and circle with the same area should have the same distance around the outside.

Additional Resources

Misconceptions in geometry: http://geometrymodule.wikispaces.com/file/view/Misconceptions.pdf

Results: Evidence of Growth in Student Learning


Results

CCSS.Math.Content.HSG-C.A.1 Prove that all circles are similar.

CCSS.Math.Content.HSG-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

CCSS.Math.Content.HSG-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

CCSS.Math.Content.HSG-C.A.4 (+) Construct a tangent line from a point outside a given circle to the circle.

Reflection

 I believe that this unit went extremely well. The students were extremely engaged in the challenge because they like to use their creativity to solve problems. The engineer visit was the best part of the unit. It helped the students to actually see what an engineer does in real life. I would add more time to the unit next time.