# Your Hood

 Author: Kevin Tucker Unit Title: Your Hood Grade: 12 Subject: Pre-Calculus Estimated Duration: 5 – 48 Minutes class periods Unit Activities: Activity 1: Essential and Guiding Questions Activity 2: Finding the area of your yard Activity 3:  Designing your neighborhood Activity 4:  Presenting your design Background Knowledge:  Students have used sine, cosine, and tangent with right triangles to find missing sides and angles.  Students know the formulas for the Law of Sines, the Law of Cosines. And the area formula for non-right triangles using sine or Heron’s formula Date: July 2013
##### The Big Idea (including global relevance)

Applying the Law of Sines and the Law of Cosines to surveying.

##### The Essential Question

What goes into designing and building a subdivision?

##### Justification for Selection of Content

Real world application of trigonometry including the Law of Sines and the Law of Cosines.

##### The Challenge

To design a subdivision given a sample plot of land.

##### The Hook

During the past 2 years the district has been building a new middles school and high school.  All of the elementary schools have been built in the last 5 years.  The students have seen a lot of construction happening.

##### Teacher's Guiding Questions
1. What does a neighborhood need?
2. How big should the lots be?
3. How will we measure the size of the lot?
4. How many lots should the neighborhood have?
5. Are there any things you can add to the neighborhood to make it more marketable?
##### ACS (Real world applications; career connections; societal impact)

A – (Real World Application):  The Law of Sines and Cosines will allow students to find the missing sides or angles of non-right triangles.  This can be used in surveying.

C – (Career Connections): Surveying.  Use of fire towers in the national forest service. Civil Engineering.

S – (Societal Impact):  If you are going to build a fence around your yard you need to know where your yard is.  If you build the fence on your neighbor’s property you will have to tear it down and start again.  When a subdivision is built you need to take into account how large of houses are to be built.  If you are building \$300,000 houses you need more land than say a \$150,000 house, because the house will have a larger footprint.

##### Engineering Design Process (EDP)

Students will subdivide a sample plot of land in order to create their own subdivision.  Students will have to research subdivision and house designs.  They will come up with a subdivision concept and then sketch out possible subdivision plans. After the groups decide on a final design they will have to build a scale survey plot and label the distances and angles.  Students will have to find the area of each plot of land.  The subdivision must be feasible.  Each house must be accessible by a street.

##### Unit Academic Standard

HSG-SRT.D.11 – Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in non-right triangles.

##### Unit Activities

Lesson 1:  Surveying and the Laws of Sines and Cosines

Lesson 1 will focus on using the Laws of Sines and Cosines in surveying.  For this project we will use plat maps as students create their own neighborhood.  Students will use the Laws of Sines and Cosines to find missing measurements on their plat maps.  Students will then find the area of their plot of land.

Activity 1: Essential and Guiding Questions for surveying and plat map

3.1.1. Your Hood_Essential Questions_KTucker_July 23 2013

Activity 2: Finding the area of your yard

3.1.2. Your Hood_The area of your yard_KTucker_July 23 2013

Lesson 2: The Plat Map:

Lesson 2 will focus on students creating their own neighborhood.  I will give students a sample plot of land that they will have to subdivide.  As students create their own neighborhood they will have to take into account where the neighborhood will be located, how large the plots of land will be.  Students will then present their neighborhood to the class.

Activity 3:  Designing your neighborhood

3.2.3. Your Hood_Designing your Subdivision_KTucker_July 23 2013

Activity 4:  Presenting your design

3.2.4. Your Hood_Presentations_KTucker_July 23 2013

##### Where the CBL and EDP appear in the Unit

The EDP will appear in lesson 2 activities 3 and 4.

Activity 3.

Identify Problem:

Students will identify the problem (designing a subdivision on a given plot of land.)  The Students will have to take into account where the neighborhood is to determine what how large to make the plots of land.

Brainstorm Ideas:

Students will have to take onto account the criteria given (must have at least 6 plots of land.) as well as constraints based on where the neighborhood is located.  Students will need to decide if their neighborhood will have any amenities (park, Dog Park, community pool, etc.).

Design:

Students will create a model of their neighborhood on a standard sheet of paper.  The group will refine their model as needed to meet the criteria.

Activity 4.

Share solution:

The group will build their final plat map on a 36 in by 48 in poster (scale 1in = 12 feet).  For each plot of land the groups will have to calculate the area and label the dimensions and angles.  The groups will then present their proposed neighborhood to the class.  In the presentation the groups will talk about the criteria they used and why they made the decisions they did in the design of their neighborhood.

##### Misconceptions

In the real world application we typically do not have right triangles, and rectangles.  Surveyors use simple trig to map out plots of land.

##### Additional Resources

Plat maps of local neighborhoods (I was unable to get Plat Maps for the local neighborhoods.

I found these resources online.

http://activerain.com/image_store/uploads/1/7/0/6/0/ar126892937606071.jpg

http://am-engineering-surveying.com/wp-content/uploads/2011/12/Residential_Subdivision_EX.jpg

http://trustlands.utah.gov/development/maps/ShelterCoveMapSubdivisionPlat.jpg

##### Results: Evidence of Growth in Student Learning

After analyzing the Pre-Assessment and Post-Assessment data.  I noticed that the grades increased significantly.  The assessment was only 3 questions for each with a possible 25 points.  The 1st 2 questions were the based on the law of sines.  The 3rd question used the law of sines the law of cosines and the area formula for a non-right triangle.  The average score on the pre-assessment was an 8.9 and the average score on the post assessment was an 11.54.  This was a 29.6% increase.  On the Pre-Assessment most students scored well on questions 1 and 2 but made almost no progress on question 3.  On the post assessment over 50 percent of the class made progress on question 3.  One of the issues was that the Unit took Longer than anticipated so the post assessment came 1 week after all of the final calculations were made do to presentations and snow days.

##### How to Make This a Hierarchical Unit

For a Middle School Unit the groups can create their neighborhood using specific shapes with known area formulas (rectangle, triangle, trapezoid, square, and circle.)

##### Reflection

The success of the lesson is that the students had to put in the time and the effort to learn the material.  Much of the class time had students discussing ideas and working together as a team to find possible solutions and share ideas, and concerns.  Since this was the second unit I taught from the CEEMS project I felt that going over the essential and guiding questions went much better this time around.  I had the students work in their groups to come up with a list of questions.  I gave the students about 8 minutes to come up with their list of questions and had each group share 2 or 3 of their questions.  As a class we decided if it is an essential or a guiding question.  After each group shared I asked if there were any other questions they would like to add.  This worked better because each group was forced to contribute something to the conversation and by allowing the students to add at the end everyone could have their ideas heard.

A short coming for the lesson was students managing their time (me helping them to manage their time).  At the end of the week (on a Friday) we discussed that the groups should finalize their plans so they can start to draw out their subdivision then next week.  We had a snow day on Monday and 75% of the groups spent Tuesday finalizing their sketches and did not start drawing the actual subdivision until Wednesday.  I should have made the sketches work points and collected it on Monday (Tuesday).  I realized though this project that I need to give the students mini deadlines to help keep them on track.

Another shortcoming of the lesson was deciding how much guidance or correction to give each group in creating their subdivision.  The math behind the lesson was not the issue as much as the underlying issues that arise when creating a subdivision.  Many of the students wanted to create a subdivision for mansions but were only given about 4.25 acres that had to be divided into a least 6 plots.  I kept suggesting to groups to find sample floor plans and check the dimensions to make sure that the house will fit.  Which they did to some degree.  But when it came time for presentations they talked about how much yard you would have and you could do all of this stuff in your yard but did not actually calculate it or draw the house on the property.  One group had a 4900 sq.ft. house on 8100 sq.ft.  They were surprised to find that this means they have about 10 ft of yard all the way around the house (not much space).  On the plus side this gave us some topics to discuss after each group had presented and if time permitted students would have been able to make some changes and redesign their properties.  Next time I will also assign students with a price range for the housing.  Almost every group was designing for \$500,000-\$1,000,000 Houses.

As with the 1st lesson another short coming of the lesson was time.  Again this lesson was supposed to take 5 days.  In reality it was more like 15.  This time some of the issues were out of my control.  We had 2 snow days and the school was on a late arrival schedule (due to the Ohio Graduation Test) so I only saw one of the classes twice during the week and the other class I only saw once.