CT-STEM

Modeling U.S. Census Housing Data With Sinusoidal Functions

Modeling U.S. Census Housing Data With Sinusoidal Functions

Subject: Mathematics
Time: 2-3 Class Periods
Level:

Algebra 2, Pre-Calculus, Statistics


Overview

The 2-3 day lesson has three related components. The first activity teaches students how to create a spreadsheet that will allow them to calculate the least squared error of a sample data set. The second activity will be to ensure that students understand the effect of the constants in a sinusoidal function, Asin(Bx+C)+D, as well as how to incorporate a general trend line with the sinusoidal function. The third activity will involve downloading data from the Census Bureau website, fitting a curve to the data and analyzing the model by examining the sum of the squared errors.

Background

Housing-starts data for residential construction is a key leading economic indicator.  Decline in the housing market is often used by economists as a signal that economic difficulties are looming.  Successfully modeling these trends, both on a short-term and long-term basis, can help people make decisions regarding the economy and financial markets.

Compatible With


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tablets

What's Next?

Standards

Computational Thinking in STEM
  • Modeling and Simulation Practices
    • Assessing Computational Models
    • Using Computational Models to Find and Test Solutions
    • Using Computational Models to Understand a Concept
  • Computational Problem Solving Practices
    • Developing Modular Computational Solutions
    • Troubleshooting and Debugging
    • Preparing Problems for Computational Solutions
  • Data Practices
    • Analyzing Data
    • Collecting Data
    • Creating Data
    • Manipulating Data
    • Visualizing Data

Comments, Feedback, and Quesitons

Modeling U.S. Census Housing Data With Sinusoidal Functions

Teacher Notes

Learner Objectives:

  • Students will understand how changes in the constant values A, B, C, and D impact the function Asin(Bx+C)+D.
  • Students will analyze the strength of their model by minimizing the sum of the squared errors.
  • Students will learn how to incorporate a trend line into the sinusoid in the form Asin(Bx+C)+mx+b.

 

Prerequisites

  • In Activity 1, it is assumed that students know how to enter data into their calculator and can find an equation of a line that models the data.
  • Most students will need to be taught how to create a spreadsheet to calculate the sum of the squared errors of a model. 
  • Students who have no familiarity with sinusoidal functions may need to spend more time examining the transformations of the sine function (Activity 2).

Background

Housing-starts data for residential construction is a key leading economic indicator.  Decline in the housing market is often used by economists as a signal that economic difficulties are looming.  Successfully modeling these trends, both on a short-term and long-term basis, can help people make decisions regarding the economy and financial markets.

 

Teaching Notes

The 3 different student activities are as follows:

  1. Learning to enter data into a spreadsheet and calculate the sum of the squared errors.
  2. Learning about the effect of transformational parameters on sinusoidal functions.
  3. Transforming a sinusoidal function to model data gathered from New Residential Construction.

Teachers will need to adjust timing and guidance depending upon the technological and mathematical sophistication of the students.

 

Pre-class Preparation

Teacher should familiarize themselves with the handouts (see below), Census Data website (site), and the online math modeling tool (https://www.desmos.com/calculator).

 

Materials and Tools:

  • Internet access
  • Spreadsheet software

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