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# Predicting the Height of a Criminal (Day 1 of 2)

Lesson 16 of 20

## Objective: SWBAT collect data, create a scatter plot, draw a line of best fit, and write a prediction equation to predict the height of a criminal.

## Big Idea: The fun part of this lesson is to introduce to students that the femur length of a person is directly proportional to their height.

*55 minutes*

#### Introduction

*10 min*

Materials needed:

- Femur project data sheet
- Meter sticks
- Graph paper
- Ruler
- Graphing calculator

I introduce this lesson by reading the first 2 paragraphs of the Femur project while displaying the worksheet in front of the class. The first paragraph connects Forensic Science to solving a crime scene. I may begin class by introducing the career of Forensic Science with a video, depending on the interests of my students.

In a previous lesson, students learned that the measurements of some parts of the human body are proportional. Today I announce to the class that tomorrow they will use this type of reasoning to predict the height of the criminal. Today we will begin working on solving the mystery with an investigation of femur length and height. I expect students to finish Femur Project Day 1 in class today.

It is important to discuss measurement precision when introducing this lesson (Mathematical Practice #6). As a class we discuss the measurement process. We will be measuring in centimeters. If necessary, I model the conversion of feet and inches to centimeters on the board.

For this lesson, I assign students heterogeneously in groups of four to collect their own data. Measuring may be difficult for some students and may need to be modeled by other students for every one to be successful. Each student measures the length of his/her femur from the center of the knee cap to the hip bone. Some students already know their height in feet and inches. If not, this measurement needs to be made as well. The students collate and synthesize the data together by entering it into a single spreadsheet. I will use google docs in my classroom and project the data for all of the students on the wall.

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#### Collect the Data

*30 min*

More time is needed in a lesson when students collect data on their own, but it is worth it for the connections that they make by thinking about the correlation between two variables. In this lesson, identifying the femur length and writing an equation that will predict height based on femur length makes provides a meaningful way for students to engage in modeling linear functions.

As the students work in groups, each student measures their own femur and height in centimeters. One student in each group should be the recorder and enter the group data into the sheet provided. After all of the data is collected a different person from the group enters the data into the class spreadsheet that is displayed on the projector. After all of the data has been collected and entered, I save the spreadsheet (Sample project data) under the class name, for example, Algebra I crime scene data, period 1, and save it to the agenda that every student has access.

**Instructional Notes:**

- Most of my students could not correctly identify the femur bone when at the start of the activity.
- Because we were using their own data, students had fun using the prediction equation to see if it predicts their height accurately.

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After the data table for the class is created, each student must draw and scale their graph. All students need to scale the graph based off of the low and high data points to ensure that all data points are on the graph. As the students work individually I encourage them to plot their points precisely. After all of the points are plotted, the students reflect on the correlation between femur length and height. Then, I ask the students draw the line of best fit through the data points.

My expectation for the students today is for each one of them to: (a) complete their scatter plot, (b) draw the line of best fit, and (c) write the equation for the line of best fit. If students do not complete these tasks, I instruct for them to complete the assignment for homework.

It is important for all of the students to complete this assignment today, so that on Day 2 the class can focus on creating the prediction equation. Students will create prediction equations by hand and with a calculator. Tomorrow the students will compare the results from the two methods of writing the prediction equation. An important element of the analysis is to consider the difference in the accuracy of the prediction equation with each method. I hope that students will be able to compare the results of each method and explain their reasoning (Mathematical Practice #3).

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Sequences
- LESSON 2: The Recursive Process with Arithmetic Sequences
- LESSON 3: Recursive vs. Explicit
- LESSON 4: Increasing, Decreasing, or Constant?
- LESSON 5: Change Us and See What Happens!
- LESSON 6: Why are lines parallel?
- LESSON 7: Get Perpendicular with Geoboards!
- LESSON 8: Dueling Methods for Writing the Equation of a Line
- LESSON 9: Comparing Linear Combinations in Ax +By= C to y=mx +b
- LESSON 10: Equations for Parallel and Perpendicular Lines.
- LESSON 11: Assessment of Graphing Lines through Art!
- LESSON 12: Are x and y Directly or Inversely Proportional? (Day 1 of 2)
- LESSON 13: Are x and y Directly or Inversely Proportional? (Day 2 of 2)
- LESSON 14: Writing, Graphing, and Describing Piecewise Linear Functions
- LESSON 15: Introduction to Scatter Plots, Line of Best Fit, and the Prediction Equation
- LESSON 16: Predicting the Height of a Criminal (Day 1 of 2)
- LESSON 17: Predicting the Height of a Criminal (Day 2 of 2)
- LESSON 18: Predicting Bridge Strength via Data Analysis (Day 1 of 2)
- LESSON 19: Predicting Bridge Strength via Data Analysis (Day 2 of 2)
- LESSON 20: Linear Assessment