# Algebra Concepts and Inequalities Lesson Plan: Height Versus Arm Span

In this lesson plan, which is adaptable for grades 4-8, students use BrainPOP resources to explore inequalities and other related algebra concepts. Students design and conduct an investigation in order to determine and explain the relationship between a person’s height and their arm span. Students will also apply graphing skills to real-world problem solving.

### Students will:

- Design and conduct an investigation in order to determine and explain the relationship between a person’s height and their arm span.
- Apply knowledge of inequalities to real-world problem solving.
- Apply graphing skills to real-world problem solving.

### Materials:

- Posters
- Meter sticks
- Computer with internet access for BrainPOP
- Interactive whiteboard (or just an LCD projector)

### Preparation:

This end-of-unit assessment should follow the teaching of inequalities, graphing and solving inequalities.### Lesson Procedure:

- Build background on the concepts covered in this lesson by showing the related BrainPOP movies as needed.
- Tell students they will conduct an experiment to find out the relationship between height and arm span, and display their findings on a poster. To collect the data, they'll need to measure the height and arm span length of 15 males and 15 females and record the data in a table. They will then calculate averages for heights and arm span lengths. Assign this task for homework.
- Discuss the results in class and help students make inferences based on their data.
- Ask students to create two scatter plots (one for males and one for females). Each scatter plot should include all individuals’ heights and their arm span lengths. Students should label the graph and use appropriate scales. They should also explain any relationships they notice in the data in terms of inequalities. (For example: The height of the average male is (greater than, equal to, or less than) the height of the average female.)
- Students should then determine the linear equation for each scatter plot of data and explain how they arrived at those two equations. Have students solve this system of equations algebraically and explain the meaning of each equation in terms of the context of the situation. They should include the meaning of each variable, slope, and y-intercept.
- Have students graph both equations on one coordinate plane and answer the following questions using correct unit labels: Based on your linear equations, at what height would a girl’s arm span and a boy’s arm span be equal? Based on your linear equations, if a boy was 5’6” tall what would you predict his arm span to be? Based on your data if a girl was 5’6” tall what would you predict her arm span to be? Based on your data if a boy’s arm span is 175 cm what would you predict his height to be? Based on your data if a girl’s arm span is 175 cm what would you predict her height to be?
- Remind students to show all of this information on their posters neatly and creatively.
- After the project is complete, students should write in their reflection journals. Sample topics include: How well does this project represent your knowledge and understanding of algebra? Did this project show you how algebra can be used in the real world? Why or why not? What additional resources would have been helpful in completing this project?