# What Does This Graph Tell You

## Unit Summary

Students choose natural phenomena to research, and then design and conduct experiments or simulations, if applicable. They predict, gather, and analyze data, and then graph the results using spreadsheet software. Students share their findings with the class through a multimedia presentation. A class wiki is created for people in the community to test their skills at interpreting graphs. In an assessment following the presentations and wiki creation, students play a matching game, where they must determine the relevant graphs from sets of clue cards.

## Curriculum-Framing Questions

**Essential Question**Why is studying change important?

**Unit Questions**How do we represent change?

How do we model natural phenomena?

How do we conduct scientific research?**Content Questions**What does this graph tell you?

What functions or equations are represented

## Assessment Processes

View how a variety of student-centered assessments are used in the What Does This Graph Tell You? Unit Plan. These assessments help students and teachers set goals; monitor student progress; provide feedback; assess thinking, processes, performances, and products; and reflect on learning throughout the learning cycle.

## Instructional Procedures

**Day 1**

Pose the Essential Question, *Why is studying change important?* Ask students to think individually about the question and then discuss their responses with each other. Ask for volunteers to share responses with the whole class.

Introduce the following Unit Questions:

*How do we represent change?**How do we model natural phenomena?**How do we conduct scientific research?*

Explain to students that they will be exploring these questions throughout their work on the project.

Divide students into small groups, pass out the What Do These Graphs Tell You? worksheet and ask students to analyze the graphs and share interpretations. Use this activity to assess students’ prior knowledge of graphical information, data interpretation, and analysis of bivariant data. The information you gather from listening to the students analyze and discuss the graphs will allow you to tailor the unit more closely to students’ learning needs. For example, you may find out that students need more experience in analyzing functions that *fit* the data well and may decide to provide them with more opportunities to do this.

**Day 2
**Ask students to brainstorm a list of natural phenomena that they could gather data on in a lab setting. You may need to define

*natural phenomena*(non-artificial events, in the physical sense, that are not produced by humans, such as volcanic eruptions, weather decay, bacteria, aging, and natural disasters). Have students choose three natural phenomena they would like to research and then design experiments to simulate the phenomena.

Place students in groups of three or four based on interest. Remind students to take some details into consideration as they design experiments, such as the selection of experimental units, issues of randomization, factors in simulating natural phenomena, and the number of trials needed to make a generalization.

Review how to use spreadsheets if necessary, especially choosing the best trendline for scatterplot data. Print and pass out the trendline spreadsheet help document as a resource for students.

**Days 3 through 7**

Instruct students to use the following six phases as a

*general*procedure in working on their projects:

- Devise a research question.
- Research the phenomena on the Internet.
- Design the experiment.
- Collect data.
- Produce a scatterplot, analyze it, choose a function over the scatterplot using spreadsheet software, and write an equation.
- Continue research and find phenomena that produce similar graphs and equations.

Note*: You may find it useful to create a chart or document with the guidelines so students have it to follow.*

Distribute the science research process rubric and review with students so that they understand the expectations for conducting research and designing their experiments.

While the students are working during the first four phases of their experiments, use the graphing student observation sheet to make notes and assess students’ work habits, ideas, communication, and cooperation.

During the final two phases of work, use the students observing thinking structured observation as a means to help students see and understand their own thinking and the thinking of others.

**Day 8**

Ask students to prepare a multimedia presentation that addresses:

- Experimental design used
- Graphical representation of the data
- Other phenomena that produce the same graphic results
- How to find the function or equation of the graph
- Why the phenomena is important to study

Refer students back to the science research process rubric and review it with them so that they understand the expectations for the multimedia presentation.

**Day 9**

Instruct students to take notes during the presentations in preparation for the final assessment, which is a graph matching game.

**Day 10**

Copy and cut out the graphs and clue cards from the match game document.

Ask each student to pin one of the graphs onto the back of another student (students should not see their own graphs). Instruct each student to randomly choose from three to five of the “clue cards” that describe the graphs. Encourage students to wander among each other trying to match their clue cards to the correct graphs. Remind students that when they find a match, they should write down the name of the person wearing the graph that matches the clue card directly onto the clue card and then continue until all the clue cards are matched with names. Reinforce the idea that students should not reveal to their classmates which graph is on their back.

**Note: A student might receive a card that matches the graph that the student is wearing. In that case, the student will not be able to find a person wearing the graph. The student should hold onto the card and at the end of the activity determine whether indeed the clue card matches the graph the student is wearing.*

Collect the clue cards at the end and separate them by name of student. Students should then determine what their graphs look like by reading the clue cards with their name. Discuss any discrepancies.

**Day 11
**Have students create a class wiki describing each of the different types of graphs they’ve studied (linear, logarithmic, polynomial, power, exponential, etc.). Ask them to create the wiki so that people from the community can guess the natural phenomena that the different types of graphs represent and then go to a page for solutions. Students can gather data from responses and find which types of graphs are the easiest or most difficult for people to interpret.

## Prerequisite Skills

- Enter data into a spreadsheet
- Write a simple formula for a spreadsheet
- Make scatterplots using technology
- Find regression equations using technology
- Find regression coefficients and evaluate the fit of a regression equation for a scatterplot
- Understand the relationships among various functions and graphs
- Recognize linear, quadratic, higher-degree polynomial, exponential, and trigonometric functions

## Differentiated Instruction

**Resource Student**

- Allow more time as needed
- Provide peer tutoring opportunities before or after school

**Gifted Student**

- Challenge the student to design multiple and varied experiments and situations that result in the same graphic results

**English Language Learner**

- Allow the student to access Internet sites in the student’s first language
- Pair the student with a peer in groups
- Use visuals as a means for explaining the assignments

## Credits

A teacher participated in the Intel® Teach Program, which resulted in this idea for a classroom project. A team of teachers expanded the plan into the example you see here.

#### At a Glance

**Grade**: 9–12**Subjects**: Math, Science**Topics**: Data Analysis, Functions, Trendlines, Modeling**Higher-Order Thinking Skills**: Analysis, Interpretation, Synthesis**Key Learnings**: Interpreting Graphs, Analysis of Bivariant Data, Modeling Phenomena, Representing Change**Time Needed**: 10 class periods, 50-minute classes

#### Mobile Learning

Mobile apps, reviewed by professional educators for related instructional content.

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#### Common Core Alignment

This unit is aligned to Common Core State Standards for Math.

Math: S-ID Interpreting Categorical and Quantitative Data, S-IC Making Inferences and Justifying Conclusions, S-CP Conditional Probability, S-MD Using Probability to Make Decisions