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The Arizona STEM Acceleration Project

The Impact of Rainfall on Tree Growth

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The Impact of Rainfall on Tree Growth

An 8th Grade STEM Lesson

Jennifer Cooke

March 2023

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Notes for Teachers

Context: This lesson takes place in a digital classroom for one period.
This lesson can be adapted for synchronous or asynchronous instruction.
Students must be fluent in the use of Google classroom and the use of calculators.
Students may work in small groups of 2-4.
Quality assurance looks like ensuring students’ graphs are consistent and accurate.
This is the 4th lesson in a series of 4. Links to other lessons are in the Speaker Notes below.

List of Materials

Virtual Project (linked)
Chromebook, laptop or tablet (one per student)
Reliable internet connection
Online graphing calculator
Table of data
Google Classroom (pre-made by teacher, with resources linked)
Online Whiteboard

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Math Standards

8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate and describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8.MP.4 Model with mathematics.

Math Standards, cont.

8.SPA.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

8.SPA.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. 8.MP.2 Reason abstractly and quantitatively

8.MP.8 Look for and express regularity in repeated reasoning..

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Ed Technology Standards

6-8.1.b. Students identify and begin to develop online networks of experts and peers to customize their learning environments in accordance with school policy.

6-8.3.c. Students locate and collect a variety of resources and organize information to make meaningful connections.

6-8.7.a. Students use digital tools to interact with others to develop a richer understanding of different perspectives and cultures.

6-8.7.c. Students perform a variety of roles within a team, using age-appropriate technology to complete a project or solve a problem.

6-8.6.c. Students create artifacts using digital tools to communicate complex ideas textually, visually, graphically, and auditorily.

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Select Web Resources

Whiteboard Whiteboard.fi

Graphing Calculator Desmos | Graphing Calculator

Padlet https://padlet.com/

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Objective(s):

Today we will analyze the relationship between rainfall and tree growth for your sample.

Today we will graphically model that relationship.

Today we will extend and reflect on the entire project.

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Agenda (60 minutes)

Produce Rainfall and Tree Age Tables (20 min)

Model this Relationship (20 min)

Extend and Reflect (20 min)

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Collect Rainfall Data Activity (20 min)

Quality assurance on the process (5 min)

Complete your table via Virtual Project

Teaching Notes

Before releasing students, explain how to fill in the table: they count how many trees in their sample that fall within each age band in the table. Next, explain how to use Desmos graphing calculator to produce a scatterplot. If you have not done this yourself, it’s best to practice beforehand. ��Activity: Students complete their personal age to rainfall table in their journal. Once all students finish, facilitate a discussion on the results:�* Do you expect everyone to have the same number of trees in each age group? Why not? (We each traveled to a different place to sample, the trees one student picked are not the same age as another randomly; because all trees aren’t the same age.)

* Raise your hand if you have the most in (and then call out each Age group 3-6, 7-10, and so forth). Mark these results on the whiteboard at the front of class or on Whiteboard.fi for digital class.��* Do you think there is a pattern? Why or why not?��* Do you think our class’s samples represent a random sample of all the trees in our area? Where would you draw the “boundary line” of that area where the sample is no longer representative? Why?

Source: AZ Precipitation Data, ASU Climate website, http://azclimate.asu.edu/

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Teacher Reference

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Differentiation for Tables

If students do not understand how to complete the table, offer to show them a complete table for reference. Do not re-explain the process. Instead, showing a complete table allows them to make connections and strengthens their reasoning and problem solving.

Remediation

Extension/Enrichment

Students who are done with the tables can act as class facilitators for the summary discussion questions. If you break students into small groups, have the student who finishes first be the Recorder on their whiteboard.fi for the rest of their classmates, taking a leadership role.

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Example of Completed Table

Teaching Notes

Hide this slide from students. Remediation for students who do not understand how to complete the table is rather than explain it, instead show them this completed table. Encourage them to observe the table to learn for themselves on how to complete it. This stretches their own reasoning and problem-solving.

If you use a two-day cycle, first teach students what data to gather and how to collect it in a table. Emphasize they must measure to the tenth. Many students will forget this unless you walk through how to read the tape measure first. Next, assign students to small groups. Using Padlet or Jamboard, have students post images of these southwestern tree species. This front-loads students so that evening, they know what type of tree species to look for. Assign students the task of data gathering that night. The following day, pick up with instruction on how to complete Lesson 2 by calculating their sample’s estimated ages.

If students have already gathered their minimum number of measurements which is at least 20 tree circumferences, then move on to Calculation. �

Instructional Strategy: After students have gathered their sample and prior to calculation, ask students to share out what tree species they used. This is a critical quality assurance check, because some students will not have picked a tree; they will have picked a bush. In those cases, students should be given another day to collect correct tree data. ��For Calculation Activity: Recommend grouping like-species groups together to complete the Calculation activity as small groups, since their growth factor will be the same within each species group.

Also consider an enrichment activity in which you teach students that this similarity grouping is exactly how statisticians use a sampling design called “stratified sampling” in order to control for known variation. Ask students what known variation there is in their groupings.

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Modeling Example

Average Rainfall(in.)

Number of Trees

predicted y = - 0.98x + 14.8

where y = number of trees

where x = ave. rainfall (in.)

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Analyze and Extend

Interpret the line of best fit - do total trees increase or decrease as the average rainfall increases or decreases?
What does this suggest will happen to your tree growth for future rainfall averages? Does this concern you?

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Project Summary

Complete your project summary.

You must write in complete sentences and use clear writing style and punctuation.