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# Summer SAVY, Session 3 Day 5, The One to Beat (3rd – 4th)

Posted by on Friday, June 28, 2024 in blog, SAVY.

Hello SAVY parents,

Today, students learned about several types of graphs that can be used to record data. New vocabulary terms to study include linear relationships, average, slope, intersecting line, horizontal line, vertical line, scatterplot, and slope. I am incredibly pleased with how the students have been using the mathematical terms learned during whole group discussions.

In the morning lesson, students investigated linear relationships by assuming a constant rate of speed for a man walking across the ocean.  They completed a table and a scatter plot (a graph of unconnected dots representing the ordered pairs from the table) showing the relationship of time to distance.  The students noticed that the rate of change was constant, which meant that all points would lie on the same line.  Students made a table for this scenario and then graphed the distance traveled against the time for an additional scenario and compared the two graphs, paying careful attention to the steepness or slope of the lines and what the difference in the steepness indicates.  In both cases, because of the assumed constant rate of travel, students were able to explain why the points for each graph all lie on the same line when they are plotted, and the students understood the term linear relationships.

In the afternoon lesson, students investigated a world record that was set as a community effort by students, Girl Scout troops, senior citizens groups, and others as part of a fund-raiser for a community college. The proceeds of the fundraising went toward college scholarships.  The record that the students investigated involved making a chain of paper links.  Students made their own chains, timed themselves, measured their chains, and determined the chain lengths that they could make in different amounts of time.

In this lesson, we also investigated linear relationships that result from building a chain at a constant rate.  We graphed the data and looked at the steepness of a line (slope) and determined what would happen if the rate changed.  We discussed differences in the starting point (y-intercept) and in steepness (slope). Looking at the shape of the graphs allowed the students to determine the rate at which the participants were working.  A curved line would indicate a non-linear relationship between the variables.  The curved lines are also the results of graphing rates that show when someone has slowed down, sped up, or stopped altogether.  We also looked at a scatter plot and determine the line of best fit and the purpose of that line.

Thank you so much for another successful week of Summer SAVY and I hope every child walks away with a newfound love for mathematics!

Guiding Questions:

• What are some differences in a scatter plot, table, and line graph?
• What kind of graph would be best used to represent the results of two variables each changing at a constant rate?
• Can you produce a real-world scenario that would represent a scatter plot with no correlation?
• How can various graphs be used to represent and analyze data?
• What kind of scatter plot would be used to demonstrate the relationship between the amount of gas in your boat and the time you spend water skiing?

Thank you so much!

–D. Fuller