Look for: close to 1.0 g/mL for water,

9.A.1 Use mathematical and computational thinking by graphing mass vs. volume data for different substances and finding the ratio of mass to volume (a unit rate) (scale, proportion, quantity) for the samples measured to determine the density of different clear liquids.

Small group work determining mean (average) densities across samples from multiple groups that yields:

close to 1.0 g/mL for water,

close to 0.78 g/mL for rubbing alcohol, and

• close to 1.26 g/mL for glycerin.
• Though some classes may have results that are within a range of +/- 0.1 g/mL of these values, students in any single class should all find the same relationship between values using data from their particular class.

If students struggle with finding or using unit rates in the context of density or averages you could:

• Provide additional measurements of water or alcohol for students to practice determining unit rates.
• Coordinate with the grade level math teacher to provide other examples and practice finding unit rates students have been working with (or will be working with) in math class.

Show slide I. Orient students to the places where the posters for the three different substances are located. Explain that they should form a line in front of the poster for one of the substances they tested, place their magnet at the appropriate coordinates, and then move to the right and post their sticky notes on the table, allowing the next person to post their magnets and sticky notes. Ask the students who have data for glycerin to start with that poster, students who have data for rubbing alcohol to start with that poster, and the second person of each sub-group pair, should post data for water. This should take about three minutes to post all the data.

Example of the water data to the right.

Analyze and interpret patterns in the graphs and tables. Show slide J. Allow students 3 minutes to record what patterns they notice in the data on a new page of their science notebooks.

Ask students to share out some of the patterns they noticed. Start with patterns within the graph and table for one substance and then shift to having students compare the graphs and tables of different substances.

SUPPORTING STUDENTS IN MAKING CONNECTIONS IN MATH

The goal of this discussion is to make connections to the work that students are doing in their 7th grade math classes, related to two ideas. Students should:

• Decide that mass and volume are in a directly proportional relationship for each substance (for example, this might be demonstrated by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin).
• Identify the constant of proportionality (the unit rate) from tables, graphs, or an expression and identify this unit rate (mass divided by volume) as the density of that substance.

Suggested prompt

Sample student response

What patterns do you notice about the shape of each of the graphs?

They form nearly straight lines.

How does the steepness of the line in each of the three graphs compare?

The line for glycerin is the steepest and the line for rubbing alcohol is the least steep.

Looking at the table for water, what would you say is the increase in grams for each additional mL of the liquid?

Water is about an extra 1 g for every 1 mL.

Looking at the table for glycerin, what would you say is the increase in grams for each additional mL of the liquid?

Glycerin goes up about 1.2 grams for every additional mL.

Looking at the table for rubbing alcohol, what would you say is the increase in grams is for each additional mL of the liquid?

Rubbing alcohol goes up about 0.8 grams for every additional mL.

Say, You’ve seen straight line relationships like this before in math. It looks like this line goes through 0, 0 (zero mL of the substance is 0 grams). When that is the case, we call this sort of pattern a directly proportional relationship. Directly proportional relationships have a constant unit rate—that means as one quantity changes, the other changes in a predictable way. We can find the unit rate for this graph by taking any coordinate point on the graph and dividing the y-value by the corresponding x-value. In our case, that would be any amount of mass in grams divided by a corresponding amount of volume in mL. This will give us the unit rate in grams per mL, which will be the density of the substance. Let’s find the density of water from the relationship between mass and volume for a few different coordinates from our graph.

Add a third column next to each table using a sheet of chart paper that can later be removed. Title this column “mass (C) / volume (D) = density, which…