July/August 2017 – Vol. 29 No. 8

What Do Math, Science, and Brownies Have in Common? Lab

Posted: Wednesday, June 1st, 2011

by Jeff Bradbury

Question: As an item of food is eaten, does this change its mass, volume, or density?

Purpose: To determine the density of different objects.

Click here for a PDF of the lesson, including formatted handouts.

Part 1 Introduction:

Background Information:

In this lab you will be working in groups of three.

Density is the ratio of mass to volume. It’s a concept with which many students struggle. They have a difficult time doing the mathematical manipulations but they also have a difficult time thinking about how density varies as the size or shape of an object changes. This activity will have us looking at the density of brownies and apples as they are consumed. We’ll try to figure out how the density changes as we eat them.

Example:

A gold nugget has a volume of 35.7 cm3 and a mass of 689.01 g. What is the density of the gold nugget?

Answer: ___________________

What would be the mass of 100 ml of gold?

Answer: ____________________

Brownies:

Does the mass of a brownie change as it is being eaten?

Does the volume of a brownie change as it is being eaten?

Does the density of a brownie change as it is being eaten?

Using a ruler you will measure the length, width, and height of a brownie so that you can calculate its volume. Use the electronic balance to find the brownie’s mass.

For sanitary reasons we’ll use a knife to cut the brownies rather than taking individual bites.

Mass of brownie Volume of brownie Density of brownie
Whole Brownie
After 1st “bite”
After 2nd “bite”
After 3rd “bite”
After 4th “bite”

What conclusion can you make about the density of a brownie as it is being eaten?

Apples:

Does the mass of an apple change as it is being eaten?

Does the volume of an apple change as it is being eaten?

Does the density of an apple change as it is being eaten?

For sanitary reasons we’ll use a knife to cut the apples rather than taking individual bites.

We can’t measure the volume of an apple using a ruler, even if we wanted to approximate the apple as a sphere. To measure its volume we will use an overflow cup to examine the water displacement.

Mass of apple Volume of apple Density of apple
Whole apple
After 1st “bite”
After 2nd “bite”
After 3rd “bite”
After 4th “bite”

What conclusion can you make about the density of apple as it is being eaten?

On the piece of graph paper please plot your brownie data and your apple data. For each, draw in the best fit line.

We can find the mass and volume of objects and predict whether they will float or sink. Simply plot them on our graph and see where they are relative to the density of water.

If we make a density column we can see relative densities of different liquids. We can test unknowns in our density column to figure out relative densities of unknown objects.

Density Columns and Density Column Experiments:

Material Density
Dark Karo syrup or maple syrup 1.37
Light Karo syrup 1.33
Water with food coloring 1.00
Glycerin (colorless) 1.26
Vegetable Oil (yellow) 0.91
Dawn dish washing liquid (blue) 1.03
Rubbing alcohol (colorless) 0.87
Lamp oil 0.80
Honey 1.36
Baby Oil 0.82

The same volume of two different liquids will have different masses. Also, the liquids that have a higher density will sink below the liquids that have a lower density. To test this, you might want to set up a scale and measure the mass of each of the liquids before pouring into your column. Make sure that you are measuring the masses of equal volumes of each liquid. You should find that the masses of the liquids with lower density will be less than the masses of equal volumes of liquids with greater density.

Typical misconceptions students have about density (and sinking and floating):

  • For an object to float it must contain air.
  • When you change the shape of something you change its mass.
  • Mass (heaviness) is the most important factor determining whether an object will sink or float. (For example, kids think big blocks of ice will sink because they are big.)
  • A clay ball, which will sink in water will displace more water than a clay boat made out of the same ball.

Because atoms and molecules are so small we cannot see them. Even with the best microscopes, we are given a very limited view of molecules. Scientists must resort to indirect evidence to create models of what molecules might look like. This kind of science is like having a “Black Box” that cannot be opened. That box contains something that, although it cannot be seen, one can use other ways of discovering what is in the box. The box could be shaken or probed etc. Although it is not perfect knowledge, one can get good approximations or models. Density is one way of “probing” at matter. Now you can come up with a model that helps yourself and others see what causes an object to have density. Use your imagination to draw a diagram of what it might look like at the smallest particle level of each of these objects. Draw “Black Box” diagrams into the space below.

Air Lead

Conclusions and Reflections:

What did you learn about density that you did not know before?

What is something from the lab today that helped you understand density a little better?

Can you say you really understand density if you memorize the definition? Explain.

Click here for a PDF of the lesson, including formatted handouts.

Jeff Bradbury is a professor of chemistry at Cerritos College in Norwalk and is community college director for CSTA.

Written by California Science Teachers Association

California Science Teachers Association

CSTA represents science educators statewide—in every science discipline at every grade level, Kindergarten through University.

3 Responses

  1. Density table needs units.
    I would stay away from “mass (heaviness)” as it hints toward the misconception of mass = force… There are other ways, still simplistic, however more correct to define mass.

  2. Thank you for a fun way to show density in a new way. Can’t wait to do this next year.

  3. Great fun density activity! I suggest using this forum to present actual definition of mass=”the amount of matter in an object…….. “- To help clear this misconception/confusion between mass and weight/force.

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The Commission on Teacher Credentialing (CTC) and Evaluation Systems group of Pearson are currently seeking California science educators to participate in a Science Standard Setting Conference for the California Subject Examinations for Teachers (CSET) program. Each standard setting panel is scheduled to meet for one-day, in Sacramento, California. The fields and dates are listed below:

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