Experimental science looks at cause and effect types of relationships. Controlled experiments vary one of the factors or traits to observe the effect on another factor or trait. These factors are called variables. A dependent variable is something that is observed and expected to change as a result of modifying another factor in the experiment. That is to say, the outcome depends on another factor. Another name for dependent variable is responding variable. The independent variable is the factor or condition that is changing or being changed by the experimenter. Sometimes waiting is the the condition that is changing, making the independent variable : time. Since we change the independent variable, it is also called the manipulated variable.

Graphing a line

A line can be described mathematically by the equation:

This is referred to as the slope-intercept form. The 2 variables y and x refer to coordinates along each axis. The term m refers to the change in the y-values over the change in the x-values. This is referred to as the slope of the line. The term b, the y-intercept, is the y-value where the line crosses the y-axis.

OR
This is how the slope of a line (m) is determined.

The slope of the line indicates the relationship between the two variables, x and y. The equation of the line indicates to us that “y” occurs as a function of changes to “x”. Sometimes this is represented by the equation . Since “y” depends on “x”, “y is the dependent variable and “x” is the independent variable. As “x” changes, how does “y” change in response? This is what the slope reveals to us.

What does this scatterplot tell us about the relationship between consumption of mozzarella in relationship to years?

How would this graph influence the way you invest in a mozzarella cheese company? Can you predict anything about the future of cheese consumption?

What does the slope of this line indicate to you?

Use mathematics to illustrate this point.

The slope has a unit related to “lbs.” and “year”, what is this unit?

Creating a Line of Best Fit

Not all points collected will fall on a straight line. A Line of Best Fit or a Trendline approximates the average of those points through a mathematical process called the least squares method. While one could “eyeball” this line, the least squares method uses the data to minimize the distance from all those points to the line to have an averaging effect.

Create a column of data for “x” values, “y” values, x^{2} and xy

At the bottom of these columns, sum the data. Σx, Σy, Σx^{2}, Σxy

Take 3 blocks of agar of different size (1cm, 2cm, 3cm) → these are our cell models

Measure the length, width and height of each cube using a ruler

Calculate the area of each face of the cubes and add all the areas together for a single cube

a cube has 6 faces → the total surface area is the same as the area of one side multiplied by 6

Calculate the volume of each cube

Report the surface area-to-volume in the table below

Data Table: Calculating Surface Area-to-Volume Ratio

Cell Model (cube)

Length

Width

Height

Total Surface Area

Volume of cell

Surface Area: Volume

1

2

3

Stop and think:

Which cube has the greatest surface area:volume ratio?

Which cube has the smallest surface area:volume ratio?

Hypothesize: In an osmosis or diffusion experiment, which cube size would have the greatest diffusion rate?

Procedures:

Each group will aquire three agar cubes: A 3cm cube, a 2cm cube, and a 1cm cube. CUT AS ACCURATELY AS POSSIBLE . (This may be already completed for you.)

Place cubes into a beaker and submerge with 200 ml NaOH

Let the cubes soak for approximately 10 minutes.

Periodically, gently stir the solution, or turn the cubes over.

After 10 minutes, remove the NaOH solution

Blot the cubes with a paper towel.

Promptly cut each cube in half and measure the depth to which the pink color has penetrated. Sketch each block’s cross-section.

Record the volume that has remained white in color.

Do the following calculations for each cube and complete the following data table:

We’re all familiar with gelatin (like the Jello brand). Gummy candies are are made of gelatin. Gelatin is a protein that exists as long fibers. When gelatin is dissolved in a liquid and cooled, the gelatin fibers tangle together in a mesh-like network. The space in between the gelatin molecules is filled with the fluid it was dissolved in. Gummy candies are considerably more firm than the gelatin molds we have as desserts because they contain a lot less fluid. Nonetheless, gummy candies are filled with a sugary solution with coloring. Like a cell, a gummy candy placed in solution will be affected by the properties of osmosis when submerged in different solutions.

Stop and think

Is distilled water hypertonic, hypotonic or isotonic compared to the sugar solution inside a gummy candy?

Based on your answer, hypothesize if a gummy candy submerged in distilled water or 40% salt solution will swell faster? Label the diagram below with your hypothesis.

Procedures

Obtain 2 gummy bears and place them in 2 different small flasks.

Drown 1 bear in distilled water and drown the other in 40% salt solution.

At the end of the lab session, remove the bears from solution and document the size difference with your mobile phone.

Hypothesized swelling of the bear based on tonicity