Active Learning Modules for Math & Chemistry

Jordan Hasler, PhD & Jason Sonnenberg, PhD 
Wolfram|Alpha

Math Modules

Fractions

N[(6/5)]

N[(11/12)]

Fitting data to a line

Two points determine a line:

Visualize the line:

Suppose that a set of data has been collected. Set the data

Obtain the line of best fit that approximates the line as best as possible (usually some points will be above and some points will be above):

LinearModelFit[data,{x},{x}]

Obtain the RSquared value:

%299["AdjustedRSquared"]

Visualize the line along with the data:

Show[ListPlot[data,PlotStyle->Red],Plot[%299[x],{x,0.95`,4.5`}]]

Obtain analysis of variance for the data:

%299["ANOVATable"]

Solving equations

Recall that adding zero to an equation preserves its solution:

Solve the equation 2x + 3 = 5:

Try adding something to both sides:

This made it more difficult to solve. Let’s try something else. Recall the additive identity doesn’t change the answer to an equation. Set equation back to 2x+3=5:

Try adding negative 3 to both sides:

Note that the equation now has the variables on the left side and the numerical quantities on the right side. Try to handle the 2 from both sides:

Multiply both sides of 2/a = a/2 by a:

Multiply both sides of 2 = a^2/2 by 2:

Solve for a:

Properties used to handle the multiplication properties:

Quadratic equation solutions

Solve a quadratic equation:

Numericize the roots:

N[{{x->(1/2) (-5-(Sqrt[13]))},{x->(1/2) (-5+(Sqrt[13]))}}]

Solve the general quadratic equation a a (x^2)+b x + c:

Logs and Exponents

Find the log of a list with 10, 100, 1000, 10000:

Compute the pH:

Plot the pH curve:

Define pH:

Solve pH for the corresponding Hydrogen ion concentration:

Check answer:

Polynomials

What are the zeros of x^2+3x+2?

Using the zero product, we see that the zeros are:

Plot a function with zeros at x = -1, -2, and -3:

Notice the point goes through the line y = 0 for each. What happens if we squared a term:

What if we squared the x+2 term instead?

Why was this point below the axis and the first was above the axis when squared?

Plot a function which goes through the axis at x = 3, 5 and “bounces” away from the axis at x=-2:

What happens for large values of x in x^2+2x+3?

Get an overview of the function properties of x^2+2x+3:

Get an interactive property analysis for x^2+2x+3:

Trigonometry

Define a trigonometric function:

Plot the equation f(x) from 0 to 2π:

Determine the maximum:

Determine the minimum:

Suppose that instead we have g(x) = a cos(x) how does the coefficient of cos(x) change the behavior of the function?

Create an interactive plot for g(x):

Increasing a for a > 0 will ______ (increase / decrease) the maximum?

Determine the maximum for a = 3:

Associated Common Core Standards

List the common core standards dealing with fractions:

List a third grade common core standard dealing with fractions:

List a fourth grade common core standard on fractions:

List the standards dealing with algebra:

Return information on reason with equations and inequalities:

More fraction examples:

More algebra examples:

Chemistry Modules

Chemical Conversions

Average Atomic Mass

Compute the average atomic mass of Si.

Gather the abundances for stable isotopes:

Convert from percent abundance to fractional abundance:

The average atomic mass is the sum of fractional abundance times its corresponding isotopic mass:

Check your work:

Clear the variables:

Chemical Structure

How many atoms are in one molecule of (Subscript[C, 8])(Subscript[H, 10])(Subscript[N, 4])(Subscript[O, 2])?

What is the mass percent of nitrogen in this molecule?

Caffeine is a molecule with the formula (Subscript[C, 8])(Subscript[H, 10])(Subscript[N, 4])(Subscript[O, 2]). What is the Lewis structure of caffeine?

How does the Lewis structure compare to the structure diagram?

Type your answer here using full sentences with correct grammar and spelling.

What is the three-dimensional structure of caffeine?

How does that compare with the stick and space-filling plots of caffeine?

Type your answer here using full sentences with correct grammar and spelling.

Reaction Enthalpy

Use bond energies to estimate the change in energy for the reaction of ethene with hydrogen to produce ethane. Then compare the results to experimental data.

Balance the chemical reaction:

Draw the Lewis structure for all chemical species:

Determine which bonds break during the reaction and compute the total bond energy for those bonds:

Determine which bonds form during the reaction and compute the total bond energy for those bonds:

Subtract the total energy of the bonds formed from the total energy of the bonds broken to estimate the reaction energy:

Compare to experimental data:

Titration Analysis of Vinegar

Academic Integrity

By typing my name below, I acknowledge awareness of and adherence to the policies on academic integrity. Furthermore, I certify that the submitted work is entirely my own. I pledge to neither give nor receive any unauthorized assistance on this activity.

Enter full name here.

Data Collection

Record the titrant concentration in moles per liter using SetPrecision to enter the number of significant digits. Assign the results to baseMolarity.

Record the volume of acetic acid in milliliters for each trial as a List using SetPrecision to enter the number of significant digits. Convert the volumes to liters and assign the results to acidVolume.

Record the initial buret reading in milliliters for each trial as a List using SetPrecision to enter the number of significant digits. Assign the results to buretInitial.

Record the final buret reading in milliliters for each trial as a List using SetPrecision to enter the number of significant digits. Assign the results to buretFinal.

Data Analysis

Compute the volume of titrant in mL used in each trial. Assign the results to baseVolume.

Compute the amount of titrant in moles for each trial. Assign the results to baseAmount.

Compute the acid concentration in moles per liter for each trial. Assign the results to acidMolarity.

Results

Compute the average acid concentration in moles per liter. Report your average molarity to the correct number of significant digits.

Type your answer here using full sentences with correct grammar and spelling.

Look up the density of an acetic acid solution with a concentration equal to the average acid molarity. Use SetPrecision to enter the correct number of significant digits in the query.

Convert the the average acid molarity to mass percent using the solution density and the molar mass of acetic acid. Use SetPrecision to enter the correct number of significant digits in the query. Report your average molarity to the correct number of significant digits.

Type your answer here using full sentences with correct grammar and spelling.

Clear the variables used.

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