Foil and Unfoil Practice

Objectives:
-Students will foil (multiply) two binomials.
-Students will unfoil (factor out) binomials from a quadratic.
-Students will correct and critique other student work.

Introduction:
This lesson was created through a game I and my family use to play when we were younger in which one person would write a story and the other person would illustrate that story. We would then pass the paper, hiding the original story while revealing the illustration and have another person try to guess what the original story was based solely of the picture. It was fun to see how the story evolved and digressed from the original.

This activity involves playing this very game , and then adapting the game to allow students to practice foiling and unfoiling polynomials.

After a sufficient number of passes students will then receive their original paper and have an opportunity to correct any mistakes that were made during the activity, thus appealing to a higher order of thinking.

Introductory Game:
Have every student get a piece of paper out and fold it horizontally 3-5 times. Their paper should look like this. You don’t need to many folds, and want enough space for the students to write and draw pictures.

Have each student write a silly (appropriate) short sentence in the top rectangle of the paper accompanied with their name. An example could be: “I drank a grape soda and my hair turned purple.”

After every student has written a quick sentence have everyone pass their paper to the person to their left (or right, or however you want them to exchange papers.) Have the students then draw a picture for the story. The picture can not contain any words itself for example a student should not’t draw a person with a can of soda and the words “grape soda”.

Once every one is done drawing their pictures have the students fold the top rectangle back, hiding the original text and only showing the picture, and then pass the paper once again to the person to their left. Every student should now have a new piece of paper only revealing an illustration. After receiving the new piece of paper the students then write a sentence about what they think the illustration is about. After everyone is done writing the sentence, they fold the picture back, so only the sentence is revealed and then pass the paper again.

You have the class repeat this behavior as many times as you want, having the students alternate between reading a sentence and drawing a picture and looking at a picture and writing a sentence. You can do this activity for as however long you want, but I find that about 8-10 minutes is sufficient. Have the students return the paper to the original owner. Let the students laugh about how the sentence evolved and at some of the silly drawings. Now that everyone is engaged and understands how the game works you adapt it to help your students practice foiling and unfoiling.

Transition into Math:
Have your students pull out a new piece of paper with their name on the top and fold it 3-5 times horizontally, just like they did before. Instead of writing a silly sentence, have the students write 2 binomials that are being multiplied together. An example is (2x+3)(x-4). Tell the students to keep it relatively simple with no decimals or extremely large numbers.

After everyone has written their binomials have them pass their papers to the left. On the paper, in the second section, have the students multiply (FOIL) the binomials together. Once all the students are done have them fold the top backwards, thus hiding the original problem from view while still showing the most recent work. Have all the students pass the papers and UNFOIL the quadratic that is visible. Once they have UNFOILED the quadratic have the students fold the top section backwards and then once again pass their papers. The students will repeat FOILing and UNFOILing the problem several times. When you believe your students have practice foiling and unfoiling sufficiently, have the students return the paper back to the original creator.

With their original papers the students now look whether or not their binomials were FOILed or UNFOILed correctly. Have them correct any mistakes and write a short explanation of what was done wrong. You can then collect the corrections as homework.

Expected Student Behavior:
Students love the game and it will get them talking and laughing. When you transition in UNFOILing and FOILing the students will understand the process and work quite well. Make sure not to go to long on either section of the activity though or else the repetitive nature of the activity will claim the attention and dedication of a few of your students.

Modifications:
You can use this same idea for any math concept that goes two ways, for example you could replace FOILing and UNFOILing with factoring and distributing; or derivatives and integrals.

Feedback:
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If you have a minute or two to spare and would like to share how this activity went in your classroom or if you have any questions, think that the activity could be clearer, find a typo or a mistake, or have any other great lesson plan ideas that you would like to share please e-mail us at: teacherresources@unpracticalmath.com