My algebra students need extra practice with the concept of multiplying and dividing monomials, because the new knowledge often interferes with what they "knew" earlier. For instance, an expression such as 2^3+2^4 will often result in the incorrect 2^7, because the students absentmindedly add the exponents.
This worksheet gives them mixed practice in the hopes of fixing those misunderstandings before a summative assessment.
To open this lesson, I work through a single example with them: I make up a problem similar to problem 12. Then I set them to work in cooperative groups, and I ask them to check their answers with one another as they work. I level with them, and acknowledge that it is uncommon for everyone to work at the same pace. However, when the "slowest-paced" student finishes a problem, they are all expected to check their answers with one another. If they can't come to a resolution, I ask them to call me over, with the caveat that if Marcy has a question, I will say to Timmy, "Timmy, what is Marcy's question?", which forces them to discuss one another's questions first.
As they finish up the first block of problems, I ask them if any of their group members caught any errors, in virtually every student says that yes, their group did find an error in their work.
I encourage my students, "When in doubt, write it out!" to help them correctly simplify many of the expressions on this worksheet.
I have included some spiral review problems, such as a tree diagram. (If your students haven't done that yet, you may edit it out or replace it with something you've studied recently.)
This worksheet is intended for students to show their work on a separate sheet of paper.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may edit for your students.
Keywords: monomials, multiplying monomials, dividing monomials, algebra, exponents, rules of exponents, compound interest, tree diagrams, conditional probability, Jonnard