Tag Archives: simplifying

Dividing a Binomial

If you have taught algebra, you have likely experienced this error. We know many students will make this type of error and we can help many students avoid it by being proactive.

Below are excerpts from a Google Jamboard that can be used to unpack the underlying concept of the division or simplifying shown above. First, start with prior knowledge students can relate to, presented as manipulatives.

Then move, in a CRA fashion, a step towards more symbolic representation of the concept.

Finally, represent the situation in symbolic form. The focus here is to show the problem as two separate division problems to emphasize that both terms are divided. Then write out the simplified expression below.

The approach shown above is an entry point to simplifying rational expressions, with the same type of common errors we see there as well.

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Simplifying Expressions (Combine Like Terms)

Simplifying expressions (see photo below) is one of the most challenging algebra tasks for many students receiving special education services. A major problem is that it is typically presented as symbol manipulation…addressed in very symbolic form.

combine like terms

My approach is to make math relevant and more concrete. Below is a scaffolded handout I use to help unpack the concept. In the handout I start with items the student intuitively understands, tacos and burritos or tacos and dollar bills. In the top left of this handout the student is asked how many tacos he or she has. 3 tacos eventually is written as 3T. See next photo to see how the handout is completed as NOTES for the students.

simplifying expressions tacos

As I work with the problems below I remind the student that the “T” stands for taco so “3T” stands for 3 tacos. This takes the student back to a more concrete understanding of what the symbols mean.

simplifying expressions tacos completed

To address negatives I use photos of eating a taco or burrito. “-2T” is eating 2 tacos.

So “3T – 2T” means I have 3 tacos and ate 2. I have 1 taco left… 1T. For students who may need an even more concrete representation, use actual tacos or other edible items.

simplifying expressions tacos with negatives

 

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Combining Like Tacos (scaffolded handout)

tacos for combining like terms

Here is a snippet of a scaffolded handout I use to teach students how to combine like terms. The tacos bring in prior knowledge and makes the concept more concrete. The scaffolding guides the students as to where and what to write. The full handouts are available by following the links below. I’ve included my webpage address. I don’t care about getting credit but please leave the address on there if you share these handouts. If anyone has follow up questions they know where to find me.

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