Factoring Binomials

Students enter silently according to the Daily Entrance Routine. Their Do Now assignments are already on their desk and they begin working silently. Today’s warm up assignment includes questions that will assess student understanding of important vocabulary. Much of my questioning for today’s lesson hinges on student understanding of these terms. There are 5 minutes set on the timer for students to complete the questions independently.

At the end of 5 minutes I let students know that this is the same type of vocabulary and questioning that will be included on tomorrow’s quiz. Through these questions I want students to continue thinking through the difference between factors and multiples while also reviewing the definitions of prime numbers, composite numbers, and other related terms. The question that asks about dimensions in a rectangle is placed in this assignment as a result of a question asked in a previous lesson. We were discussing finding the dimensions of a rectangle and one student asked for the definition of the word dimensions. I called on another student to explain only to find that most of the students in the class did not know the definition. It was an important lesson for them and me: never assume. Students assumed they were the only one who didn’t know and I assumed they all knew. We reviewed the definition that day and I am checking for understanding again through question 7 on this assignment.  

I have one student read the aim. I explain that factoring is the opposite of the distributive property and that I will be using integers to show how I factor out a GCF to re-write equivalent expressions.

Sometimes, after we use integers to prove certain theorems and properties, students ask things like, “why don’t you just add 2  and 8 for #1?”. This indicates that students do not understand that I am using an integer expression with two terms to show how I would distribute a binomial. Rather than stating this and confusing the student even more with additional vocabulary, I ask them to take a look at #3. What if a question asked students to find an equivalent expression by factoring?

Once students have seen these first three examples they usually understand the purpose of factoring. I ask all students to work with their partner to factor the GCF out of the rest of the problems, re-writing as an equivalent expression with parentheses. I check for understanding during this time by checking in with students who did not participate during the previous discussions.

At the end of 5 minutes we check all of our answers by having students call out the equivalent expressions, using the sentence guide “The GCF is ____. The equivalent expression is _____ times the quantity _______________”.

Students organize their papers into their binders as I distribute class work. Pairs of students are allowed to join another pair to make a group of 4, but they must come see me before they form a group so that I can approve. It will be explained that they all have 10 minutes to complete all three problems and will then be given a problem to solve on a large piece of chart paper where each student in the group will have a job. If they finish early they may ask me for their materials and problem assignment early. The following lists the duties I give different students in a group depending on the question I assign the group. I make it clear that there are enough steps to be completed in each problem to give everyone in the group an opportunity to show some work.

Question 1:

• All students must multiply 4(5.5) to simplify the right side of the equation entirely.
• One student must copy the problem on the chart paper
• One student must show how to simplify answer choice A
• Another student must show how to simplify answer choice B
• Another student must show how to simplify answer choice C
• Another student must show how to simplify answer choice D

Question 2:

• One student must draw and label the known information o. the chart paper.
• One student must show how they will use the area and the 2 inches to figure out the length of the rectangle.
• Another student must show a check step that proves the answer.
• Another student must write the answer in a complete sentence, making sure to echo the question.

Question 3:

• One student must draw the first rectangle and label it according to the information given in the problem.
• The other student must show the work that shows how to reduce the length so it’s half as long
• Another students must show w check step that proves this answer (encourage a bar model)
• Another student must draw and label the new garden and write the answer in a complete sentence.

During this time I am walking around making sure students are working well together, listening for common errors and asking other students to catch and correct theses errors. I begin encouraging students to place they’re finishing touches within the last 5 minutes of this section as we begin taping the chart papers around the room. We will be using these during a gallery walk.