blogs.baruch.cuny.edu€¦  · Web viewFactor Trinomials of the Form . Factor out the greatest common factor and then factor a trinomial of the form . Length of lesson: 45-50mins

Lesson Plan: Section 6.2: Factoring Trinomials: Leading Coefficient of A=1

Teaching point / Objectives:

Factor Trinomials of the Form

Factor out the greatest common factor and then factor a trinomial of the form

Length of lesson: 45-50mins

Materials: Text: Beginning and Intermediate Algebra 6 th Edition-Elayne Martin Gay (pgs. 387- 393)Active Learning Strategy proceduresNumber Puzzle Activity (Print page 32 here)

Active learning strategies that this lesson employs:

1) Number Puzzle- The goal of this puzzle is to prepare students to achieve the goal of this lesson, factoring! However, in a fun and engaging way. Students

are most likely familiar with complete puzzles so here is a way for students to achieve the objective in a way such that they are activating prior knowledge and challenging themselves. (See number puzzle in stage 1 below and/or click on the link to the resource provided above to print a copy for each student to receive at the beginning of class).

2) Group Quiz- After students complete the number puzzle activity and you’ve conducted your mini-lecture, it is time for a 15-20min group quiz. This is a great way to keep the momentum going in the 40mins you have to conduct this lesson and a great to assess mastery of content before beginning the tougher concepts in next class session. The way you will like to conduct the group quiz is up to you, here is a description of the different ways you can do it from Blogs at Baruch’s website:

Activity description: Group quizzes can be conducted in various ways. All methods require that students are divided into groups.

In the first approach, the teacher creates the questions before class. During class, once students are divided into their groups, the teacher poses the questions and gives students time to discuss and record their group’s answers. If using clickers, the teacher may want to present questions one-by-one, giving students time in between questions to discuss (or solve a problem) and submit their answer using the clicker.A more lively approach involves breaking students into teams of 4-5 students. To prepare for this activity, the teacher may want to create a comprehensive outline of material covered in class to be used on the quiz (students could assist in this effort in a previous class). At the beginning of the class, each student would be given a copy of the outline, several notecards, and assigned to a team.Using the outline for guidance, each team creates questions for the quiz. Teams write their questions on the notecard and also include their team

letter in the upper corner of the notecard (to ensure that they do not answer this question). While creating questions teams should also be given time to study for the quiz. After the teams have created a specified number of questions, they turn in their questions and outlines to the teacher.With the class clearly and physically divided into their teams, the teacher presents Team A with a question. If Team A misses the question, Team B gets a chance to answer the question, the question circulates between teams until the right answer is given. The next question goes first to Team B and missed questions circulates to Team C and so on.At the end of the quiz, each team tallies the number of questions they answered correctly.Optional: The teacher could decide to select student-created questions to include in the actual test. This would reward students’ attendance, class participation, and attentiveness.

Real-world connection / focus / word problem connecting lesson to real-world: (What is the connection between this content and a student’s future study or the “real world”? What is the context of this lesson? What problem will you use to hook students into the lesson to make a real-world connection to content that they are going to learn today?)

How are you using this context to introduce or reinforce the teaching point?

“Suppose you're running a factory. There are a number of workers who do certain tasks, many of them requiring a particular tool (e.g., a certain kind of file). Each guy, when he needs a tool, leaves what he's doing and walks over to the place where they keep the tools, checks out the tool, walks back to where he's working, uses the tool, walks back to the place where they keep the tools, and checks it back in. This can happen several times a day. If you're familiar with factoring common monomials, you might think about this: Is it easier to compute 3*19 + 12*19 + 2*19 + 5*19 or (3 + 12 + 2 + 5)*19 ? It's obvious that it's easier to compute the latter, because it requires fewer steps. So you might consider, can the underlying idea be applied to what's happening in the factory? In fact, it can: You could have each worker check out the tools that he needs one time, at the beginning of the shift, and check them back in one time, at the end of the shift. It's really the same kind of reasoning, except one deals with mathematical expressions, and the other deals with manufacturing processes. Do you _need_ to have studied monomial factoring in order to come up with this solution? Not necessarily. But if you've spent several years in math classes, learning to look for ways to eliminate wasted operations, you're much, much more likely to think to look for a solution in the first place, which is the first step to finding one."

Source: http://mathforum.org/library/drmath/view/60957.html

Anticipated time Stage and aim Procedure

15-20mins Task Setting- To give students an active way of engaging with the lecture content so that the teacher can later evaluate understanding

Have students complete the following number puzzle (individually, in peers, or in groups)

5-10mins Presentation of new concept- To clarify/ present the new

You can hook/ transition students into the lesson by saying “factoring a trinomial is the similar to completing a number puzzle!”

material (as students work on something active)

Teacher can continue to present this to students by saying “When you see a trinomial in the form , in order to write it in factored form (you can elaborate a little here on what is factored form- which may look like the following

) )/ a product of two binomials), you have to find two terms that will give you the product of c AND the sum of b.”

Teacher continues by going through an actual example “lets say we had to factor: ”

This is an example from the book and you can go through similar steps with your students:

Teacher continues, “there are also two scenarios you should be aware of when factoring trinomials.”

1. Sometimes it may not be factorable. For example: Factor: . This cannot be factored because there are no two numbers whose sum is 2 and product is 10. So we call this a prime

polynomial.2. Other times, the polynomial may have a common

factor in each term! If this is the case, factor out the greatest common factor before writing the polynomial in factored form. Note: The first step in factoring any polynomial is to factor out the greatest common factor- if there is one other than 1 or -1. For example:

Factor:

1. Factor out the greatest common factor, 3,

2. Now we factor by looking for two factors of -20 whose sum is -8. The factors are -10 and 2. Therefore, the complete factored form is:

15-20mins Test Group Quiz:

Choose 5 out of 20 questions below for students to factor in their groups for the group quiz (pg.392 of textbook). Or as mentioned above, have students create the questions for the quiz and complete the quiz in the manner mentioned above.

Anticipated problems and potential solutions in this lesson (These can be either problems with logistics / timing, or problems to anticipate with students’ knowledge / grasp of the content. Where will students have difficulties? What would you want a newer teacher to anticipate?)

Students may encounter difficulty seeing the connection this lesson has to the real world because in this lesson they are focused on learning how to factor equations. So it will be helpful to make as much connections with students as you can about how they will see these concepts reoccur in upcoming semesters/ future math courses.

Differentiation: In what places in the lesson are you differentiating for students in different ability groups?

Active learning strategies aid all types of learners and the various levels of questioning throughout the lessons aid learners at different levels.

Where are these on your lesson plan?

· Throughout the lesson

Students can also be grouped homogeneously or heterogeneously based on mathematical ability during activities.

Ideas for extensions, notes, considerations, or alternative plans:

When completing the number puzzles, students may not need to spend 10-15 minutes on the puzzle, it can be used as a lead-in to the presentation stage of your lesson.

For the number puzzle, you might have them complete it individually and then check in pairs while you monitor.