Title of Lesson: Reviewing and Relearning The Distributive Property
Grade Level: 6-9
Length of Lesson: 25-35 minutes
Day 1: 5-15 minutes
Day 2: 15-20 minutes
Context of Lesson: This lesson would take place during first part of a trimester and be introduced at the end in the last 10-15 minutes of a class hour, as a pre-assessment is handed out to the class and a link then given to the class. Though students have likely been exposed to this concept in previous grades, the targeted population will have demonstrated difficulty with the process of simplifying expressions. Some middle school Special Ed. students however, may have made a transition from a middle school resource room math to a high school Algebra 1 Fundamentals type of class. In this case, they may not be familiar with this concept.
The primary audience for the lesson would be students in Fundamental Algebra courses (probably in 9th grade) and special education students who have had difficulty following proper procedure in math class. The purpose of the lesson is to ensure the students understand that applying “Orders of Operation,” to expressions such as 3(5x +2) can cause problems when the terms in the expression are not like terms, as those terms may not be combined through the operations of addition and subtraction.
Materials/Resources:
Paper
Writing utensils
Access to calculating device
Internet access via computer, cell phone, tablet, to view video accessible on YouTube or
teacher website
One of the following: white/chalkboard, overhead projector, document camera, LCD projector
Overview: While the lesson may be a review a to a select group of students, many of the students to this point have displayed a perception that “Order of Operations,” is carried out the same, regardless of expression make up. For example: Students may believe that 3(5x+2) factors out to be 21x or 15x+2. Many students also fail to show work and confuse themselves in the process. Students will likely demonstrate this misconception as they complete the in-class pre-assessments. Students will then be provided a link to access as an out of class assignment (possibly homework), with the hopes that misconceptions are addressed. The out of class assignment will then be reviewed in the next class and the
Objectives: Students will be able to identify errors in their work, related to misconceptions they began the lesson with, regarding The Distributive Property and Orders of Operations when the integration of variables takes place and only like terms may be combined.
CCSS.MATH.CONTENT.6.EE.A.2.B
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
CCSS.MATH.CONTENT.6.EE.A.3
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
CCSS.MATH.CONTENT.7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Essential Questions:
1. Is there more than one way to evaluate an expression?
2. Does Order of Operations (PEMDAS), as it is stated, always lead you to a direct answer?
3. What is The Distributive Property?
4. How does The Distributive Property provide a more accurate outcome, when dealing with variables?
Anticipated Student Conceptions or Challenges to Understanding:
It is anticipated that many of the students will be concrete in their thinking of “Orders of Operations,” applying the rules of (PEMDAS), despite the presence of variables and presenting incorrect outcomes, i.e., 3(5x+2) = 21x or 15x+2. The challenge here is that students may have missed or need to relearn the concept of combining like terms and The Distributive Property.
Assessment: Students will first be given a short (about 5-10 question) pre-assessment, which will present them with the task of solving various means of multiplying terms through the application of The Distributive Property. The class will be assessed again, the following day about midway through the class session, after reviewing and discussing the online portion.
Procedure:
- Introduction- Leaving 10-12 minutes at the end of the class, students will be given a pre-assessment of a concept which will become prevalent in much of the classwork going forward. Many of the questions will be basic multiplication in various forms, such as 5 x 8, 5(8), (5)(8), to familiarize the students with the concept of using parentheses and numbers in multiplication. Following these, problems may evolve to place two numbers in parentheses, which are being added. For example: 5(8+2), 3(5+6). Finally, variables will be integrated into problems to assess student understanding of combining like terms appropriately. Problems may present as follows: 5(3x+4), 5(x+y).
- Following completion of the quizzes, students will be given a link to access outside of class time. This link will provide a breakdown review of the Distributive Property and its application in the presence of variables. Students are expected to view this on their own time or access a teacher for assistance doing so, if this is not possible. Students will be encouraged to email or meet with one of the teachers for support, if they are confused by the online content.
- The next day, at the beginning of the class period, the class will review the video presentation and discuss The Distributive Property and its application going forward.
- Closure: Hopefully students have viewed the video at home and the following day in class. After reviewing the video in segments with the class, a short, 7-10 question assessment will be given to the class. Time allowing, students will begin work applying the concept the have just reviewed.
Accommodations: Students who do not have online access are responsible for working with a teacher or even peers to ensure they access the material prior to the next class period. Alternate viewing times will be given. Students unable to access the material due to a disability will be afforded opportunities in accordance with their Individualized Education Plans. Other students will provided support(s) as needed throughout the class period.
Notes:
Content: The content being taught here covers Orders of Operation as they may relate to The Distributive Property and could be seen as review, if it is being taught at or above the 8th grade level. Students often inaccurately apply Order of Operations while trying to use The Distributive Property. The CCSS are more in alignment with those of 6th and 7th grades, but the lesson is meant to supplement and assess student readiness for upcoming work in the course. Students will be given a pre-assessment to establish where the class is as a whole, with the expectation that a short video lesson will be viewed outside of class, reviewed again by the class the following day, accompanied by class discussion.
Pedagogy: The lesson will apply the learning theories of Cognitivism and Social Constructivism. Students will be
requested to access prior knowledge, apply previously learned concepts, and, in some cases, restructure some of
their prior knowledge as they access the “Web 2.0” portion of the lesson, in order to better grasp The Distributive
Property. These processes will involve student in both the “Information Processing,” and “Cognitive Constructivism learning theories. The following day, the process becomes more social, as the class discusses the “Web 2.0” assignment and breaks it down as a group, looking for areas of confusion or misconceptions the students had before and have after viewing the online portion of the lesson. This is where the lesson moves into the Social Constructivist theory, as it becomes group discussion, prior to the follow up assessment. Going forward, it is expected that some forms of Social Apprenticeship will evolve as students become more comfortable with the
process and are willing to seek guidance from the teacher and their peers. My hope is that this process will reach
all learners.
requested to access prior knowledge, apply previously learned concepts, and, in some cases, restructure some of
their prior knowledge as they access the “Web 2.0” portion of the lesson, in order to better grasp The Distributive
Property. These processes will involve student in both the “Information Processing,” and “Cognitive Constructivism learning theories. The following day, the process becomes more social, as the class discusses the “Web 2.0” assignment and breaks it down as a group, looking for areas of confusion or misconceptions the students had before and have after viewing the online portion of the lesson. This is where the lesson moves into the Social Constructivist theory, as it becomes group discussion, prior to the follow up assessment. Going forward, it is expected that some forms of Social Apprenticeship will evolve as students become more comfortable with the
process and are willing to seek guidance from the teacher and their peers. My hope is that this process will reach
all learners.
Content & Pedagogy: The hope is that the content is a review for much of the class, but in my experience, this is not often the case with an “Algebra 1 Fundamentals” class and it is important to expose the students to the content, while also assessing what it is they know or think they know coming into to the content. The pre-assessment will give a “ballpark” idea of where the group is in regards to accessing prior learning and any preconceived ideas students have about the concept. The online lesson should give students a different medium with which to access this concept and also give them a non-threatening means to the concept as well. Having a visual and auditory means to absorb the material, while also being able to self-pace the material should be beneficial to multiple learning styles. The following day, the class will have discussion around the lesson and work to address any misconceptions and guide those who are struggling with the general concept in the right direction. This can serve as an indirect formative assessment, though it will not address every student in the class, as the short end of the lesson assessment is intended to do.
Technology: I actually chose to integrate a few technologies we have already used, while also implementing a “Web 2.0” resource we have already used and one I’ve started to dabble with while working in this class. While I saw these as technologies for specific uses in the past, I now see them all as relatively content-general. The technologies I have selected are Keynote, Garageband, and iMovie, to be applied to YouTube. I chose these, because I would like to improve my skills in using them, but also because they are commonly used, practical, don’t seem overly complex, and all three seem to be available for free use to some scale on various platforms, which would allow me flexibility, should I not have the funding to invest in a website membership or a program in the future. While these technologies are not vital to my ability to complete the tasks, they should be beneficial in presenting the material in a different format.
As a Special Education teacher, we are rarely afforded content specific programs. This is especially the case at the high school level. This method affords me the opportunity to create supplementary material, while catering it directly to both my own and the student needs. Additionally, I almost looked at this as a lesson I could create in a co-teaching situation, where I am working to support and supplement the material already being taught in the class.
Technology & Content: Though the ideas are fundamental, they are a very key part of student success within high school mathematics. The technology will afford students another means of accessing the content even after they have left the class. The technology will also take two concepts and show how one may cause confusion in its application of the other. Additionally, students will be given a demonstration of how to properly show their work (albeit on a smaller scale). As a whole, across both the Pedagogy and Content aspects, this technology is content-general and should afford teachers the ability to be flexible in editing and refining its presentation over time.
Assessment: While the assessments will be in class, the online portion of this lesson should afford students the ability to self-assess their understanding of Orders of Operations and The Distributive Property as they go along. Though the class will be given both a pre-assessment and a post-assessment, student will be assessed formatively as the class progresses, based on their ability to apply the concept of The Distributive Property and show their work, as it relates to individual assignments.
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