Instructor: Elizabeth Proll 9th grade Algebra 1 Common Core
Lesson Title: Exponent Inquiry Date: Wednesday, October 15th
- LESSON CONTEXT AND RATIONALE
Culture and Context / The target class population consists of eight students, with 50% Hispanic, 25% Black, and 25% Caucasian and 62.5% of which receive free or reduced lunch.
I have designed this lesson to allow students to discover the properties of exponents through peer collaboration. Throughout the school year, I have encouraged and helped my students begin forming positive attitudes towards mathematics in order to enhance lesson meaning through dialogue based on prior knowledge and experiences of the students’ (Wlodkowski & Ginsberg, 1995). My students often chat with each other during the class period, and in this lesson I plan to utilize their social characteristics to discuss mathematical concepts. During this lesson, students will exhibit autonomy as they hold their partners and themselves accountable for their learning and later present their findings to their remaining peers. These activities will help promote student collaboration, dialogical learning, paraphrasing, and presentation skills which are relevant to their everyday lives and futures as they are preparing to enter the workforce.
Identity and Intellectual Development / Students are offered an opportunity to cooperate with each other as they complete their tasks, and must assume varying roles. The lesson also offers students an occasion to highlight any appropriate strength that they may have, such as an original or creative representation, explanation, or understanding during their presentation. Furthermore, this lesson promotes autonomy and conceptual understanding which pertains to the everyday life of all students.
Lesson Rationale / This lesson is a precursor for the upcoming unit which covers graphing linear and exponential functions. Therefore, this lesson is based on an 8th grade CCGSP standard in order to review this concept from middle school and prepare for using properties of exponents while graphing and evaluating exponential functions.The students have seen these properties previously, but I have observed a lack of firm understanding of them. Thus,in order to solidify student knowledge, I will teach this lesson through student inquiry in which students will explore the properties of exponents in order to formulate their own “rule” for each respective property. My intent for teaching this topic in this manner is that through student inquiry, a deeper conceptual connection in made.
Management / During this lesson, the students will transition from a whole group warm up activity, to small group exploration, and finally to a group presentation. In order to transition students between each lesson component, I will make sure to warn students of the upcoming transitions with time limit warnings and ensure that directions are clearly explained.
- STANDARDS & REQUIREMENTS
CCGSP or GPS Standard(s) / MCC8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Individual Education Plan Goal(s) and Benchmarks / As this is a mathematics resource class, each student in this class has individual education plan goals. The majority of the target class population have not met a standard score on middle grades CRCT testing and have also scored below average on the Wechsler Individual Achievement Test in mathematics. Additionally, a majority of the students within this class have curriculum mastery goals outlined in their individual education plans, such as evaluating and performing operations with real numbers and algebraic expressions/equations as measured by 80% accuracy.
Modification(s) /Accommodation(s) / All students are offered access to the use of a calculator, as defined in their IEP accommodations. Additionally, the majority of students within this class are provided with breaking material into manageable parts, additional time to respond, extra time if effort is shown, and checking work frequently to ensure understanding. Several students also require giving short and concise directions, providing a copy of all notes/study guides, graphic organizers, reading aloud, as well as presenting information visually.
Differentiation / Each pair of students will complete an individual assignment and then share/present their findings to the class. The varying exponent properties have within them varying levels of difficulty and this student pairs will be predetermined by the instructor to meet the appropriate need of each student. The instructor will observe student work for understanding and learning, give multiple means of representation, and promote autonomy of each group in order for all students to be successful with their individualized task.“One approach to meeting each student’s needs is to provide tasks within each student’s zone of proximal development and to ensure that each student in the class has the opportunity to make a meaningful contribution to the class community of learners… instruction within the zone of proximal development allows students, whether with guidance from the teacher or by working with other students, to access new ideas that are beyond what the students know but within their reach” (Small, 2010, p. 2).
The homework assignment for the evening includes two versions, with one extending student knowledge and utilizing the need to use multiple exponent properties in order to solve.
- RESOURCES
Academic Language / The key language demand of this lesson is writing and speaking. Each student will discuss with their partner their predictions for each exponent property as they write and solve their example problems. Finally, each group will also discuss their findings with the whole group during a concluding presentation.
Language Functions / The primary language functions of this lesson are to predict, evaluate, and explain. Each student pair will predict an exponent property from evaluating several examples. The groups will then explain their findings and predictions to the class as they present their property and corresponding “rule.”
Language Vocabulary / Key Vocabulary to be used throughout this lesson:
Exponent / Variable / Coefficient
Power / Product / Quotient
Multiple / Factor / Term
Expression / Equation / Inverse Operation
Like Terms / Perfect Square / Multiplicative Inverses
Materials /
- Poster Board
- Markers/colored pencils
- Calculators
- Exponent Inquiry Student Worksheets
- Exponent Rules Graphic Organizers
- Exponent Homework Versions 1 and 2
Technology / Promethean Board- Each group will be asked to fill in their corresponding box of the Exponent Rules Graphic Organizer at the board in order for other students/groups to take notes. This electronic copy of the class graphic organizer will later be uploaded to our online class portal for student reference and access at any later date.
Calculator- All students will have access to the use of a calculator if needed. A majority of the students have an accommodation of a calculator, which are kept at the front of the classroom for easy access.
- LESSON PROCEDURE
Enduring Understanding / Exponents are useful for representing very large or very small numbers.
Properties of integer exponents can be used to generate equivalent numerical expressions.
Exponent properties can be derived from expanding and simplifying numerical expressions.
Essential Question(s) / How can I apply the properties of integer exponents to generate equivalent numerical expressions?
How do I simplify and evaluate numeric expressions involving integer exponents?
How can the properties of exponents be used to solve this problem?
Lesson Objective(s) / Students will be able to use exponent properties in order to evaluate exponential expressions.
Assessment Link / Students will present their discovered properties to the whole group and explain how they derived their exponent “rule” amongst their group.
Introduction to Lesson / A warm up will be presented at the opening of the class period which asks how to expand an exponential expression, such as. A whole group discussion will follow as well as a prompt of the students to also expand an expression such as.This warm activity is relevant due to the need to expand exponential expressions in the inquiry activity in the body of this lesson.
Following the warm up activity which reinforces prior student knowledge, I will assign each student a partner and explain the body of the lesson, while also providing a visual of the directions on the classroom Promethean Board. Students will then be asked to join together with their partner and begin the exponent inquiry task, following all directions on their task sheet, making a presentation poster of their work, and preparing to present to their peers.
The introduction/warm up activity should take no more than 5 minutes to complete.
Body of Lesson / Students will form pairs to work together on completing their inquiry assignment of one of the four exponent properties. Each assignment lists specific directions as well as questions and activities to guide each group to discover a property of exponents.
I will circulate the room and oversee group dialogue, be available to answer questions or assist as needed, and to assess student comprehension. As this lesson is student centered, I will ask guiding questions of groups in order to keep on task, assist in their inquiry, and guide them to the expected property conclusions as needed. I may need to offer groups additional examples in order to derive a pattern and see the relationship, while other groups may need no assistance. I will allow extra time as needed, while also allowing accelerated groups to complete the activity on more than one property should the instance arise.
The body of the lesson will take 20 to 30 minutes to complete, depending on student needs.
Closure / Students will summarize what they have learned through a presentation to their peers. Each student small group will be expected to present their poster board corresponding to their exponent inquiry topic. Each student group will also be responsible for filling in their respective portions of the exponent graphic organizer that will be projected on the classroom Promethean Board.
The closure should take approximately 15 to 20 minutes to complete.
If any additional class time remains at the conclusion of the group presentations, I will ask students to evaluate several exponential expressions that involve the use of more than one exponent property as a means of additional practice.
Students will also be assigned a homework assignment covering the proper use of the various exponent properties. Each student will be given one of two premade homework assignments, based on their level of comprehension of the exponent rules and their level on continued practice needed.
- ASSESSMENT
Evaluation (Assessment Plan for IEP Goals and/or 504 Plans) / I will assess student learning through evaluating student participation, conceptual understanding, and appropriate language use as they discuss among their group and then present to the entire class. Feedback will be provided as I circulate the room and observe the interactions between each group. The group presentations of their exponent exploration will also serve as a formative assessment, and demonstrate if each group has learned what this lesson intended. Evidence of student understanding will be collected in the form of the overhead exponent properties graphic organizer as it will be saved in an electronic form. In order to collect student assessment of vocabulary use, I will employ the use of checklists of the key vocabulary intended for this lesson. Feedback will also be given along with each groups key vocabulary checklist during the next class period. The student homework assigned for the evening is an additional form of assessment, which will include additional feedback during its return, while a summative assessment will be given at a later date at the conclusion of the current unit.
- REFLECTION
Analyzing Teaching Effectiveness
References
Small, M. & Lin, A. (2010). More Good questions: Great Ways to differentiate secondary
mathematics instruction, Ch.1: Why and how to differentiate math instruction, 1-16. Teacher College Press: USA.
Wlodkowski, R. & Ginsberg, M.B.J. (1995). A framework for culturally responsive teaching. Strengthening Student Engagement, 53(1), pp. 17-21.