Lesson Plan #5 CANDURO! 1 of 5! Lesson Plan: Principles of Mathematics, Grade 9, Academic (MPM1D)

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Mervin Byrd
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1 Lesson Plan #5 CANDURO! 1 of 5! Lesson Plan: Principles of Mathematics, Grade 9, Academic (MPM1D) Purpose Context Standard Lesson Outcome(s) This lesson would occur near the beginning of a unit on Number Sense and Algebra, given students will be expected to derive the exponent rules for multiplying and dividing monomials, and knowledge of such rules will be required to complete problems later in the unit. Students will learn to derive the rules through the examination of patterns, and will learn to utilize the aforementioned exponent rules when dealing with expressions of more than one variable. Specifically, students will use manipulatives to expand expressions in an attempt to observe patterns in the exponents. This lesson is heavily based on student discovery, as well as on the use of manipulatives and games. Given knowledge of the exponent rules is necessary in solving later problems in the unit, this lesson occurs near the beginning of the unit. Specifically, this lesson would follow several lessons covering concepts, such as substitution into, and evaluation of algebraic expressions involving natural-number exponents, and relationships between the algebraic and geometric representation of a single variable term. Lessons which follow this lesson would cover concepts, such as derivation of the power of a power rule, simplification of numerical expressions involving integers and rational numbers, relating inverse operations to squaring and taking the square root, and performing operations on polynomials. From THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICS, Number Sense and Algebra (p.30): Derive, through the investigation and examination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents. By the end of this lesson, students will be able to: use manipulatives, paper and pencil to observe patterns in exponents when multiplying and dividing monomials, derive the exponent rules for multiplying and dividing monomials, apply such rules in simplifying expressions involving one and two variables with positive exponents.

2 Lesson Plan #5 CANDURO! 2 of 5! Lesson Assessment Performance- Based Task Students will be placed in pairs and will play a game of memory. Specifically, each pair of students will be given 32 index cards, 16 of which will have a problem involving the multiplication or division of monomials (expressions will sometimes include more than one variable), and the remaining 16 with the corresponding solutions. The cards will be sorted into two piles, based on whether a problem or solution is written on the card, and all cards will be placed face down. Students will play a game of rock, paper, scissors to determine who goes first. The student who wins (student A) will flip one of the problem cards over. Both students will then be required to write down the problem in their academic notebooks, and simplify the expression using the exponent laws previously discovered during the performance-based task. This simplification will constitute as the solution. Student A will then flip over one of the solution cards. If the solution matches the solution in the students academic notebooks, then student A will be able to keep both the problem and solution cards. If the solution on the card does not match, the cards must be flipped over and the process must be repeated until all cards are gone. The teacher will collect the students academic notebooks, and grade them based on correct use of exponent laws. Sixteen points will be possible in this assessment activity. Note that this activity was chosen as a fun way to cement in the knowledge of exponent laws, given that such rules are typically taught in a lecture fashion. Inspiration for the memory game came from Pinterest. Students will be given 10 monomial expressions involving positive exponents, including expressions with natural number bases and variable bases. Students will be asked to write such expressions in a different form. Students will also be asked to model such expressions using coloured wooden blocks. Students will then participate in a think-pair-share activity, where they are expected to compare results and work out any disagreements. The expanded form of each expression will then be provided on the board for student reference. Note that students would have covered this material in a previous lesson and so it should be review. Students will then be asked to contemplate the multiplication of any two of the previously given monomial expressions. They will be asked to illustrate such a multiplication using the coloured blocks. Students will be encouraged to discuss with neighbouring peers. After roughly 15 minutes of contemplation, students will be given a sheet showing example problems of monomial multiplication involving exponents and corresponding solutions, and students will work in pairs to determine any observable patterns, as well as to determine any exponent rules involved. Similarly, students will be given a sheet with example problems of monomials division involving exponents, and will be asked to investigate for any patterns. **See handout #1 & #2 below.

3 Lesson Plan #5 CANDURO! 3 of 5! Procedures Formative Assessment Materials Before: Direct instruction will be used to go through a quick review of the substitution into algebraic expressions involving exponents. Students will be asked to discuss the definition of a monomial (involving exponents) with their neighbouring classmates. Ten students will then be chosen to come and write an example of a monomial (involving exponents) on the board. The teacher will then go through each and will invite the class to agree or disagree. Provided that such examples include a monomial with multiple variables, these ten algebraic expressions will be used during the first part of the performance-based task. During: Students will be given a brief tutorial on how to use wooden block manipulatives, and then will be directed to complete the performance-based task. Students who are struggling with the wooden blocks or with the investigation of patterns will be paired with a student who has mastered the concepts. Students who have mastered the concepts will be asked to complete multiplication and division problems involving monomial expressions with more than two variables. After: Students will be invited to share the patterns which were found during the performance-based task in a class-wide discussion. The exponent rules for multiplication and division will then be written on the board. Students will watch the following video on Youtube, Instructions for the assessment activity will be given. The formative assessment for this lesson will be the reflections which students write after completing the performance-based task. As well, a rich discussion is expected to result during the performance-based task. Students will be evaluated for participation throughout the lesson as well as for depth of reflection and correctness of ideas. Coloured, wooden blocks (manipulatives), Pencil and paper, Academic notebooks, Computer (to show Youtube video), Playing cards for memory game, Handout from teacher (see handouts #1 and #2 below).

4 Lesson Plan #5 CANDURO! 4 of 5! Room Setup Standards for Mathematical Practice Reflection Desks will be arranged in pairs such that students are facing each other, given that the activities in this lesson are mostly collaboration-based. As well, the assessment activity requires that students work in pairs. The standards are incorporated in the following ways: (MP1): Students must make conjectures based on the problems they are given and persevere in identifying a relationship. (MP3): Students must defend the relationship they have identified, and critique those presented by others. During the game, they are expected to positively work through any disagreements until a solution is reached. (MP8): The point of the entire lesson is for students to discover a shortcut when multiplying and dividing monomials that involve exponents. After completing this lesson plan, a few things I have noticed which could be improved upon include: -Not as much emphasis is placed on the division of monomials as on the multiplication, so more time should be allowed to the former of the two. -Direct instruction should not be used to go through the review material - this should be a student-led activity given students should already know the material. -The tutorial for the block manipulative should be done during previous lessons, so that time is not taken away from content. As well, the teacher should demonstrate one or two problems using the manipulatives.

5 Lesson Plan #5 CANDURO! 5 of 5! Handout #1 & #2:

Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview

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