Unit and Lesson Plan An Artifact for Standard #7 Unit Plans for Unit 6: Following the set Winter/Spring Calendar from Algebra I teaching team: Ms. Sara Straus and Mr. Michael Costello Day
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Th F M Tu W Th F M Tu W
1/29 1/30 2/2 2/3 2/4 2/5 2/6 2/9 2/10 2/11
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8.1 Multiplying Monomials 8.2 Dividing Monomials Review Monomials 8.4 Polynomials Review Quiz on 8.1-8.4 **Graded by Choi 8.5 Adding and Subtracting Polynomials 8.6 Multiply Polynomial by Monomial 8.7 Multiply Polynomials 8.8 Squaring a binomial (special products) Word Problems (like assessment 6B #8 and#9) 12.5 dividing polynomials by monomials 9.1 Finding the greatest common factor Review sheet (We need a warmup with sci not.) Review- go over review sheet in class Test on Ch. 8 (County formative assessment) Graded by Scantron, Costello 9.2 Factoring out the greatest monomial factor 9.2 Zero product Property 9.3 Factoring Trinomials a=1 9.3 zero product property with trinomials
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Homework Assigned Unit 6 Worksheet #1 p421-423 #14-34 Unit 6 Worksheet #2 p434-435 #15-51odds Unit 6 Worksheet #3 Quiz on 8.1, 8.2, 8.4 - No Homework p441 #13-27odd, 30-31 p446-447 #15 - 43 odd p455-456 #14-34 even, 39, 43, 48 p462 #16-32 even Unit 6 Worksheet #4 p669 #4, 5, 11-14 p478 #40-60 Unit 6 Worksheet #5 p469 #20-32 Test: Chapter 8 - No homework p484 #16-28 p485-486 #48-59, 66-74 p493 #17-30 p493 #37-51 Quiz Review: Sections 9.1-9.3 (worksheet)
SNOW DAY Review p840 9.2 #22-27, 9.3 #19-30 Quiz on 9.1-9.3**Graded by Choi Quiz on 9.1-9.3: no homework 9.4 Factoring Trinomials with a not = 1 Page 499 #14-27 More 9.4, with solving the equations Page 499 #35-43, 49-50 9.5 Factoring perfect squares p505-506 #17-29 odd, 34-37, 47 Review Factoring Unit 6 review Go over Review Sheet p519 #10-15, 31-37
Unit 6 County Assessment
*Shaded cells denote days that Jacob Choi wrote the lesson plan and taught
Lesson Plan Form: Day 24 Objective: Factoring Trinomials of the Form ax2+bx+c Goal 1 Functions and Algebra The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions, and algebra. Expectation 1.1 •
The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology. o Focus on Indicator 1.1.4
The student will describe the graph of a non-linear function and discuss its appearance in terms of basic concepts of maxima and minima, roots (zeros), rate of change, domain and range, and continuity.
The objective of today’s lesson is to set up the quadratic equations to be solved for by using the Zero Product Property. Hence, this leads to the roots/zeros described in Indicator 1.1.4 on the Maryland Indicator Level.
The student will describe and apply properties of functions and relations. Students need to recognize that they are working with o A trinomial, and o A quadratic (since the highest power is 2)
The student will perform a variety of operations and geometrical transformations on functions and relations. Not as applicable today, but students need to realize that the trinomial function arises from the multiplication of two binomials. Therefore, their factoring is really an operation of division.
The student will use numerical, algebraic, and graphical representations of functions and relations in order to solve real-world problems. We will leave the graphical representation for later lessons when students will also solve the quadratics, having already factored it first. This way, they can see the relevance of solving these by
using the zero product property later, although they have already seen what the ZPP does with linear functions. Expectation 4.1
The student will describe and represent numbers and their relationships. The student needs to recognize the coefficients in today’s lesson —those are the three numbers that we need to find a relationship between, if it exists Should no relationship exist between the numbers, we call that quadratic a prime—students will be able to test for and identify prime trinomials.
Expectation 4.2 The student will estimate and compute using mental strategies, paper and pencil, and technology. (In today’s lesson, using just paper and pencil—technology has very little input today)
Factor and solve some quadratics with an a=0 coefficient. Prepare these for Activoting to record student data, as shown below:
Bonus: Think Question prepares students for the lesson today—based on the warmup! Moving into the lesson, we return to ask the think question, having rewritten the three warm-up problems without the “=0” as a hint. Anticipated answers for the question include:
They’re all trinomials They all don’t have =0
They all have the degree of 2
All the above are correct, giving us a chance to affirm the students who respond with that, but we will really hunt for
They all have only one copy of an x2 [or anything similar]*
By rolling down the screen (notice the sliding bar on the right) we will slowly reveal the words: “So today’s topic is going to be…”
Pause here and let the students guess after we have discussed this point* above
After revealing the green words students are then asked to â€œwrite down the green titleâ€? Although the green writing is necessary, it is also the same content as the purple header on this next slide, so students can also copy this title too. Once they have done so, have them write down the example, steps, and grid game since they have seen something like these before.
Students are shown that the grid game is remixed by using the same technique as our previous lessons to find the “factors of __”. However instead of just putting the c-term here, we must emphasize to the students, using perhaps a different color pen that we are using “factors of 6x5” in this example….in other words: “You have to multiply the first and last coefficients…remember that this only works in standard form!” This is our BIG POINT for the day! Given two more to try, students are free to work on their own before we try this as a class. I make sure to drill into the students that they have to use the grid to find their solutions like this: Factors of 30 1, 30 2, 15
Adds to.. 31 17 (Stop here)
As a class, we will go over the next two examples using the â€œpink gridâ€? with ample space beneath them. While the class gets about ten minutes to work on these as well as getting any clarifications on a one-on-one basis, two students can come up to the board and complete these two problems at the end of that time after having already done their example. This encourages class participation as the whole crowd can watch and be involved in the factoring process. If the student who is on the board is willing, I ask them to provide a commentary to narrate what they are doing, or else I ask for another student to narrate the steps performed. To conclude with these problems, I will narrate the steps performed in a general manner for both problems. Notice that the second problem includes negative coefficients, which the students have already seen before but not without a first coefficient that is not 1. [See next page] As the class enters its remaining minutes, we toss up some class practice for the students to work on in pairs or individually. These are more challenging problems that mimic the homework, and we have time to go over a few. Notice that there are some there are different combinations of positives and negatives involved too â€”those is tougher and students will have ample opportunities to ask about them.
Since the students already have “eggs” why don’t we do a spot-assessment? With the rivalry against English going on, the students are able to vote in how well they think they know this stuff. Looking at the Activote data later will reveal who we hope will come to Time for Academic Progress.
Lesson Plan Adjustments Throughout each unit, we strive to review previous units’ materials because the HSA demands that cumulative assessment is performed. As such, multiple skills can be tested for in the midst of other questions that revive old skills. Following the above Day 24 lesson, I added on a few buffer questions at the end of Day 25, which as the students guessed right, included an “equals sign”, meaning that they had to solve these quadratics now. Given this new purpose, two sets of buffer questions were slotted in to test them on different abilities.
Day 25—Add-on and Extensions
“It’s weird, but I like it!” said Mr. Costello, after I submitted this slide on the flipchart for Day 25, when we studied Solving Quadratic Equations in the form ax2+bx+c=0. This is one of the most difficult lessons in the whole course. As Michael Costello said to the students, “I’ve taught Algebra I for seven years now, and I can tell you right now that these six days—out of the whole year—these six days can make or break Algebra I for you. Those people who repeat Algebra I usually do so because they didn’t get this week’s material, so pay attention, because the next week’s worth of learning is way important. It’s hard, and that’s okay, because if it was easy, we’d call it English!” In this above exercise, all the students have to do is insert a positive or negative sign for each red question mark. It looks rather easy, but some will have difficulty understanding how to operate these and will need a revision of how two negatives multiplied together give a positive and so on. Although not a computational exercise, it tests the abilities of students to differentiate between possible answers being positive or negative upon distributing the binomials using FOIL, or practicing the grid game we learned today involving the first and last coefficients. CHOI, Jacob