Learning Strategies Lesson Learning Strategies Lesson According to Dr. Deshler, most students begin to experience a performance gap in the fifth grade (Laureate Education, Inc. , 2012a). The bridge to close this gap is built by changing the pedagogy of the teacher and the learning strategies of the students. The learning strategies taught to the students enable them to develop into independent thinkers and learners (Friend & Bursuck, 2009). Student-centered learning incorporates effective learning strategies with the mathematics curriculum and provides students with the means to meet their potential.
Every sixth grade student learns to transition from multiplication with numbers to variables. This transition also includes a development from the distributive property of a monomial times a binomial to the product of two binomials. Finding the product of two binomials can be a daunting task, unless students are presented the material in connection with a learning strategy that they are able to master. The lesson, found in the appendix, is designed to facilitate the evolution of multiplication of monomials and binomials.
It was taught to one struggling seventh grade student who is the product of social passing throughout her mathematical career. The mathematics was written to help the young lady succeed, despite other mathematical shortcoming that could stand in her way. The lesson was designed to begin with a review of mathematical vocabulary and the distributive property. Students learn better when new concepts are anchored to known or familiar ideas. The young lady has a solid understanding of the distributive property, but struggles with vocabulary.
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The warm-up program and Activity 1 provide the opportunity to align the vocabulary with the process that she has already mastered. This prior knowledge was then completed under a guided practice, with the student summarizing the process in her own words giving her ownership of the concept. The next step in the lesson was to connect the distributive property to multiplying binomials. Although this is an effective method for simplifying these products, it requires more writing and can be time consuming. With these hindrances in mind, the lesson moved into teaching the multiplication of binomials using the FOIL strategy.
FOIL stands for the product of the First terms plus the product of the Outer terms plus the product of the Inner terms plus the product of the Last terms. The lesson connected these products to the corresponding letters of the word. Another method was taught during the FOIL process and this method was the quickest for her to acquire. It entailed drawing the lines to connect the First terms, the Outer terms, the Inner terms and the Last terms. When drawn above and below the binomials, the lemonhead face is formed.
After numerous examples of these methods were practiced, the student completed some on her own. At the end of our time together, she went home with 10 problems assigned through our online mathematics program, Digits. Her score showed that she correctly worked 8 out of 10 problems correctly. Upon looking at her mistakes, both were errors in multiplying positive and negative numbers. According to Benson (2012), student-centered learning promotes authentic learning, helps students develop critical thinking skills and increases metacognitive awareness.
By working through a well-developed lesson, teachers have the opportunity to teach, model and cue the use of various student-centered learning strategies (Laureate Education, Inc. , 2012 b). Students, with and without special needs, struggle to attain the skills learned throughout their educational careers. By becoming strategic learners, students are able to move past their difficulties through the incorporation of effective learning strategies. References Benson, S. (2012). The Relative Merits of PBL (Problem-Based Learning) in University Education. Online Submission. Retrieved April 2, 2013.
Friend, M. , & Bursuck, W. D. (2009). Including students with special needs: A practical guide for classroom teachers (5th Ed. ). Upper Saddle River, NJ: Merrill. Laureate Education, Inc. (Executive Producer). (2012a). Content Enhancements. [Webcast]. Baltimore: Author. Laureate Education, Inc. (Executive Producer). (2012b). Learning Strategies. [Webcast]. Baltimore: Author. Appendix Lesson Plan- Multiplication of binomials Standard: 6. EE. A. 3 Apply the properties of operations to generate equivalent expressions Warm-Up Problem (WUP) What do the following words mean?
Product, sum, difference, binomial, increased by, decreased by Rewrite as 3(1+-2x) Rewrite as 3(1+-2x) Activity 1: Review the Distributive Property Directions: Multiply Ex. 1 4(5x + 7)Ex. 2 3(1 - 2x) 4(5x) + 4(7) 3(1) + 3(-2x) Rewrite as -8(-1+-9x) Rewrite as -8(-1+-9x) 20x + 28 3 + -6x = 3 - 6x Ex. 3 -2(6x + 11)Ex. 4 -8(-1 - 9x) -2(6x) + -2(11) -8(-1) + -8(-9x) -12x + -22 = -12x - 22 8 + 72x Activity 2: Try these on your own (OYO)! OYO 1 -5(x – 10)OYO 2 Write a brief summary of -5 (1x + -10)how to use the distributive property. 5(1x) + -5 (-10) -5x + 50 Activity 3: Multiply two binomials using the distributive property Ex. 5 (3x + 4)(x + 5)Ex. 6 (x + 3)(x - 12) 3x(x + 5) + 4(x + 5) x(x - 12) + 3(x - 12) 3x2 + 15x + 4x + 20 x2 – 12x + 3x -36 3x2 + 19x + 20 x2 – 9x – 36 (Continued on next page) Ex. 7 (3 – 2x)(2 – 3x)Ex. 8 (x + 2)(5x - 6) 3(2 + -3x) + -2x(2 + -3x) x(5x + - 6) + 2(5x + -6) 6 + -9x + -4x + 6x2 5x2 +-6x + 10x + -12 6x2 + -13x + 6 5 x2 + 4x – 12
Activity 4: Try these on your own (OYO)! OYO 3 (3x -1)(2x + 5)OYO 4 (x + 4)(x - 12) 3x(2x + 5) + -1(2x + 5) x(x + -12) + 4(x + -12) 6x2 + 15x + -2x + -5 x2 + -12x + 4x + -48 6x2 + 13x + -5 x2 + -8x + - 48 Activity 5: Multiply two binomials using FOIL (x + a)(x+b) F multiply the FIRST terms in the parentheses + O multiply the OUTSIDE terms in the parentheses + I multiply the INSIDE terms in the parentheses + L multiply the LAST terms in the parentheses Ex. 9 (3x + 4)(x + 5)Ex. 0 (x + 3)(x - 12) = (x + 3) (x + -12) F + O + I + LF + O + I + L (3x)(x) + (3x)(5) + (4)(x) + (4)(5) (x)(x) + (x)(-12) + (3)(x) + (3)(-12) 3x2 + 15x + 4x + 20 x2 + -12x + 3x + -36 3x2 + 19x + 20 x2 + -9x + -36 Ex. 11 (3 – 2x)(2 – 3x)Ex. 12 (x + 2)(5x - 6) (3 + -2x) (2 + -3x) (x+2)(5x+ -6) F + O + I + LF + O + I + L (3)(2) + (3)(-3x) + (-2x)(2) + (-2x)(-3x) x)(5x) + (x)(-6) + (2)(5x) + (2)(-6) 6 + -9x + -4x + 6x2 5x2 +-6x + 10x + -12 6x2 + -13x + 6 5 x2 + 4x + -12 Activity 6: Try these on your own (OYO)! OYO 5 (3x -1)(2x + 5)OYO 6 (x + 4)(x - 12) (3x + -1)(2x + 5) (x + 4) (x + -12) F + O + I + LF + O + I + L (3x)(2x) + (3x)(5) + (-1)(2x) + (-1)(5) (x)(x) + (x)(-12) + (4)(x) + (4)(-12) 6x2 + 15x + -2x + -5 x2 + -12x + 4x + -48 6x2 + 13x + -5 x2 + -8x + - 48
Activity 7: Applications Christina has a square garden. When she increases her garden’s width by 3 meters and decreases its length by 4 meters, the garden’s area is 60 m2. What are the dimensions of the garden before she changed everything? Step 1: Draw a picture and label X+3 X+3 X X X-4 X-4 X X Step 2: Write an equation A = L * W 60 = (x+3)(x-4) Step 3: Guess and Check (answer is 9 m)
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