Lesson Plan by Daniel Haffner Lesson: Factoring Trinomials Length: 50 min. Age or Grade Level Intended: Algebra 1 Unit Lesson #7 Modified for Autism Academic Standard(s): A1.6.7 Factor the difference of two squares and other quadratics Performance Objective(s): Given a 10 problems, the students will factor trinomials with a value not equal to 0 with 80% accuracy. Assessment: The students will be given 10 problems. The teacher will check to see that the student got at least 8 out of the 10 problems correct. Advance Preparation by Teacher: - Chalkboard, chalk (different color chalk) - Copies of the worksheet for each student -, you have factor cards cut out and enough for each student to have 2 of each o cards have a trinomial on them for students to answer o cards have a question that has an answer to one of the cards. Procedure Introduction: 1. Remind students that they have recently been learning how to factor trinomials. Tell the students that they will be learning how to factor trinomials again, but this time it will not equal 1. 2. Tell students that before they learn about that type of factoring, they will be playing a game of, you have factors. 3. Tell the students that they will each get four cards, two cards and two who has cards. a. The cards will need to factor the trinomial on their card. They will then need to put their names on the back of the card with their work. b. Once students finish working out the problem they will also have a card that has a question asking who has? card (the answer to their problem). Students will need to find the person who answers their two question cards and give that person his or her card cards. (Gardner s: Interpersonal, Logical-Mathematical) 4. Students will check the work on both of the cards that they received. Step by Step:
1. Have students sit back down and then write on the board 6 23 7 2. Now ask the students how they think the problem should be factored. Get different ideas from students and ask students to justify their answers or explain their thinking. Remind students that they should be trying to get the answer so no idea is wrong at this point. (Bloom s: Knowledge, Evaluation) 3. Remind students that the standard form of a trinomial is 4. Have students copy down what you write on the board. 5. Divide the board up into 4 sections with each letter of FOIL at the top of a section. a. Under the F section, tell the students that they need to find all the factors of a. b. Under the L section, tell the students that they need to find all the factors of c. c. Now students should be left with the O and U sections as empty. Tell students that they will need to take one of the factors of a and put in the O section. Tell students that they now need to take one of the factors from c and put it in the I section. The factors should be taken from the same row (so if a student takes a factor of a from row one, then they should take a factor of c from row one). d. Multiply the two numbers in each of the sections and then take the sum of the two sections. When the sum is equal to b, use the two numbers in O for the outer of each binomial, and the two numbers in I for the inner. Example: 6 23 7 F O Sum of O and I I L Factors of 6 1*7 13 1*6 Factors of 7 1*6 1*1 43 7*6 1*7 2*3 2*7 17 1*3 2*1 23 7*3 (2x+7) * (3x+1) Make sure the x terms product is equal to the a and the product of the constant is equal to the c. (Gardner s: Logical-Mathematical, Visual-Spatial) 6. Now have the students try 7 26 8, by themselves. Answer: (1x+-4)(7x+2). As a class, work through it together calling on a different student to explain each step of the problem. (Bloom s: knowledge, comprehension) 7. Now have them get with a partner and try 20 80 35. Let students work in partners for a minute or two, and then give them a hint to make the problem easier. a. Hint: factor out a monomial or GCF of all terms in the trinomial. It will reduce the number of factors you have to search for. 8. Ask students why factoring out a monomial or GCF of all terms in the trinomial makes the problem easier. Have students explain their thinking. (Bloom s: analysis, Gardner s: interpersonal)
9. As a class, work through it together calling on a different student to explain each step of the problem. (Bloom s: knowledge, comprehension; Gardner s: verbal-linguistic) Answer: 5(2x+1)(2x+7) 10. Let students work on the homework. Now give them their worksheet and have them work on it for the rest of class. If they do not finish it then it is homework. Closing 1. Take the last 5 min of class and review with the students the steps of all types of factoring they have learned. a. Standard form is when a=0 and when a does not equal 0 (like today s lesson) b. Bring back the term FOIL and discuss with students what good is it now that they learned factoring. (Bloom s: knowledge, comprehension; Gardner s: verballinguistic, interpersonal) 2. Ask the students what type of factoring they like best and have them justify their answers or explain their thinking (Bloom s: knowledge, application, evaluation; Gardner s: verbal-linguistic, interpersonal) 3. Ask the students if they are any special case factoring problems? (such as squaring a binomial, difference of squares)? (Bloom s: knowledge, application; Gardner s: verballinguistic, interpersonal, logical-mathematical). 4. Tell students that tomorrow, they will be learning more about factoring the difference of two squares and other quadratics. Adaptations Autism Provide student with a script for checking to see if a classmate has his or her card during the game. For example, the student s script could be: Student: Do you have the answer? If yes: I will give you my card. If no: Ok. I will keep looking. ---------------------------------------------------------------------------------------------------- Student: the answer. If the student does has your answer Yes, that matches my card. Thank you. If the student does not have your answer No, that does not match my card. Sorry. Provide student with a schedule for how the class will run so the student can follow along and see the routine for the day. Allow student to work by him or herself to solve the problems in class if they want to. Allow student to work in the back of the room if the noise from other students working starts to upset him or her. Provide student with a handout of the notes to follow along with. Reflections - Did I get the student s interested in the lesson? - Do the students remember information from the previous lesson? - Was the lesson too long or too short? - Were my adaptations effective? - What would make the lesson go better next time?
x 2 18x + 81. (x 10)(x + 1)? x 2 9x 10. (x + 12)(x 3)? x 2 9x 36. (x + 7)(x + 7)? x 2 + 14x + 49. (x + 2)(x 6)? x 2 4x 12. (x + 11)(x 3)? x 2 + 8x 33. (x + 8)(x + 4)? x 2 + 12x + 32. (x 15)(x 4)? x 2 19x + 60. (x 6)(x + 6)? x 2 36. (x + 2)(x + 7)? x 2 + 9x + 14. (x + 9)(x 5)? x 2 + 4x 45. (x + 1)(x + 1)? x 2 + 2x + 1. (x + 9)(x + 9)? x 2 + 18x + 81. (x + 6)(x 10)? x 2 4x 60. (x 6)(x 6)? x 2 12x + 36. (x 15)(x + 4)? x 2 11x 60. (x + 1)(x + 10)? x 2 + 11 x + 10. (x 9)(x 3)? x 2 12x + 27. (x 6)(x + 4)? x 2 2x 24. (x 8)(x 4)? x 2 12x + 32. (x 9)(x + 6)? x 2 3x 54. (x + 15)(x + 4)? x 2 + 19x + 60. (x + 7)(x + 3)? x 2 + 10x + 21. (x 8)(x 3)? x 2 11x + 24. (x + 5)(x + 9)?
x 2 + 14x + 45. (x 2)(x 10)? x 2 12x + 20. (x + 7)(x 3)? x 2 + 4x 21. (x + 9)(x + 6)? x 2 + 15x + 54. (x 8)(x 7)? x 2 15x + 56. (x + 8)(x + 5)? x 2 + 13x + 40. (x 6)(x 10)? x 2 16x + 60. (x + 6)(x + 5)? x 2 + 11x + 30. (x 12)(x + 3)? x 2 9x 36. (x 1)(x 1)? x 2 2x + 1. (x + 3)(x + 3)? x 2 + 6x + 9. (x 9)(x + 3)? x 2 6x 27. (x 7)(x + 3)? x 2 4x 21. (x 1)(x + 10)? x 2 + 9x 10. (x 6)(x 5)? x 2 11x + 30. (x 3)(x 3)? x 2 6x + 9. (x + 15)(x 4)? x 2 + 11x 60. (x + 5)(x + 7)? x 2 + 12x + 35. (x + 9)(x 3)? x 2 + 6x 27. (x + 6)(x + 10)? x 2 + 16x + 60. (x 11)(x + 2)? x 2 9x 22. (x 2)(x 7)? x 2 9x + 14. (x + 5)(x 9)? x 2 4x 45. (x + 9)(x + 3)? x 2 + 12x + 27. (x 9)(x 9)? http://www.ilovemath.org/index.php?option=com_docman&task=doc_details&gid=100
Name Worksheet Factoring Trinomials 1. 2 15 7 6. 6 25 11 2. 16 26 9 7. 8 18 9 3. 7 50 7 8. 2 3 4. 8 10 3 9. 12 20 5. 25 10 15 10. 11 77 66
Name Worksheet Factoring Trinomials 1. 2 15 7 6. 6 25 11 2. 16 26 9 7. 8 18 9 3. 7 50 7 8. 2 3 4. 8 10 3 9. 12 20 5. 25 10 15 10. 11 77 66