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Discrete Math Lesson Plans Third Nine Weeks—Week 4 1/25/10 Objectives Students will be able to translate English statements into logic using symbols. Students will be able to construct truth tables for statements containing negations, conjunctions, and disjunctions. Activities Lecture to introduce statements, symbols, and truth tables. Homework Section 1.1 in Text: 3, 5, 8, 17, 18, 20, 21, 26, 28, 29, 32, 40, 42, 43, 46, 47, 49 1/26/10 Objectives Students will be able to translate conditional statements from English to logic using symbols. They will be able to construct truth tables with statements involving conditionals. They will also be able to write the converse, inverse, and contrapositive of a conditional statement. Activities Opening problem on overhead: Show that the distributive property of logic holds. Have students put homework problems on the board for discussion. Lecture to introduce conditional statements, converses, inverses, and contrapositives. Homework Section 1.2 in Text: 2, 4, 5, 8, 11, 14, 16, 18-22, 29, 32, 35, 36 1/27/10 Objectives Students will be able to show whether an argument is valid or invalid. Students will be able to recognize the converse and inverse errors. Activities Quiz; Read section 1.3 and do problems below Homework Section 1.3 in Text: 6-11 all, 21-31 odd 1/28/10 Objectives Students will be able to use rules of inference to prove that an argument is valid. Homework Section 1.3 in Text: 36, 37, 41, 43 1/29/10 Go over homework on the board 2/1/10 Objectives Students will be able to construct simple logic circuits from Boolean expressions and input/output tables. They will also be able to construct an input/output table and Boolean expressions from a given circuit. Activities Go over homework from 1.3. Begin discussion of logic circuits in section 1.4. Homework Section 1.4 in Text: 2, 6, 10, 13-21, 24, 29, 30, 34 2/2/10 Objectives Students will be able to use Karnaugh maps to simplify circuits. Activities Quiz; Give handout on Karnaugh maps with examples for us to go through as a class. Homework Exercises 4-16 even on handout 2/3/10 Objectives Students will be able to use quantifiers to write statements mathematically. Students will be able to negate quantified statements. Activities Lecture on quantifiers (Section 2.1). Homework Section 2.1 in Text: 1, 4, 7, 8, 11, 12, 13, 16, 18, 19, 21, 23, 28, 29-36 2/4/10 Objectives Students will be able to use multiple quantifiers to write statements mathematically. Students will be able to negate universal conditional statements. Activities Quiz; Lecture on section 2.2. Homework Section 2.2 in Text: 3-17, 22-30, 32, 33, 41-43 2/5/10 Watch Breaking Vegas 2/8/10 Test—Chapter 1 2/9/10 AMC 12 2/10/10 Objectives Students will be able to use quantifiers to write statements mathematically. Students will be able to negate quantified statements. Activities Lecture on quantifiers (Section 2.1). Homework Section 2.1 in Text: 1, 4, 7, 8, 11, 12, 13, 16, 18, 19, 21, 23, 28, 29-36 2/11/10 Objectives Students will be able to use multiple quantifiers to write statements mathematically. Students will be able to negate universal conditional statements. Activities Quiz; Lecture on section 2.2. Homework Section 2.2 in Text: 3-17, 22-30, 32, 33, 41-43 2/12/10 QUIZ 2/15/10 Objectives Students will be able to determine the validity of arguments with quantified statements. Homework Section 2.3 in Discrete Text: 1, 15-19, 21-35 odd, 45-51 odd 2/16/10 Objectives Students will be able to determine the validity of arguments with quantified statements. Homework Section 2.3 in Discrete Text: 1, 15-19, 21-35 odd, 45-51 odd 2/17/10 Objectives Students will be able to determine the validity of arguments with quantified statements. Homework Section 2.4 in Discrete Text: 7-33 odd 2/18/10 Objectives Students will be able to recognize direct proofs and disproofs by counterexample. Students will attempt to construct their own proofs. Students will recognize good proof-writing techniques and will explore ways to improve proof writing. Activities Give examples of direct proofs and disproofs by counterexample. Divide students into groups to construct a proof. Have groups present proofs to class for us to critique. Homework Section 3.1 in Discrete Text: 2, 7, 9, 12, 15, 16, 21-26, 32, 35, 38-41, 46 2/19/10 Objectives Students will recognize good proof-writing techniques and will explore ways to improve proof writing. Activities Go over the homework by putting proofs on board. Define divisible, and prove transitivity of divisibility. Prove divisibility by a prime, and state the unique factorization theorem without proof. Homework Section 3.2 (Discrete) problems: 7, 11, 13, 14, 16, 17, 18, 21, 22, 25, 26, 28-32 2/22/10 Objectives Students will recognize good proof-writing techniques and will explore ways to improve proof writing. Activities Go over the homework by putting proofs on board. Homework Section 3.3 (Discrete) problems: 3, 4, 7, 8, 10, 12, 15, 17, 19-26, 36, 37, 38, 41, 42 2/23/10 QUIZ—go over homework 2/24/10 Objectives Students will understand the purpose of statistical measurement and sampling as a means of estimating parameters. Activities Go over 3.3 homework. Define parameter and statistic, sampling distribution, bias, and variability. Give an example to show the relationship between bias and variability. Give an example of a matched pairs experimental design. Homework Section 3.4 in stats book: 44-47, 48, 51, 52, 56 2/25/10 Objectives Students will be able to prove properties of floor and ceiling and to provide counterexamples for false statements. Activities Define floor and ceiling. Prove and disprove some properties of these. Homework Section 3.5 in Discrete text: 2, 3, 5, 13, 14, 17, 20-22, 25, 27-29 2/26/10 Quiz 3/1/10 3/2/10 TEST 3/3/10 Objectives Students will be able to construct indirect proofs. Activities Go over homework from section 3.5 of discrete book. Introduce section 3.6 of discrete book (proof by contradiction) by proving that the sum of any rational number and any irrational number is irrational. Do a proof by contraposition (if the square of an integer is even, then the integer is even). Homework None 3/4/10 Objectives Students will be able to design experiments and detect sources of bias. Activities Chapter 3 stats test Homework Section 3.6 (discrete): 8, 10, 12, 13, 17-24 3/5/10 Objectives Students will be able to construct indirect proofs. Activities Go over homework from section 3.6. Prove that 2 is irrational. Prove that if a prime number is a factor of a then it is not a factor of a 1 . Homework Section 3.7 (discrete): 3, 4, 7, 8, 9, 14, 15 3/8/10 Objectives Students will be able to write induction proofs. Activities Quiz; Go over homework from section 3.7 (discrete). Go over section 4.1 in discrete book (sequences and product notation). This should be a review. Introduce induction proofs by proving the formula for the sum of the first n counting numbers. Also prove the formula for the sum of the first n terms of a geometric sequence. Homework Section 4.2 in discrete book: 6-9, 12, 16, 18, 24, 27 3/9/10 Objectives Students will be able to write induction proofs. Activities Prove by induction that 3 | 2 2 n 1 for all n 1 . Prove by induction that 2n 1 2 n for all n 3 . Prove number 19 in discrete text. Homework Section 4.3 in discrete book: 3, 9, 12, 16-18, 21, 25 3/10/10 Objectives Students will be able to write series and products using sigma and pi-notations. Most of this should be a review. Activities Have students read section 4.1 in discrete math text and work on problems below. Homework Section 4.1 discrete: 1-57 odd 3/11/10, 3/22/10, 3/23/10 Objectives Students will be able to construct indirect proofs. Activities Go over homework from section 3.6. Prove that 2 is irrational. Prove that if a prime number is a factor of a then it is not a factor of a 1 . Homework Section 3.7 (discrete): 3, 4, 7, 8, 9, 14, 15 3/12/10 PD Day 3/15/10-3/19/10 Spring Break 3/24/10, 3/25/10 Objectives Students will be able to write induction proofs. Activities Quiz; Go over homework from section 3.7 (discrete) Introduce induction proofs by proving the formula for the sum of the first n counting numbers. Also prove the formula for the sum of the first n terms of a geometric sequence. Homework Section 4.2 in discrete book: 6-9, 12, 16, 18, 24, 27 3/28/10, 3/29/10 Objectives Students will be able to write induction proofs. Activities Prove by induction that 3 | 2 2 n 1 for all n 1 . Prove by induction that 2n 1 2 n for all n 3 . Prove number 19 in discrete text. Homework Section 4.3 in discrete book: 3, 9, 12, 16-18, 21, 25 3/30/10-3/31/10 Review and begin stats review 4/1/10 TEST 4/2/10 Go over AP MC 2007 4/5/10 Assign review project—due 4/13/10 1997 FR 4/6/10 1997 FR 4/7/10 Time to work on project 4/8/10 Go over 1997 MC 4/12/10 No School 4/13/10 Review Project Due 4/14/10 Time to work on senior research 4/15/10 Senior Research 4/16/10 Go over 1997 MC 4/19/10 Go over 1997 FR 4/20/10 1998 FR 4/21/10 1999 FR 4/22/10 2000 FR 4/23/10 2001 FR 4/26/10 2002 FR 4/27/10 2002 MC 4/28/30 2003 FR 4/29/30 2006 FR 4/30/10 General AP Review 5/3/10 AP Review 5/4/10 AP Exam