Discrete Math Lesson Plans by IlsqWsUD

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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

								
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