# 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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