Lesson Plan Title:



Technology Integrated Lesson Plan

SECTION A

Your Name: Mikel Thompson

Date: 7/5/2010

Grade Level: high school, grades 10-12

Lesson Plan Title: L1.1 – Real Numbers: Order and Absolute Value

Concept / Topic To Teach: Real number system review

Standards Addressed: Washington State EALRs

• A.2.1.B Solve problems represented by systems of equations and inequalities.

• A.2.2.A Explain how whole, integer, rational, real and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved. 

General Goal(s):

This is the first formal unit of the course and provides a review of the basics of real numbers. Students will be able to classify real numbers, order them on the number line, and evaluate the absolute value of numbers. 

Specific Objectives:

Students will be able to:

• Define sets and use them to classify numbers as natural, integer, rational or irrational.

• Plot numbers on the real number line.

• Use the real number line and inequality symbols to order real numbers.

• Find the absolute value of a number.

Required Materials:

1. Math text book

2. Lined paper, pencil and eraser

3. TI-83/84 calculator 

4. An open mind ready to learn!

Anticipatory Set (Lead-In):

• Ask “What are numbers?”

o Clarify difference between meaning and use

o Look for:

▪ Idea that numbers are symbols

▪ There are different types of numbers

• Ask “Where do numbers come from?”

o Deeper question: “Did man create numbers?” … some mathematicians think so but many believe we discover the mathematics that God created.

• Ask “Are numbers dangerous?”

o Myth has it the Greek Hippasus was drowned for discovering irrational numbers.

o Each discovery of a new type of number has spurred tremendous advances but has required people to stretch their thinking significantly. 

Step-By-Step Procedures:

Lesson is sequenced primarily by SMART Notebook slides. Class is 75 minutes long.

1. (2 min) Introduce the mathematical concept of a set and its notation.

a. Identify the set of males then females in the classroom (stand up)

b. Identify the set of students currently taking English (stand up)

c. Identify the real number system as a set

2. (10 min) Identify the subsets of the real number system using visuals in slides:

a. Natural numbers

b. Whole numbers (naturals plus zero)

c. Integers (whole numbers plus negatives)

d. Rational numbers (integers plus fractions/decimals)

e. Irrational numbers (discovery of and examples)

f. Real numbers (rationals plus irrationals)

g. Checkpoint formative assessment with Senteo clicker question classifying real numbers

h. Practice classifying real numbers (homework problems 1-3 page 9)

3. (5 min) Identify the real number line:

a. Parts (origin, positive numbers, negative numbers)

b. Plotting

c. Demonstrate using Gizmos activity widget

d. Practice plotting numbers on the real number line (problems 5-7 page 9)

4. (10 min) Review order of real numbers:

a. Concept of less than and greater than

b. Symbology (, ≤, ≥)

c. Use of number line to determine order

d. Ordering integers

e. Ordering fractions

• Common denominator

f. Ordering decimals

• Can convert fractions to decimal when comparing

g. Checkpoint formative assessment with Senteo clicker question ordering real numbers of mixed type.

h. Practice ordering real numbers (homework problems 9-15 page 9)

5. (3 min) Introduce expressions

a. Define expression: collection of numbers, operators or symbols (basic math sentence)

b. Define evaluate: find the number equal to the expression

c. Demonstrate evaluating simple arithmetic expressions

6. (15 min) Introduce absolute value:

a. Ask “what number do you think is the opposite of 5?”

b. Define opposites of real numbers as numbers same distance from but on opposite sides of the origin (zero)

• Practice finding opposites of numbers (problems 25-27 page 9)

c. Define absolute value as distance from origin on number line

• Practice finding the distance from a number and the origin (problems 21-22, 31-32 page 9)

d. Identify absolute value notation

e. Demonstrate evaluating absolute value expressions

f. Checkpoint formative assessment with Senteo clicker questions evaluating absolute value expressions

g. Practice evaluating absolute value expressions (problems 35-39 page 9) 

7. (15 min) Independent practice

a. Homework assignment: Page 9, #1-60 (they have already done 25 of these)

Plan For Independent Practice:

Students will engage in short independent practice after each concept is introduced or reviewed by completing selected problems from their homework assignment. Once all concepts are covered and students evidence sufficient mastery, they will continue working on their homework assignment (independent practice) while teacher circulates among the students monitoring and guiding as necessary. Unfinished homework assignment problems will be completed at home that evening.

Once students complete their homework assignment, they will grade and correct their assignment, complete with work shown. They will also update their online study skills portfolio including indicating which problems were difficult (“Muddiest Point”).

Closure (Reflect Anticipatory Set):

• (5 min) Give each table group (quad) one of the following questions: Give a real-life example of when you use:

o Natural numbers (example: counting the number of homework problems)

o Whole numbers (example: counting the number of dates you will get with a movie star – zero)

o Integers (example: temperature – can be negative)

o Rational numbers (example: the cost of an item at the store in dollars)

o Absolute value (example: the distance from home to school)

Biblical Integration:

Genesis 1: God created the universe and the laws that hold it together. This includes the mathematics that underlie and describe how the world works (the science of physics).

“Mathematics is the language in which God wrote the universe.” Galileo Galilei.

Best Practices Used:

1. Identifying similarities and differences

2. Summarizing and note taking

3. Homework and practice

4. Cooperative learning

SECTION B

Technology

(Outline what type of technology will be incorporated in your lesson.)

• SMART Sympodium with LCD projector

• SMART Notebook lesson slides. Lesson slides with in-class notation and work shown will be made available online (class website) for student review at home.

• Gizmos (): Real number line activities A and B (online flash activities allowing points to be moved on the number line with opposites and absolute value compared).

• Senteo clicker formative question response to determine mastery of key concepts.

• Lesson will be recorded using SMART Notebook recording feature with the resulting video made available online (class website) for student review at home.

• Online study skills portfolio updated by students as they complete their daily homework assignments.

• Daily homework assignment (page and problem set) are Twittered to students daily with students getting a text update to their cell phone.

Positive Learning Benefits

(Outline or summarize the potential positive benefits of using this technology.)

• Lesson slides and video provide excellent review and study opportunity for learners with different learning modalities (auditory, visual, and linguistic).

• Dynamic nature of Gizmos activity widget captures student attention and makes the number line and related concepts “come alive.”

• Senteo clicker formative evaluation provides immediate and comprehensive insight into concept mastery.

• Ability for students to review lesson slides and video at home provides for students who were absent or who need more processing time than the bell schedule allows.

• Students are able to update and view their online study skills portfolio at any time.

SECTION C

Online Component:

• Lesson slides and video are available for review on class website.

• Gizmos activity widget is available for student access and manipulation at home.

• Online study skills portfolio.

Youth Culture Trends (How will this lesson motivate today’s youth?):

• Use of SMART Notebook slides allows use of color and dynamic content. Further, the lesson slides allow students to see the step-by-step process progress of concept development and problem solution.

• Senteo clickers make a game of learning and provide an integrated “gadget” for students to use providing immediate individual and group mastery feedback.

• Use of Gizmos activity widget allows students to directly manipulate points on the number line with immediate feedback.

• “Tweeting” homework assignments allows students to receive a text message that brings the math classroom into their every-day life and gives them a readily accessible record of their assignment.

SECTION D

Assessment Based On Objectives:

• Formative assessment using Senteo clickers.

• Formative assessment as students complete selected homework problems reviewing the concept just taught.

• Textbook based homework assignment.

• “Muddiest point:” students identify most difficult problems in online study skills portfolio.

SECTION E

Adaptations (For Students With Learning Disabilities):

• Students with plan for success indicating writing challenges are allowed to complete lecture notes at home using provided online lecture slides and lesson video.

• Students work in quads allowing for peer teaching and explanations.

Extensions (For Gifted Students):

• I would challenge interested students to determine which number system sets are closed with respect to addition, subtraction, multiplication and division. This exploration provides a preparatory exposure to college level number theory and abstract algebra classes.

• Interested students could research one other interesting mathematicians or events:

o

o

Possible Connections To Other Subjects:

• History of mathematics

• Mathematics as a language with sentence structure

• Mathematics is a language that can be translated to or from English

 

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