Download Curriculum Unit Overview Tiffany Roth Curriculum Development

Curriculum Unit Overview
Tiffany Roth
Curriculum Development
Southwestern College
Dr. Dana LaMantia
August 16, 2009
Title: Powers and Roots
Subject: Applied Algebra I
Grade Level: 9
Time Period: Three 90 Minute Class Periods
Kansas State Standards:
KS2004.M.9-10.1 – STANDARD: Number and Computation – The student uses numerical and
computational concepts and procedures in a variety of situations.
KS2004.M.9-10.1.1 – BENCHMARK: Number Sense – The student demonstrates number sense
for real numbers and algebraic expressions in a variety of situations.
KS2004.M.9-10.1.1.K.1 – KBI: knows, explains, and uses equivalent representations for real
numbers and algebraic expressions including integers, fractions, decimals, percents, ratios;
rational number bases with integer exponents; rational numbers written in scientific
notation; absolute value; time; and money (2.4.K1a), e.g., –4/2 = (–2); a(-2) b(3) = b3/a2.
KS2004.M.9-10.1.4 – BENCHMARK: Computation – The student models, performs, and
explains computation with real numbers and polynomials in a variety of situations.
KS2004.M.9-10.1.4.K.1 – KBI: computes with efficiency and accuracy using various
computational methods including mental math, paper and pencil, concrete objects, and
appropriate technology (2.4.K1a).
KS2004.M.9-10.1.4.K.2 – KBI: performs and explains these computational procedures
(2.4.K1a):
KS2004.M.9-10.1.4.K.2.1 – addition, subtraction, multiplication, and division using the order of
operations
KS2004.M.9-10.1.4.K.2.8 – simplification of radical expressions (without rationalizing
denominators) including square roots of perfect square monomials and cube roots of
perfect cubic monomials;
KS2004.M.9-10.1.4.K.2.9 – simplification or evaluation of real numbers and algebraic monomial
expressions raised to a whole number power and algebraic binomial expressions squared or
cubed;
KS2004.M.9-10.1.4.K.2.10 – simplification of products and quotients of real number and
algebraic monomial expressions using the properties of exponents;
KS2004.M.9-10.1.4.A.1 – AI: generates and/or solves multi-step real-world problems with real
numbers and algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
concepts with:
KS2004.M.9-10.3 – STANDARD: Geometry – The student uses geometric concepts and
procedures in a variety of situations.
KS2004.M.9-10.3.1 – BENCHMARK: Geometric Figures and Their Properties – The student
recognizes geometric figures and compares and justifies their properties of geometric
figures in a variety of situations.
KS2004.M.9-10.3.1.K.5 – KBI: uses the Pythagorean Theorem to (2.4.K1h):
KS2004.M.9-10.3.1.K.5.1 – determine if a triangle is a right triangle,
KS2004.M.9-10.3.1.K.5.2 – find a missing side of a right triangle.
Purpose/Goals: On completion of this unit students will be able to:
1. Simplify expressions using both positive and negative exponents.
2. Simplify and solve expressions and equations that contain a square root symbol.
3. Find a missing side length of a right triangle.
Outline of Unit Content:
Day 1 – Power, Exponents, and Multiplying and Dividing Exponents
Day 2 – Negative Exponents and Square Roots
Day 3 – Pythagorean Theorem
Day 4 – Unit Review – Candyland Activity
Day 5 – Unit Test
Unit Objections:
1. TSWBAT show powers in expressions. (Knowledge/Comprehension)
2. TSWBAT solve expressions by multiplying and dividing powers. (Application)
3. TSWBAT simplify expressions containing negative exponents. (Analysis)
4. TSWBAT solve radical expressions using the Product and Quotient Properties of Square
Roots. (Synthesis)
5. TSWBAT determine missing right triangle lengths using the Pythagorean Theorem.
(Evaluation)
Blooms Taxonomy:
_x_ Knowledge
_x_ Comprehension
_x_ Application
_x_ Analysis
_x_ Synthesis
_x_ Evaluation
Multiple Intelligences:
_x_ Verbal/Linguistic
_x_ Mathematical/Logical
_x_ Visual/Spatial
_x_ Musical/Rhythmical
_x_ Body/Kinesthetic
_x_ Interpersonal
_x_ Intrapersonal
___ Naturalist
Textbook: Cummins, J., Malloy, C., McClain, K., Mojica, Y., & Price, J. (2006) Algebra:
concepts and Application. Glencoe Mathematics: Illinois.
Materials: Calculators, construction paper, gird paper, LCD projector, notebook paper, ruler,
scissors, textbooks, uncooked spaghetti, whiteboard, whiteboard markers and erasers, and
writing utensils.
Prior Knowledge: Before beginning this unit, students need to be able to simplify both proper
and improper fractions and be able to find the product and quotient of a numeric expression.
Plan Sequence of Daily Lessons:
1. Bell-Ringer – Students are to write a paragraph of three or more sentences of reflection
on the quote of the day.
2. Anticipatory Set – Explore/Working Together
3. Input/Modeling – Building Understanding
- Example problems will be modeled in a 2x2 fashion. The teacher does two examples
then the students do two.
4. Checking for Understanding/Guided Practice - Practice
5. Independent Practice – Extend, Think Critically, Project Connection/Mixed Review
6. Closure
Assessment:
1. Informal Assessment
o As students work on practice problems
o Questions students ask and answers given to teacher’s questions
o Students body language
o Observe students’ work while completing practice problems
2. Formal Assessment
o Grades on daily assignments turned in
o Unit Test
Incorporation of Technology:
- Calculators
- Foldable/Graphic Organizers
- Geometers
- LCD projector for PowerPoint Presentations
- Overhead projectors
Plan for Adaptations:
1. Visual needs:
o Enlargement of textbook material and pre-made notes
o Write largely on the board and/or overhead
o Have students set in the front of the room
2. Hearing needs:
o Have students sit in the front of the room
3. Disruptive students:
o Motor progress
o Separate from group work as needed
4. Any others:
o Will be handled with care as they arise
Unit Daily Lesson Plans: Day 1
Lesson: Powers, Exponents, and Multiplying and Dividing Exponents
Standards:
KS2004.M.9-10.1 – STANDARD: Number and Computation – The student uses numerical and
computational concepts and procedures in a variety of situations.
KS2004.M.9-10.1.1 – BENCHMARK: Number Sense – The student demonstrates number sense
for real numbers and algebraic expressions in a variety of situations.
KS2004.M.9-10.1.1.K.1 – KBI: knows, explains, and uses equivalent representations for real
numbers and algebraic expressions including integers, fractions, decimals, percents, ratios;
rational number bases with integer exponents; rational numbers written in scientific
notation; absolute value; time; and money (2.4.K1a), e.g., –4/2 = (–2); a(-2) b(3) = b3/a2.
KS2004.M.9-10.1.4 – BENCHMARK: Computation – The student models, performs, and
explains computation with real numbers and polynomials in a variety of situations.
KS2004.M.9-10.1.4.K.1 – KBI: computes with efficiency and accuracy using various
computational methods including mental math, paper and pencil, concrete objects, and
appropriate technology (2.4.K1a).
KS2004.M.9-10.1.4.K.2 – KBI: performs and explains these computational procedures
(2.4.K1a):
KS2004.M.9-10.1.4.K.2.1 – addition, subtraction, multiplication, and division using the order of
operations
KS2004.M.9-10.1.4.K.2.8 – simplification of radical expressions (without rationalizing
denominators) including square roots of perfect square monomials and cube roots of
perfect cubic monomials;
KS2004.M.9-10.1.4.K.2.9 – simplification or evaluation of real numbers and algebraic monomial
expressions raised to a whole number power and algebraic binomial expressions squared or
cubed;
KS2004.M.9-10.1.4.K.2.10 – simplification of products and quotients of real number and
algebraic monomial expressions using the properties of exponents;
KS2004.M.9-10.1.4.A.1 – AI: generates and/or solves multi-step real-world problems with real
numbers and algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
concepts with:
Objective:
1. TSWBAT show powers in expressions. (Knowledge/Comprehension)
2. TSWBAT solve expressions by multiplying and dividing powers. (Application)
Example of Relevance:
- Exponents are found in multiple formulas used by architects, engineers, and mathematics.
- The movie industry measures the intensity of sound by a decibel which is a unit that is
based on the powers of ten.
Materials: Calculators, LCD projector, notebook paper, textbooks, whiteboard, whiteboard
markers and erasers, and writing utensils.
Early Preparation:
1. Set out the students’ whiteboard markers and erasers.
2. Prepare LCD projector and make sure the PowerPoint Presentation is working correctly.
The PowerPoint Presentation will be used during the anticipatory set, input/modeling,
and checking for understanding/guided practice portions.
3. Make copies of problem rubric.
4. Make copies of notes for special education students.
Procedure:
1. Bell-Ringer
o Quote of the day reflection
2. Anticipatory Set
o Problems to review simplifying fractions
o Making Real-World connections
3. Input/Modeling
- Powers and Exponents
o Definitions of perfect square, exponent, base, and powers.
o Examples of writing expressions using exponents.
o Examples of writing powers as multiplication expressions.
o Evaluating expressions with substitution parts
- Multiplying and Dividing Exponents
o Hand out problem rubric.
o Product of Powers Rule
 Examples of simplifying expressions using the Product of Powers Rule
o Quotient of Powers Rule
 Examples of simplifying expressions using the Quotient of Powers Rule
4. Checking for Understanding/Guided Practice
o Last Person Standing: Every student has a whiteboard, whiteboard maker, and
eraser. Everyone begins by standing. Problems are given for students to solve. If a
student does not have the right answer they must set down. Once the student is
setting down then the teacher/para can help him/her with the problems.
5. Independent Practice
o Homework assignment
o Have music playing during this time
6. Closure
o Recap of lesson
Problem Rubric for Multiplying and Dividing Powers
Steps
Completed
State the rule that will be used in evaluation the problem.
Rewrite the problem.
Write out each step used in evaluating the problem.
Finished problem with the correct answer.
*Each problem is worth 4 points.
1
1
1
1
Particularly
Completed
1/2
1/2
1/2
--
Did Not
Complete
0
0
0
0
Unit Daily Lesson Plans: Day 2
Lesson: Negative Exponents and Square Roots
Standards:
KS2004.M.9-10.1 – STANDARD: Number and Computation – The student uses numerical and
computational concepts and procedures in a variety of situations.
KS2004.M.9-10.1.1 – BENCHMARK: Number Sense – The student demonstrates number sense
for real numbers and algebraic expressions in a variety of situations.
KS2004.M.9-10.1.1.K.1 – KBI: knows, explains, and uses equivalent representations for real
numbers and algebraic expressions including integers, fractions, decimals, percents, ratios;
rational number bases with integer exponents; rational numbers written in scientific
notation; absolute value; time; and money (2.4.K1a), e.g., –4/2 = (–2); a(-2) b(3) = b3/a2.
KS2004.M.9-10.1.4 – BENCHMARK: Computation – The student models, performs, and
explains computation with real numbers and polynomials in a variety of situations.
KS2004.M.9-10.1.4.K.1 – KBI: computes with efficiency and accuracy using various
computational methods including mental math, paper and pencil, concrete objects, and
appropriate technology (2.4.K1a).
KS2004.M.9-10.1.4.K.2 – KBI: performs and explains these computational procedures
(2.4.K1a):
KS2004.M.9-10.1.4.K.2.1 – addition, subtraction, multiplication, and division using the order of
operations
KS2004.M.9-10.1.4.K.2.8 – simplification of radical expressions (without rationalizing
denominators) including square roots of perfect square monomials and cube roots of
perfect cubic monomials;
KS2004.M.9-10.1.4.K.2.9 – simplification or evaluation of real numbers and algebraic monomial
expressions raised to a whole number power and algebraic binomial expressions squared or
cubed;
KS2004.M.9-10.1.4.K.2.10 – simplification of products and quotients of real number and
algebraic monomial expressions using the properties of exponents;
KS2004.M.9-10.1.4.A.1 – AI: generates and/or solves multi-step real-world problems with real
numbers and algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
concepts with:
Objective:
1. TSWBAT simplify expressions containing negative exponents. (Analysis)
2. TSWBAT solve radical expressions using the Product and Quotient Properties of Square
Roots. (Synthesis)
Example of Relevance:
1. Electricians measures electric currents using the prefixes micro and milli. Micro is 10-6
and milli is 10-3.
2. Pilots use a distance formula to find how far they are from the horizon. This distance
formula contains a square root symbol.
Materials: Calculators, construction paper, notebook paper, scissors, textbooks, whiteboard,
whiteboard markers and erasers, and writing utensils.
Early Preparation:
1. Set out the students’ whiteboard markers and erasers.
2. Make copies of problem rubric.
3. Make copies of Mingo cards.
4. Cut out 25 Mingo markers for each student using construction paper.
5. Make copies of notes for special education students.
Procedure:
1. Bell-Ringer
o Quote of the day reflection
2. Anticipatory Set
o Go over homework questions
o Making Real-World connections
3. Input/Modeling
- Negative Exponents
o Hand out problem rubric.
o Examples of writing numbers with negative exponents using positive exponents
o Examples of simplifying expressions that have negative exponents
o Examples of simplifying expressions that have both positive and negative
exponents.
- Square Roots
o Definition of square root, radical sign, and perfect square.
- Examples of simplifying perfect squares expressions.
o Definition of radical expression, prime number, composite number, and prime
factorization.
o Product Property of Square Roots
- Examples of simplifying expressions using the Product Property of Square
Roots
o Quotient Property of Square Roots
- Examples of simplifying expressions using the Quotient Property of Square
Roots
4. Checking for Understanding/Guided Practice
o Mingo – Math Bingo. Each student will need a Mingo card and 25 colored Mingo
markers. Give students a list of 24 answers that they are to put on their Mingo
card. Students are to work problems out on their whiteboards.
5. Independent Practice
o Homework assignment
o Have music playing during this time
6. Closure
o Recap of lesson
Problem Rubric for Solving Problems with Exponents
Steps
Completed
State the property that will be used in evaluation the
1
problem.
Rewrite the problem.
1
Changed negatives to positive exponents.
1
Write out each step used in evaluating the problem.
1
Finished problem with the correct answer.
1
*Each problem is worth 5 points.
Particularly
Completed
1/2
Did Not
Complete
0
1/2
1/2
1/2
--
0
0
0
0
Unit Daily Lesson Plans: Day 3
Lesson: Pythagorean Theorem
Standards:
KS2004.M.9-10.1 – STANDARD: Number and Computation – The student uses numerical and
computational concepts and procedures in a variety of situations.
KS2004.M.9-10.1.1 – BENCHMARK: Number Sense – The student demonstrates number sense
for real numbers and algebraic expressions in a variety of situations.
KS2004.M.9-10.1.1.K.1 – KBI: knows, explains, and uses equivalent representations for real
numbers and algebraic expressions including integers, fractions, decimals, percents, ratios;
rational number bases with integer exponents; rational numbers written in scientific
notation; absolute value; time; and money (2.4.K1a), e.g., –4/2 = (–2); a(-2) b(3) = b3/a2.
KS2004.M.9-10.1.4 – BENCHMARK: Computation – The student models, performs, and
explains computation with real numbers and polynomials in a variety of situations.
KS2004.M.9-10.1.4.K.1 – KBI: computes with efficiency and accuracy using various
computational methods including mental math, paper and pencil, concrete objects, and
appropriate technology (2.4.K1a).
KS2004.M.9-10.1.4.K.2 – KBI: performs and explains these computational procedures
(2.4.K1a):
KS2004.M.9-10.1.4.K.2.8 – simplification of radical expressions (without rationalizing
denominators) including square roots of perfect square monomials and cube roots of
perfect cubic monomials;
KS2004.M.9-10.1.4.K.2.9 – simplification or evaluation of real numbers and algebraic monomial
expressions raised to a whole number power and algebraic binomial expressions squared or
cubed;
KS2004.M.9-10.1.4.K.2.10 – simplification of products and quotients of real number and
algebraic monomial expressions using the properties of exponents;
KS2004.M.9-10.1.4.A.1 – AI: generates and/or solves multi-step real-world problems with real
numbers and algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
concepts with:
KS2004.M.9-10.3 – STANDARD: Geometry – The student uses geometric concepts and
procedures in a variety of situations.
KS2004.M.9-10.3.1 – BENCHMARK: Geometric Figures and Their Properties – The student
recognizes geometric figures and compares and justifies their properties of geometric
figures in a variety of situations.
KS2004.M.9-10.3.1.K.5 – KBI: uses the Pythagorean Theorem to (2.4.K1h):
KS2004.M.9-10.3.1.K.5.1 – determine if a triangle is a right triangle,
KS2004.M.9-10.3.1.K.5.2 – find a missing side of a right triangle.
Objective:
1. TSWBAT determine missing right triangle lengths using the Pythagorean Theorem.
(Evaluation)
Example of Relevance: Carpenters use the Pythagorean Theorem to determine if corners of a
desk are right angles. Construction workers constantly use special right triangles when building
buildings.
Materials: Calculators, grid paper, LCD projector, notebook paper, ruler, scissors, textbooks,
uncooked spaghetti, whiteboard, whiteboard markers and erasers, and writing utensils.
Early Preparation:
1. Set out the students’ whiteboard markers and erasers.
2. Prepare LCD projector and make sure the PowerPoint Presentation is working correctly.
The PowerPoint Presentation will be used during the anticipatory set, input/modeling,
and checking for understanding/guided practice portions.
3. Make copies of problem rubric.
4. Make copies of notes for special education students.
Procedure:
1. Bell-Ringer
o Quote of the day reflection
2. Anticipatory Set
o Go over homework questions
o Making Real-World connections
7. Input/Modeling
- Investigation of Pythagorean Theorem
o Using different lengths of uncooked spaghetti to create different diagonals of
rectangles. Students will exam the relationships between the height and length of
each rectangle.
- Pythagorean Theorem
o Hand out problem rubric.
o Labeling parts of a right triangle and Pythagorean Theorem
o Examples of determining whether or not three given side lengths create a right
triangle. (converse of the Pythagorean Theorem)
o Given examples of special right triangles.
o Examples of finding the missing length of a given right triangle.
8. Checking for Understanding/Guided Practice
o Last Person Standing
9. Independent Practice
o Homework assignment
o Have music playing during this time
10. Closure
o Recap of lesson
Problem Rubric for Solving Problems with a missing length using the Pythagorean Theorem
Particularly Did Not
Steps
Completed
Completed Complete
State which part of the triangle you are solving for.
1
1/2
0
Rewrite the problem.
1
1/2
0
Write out each step used in evaluating the problem.
1
1/2
0
Finished problem with the correct answer.
1
-0
*Each problem is worth 4 points.