Mathematics – Algebra 1
Unit 7: Polynomials
Third Grading Period – Week 1-4(14 Days)CURRICULUM OVERVIEW
Big Idea / Unit RationaleAll numerical operations with polynomials – adding, subtracting, multiplying and dividing – including factoring and problem-solving applications.
The geometric property of similarity for both 2-D and 3-D figures and the related concept of proportionality.
Graphical representations of transformations – translations, reflections and dilations. / Polynomial expressions easily lend themselves to modeling real-world situations and processes from ticket sales at a football game to energy levels in the nucleus of an atom. Students must learn to be comfortable working with these algebraic expressions to reveal many of the world’s secrets.
Scale factors and the associated concept of similarity have wide usage in engineering, architecture and art.
TEKS / TEKS Specificity - Intended Outcome
Concepts / 8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:
8.3B estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.
8.6 Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to:
8.6A generate similar figures using dilations including enlargements and reductions: and
8.6B graph dilations, reflections, and translations on a coordinate plane.
8.7 Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:
8.7B use geometric concepts and properties to solve problems in fields such as art and architecture: and
8.7D locate and name points on a coordinate plane using ordered pairs of rational numbers.
8.9 Measurement. The student uses indirect measurement to solve problems. The student is expected to: / ” I CAN” statements highlighted in yellow should be displayed for students.
I can:
- estimate and find solutions to real-life problems involving percents and proportional relationships such as similarity and rates. (8.3B)
- generate similar figures through dilations which either enlarge or reduce the original shape (8.6A)
- graph dilations, reflections, and translations on a coordinate plane (8.6B)
- use geometric concepts and properties to solve real-world problems (8.7B)
- locate and name points on a coordinate plane using ordered pairs of rational numbers (8.7D)
- use proportionality to find the missing measurements in two-dimensional or three-dimensional figures. (8.9B)
- describe the changes on perimeter and area when the dimensions of a shape are altered proportionally (8.10A)
- evaluate polynomial expressions for a given value of the variable (A.4A)
- identify monomials, binomials, and trinomials (A.4A)
- add polynomials(A.4A)
- subtract polynomials (A.4A)
- multiply monomials (A.4A)
- use the commutative, associative, and distributive properties to simplify algebraic expressions (A.4B)
- multiply binomials using the F.O.I.L method (A.4A)
- multiply polynomials using laws of exponents (A.11A)
- divide polynomials using the laws of exponents (A.11A)
- understand the properties of exponents(A.11A)
- solve a polynomial equation using factoring (A.10A)
8.9B use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.
8.10 Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to:
8.10A describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally.
A.4Foundations for Functions. The student understands the importance of the skills to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to:
A.4A. find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations; and
A.4B. use the commutative, associative, and distributive properties to simplify algebraic expressions.
A.10 Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to:
A.10Asolve quadratic equations using concrete models, tables, graphs, and algebraic methods.
A.11 Quadratic and other nonlinear functions: The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situation. The student is expected to:
A.11Ause patterns to generate the laws of exponents and apply them to problem-solving situations.
Evidence of Learning
At least 80% of the time, students will demonstrate on paper or use modelsto show they can
- estimate and solve application problems involving percents and other proportional relationships
- generate similar figures using dilations
- graph dilations, reflections, and translations on a coordinate plane
- solve problems using geometric concepts and properties
- locate and name points on a coordinate plane using ordered pairs of rational numbers
- use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements
- describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally
- simplify a polynomial expression to transform and solve an equation
- use the commutative, associative and distributive properties to simplify a mathematical expression
- solve a polynomial equation by factorization
- express patterns of the variable with exponents for problem applications
Mathematics – Algebra 1
Unit 7: Polynomials
Third Grading Period – Week 1-4 (14 Days) CURRICULUM GUIDE
Essential Questions / Essential Pre-requisite Skills- How do I add and subtract polynomials?
- How do I multiply and divide monomials?
- How do I factor multi-termed polynomials?
- What are the rules for multiplying and dividing mathematical expressions that contain exponents?
- How do I order rational numbers when expressed as integers, percents, decimals and fractions?
- What are the various procedures to transform a geometric figure on a coordinate plane?
- How do I use geometric properties and concepts to solve real-world problems?
- How do I use proportionality to solve for missing dimensions or other measures in geometric figures?
- compare and order integers and positive rational numbers (7.1A)
- convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator (7.1B)
- simplify numerical expressions involving order of operations and exponents (7.2E)
- estimate and find solutions to application problems involving percent (7.3A)
- estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units (7.3B)
- use critical attributes to define similarity (7.6D)
- locate and name points on a coordinate plane using ordered pairs of integers (7.7A)
- graph reflections across the horizontal or vertical axis and graph translations on a coordinate plane (7.7B)
- estimate measurements and solve application problems involving length and area of polygons and other shapes (7.9A)
- find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change) (8.5B)
- use the Pythagorean Theorem to solve real-life problems (8.9A)
- communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models(8.15A)
- make conjectures from patterns or sets of examples and non-examples (8.16A)
The Teaching Plan
Instructional Model & Teacher Directions
The teacher will… / So students can demonstrate competency,
the students will …
Jan 21 – Jan 23, 2009
These days are set aside for any or all of the following objectives:
- Set the stage for a focused approach to significantly improving all students’ TAKS performance
- Student awareness of the significance of improved scores for the campus accountability
- Student awareness of his/her specific math TAKS scores for the previous three years and need to develop a plan for improvement
- Review Jan 12-15 Benchmark results with students for teacher and students to know student’s individualTAKS strengths and weakness
- Review 2008 FMA results with students for teacher and students to know student’s individualcourse TEKS strengths and weakness
- Review campus/class 2008 TAKS resultsfor teacher and students to know student’s individual previous strengths and weakness
- Re-teach any Unit 6 Systems of Equations unfinished lessons or areas needing emphasis
- Improve students graphing calculator skills
- Either assign or solicit volunteers (students) to become the class experts in one or two TAKS student expectations
- Ensure that a copy of Margaret Kilgo’s historical TAKS question material is made available to the student experts
These days are set aside for any or all of the following objectives:
- Set the stage for a focused approach to significantly improving all students’ TAKS performance
- Student awareness of the significance of improved scores for the campus accountability
- Student awareness of his/her specific math TAKS scores for the previous three years and need to develop a plan for improvement
- Review Jan 12-15 Benchmark results with students for teacher and students to know student’s individualTAKS strengths and weakness
- Review 2008 FMA results with students for teacher and students to know student’s individualcourse TEKS strengths and weakness
- Review campus/class 2008 TAKS resultsfor teacher and students to know student’s individual previous strengths and weakness
- Re-teach any Unit 6 Systems of Equations unfinished lessons or areas needing emphasis
- Improve students graphing calculator skills
- Either assign or solicit volunteers (students) to become the class experts in one or two TAKS student expectations
- Ensure that a copy of Margaret Kilgo’s historical TAKS question material is made available to the student experts
Day 1
TEA TAKS Study Guide Grade 9 Objective 9
SE 8.7B
Engage/Explore (5-10 minutes)
- Ask students in pairs “What is the percent equivalent of ¼? of 7/8? of 4/7?”
- How do I answer these questions using proportionality?
- Explain the strategy to solve problems involving proportional relationships from page 168 with the example on page 169
- Have the student pairs complete the Try It on page 170 for guided practice, as well as Questions 70, 71, and 72 on page 191.
- Assign problems 38-44 in McDougal Littell Algebra 1 on page 195 for in-class completion in pairs.
TEA TAKS Study Guide Grade 9 Objective 9
SE 8.7B
Engage/Explore (5-10 minutes)
- What is the percent equivalent of ¼? of 7/8? of 4/7?
- How do I answer these questions using proportionality?
- Take notes on the strategy to solve problems involving proportional relationships from page 168 with the example on page 169
- Complete with a partner the Try It on page 170 for guided practice, as well as Questions 70, 71, and 72 on page 191.
- Assign problems 38-44 in McDougal Littell Algebra 1 on page 195 for in-class completion in pairs.
Day 2
Adding and Subtracting Polynomials
McDougal Littell, Algebra 1, Section 9.1
Engage/Explore (10 minutes) Collecting Like Objects (Terms)
- Make connections to prior knowledge – collecting like terms.
- From a deck of cards, give a different one to each student as they enter your classroom.
- When ready, have the students on their own group themselves by suit.
- Upon completion, then have them group themselves by card value – aces, twos,…, queens and kings.
- Conduct a discussion on grouping by “labels”
- Using Examples 1 and 2, define polynomials(monomial, binomial, and trinomial) and give examples. Ask the students to give examples.
- Have students take notes and generate the Frayermodel for each of the above four terms.
- Explain that the coefficients of like terms (same variables and same degree) are added and subtracted like integers using Examples 3 and 4
- Using problems from the McDougal-Littell, Ch.9.1, pages 557, #17-26 have students practice how to add and subtract polynomials
- Monitor student activity for understanding throughout the class session.
- Consider the option of collecting the activity for either a grade or a completion check
Adding and Subtracting Polynomials
McDougal Littell, Algebra 1, Section 9.1
Engage/Explore
- Make connections to prior knowledge (collecting like terms) with playing cards sorted by suit or card value with other students.
- Using the Frayer model, add the termspolynomial, monomial, binomial, and trinomial to your vocabulary
- Take noteson the teacher’s presentation on adding and subtracting polynomials (A.4A, A.4B)
- Complete problems 17-26 on page 557 for a check on understanding. (A.4A, A.4B)
Day 3
Exponents, Multiplication/Division
McDougal Littell, Algebra 1, Section 8.1/8.2
Engage (5-7 minutes) KWL on Exponents
- KWL with students in groups of 3-4 on their knowledge of exponents with this question - What is the purpose of an exponent mathematically?
- Have students put there K and W on sticky notes - 1 per sticky note. Put on a previously prepared KWL chart paper.
- Have students in their groups do Activity 8.1 on page 488, “Product of Powers.”
- Confirm students’ conclusions about exponents by presenting the Key Concepts – Product of Powers Property on page 489 and Power of a Power Property on page 490.
- For guided practice, assign 9-12 on page 491.
- Present Key Concepts Quotient of Powers Property on page 495 and Power of a Quotient Property on page 496.
- For guided practice, assign 5-8 on page 497.
- Monitor the students throughout the class for understanding
- (last 5 minutes of class) Have students add to W column on KWL chart paper
- Assign for homework
Pages 498/499 – 9, 13, 17, 21, 27, 31, 33
Alternate Lesson: Multiplying Monomials Rules Notes, Multiplying Monomials Rules Assignment, Quotient of Powers Notes, Quotient of Powers Assignment / Day 3
Exponents, Multiplication/Division
McDougal Littell, Algebra 1, Section 8.1/8.2
Engage
- Using a KWL activity, review your current knowledge of exponents. Put K’s and L’s on sticky notes (1 per sticky) and apply to class KWL chart.
- Complete“Product of Powers” activityon page 488 to draw conclusions from patterns recognized (A.11A)
- Take notes on 4 Key Concepts presented by teacher – 2 on multiplying and 2 on dividing C
- Work guided practice problems to check for understanding (A.4A, A.4B, A.11A)
- As a class learning summary, add “L” sticky notes to class KWL chart.
- Complete homework assignment. (A.4A, A.4B, A.11A)
Day 4
Exponents, Zero & Negative
McDougal Littell, Algebra 1, Section 8.3
Engage (10 minutes)
- Review homework assignment
- Have students do Activity 8.3, page 502 to gain an understanding and insight intoZero and Negative Exponents
- Present two Key Concepts – Definition of Zero and Negative Exponents on page 503 and Properties of Exponents on page 504.
- Present desired parts of examples 1-3 to model the use of the properties
- Assign for guided practice on pp 503/4/5: 1, 3, 6, 7, 9
- For homework , have students choose one of the following as a notebook entry:
- make a flip chart for all the Laws of Exponents (page 504) with the rules and examples to each rule.
- put all the Laws of Exponents (page 504) into your own words with examples of each.
Exponents, Zero & Negative
McDougal Littell, Algebra 1, Section 8.3
Engage
- Review homework assignment
- Complete Activity 8.3, page 502 to gain an understanding of Zero and Negative Exponents(A.3.B, A.11.A) by drawing conclusions from recognized patterns (A.11A)
- Take notes on the Key Concepts associated with zero and negative exponents (A.11A)
- Complete guided practice to check for understanding (A.11A)
- For homework either (A.11A)
- make a flip chart for all the Laws of Exponents with the rules and examples for each rule, or
- put all the Laws of Exponents (page 504) into your own words with examples of each.
Days 5 & 6
Closing the Distance Grade 9 Lesson 1 – Coordinate Plane
SEs 8.6B, 8.7D
Engage (10 minutes) Ordering Rational Numbers in Different Forms
- Prepare and distributeCruising the Number Line Cards and begin the activity
- Use the Facilitation Questions on page 4 to ensure depth of understanding
- Distribute Part A and Part B to each student
- Divide students in group of 3-4 and complete activity in these groups
- Actively monitor each group’s progress
- Use the Facilitation Questions on pages 5 and 6 to ensure depth of understanding
- Distribute to each group either transparency of Part A or Part B for class presentation
- Chose 1 group to present Part A and another group to present Part B
- Use the Facilitation Questions on pages 7 and 8 to ensure depth of understanding
Elaborate (20 Minutes) Transformation Activity
- Distribute Bobby’s Transformation to each student
- Have students complete in their same groups as before.
- Use the Facilitation Questions on page 9 to ensure depth of understanding
- Distribute Evaluate: Coordinate Plane to each student
- Have students complete individually showing all work on the pages
- Have student trade pages for grading
- Have students journal their strengths and weaknesses regarding plotting and transforming rational ordered pairs.
- Collect assessments for further analysis on need to re-teach.
Closing the Distance Grade 9 Lesson 1 – Coordinate Plane
SEs 8.6B, 8.7D
Engage (10 minutes) Ordering Rational Numbers in Different Forms
- Order rational numbers via kinesthetic movement
- Answer questions related to the strategies of numerical ordering
- Plot rational pairs on a coordinate plane in small groups (8.7D)
- Reflect and translate geometric figures on a coordinate plane (8.6B)
- Answer questions related to the details of the plotting process