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LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
1 Draft as of 8/10/2015
ALG
EBR
A I
Quarter 1
Unit 1
Arithmetic to Algebra
Unit 2
Expressions and Equations
Unit 3
Graphs
Quarter 2
Unit 4
Lines
Quarter 3
Unit 5
Introduction to Functions
Unit 6
Exponents and Radicals
Quarter 4
Unit 7
Polynomials
Unit 8
Quadratics
Course Overview
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
2 Draft as of 8/10/2015
The following are a list of essential standards for this course and a brief map of where they will be addressed. These have been identified by the
MA DESE as content standards for Model Algebra I courses. Those standards in bold are assessable on MCAS.
Standard Quarter 1 Quarter 2 Quarter 3 Quarter 4
N.RN.1, N.RN.2, N.RN.3- The Real Number System; working with Rational Exponents and Irrational Numbers
X
N.Q.1, N.Q.2, N.Q.3- Quantities; Reason and Use Units to Solve Problems X X
A.SSE.1, A.SSE.2- Seeing Structure in Expressions X X X
A.SSE.3, A.SSE.4- Write Expressions in Equivalent Forms to Solve Problems X X
A.APR.1- Perform Arithmetic Operations on Polynomials X
A.APR.3- Identify Zeros of Polynomials X
A.APR.4, A.APR.5- Use Polynomial Identities to Solve Problems X
A.CED.1, A.CED.2, A.CED.3, A.CED.4- Create Equations that Describe Numbers or Relationships
X X X X
A.REI.1, A.REI.2- Understand Solving Equations as a Process of Reasoning and Explain X X X X
A.REI.3, A.REI.4- Solve Equations and Inequalities X X X
A.REI.5, A.REI.6, A.REI.7- Solve Systems of Equations X X
A.REI.10, A.REI.11, A.REI.12- Represent and Solve Equations and Inequalities Graphically X X
F.IF.1, F.IF.2, F.IF.3- Understand functions and their notation X
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
3 Draft as of 8/10/2015
Standard Quarter 1 Quarter 2 Quarter 3 Quarter 4
F.IF.4, F.IF.5, F.IF.6- Using functions and their graphs to model relationships X X
F.IF.7, F.IF.8, F.IF.9, MA.F.IF.10- Analyze functions using different representations X X X
F.BF.1, F.BF.2- Build functions to model a relationship between two quantities X
F.BF.3, F.BF.4- Build functions from existing functions X X
F.LE.1, F.LE.2, F.LE.3- Construct and compare linear, quadratic, and exponential models X X
F.LE.5- Interpret expressions for functions in terms of the situation they model X X
S.ID.1, S.ID.2, S.ID.3, S.ID.4- Summarize, represent, and interpret data on a single variable X
S.ID.5, S.ID.6- Summarize, represent, and interpret data on two variables X X
S.ID.7, S.ID.8, S.ID.9- Interpret linear models X X
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
4 Draft as of 8/10/2015
Quarter 1: Unit 1 Arithmetic to Algebra Investigations 1A, 1B, and 1C
Learning Goals: Review basic operations on different types of real numbers and investigate why algorithms work SWBAT:
Add, subtract, multiply, and divide positive and negative integers
Apply the basic rules of arithmetic to integers
Compare and order rational numbers
Extend arithmetic to apply to real numbers including radicals
Essential Questions
What are the rules for multiplying and dividing positive and negative integers? What are the rules for adding and subtracting positive and negative integers? How are addition and subtraction related? How are multiplication and division related? What are some real life situations where it is important to be able to add and subtract positive and negative integers? How are exponents and radicals related?
Standards 6.EE.3, 6.NS.3, 6.NS.6, 7.NS.1, 7.NS.2, 7.NS.3, 8.NS.2 Tier II Vocabulary addition, subtraction, multiply, divide, distributive, opposite, positive, negative, factor, base, exponent, power, squared, cubed,
radical, roots, increase, decrease, up, down, left, right, reciprocal Tier III Vocabulary additive identity, additive inverse, integers, perfect square, exponential form, standard form, expanded form, square root,
algorithm Assessments CIA: 10/26-10/30/15 Data Meeting: 11/9/15
Summative assessments: Formative assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Texts/Resources CME Algebra 1 Text
- Chapter 1 LHS Math Website (includes study guides, performance tasks, formative and summative assessment ideas) http://www.virtualnerd.com/algebra-1/algebra-foundations/powers-square-roots
Notes Chapter 1 is a pre-Algebra review to ensure students remember how to perform operations on rational numbers. This should be no more than 2 WEEKS of class time. If students need more help, they will need differentiated assignments and more spiral review as they move to the other concepts.
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
5 Draft as of 8/10/2015
Quarter 1: Unit 2 Expressions and Equations Investigations 2A, 2B, and 2C (see Notes)
Learning Goals: Writing and evaluating expressions and equations SWBAT:
State the need for variables and expressions
Determine the order of operations
Express word problems using variables and mathematical notation
Explain the relationship between an equation and its solutions
Evaluate and simplify expressions
Solve equations
Essential Questions
How does the value of an expression chance if one does not follow the correct order of operations? Why is it important to follow the order of operation? (Left to right, PEMDAS) Why is the order of multiplication and division interchangeable? Why is the order of addition and subtraction interchangeable? Why is the order of addition and multiplication as well as the order of addition and division NOT interchangeable? Why is the order of subtraction and multiplication as well as the order of subtraction and division NOT interchangeable? Why is it important to be able to translate word phrases into arithmetic and variable expressions?
Standards 7.EE.1, A.CED.1, A.CED.2, A.CED.3, A.CED.4, A.REI.1, A.REI.3, A.SSE.1, A.SSE.2, N.Q.1 Tier II Vocabulary expression, parentheses, nested parenthesis, brackets, sum, product, quotient, difference, less than, greater than, more than, plus,
minus, increase, decrease, variable, times, multiplied by, divided by, linear, theorem, solution, operation
Tier III Vocabulary order of operations, arithmetic expression, algebraic expression, like terms, equations, binary operation, empty set Assessments CIA: 10/26-10/30/15 Data Meeting: 11/9/15
Summative assessments: Formative assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Texts/Resources CME Algebra 1 Text
- Chapter 2 http://www.mathsisfun.com/operation-order-pemdas.html http://www.math-aids.com/Order_of_Operations/Order_of_Operations.html
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
6 Draft as of 8/10/2015
http://www.math-aids.com/Algebra/Algebra_1/Basics/Writing_Variable.html http://www.math-aids.com/Algebra/Algebra_1/Basics/Evaluating_Expressions.html http://www.math-aids.com/Algebra/Pre-Algebra/Expressions/ http://www.lavc.edu/math/math112/Worksheets/lineqnvarbothsides.pdf http://www.worksheetworks.com/math/pre-algebra/equations-mixed.html
Notes: Omitting section 2D and focus instead on MCAS Open Response
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
7 Draft as of 8/10/2015
Quarter 1: Unit 3 Graphs Investigations 3A and 3C, postpone 3B (see Notes)
Learning Goals: Graphing equations in the coordinate plane and understanding statistical data SWBAT:
Plot points and read coordinates on a graph
Describe the effects of a transformation
Use absolute value and relate it to distance
Connect graphs to data sets
Determine mean, median, mode
Build and compare data graphs
Graph equations
Test points to determine whether it is on the graph of an equation
Write equations from a graph
Decide whether a situation represents direct or inverse variation
Essential Questions
Why is it important to not confuse x and y coordinates? What is the benefit of graphing data? Why is it useful to have a graph for every value of x? How are equations and graphs related? How does recognizing a pattern help?
Standards 8.G.8, A.CED.3, A.REI.10, A.REI.11, A.REI.6, A.REI.7, F.BF.3, F.IF.7, N.Q.1, N.Q.3, S.ID.1, S.ID.2, S.ID.3, S.ID.5, S.ID.6, S.ID.8, S.ID.9
Tier II Vocabulary coordinate, graph, origin, plane, transformation, quadrants, association, table, range, maximum, minimum, mode, mean, median, outlier
Tier III Vocabulary x-axis, y-axis, ordered pair, absolute value, quartile, correlation coefficient, negatively associated, positively associated Assessments CIA: 10/26-10/30/15 Data Meeting: 11/9/15
Summative assessments: Formative assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies 7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around Texts/Resources CME Algebra 1 Text
- Chapter 3
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
8 Draft as of 8/10/2015
http://www.mathsisfun.com/data/cartesian-coordinates.html http://www.math-aids.com/Graphing/ http://www.worksheetworks.com/math/geometry/graphing/coordinate-pictures.html
Notes: Since most students in Alg 1 are repeaters, we are recommending Chapters 1-3 in Quarter 1 to leave more time for Chapters 4-8. 3A and 3C are essential at this point in the year 3B can be placed closer to MCAS in order to review Statistics standards prior to the test 3D is visited again in Algebra II, so could be omitted here if time dictates
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
9 Draft as of 8/10/2015
Quarter 2 : Unit 4 Lines Investigations 4A, 4B, 4C, and 4D
Learning Goals: Analyzing linear equations and graphs SWBAT:
Describe slope as a rate of change
Write linear equations
Solve systems of equations
Graph the solutions to an inequality
Essential Questions
What are some uses of linear equations? What is the significance of an intersection? What is the purpose of finding a line of best fit?
Standards 8.EE.6, A.CED.1, A.CED.2, A.CED.3, A.CED.4, A.REI.1, A.REI.3, A.REI.5, A.REI.6, A.REI.11, A.SSE.1, A.SSE.2, F.IF.6 , F.IF.7, F.LE.2, F.LE.5, G.GPE.5 N.Q.1, N.Q.2, N.Q.3, S.ID.6, S.ID.7
Tier II Vocabulary rise, run, slope, subscript, parallel, intersection, elimination, substitution, inequality Tier III Vocabulary collinear points, x-intercept, y-intercept, systems of equations, linear regression, line of best fit
Assessments Midterms: 1/19-1/22/16 Data Meeting: 2/1/16
Summative assessments: Formative assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME Algebra 1 Text - Chapter 4
Notes: This chapter is essential for High School Mathematics, so students need to complete all 4 investigations and master the concepts of linear equations and graphs.
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
10 Draft as of 8/10/2015
Quarter 3 : Unit 5 Introduction to Functions Investigation 5A (see Notes)
Learning Goals: Begin to understand functions and their various forms SWBAT:
Build a function from a word problem
Create input-output tables
Graph a function
Describe a recursive rule
Essential Questions
How do you find a function rule from an input-output table? What is the benefit of determining a recursive rule?
Standards F.IF.1, F.IF.8, A.CED.1, F.BF.1, F.IF.2, F.BF.4, F.IF.4, F.IF.9, F.IF.7, A.CED.1, F.IF.3, F.BF.2, F.LE.1 Tier II Vocabulary composition, function, domain, range, input, output, period
Tier III Vocabulary delta, recursive rule Assessments CIA: 4/4-4/8/16 Data Meeting: 4/25/16
Summative assessments: Formative assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME Algebra 1 Text - Chapter 5
Notes: Investigation 5A introduces Functions and is an important Algebra concept. 5B and 5C can get students bogged down so they can be omitted or postponed to the year end.
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
11 Draft as of 8/10/2015
Quarter 3 : Unit 6 Exponents and Radicals Investigations 6A, 6B, and 6C (see Notes)
Learning Goals: SWBAT:
simplify expressions involving integral exponents
distinguish between rational and irrational numbers
use exponential functions to solve problems
Essential Questions
What is the benefit to using scientific notation? How can numbers be classified between rational and irrational?
Standards A.REI.2, 8.EE.2, F.IF.2, N.RN.2, N.RN.3, N.RN.1, A.CED.1, F.IF.8, F.LE.1, F.LE.2, A.SSE.3, F.IF.7, F.LE.5, F.IF.4, F.LE.3, F.IF.3, F.BF.2
Tier II Vocabulary base, cube, identity, radical
Tier III Vocabulary annual percentage rate, compound interest, constant ratio, exponent, scientific notation, square root Assessments CIA: 4/4-4/8/16 Data Meeting: 4/25/16
Summative assessments: Formative assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME Algebra 1 Text - Chapter 6
Notes: This is also the place where Investigation 3B can be taught so students are prepared for MCAS.
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
12 Draft as of 8/10/2015
Quarter 4 : Unit 7 Polynomials Investigations 7A, 7B, and 7C
Learning Goals: SWBAT:
factor expressions and polynomials
add, subtract, and multiply polynomials
use factoring to solve equations
Essential Questions
Why should you consider more than one strategy? How do you determine whether two different expressions define the same function? Why is it a good idea to write polynomials in normal form?
Standards A.SSE.1, A.SSE.4, A.APR.4, A.APR.5, F.IF.8, A.SSE.2, A.SSE.3, A.CED.3, F.IF.2, A.APR.3, A.CED.4, A.REI.4, A.APR.1 Tier II Vocabulary factor, expand, identity, parameter, degree
Tier III Vocabulary annulus, binomial, coefficient, monic, monomial, polynomial, trinomial Assessments Finals: 6/7-6/10/16*
Summative assessments: Formative assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME Algebra 1 Text - Chapter 7
Notes: *Dates may be adjusted according to inclement weather cancellations
LAWRENCE HIGH SCHOOL ALGEBRA I CURRICULUM MAP 2015-2016
13 Draft as of 8/10/2015
Quarter 4 : Unit 8 Quadratics Investigations 8A and 8B (see Notes)
Learning Goals: SWBAT:
use the quadratic formula to solve equations
construct a quadratic equation given the equation's two roots
factor nonmonic quadratics
graph quadratic functions
sketch the solutions of inequalities
Essential Questions
When can the quadratic formula be used?
Standards A.REI.4, F.IF.2, A.APR.3, A.SSE.1, A.CED.1, A.CED.2, A.CED.3, A.SSE.3, F.IF.4, F.IF.5, F.IF.7, F.IF.8, F.IF.9, N.Q.1, A.REI.1, F.IF.1, A.REI.7, A.REI.11, A.REI.12, F.BF.1, F.LE.1, F.LE.2
Tier II Vocabulary vertex
Tier III Vocabulary line of symmetry, parabola, nonmonic Assessments Finals: 6/7-6/10/16*
Summative assessments: Formative assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME Algebra 1 Text - Chapter 8
Notes: *Dates may be adjusted according to inclement weather cancellations 8C can be omitted if time dictates End of year can be used to review any topics identified as problem areas