quarter unit 2 1 expressions and equations unit 3 … high school algebra i curriculum map 2015-2016...

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


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


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


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.


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





- Chapter 2 http://www.mathsisfun.com/operation-order-pemdas.html http://www.math-aids.com/Order_of_Operations/Order_of_Operations.html


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


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





- Chapter 3


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


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




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.


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




RETELL Strategies



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.


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




RETELL Strategies



Notes: This is also the place where Investigation 3B can be taught so students are prepared for MCAS.


12 Draft as of 8/10/2015

Quarter 4 : Unit 7 Polynomials Investigations 7A, 7B, and 7C


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*




RETELL Strategies



Notes: *Dates may be adjusted according to inclement weather cancellations


13 Draft as of 8/10/2015

Quarter 4 : Unit 8 Quadratics Investigations 8A and 8B (see Notes)


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*




RETELL Strategies



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

quarter unit 2 1 expressions and equations unit 3 … high school algebra i curriculum map 2015-2016...

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