Honors Algebra 1-2 Scope and Sequence

General Information

  • Engageny suggested Pacing is 1 lesson per day, but Honors pacing may be a bit faster, depending on the material covered. We recommend that teachers review the lessons prior to determine ones that could be melded together.
  • Each lesson has an exit ticket that may be used as a formative assessment.

Suggestions

  • Teachers may create additional assessments as they feel necessary.
  • Modules (student materials) may be printed and bound for students to use as a workbook.
  • Common Core belief is to provide students with answer keys to practice correctly.

Required Materials – Per Common Core

  • Graphing Calculators

Quarter 1

Module 1: Relationship Between Quantities and Reasoning with Equations and Their Graphs
Topic A: Introduction to Functions Studied this Year
In Topic A, students explore the main functions that they will work with in Grade 9: linear, quadratic, and exponential. The goal is to introduce students to these functions by having them make graphs of situations (usually based upon time) in which the functions naturally arise (A-CED.2). As they graph, they reason abstractly and quantitatively as they choose and interpret units to solve problems related to the graphs they create (N-Q.1, N-Q.2, N-Q.3).
Lessons / Description – Student Outcome(s) / Mathematical Practice(s)
1: Graphs of Piecewise Linear Functions /
  • Students define appropriate quantities from a situation (a “graphing story”), choose and interpret the scale and the origin for the graph, and graph the piecewise linear function described in the video. They understand the relationship between physical measurements and their representation on a graph.
/ MP.1
MP.3
MP.6
2: Graphs of Quadratic Functions /
  • Students represent graphically a non-linear relationship between two quantities and interpret features of the graph. They will understand the relationship between physical quantities via the graph.
/ MP.1
MP.4
3: Graphs of Exponential Functions /
  • Students choose and interpret the scale on a graph to appropriately represent an exponential function.
  • Students plot points representing number of bacteria over time, given that bacteria grow by a constant factor over evenly spaced time intervals.
/ MP.4
MP.6
4: Analyzing Graphs –
Water Usage During a Typical Day at School /
  • Students develop the tools necessary to discern units for quantities in real-world situations and choose levels of accuracy appropriate to limitations on measurement. They refine their skills in interpreting the meaning of features appearing in graphs.
/ MP.1
MP.2
MP.3
5: Two Graphing Stories /
  • Students interpret the meaning of the point of intersection of two graphs and use analytic tools to find its coordinates.
/ MP.1
MP.3
Topic B: The Structure of Expressions
In middle school, students applied the properties of operations to add, subtract, factor, and expand expressions (6.EE.3, 6.EE.4, 7.EE.1, 8.EE.1). Now, in Topic B, students use the structure of expressions to define what it means for two algebraic expressions to be equivalent. In doing so, they discern that the commutative, associative, and distributive properties help link each of the expressions in the collection together, even if the expressions look very different themselves (A-SSE.2). They learn the definition of a polynomial expression and build fluency in identifying and generating polynomial expressions as well as adding, subtracting, and multiplying polynomial expressions (A-APR.1). The Mid-Module Assessment follows Topic B.
Lessons / Description – Student Outcome(s) / Mathematical Practice(s)
6: Algebraic Expressions –
The Distributive Property /
  • Students use the structure of an expression to identify ways to rewrite it.
  • Students use the distributive property to prove equivalency of expressions.
/ MP.7
7: Algebraic Expressions –
The Commutative and Associative Prop. /
  • Students use the commutative and associative properties to recognize structure within expressions and to prove equivalency of expressions.
/ MP.8
8: Adding and Subtracting Polynomials /
  • Students understand that the sum or difference of two polynomials produces another polynomial and relate polynomials to the system of integers; students add and subtract polynomials.

9: Multiplying Polynomials /
  • Students understand that the product of two polynomials produces another polynomial; students multiply polynomials.

Mid – Module Assessment Task – Topics A through B (recommended assessment 1-2 days)
Topic C: Solving Equations and Inequalities
Throughout middle school, students practice the process of solving linear equations (6.EE.5, 6.EE.7, 7.EE.4, 8.EE.7) and systems of linear equations (8.EE.8). Now, in Topic C, instead of just solving equations, they formalize descriptions of what they learned before (variable, solution sets, etc.) and are able to explain, justify, and evaluate their reasoning as they strategize methods for solving linear and non-linear equations (A- REI.1, A-REI.3, A-CED.4). Students take their experience solving systems of linear equations further as they prove the validity of the addition method, learn a formal definition for the graph of an equation and use it to explain the reasoning of solving systems graphically, and graphically represent the solution to systems of linear inequalities (A-CED.3, A-REI.5, A-REI.6, A-REI.10, A-REI.12).
Lessons / Description – Student Outcome(s) / Mathematical Practice(s)
10: True and False Equations /
  • Students understand that an equation is a statement of equality between two expressions. When values are substituted for the variables in an equation, the equation is either true or false.
  • Students find values to assign to the variables in equations that make the equations true statements.
/ MP.8
11: Solution Sets for Equations and Inequalities /
  • Students understand that an equation with variables is often viewed as a question asking for the set of values one can assign to the variables of the equation to make the equation a true statement. They see the equation as a “filter” that sifts through all numbers in the domain of the variables, sorting those numbers into two disjoint sets: the Solution Set and the set of numbers for which the equation is false.
  • Students understand the commutative, associate, and distributive properties as identities, e.g., equations whose solution sets are the set of all values in the domain of the variables.
/ MP.1
MP.2
MP.3
12: Solving Equations /
  • Students are introduced to the formal process of solving an equation: starting from the assumption that the original equation has a solution.
  • Students explain each step as following from the properties of equality. Students identify equations that have the same solution set.
  • Honors should extend and include solving radical equations
/ MP.1
MP.2
MP.3
13: Some Potential Dangers when Solving Equations /
  • Students learn “if-then” moves using the properties of equality to solve equations. Students also explore moves that may result in an equation having more solutions than the original equation.
/ MP.3
14: Solving Inequalities /
  • Students learn if-then moves using the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line.
/ MP.1 MP.3
MP.2
15: Solution Sets of Two or More Equations (Inequalities) Joined by “And” or “Or” /
  • Students describe the solution set of two equations (or inequalities) joined by either “and” or “or” and graph the solution set on the number line.
/ MP.2
MP.6
16: Solving and Graphing Inequalities Joined by “And” and “Or” /
  • Students solve two inequalities joined by “and” or “or,” then graph the solution set on the number line.
/ MP.1
MP.3
17: Equations Involving Factored Expressions /
  • Students learn that equations of the form (?−?)(?−?)=0 have the same solution set as two equations joined by “or:” ?−?=0 or ?−?=0. Students solve factored or easily factorable equations.
/ MP.6
MP.7
MP.8
18: Equations Involving a Variable Expression in the Denominator /
  • Students interpret equations like 1? = 3 as two equations “1?= 3” and “? ≠ 0” joined by “and.” Students find the solution set for this new system of equations.
  • Honors should extend solving rational equations
/ MP.3
19: Rearranging Formulas /
  • Students learn to think of some of the letters in a formula as constants in order to define a relationship between two or more quantities, where one is in terms of another, for example holding V in V = IR as constant, and finding R in terms of I.
/ MP.3
20: Solution Sets to Equations and Inequalities with 2 Variables - Part 1 /
  • Students recognize and identify solutions to two-variable equations. They represent the solution set graphically. They create two variable equations to represent a situation. They understand that the graph of the line ax + by = c is a visual representation of the solution set to the equation ax + by = c.
/ MP.2
MP.6
21: Solution Sets to Equations and Inequalities with 2 Variables - Part 2 /
  • Students recognize and identify solutions to two-variable inequalities. They represent the solution set graphically. They create two variable inequalities to represent a situation.
  • Students understand that a half-plane bounded by the line ?? + ?? = ?is a visual representation of the solution set to a linear inequality such as ?? + ???. They interpret the inequality symbol correctly to determine which portion of the coordinate plane is shaded to represent the solution.
/ MP.1
22: Solution Sets to Simultaneous Equations P1 /
  • Students identify solutions to simultaneous equations or inequalities; they solve systems of linear equations and inequalities either algebraically or graphically.
/ MP.7
23: Solution Sets to Simultaneous Equations P2 /
  • Students create systems of equations that have the same solution set as a given system.
  • Students understand that adding a multiple of one equation to another creates a new system of two linear equations with the same solution set as the original system. This property provides a justification for a method to solve a system of two linear equations algebraically.

24: Applications of Systems of Equations and Inequalities /
  • Students use systems of equations or inequalities to solve contextual problems and interpret solutions within a particular context.
/ MP.1
MP.3
MP.6
Topic D: Solving Equations and Inequalities
In Topic D, students are formally introduced to the modeling cycle (see page 61 of the CCLS) through problems that can be solved by creating equations and inequalities in one variable, systems of equations, and graphing (N-Q.1, A-SSE.1, A-CED.1, A-CED.2, A-REI.3). The End-of-Module Assessment follows Topic D.
Lessons / Description – Student Outcome(s) / Mathematical Practice(s)
25: Solving Problems in 2 ways – Rates and Algebra /
  • Students investigate a problem that can be solved by reasoning quantitatively and by creating equations in one variable.
  • They compare the numerical approach to the algebraic approach.
/ MP.1
MP.2
26: Recursive Challenge Problem – Double and Add 5 Game – Part 1 /
  • Students learn the meaning and notation of recursive sequences in a modeling setting.
  • Following the modeling cycle, students investigate the double and add 5 game in a simple case in order to understand the statement of the main problem.
/ MP.1
MP.4
27: Recursive Challenge Problem – Double and Add 5 Game – Part 2 /
  • Students learn the meaning and notation of recursive sequences in a modeling setting.
  • Students use recursive sequences to model and answer problems.
  • Students create equations and inequalities to solve a modeling problem.
  • Students represent constraints by equations and inequalities and interpret solutions as viable or non-viable options in a modeling context.
/ MP.2
MP.3
MP.4
28: Federal Income Tax /
  • Students create equations and inequalities in one variable and use them to solve problems.
  • Students create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales.
  • Students represent constraints by inequalities and interpret solutions as viable or non-viable options in a modeling context.
/ MP.1
MP.2
MP.4
End – Module Assessment Task – Topics A through D (recommended assessment 1-2 days)

Focus Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them. Students are presented with problems that require them to try special cases and simpler forms of the original problem in order to gain insight into the problem.

MP.2 Reason abstractly and quantitatively. Students analyze graphs of non-constant rate measurements and reason from the shape of the graphs to infer what quantities are being displayed and consider possible units to represent those quantities.

MP.3 Construct viable arguments and critique the reasoning of others. Students reason about solving equations using “if-then” moves based on equivalent expressions and properties of equality and inequality. They analyze when an “if-then” move is not reversible.

MP.4 Model with mathematics. Students have numerous opportunities in this module to solve problems arising in everyday life, society, and the workplace from modeling bacteria growth to understanding the federal progressive income tax system.

MP.6 Attend to precision. Students formalize descriptions of what they learned before (variables, solution sets, numerical expressions, algebraic expressions, etc.) as they build equivalent expressions and solve equations. Students analyze solution sets of equations to determine processes (like squaring both sides of an equation) that might lead to a solution set that differs from that of the original equation.

MP.7 Look for and make use of structure. Students reason with and about collections of equivalent expressions to see how all the expressions in the collection are linked together through the properties of operations. They discern patterns in sequences of solving equation problems that reveal structures in the equations themselves: 2? + 4= 10, 2(? − 3) + 4= 10, 2(3? − 4) + 4= 10, etc.

MP.8 Look for and express regularity in repeated reasoning. After solving many linear equations in one variable (e.g., 3? + 5=8? − 17), students look for general methods for solving a generic linear equation in one variable by replacing the numbers with letters: ?? + ? = ?? + ?. They have opportunities to pay close attention to calculations involving the properties of operations, properties of equality, and properties of inequality as they find equivalent expressions and solve equations, noting common ways to solve different types of equations.

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Dysart USD – engageny2014 ~ 2015