Download Unit B: Equations and Inequalities

Algebra 1 Unit B: Equations and Inequalities
Math Florida Standards
Unit Overview
Content Standards
(bold are directly
assessed)
You can represent an equation/inequality in many ways. You can use properties of numbers and equality to transform
equations/inequalities into equivalent, simpler equations/inequalities and find solutions. Real-world relationships can be
modeled using equations/inequalities. In a proportional relationship the relationship between two quantities are equal.
You can use this relationship to describe similar figures, scale models, and rates.
Textbook Resources
Pearson Prentice Hall Algebra 1 copyright 2011
Pearson SuccessNet
Sections:
1.8, 2.1 – 2.5, 2.5 Concept Byte, 2.6 – 2.8, 2.10,
3.2 – 3.4, 3.6, 3.7
Mathematics Formative Assessment System
The system includes tasks or problems that teachers can
implement with their students, and rubrics that help the
teacher interpret students' responses. Teachers using MFAS
ask students to perform mathematical tasks, explain their
reasoning, and justify their solutions. Rubrics for
interpreting and evaluating student responses are included
so that teachers can differentiate instruction based on
students' strategies instead of relying solely on correct or
incorrect answers. The objective is to understand student
thinking so that teaching can be adapted to improve student
achievement of mathematical goals related to the
standards. Like all formative assessment, MFAS is a process
rather than a test. Research suggests that well-designed and
implemented formative assessment is an effective strategy
for enhancing student learning.
MAFS.912.A-CED.1.1
MAFS.912.A-CED.1.4
MAFS.912.N-Q.1.1*
MAFS.912.N-Q.1.2*
MAFS.912.N-Q.1.3*
*(all N-Q are assessed
throughout)
MAFS.912.A-SSE.1.1b
MAFS.912.A-REI.1.1
MAFS.912.A-REI.2.3
Highlighted Standards
for Mathematical
Practice
MAFS.K12.MP.1.1
MAFS.K12.MP.2.1
MAFS.K12.MP.4.1
MAFS.K12.MP.6.1
MAFS.K12.MP.8.1
Other Resources
Algebra Nation
Online Graphing Calculator
Canvas Mathematics Website
Algebra Balance Scales
Paying the Rent
Planes and Wheat
Mathematics Formative Assessment System Tasks
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 1 Unit B: Equations and Inequalities
Unit Scale (Multidimensional) (MDS)
The multidimensional, unit scale is a curricular organizer for PLCs to use to begin unpacking the unit. The MDS should not be used directly with students and is not for
measurement purposes. This is not a scoring rubric. Since the MDS provides a preliminary unpacking of each focus standard, it should prompt PLCs to further explore question #1,
“What do we expect all students to learn?” Notice that all standards are placed at a 3.0 on the scale, regardless of their complexity. A 4.0 extends beyond 3.0 content and helps
students to acquire deeper understanding/thinking at a higher taxonomy level than represented in the standard (3.0). It is important to note that a level 4.0 is not a goal for the
academically advanced, but rather a goal for ALL students to work toward. A 2.0 on the scale represents a “lightly” unpacked explanation of what is needed, procedural and
declarative knowledge i.e. key vocabulary, to move students towards proficiency of the standards.
4.0
In addition to displaying a 3.0 performance, the student must demonstrate in-depth inferences and applications that go beyond what was taught within these
standards. Examples:

Create a word problem involving a real-life relationship. Choose and define appropriate variables and use them to create an equation that models the
relationship. Solve the equation, justifying each step, and explain its meaning in the context of the problem.
3.0
The Student will:
 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple
rational, absolute, and exponential functions. (MAFS.912.A-CED.1.1)
 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight
resistance R. (MAFS.912.A-CED.1.4)
 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and
interpret the scale and the origin in graphs and data displays. (MAFS.912.N-Q.1.1)
 Define appropriate quantities for the purpose of descriptive modeling. (MAFS.912.N-Q.1.2)
 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. (MAFS.912.N-Q.1.3)
 Interpret expressions that represent a quantity in terms of its context.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret
as the product of P and a
factor not depending on P. (MAFS.912.A-SSE.1.1b)
 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the
original equation has a solution. Construct a viable argument to justify a solution method. (MAFS.912.A-REI.1.1)
 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (MAFS.912.A-REI.2.3)
2.0
The student will recognize or recall specific vocabulary, such as:
 Linear equation, linear inequality, properties of equality for real numbers, at most, at least, more than, less than, number line
The student will perform basic processes, such as:
 Solving a linear equation and an inequality, graphing on a number line
1.0
With help, partial success at 2.0 content but not at score 3.0 content
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 1 Unit B: Equations and Inequalities
Unpacking the Standard: What do we want students to Know, Understand and Do (KUD):
The purpose of creating a Know, Understand, and Do Map (KUD) is to further the unwrapping of a standard beyond what the MDS provides and assist PLCs in answering question
#1, “What do we expect all students to learn?” It is important for PLCs to study the focus standards in the unit to ensure that all members have a mutual understanding of what
student learning will look and sound like when the standards are achieved. Additionally, collectively unwrapping the standard will help with the creation of the uni-dimensional
scale (for use with students). When creating a KUD, it is important to consider the standard under study within a K-12 progression and identify the prerequisite skills that are
essential for mastery.
Domain: Algebra: Reasoning with Equations & Inequalities
Cluster: Understand solving equations as a process of reasoning and explain the reasoning- (Major Cluster)
Standard: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the
original equation has a solution. Construct a viable argument to justify a solution method. (MAFS.912.A.REI.1.1)
Understand
“Essential understandings,” or generalizations, represent ideas that are transferable to other contexts.



When or why steps are completed in a certain order.
Arguments about equality are used to justify solutions to equations.
There is a justifiable process for solving equations in which the equality of expressions must be maintained.
Know
Declarative knowledge: Facts, vocab., information









steps for solving
solution
no solution
addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality
distributive property
like terms
Do
Procedural knowledge: Skills, strategies and processes that are transferrable to other contexts.
Retrieval
 Identify properties of equality
Comprehension
 Explain each step
Analysis
 Construct a viable argument to justify solution
Prerequisite skills: What prior knowledge (foundational skills) do students need to have mastered to be successful with this standard?
inverse operations, expressions, order of operations, variables
Moving Beyond: Solving polynomial and trigonometric equations
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 1 Unit B: Equations and Inequalities
Uni-Dimensional, Lesson Scale:
The uni-dimensional, lesson scale unwraps the cognitive complexity of a focus standard for the unit, using student friendly language. The purpose is to articulate distinct levels of
knowledge and skills relative to a specific topic and provide a roadmap for designing instruction that reflects a progression of learning. The sample performance scale shown
below is just one example for PLCs to use as a springboard when creating their own scales for student-owned progress monitoring. The lesson scale should prompt teams to
further explore question #2, “How will we know if and when they’ve learned it?” for each of the focus standards in the unit and make connections to Design Question 1,
“Communicating Learning Goals and Feedback” (Domain 1: Classroom Strategies and Behaviors). Keep in mind that a 3.0 on the scale indicates proficiency and includes the
actual standard. A level 4.0 extends the learning to a higher cognitive level. Like the multidimensional scale, the goal is for all students to strive for that higher cognitive level,
not just the academically advanced. A level 2.0 outlines the basic declarative and procedural knowledge that is necessary to build towards the standard.
Standard:
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original
equation has a solution. Construct a viable argument to justify a solution method. (MAFS.912.A.REI.1.1)
Learning Progression
Sample Tasks
Score
4.0
3.5
3.0
2.5
I can…
Given a simple equation such as -3(2x - 5) = 39 , generate multiple solution

methods and construct viable arguments to justify each solution method.
Experiment with a simple equation to generate multiple solution methods
and construct viable arguments to justify each solution method
 Investigate errors in solution methods given an equation and multiple
solutions
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.
I can…
Solve the following equation and justify each step:
 Explain each step in solving a simple equation
 Construct a viable argument to justify the solution
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
I can…



Solve a simple equation
Identify properties of equality
Recognizing a viable argument
Solve the following equation:
2
4
x - 2 = - (x + 3)
3
3
5x + 2 = 2(x + 7)
Which property of equality is demonstrated as the first step in solving the
following equation?
2.0
Key Vocabulary such as: solution, no solution, simple equation, addition
property of equality, subtraction property of equality, multiplication property
of equality, division property of equality, distributive property, like terms
1.0
7
k +1 = 2k - 5
2
7
2( k +1) = 2(2k - 5)
2
I need prompting and/or support to complete 2.0 tasks.
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015
Algebra 1 Unit B: Equations and Inequalities
Sample High Cognitive Demand Tasks:
These task/guiding questions are intended to serve as a starting point, not an exhaustive list, for the PLC and are not intended to be prescriptive. Tasks/guiding questions simply
demonstrate one way to help students learn the skills described in the standards. Teachers can select from among them, modify them to meet their students’ needs, or use them
as an inspiration for making their own. They are designed to generate evidence of student understanding and give teachers ideas for developing their own activities/tasks and
common formative assessments. These guiding questions should prompt the PLC to begin to explore question #3, “How will we design learning experiences for our students?”
and make connections to Marzano’s Design Question 2, “Helping Students Interact with New Knowledge”, Design Question 3, “Helping Students Practice and Deepen New
Knowledge”, and Design Question 4, “Helping Students Generate and Test Hypotheses” (Domain 1: Classroom Strategies and Behaviors).
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic
MAFS Content Standard(s)
functions, and simple rational, absolute, and exponential functions. (MAFS.912.A-CED.1.1)
Design Question 1; Element 1
MAFS Mathematical Practice(s)
Make sense of problems and persevere in solving them. (MAFS.K12.MP.1.1)
Attend to precision. (MAFS.K12.MP.6.1)
Design Question 1; Element 1
Marzano’s Taxonomy
Knowledge Utilization
Teacher Notes
Questions to develop mathematical
thinking, possible
misconceptions/misunderstandings
, how to differentiate/scaffold
instruction, anticipate student
problem solving strategies
Task
*These tasks can either be teacher
created or modified from a
resource to promote higher order
thinking skills. Please cite the
source for any tasks.
Licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
This a working document that will continue to be revised and improved taking your feedback into consideration.
Pasco County Schools, 2014-2015