Download durham public schools 2012-2013

DURHAM PUBLIC SCHOOLS 2012-2013
UNIT 2 PLAN FOR MATHEMATICS I
Unit Overview:
Quarter x One
Three
Instructional Time: approximately 35 days (based on 90-minute classes)
x Two
Four
Grade Level: Common Core Mathematics 1
Unit Theme: Modeling with Linear and Exponential Relationships
Depth of Knowledge: Level 3, Strategic Thinking
Unit Summary: This unit takes students through creating equations with one-variable, solving literal equations and formulas, and creating
equations with two-variables given the context. Students will use real world context to create linear and exponential equations and identify the
graphs of linear and exponential functions by their shapes and specific characteristics. Students will create lines of best fits taking into account
residuals. Students will examine correlation coefficients and the connection between correlation and causation. Lastly, students will solve for onevariable in terms of the other. Using this framework, students will solve for y, in terms of x, in order to help students see the connection between
the terms; as well as identify the slope and y-intercept of the equation (given contextual information).
Critical Area of Concentration: (1) Create equations that describe numbers or relationships, (2) Understand solving equations as a process of
reasoning and explain the reasoning, (3) Solve equations and inequalities in one variable, (4) Interpret functions that arise in applications in terms
of the context
North Carolina Information and Technology Essential Standards:
HS.TT.1
Use technology and other resources for assigned tasks.
HS.TT.1.3
Use appropriate technology tools and other resources to design products to share information with others (e.g. multimedia presentations, Web 2.0
tools, graphics, podcasts, and audio files).
HS.SE.1
Analyze issues and practices of responsible behavior when using resources.
Common Core State Standards
Functions: Linear, Quadratic, and Exponential Models Construct and compare linear and exponential models and solve problems
F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
a. Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over
equal intervals.
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or
two input-output pairs (include reading these from a table).
Algebra: Creating Equations Create equations that describe numbers or relationships
A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Instructional focus should include equations arising
from linear functions
A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels
and scales.
A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Algebra: Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoning
A-REI.1 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.
Algebra: Reasoning with Equations and Inequalities Solve equations and inequalities in one variable
A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Functions: Building Functions Build a function that models a relationship between two quantities
F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate
between the two forms. Formal recursive notation is not used.
Interpreting Categorical and Quantitative Data - Summarize, represent, and interpret data on two categorical and quantitative variables
S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data
(including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function
suggested by the context. Emphasize linear and exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for scatter plots that suggest a linear association.
Interpreting Categorical and Quantitative Data - Interpret linear models
S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
S-ID.9 Distinguish between correlation and causation.
Italicized standards notate Gap Standards that are new for North Carolina.
Bold standards notate Power Standards that are heavily weighted on Standardized Tests.
Italicized and Bold indicates the standard is both a Gap and a Power Standard.
Essential Question(s):
 How would creating a table help you see the pattern of a set of data?
 How do equations help us in finding missing information?
 How do addition and multiplication properties help us solve for unknowns?
 Why is the idea of balance so important in solving equations?
 How do you write inequalities and what do they mean?
 How do you represent solutions for inequalities on a number line?
 How do we identify and describe patterns?
 How do we use patterns to make predictions and solve problems?
 How can you identify equal changes in intervals from a table, a graph, or a linear function?
 How do linear functions compare to exponential functions?
 What is a function?
 What are the different ways that functions may be represented?
 How can functions be used to model real world situations, make predictions, and solve problems?
 How can technology help us analyze sequences and functions?
 How can you identify changes that grow by equal factors in intervals from a table, a graph, or an exponential function?
 How do we use residuals to help create a line of best fit?
 How do we find and interpret a correlation coefficient for a linear equation?
 How do we distinguish between correlation and causation?
Enduring Understanding(s):
 Linear equations and inequalities represent real-world problems and situations which grow by equal differences over equal intervals.
 There is a clear relationship between the variables in a function and that relationship is evident in tables, equations and graphs.
 Each step in solving an equation corresponds with an algebraic property.
 There are specific characteristics of linear functions and equations.
 There are specific characteristics of exponential functions and equations.
 Functions are a mathematical way to describe relationships between two quantities that vary.


Exponential equations represent real-world problems and situations which grow by equal factors over equal intervals.
Correlation does not necessarily imply causation.
I Can Statement(s):
 I can create one-variable linear equations and inequalities from contextual situations.
 I can create one-variable exponential equations and inequalities from contextual situations.
 I can solve and interpret the solution to multi-step linear equations and inequalities in context.
 I can justify the steps in solving equations by applying and explaining the properties of equality, inverse and identity.
 I can use the names of the properties and common sense explanations to explain the steps in solving an equation.
 I can justify the fact that linear functions grow by equal difference over equal intervals using tables and graphs.
 I can justify the fact that exponential functions grow by equal factors over equal intervals using tables and graphs.
 I can find the correlation coefficient—and interpret it—for a linear equation.
 I can distinguish between correlation and causation.
 I can find the line of best fit for a set of linear or exponential data.
Vocabulary:
greater than
less than
at most
=, <, >,
equations
variables
no less than
no more than
at least
inequalities
function
exponential
coordinate plane
constant
coefficient
properties of
operations
linear functions
exponential functions
like terms
variable
evaluate
justify
viable
properties of
equalities
constant rate of
change
interval
rate
literal equation
relationship
sequences
arithmetic sequence
geometric sequence
arithmetic
geometric
recursive
explicit
slope
scale
independent variable
dependent variable
Transdisciplinary Connections
domain
range
input
output
correlation coefficient
residual
Unit Implementation:
The primary resource for Unit 2 is: Core-Plus (Glencoe; 2008; Course 1). The estimated days are based on 90-minute periods and include review time and a period for
assessment in each block of time.
Days 1-10: Unit 1: Patterns of Change: Lessons 3, 4 (Looking Back)
Days 11-22: Unit 3: Linear Functions: Lessons 1, 2, 3, and 4 (Looking Back)
Days 23-35: Unit 5: Exponential Functions: Lessons 1, 2, and 3 (Looking Back)
Evidence of Learning (Formative Assessment):
 Daily Math Journal/Reflective Blog Entries
 Q&A
 Graphics Design
 HW responses
Summative Assessment:
 End of Unit Assessment