Download 4th 9 weeks

2016.17, Algebra I, Quarter 4
The following practice standards will be used throughout the quarter:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Ongoing Standards
Note to Teachers: The following ongoing standards will be practiced all year long and embedded into your instruction instead of being taught
in isolation.
AI.WCE.1 Evaluate expressions and solve equations fluently using substitution to verify solutions.
AI.WCE.2 Understand the relationships of numbers and number sets within the real number system.
AI.WCE.3 Convert unit rates of measurements in multistep arithmetic problems. (i.e. feet per second to miles per hour.)
AI.WCE.4 Identify the independent and dependent variables in situations represented by linear functions.
AI.WCE.5 Add, subtract and multiply radicals to simplify expressions.
AI.WCE.6 I can differentiate between linear and non-linear functions.
AI.WCE.7 I can move fluently between different representations of numbers, such as graphs, tables and equations.
**Unless otherwise noted, all resources are from HMH Algebra I, 2015 Edition.
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Standards
Student Friendly “I Can” Statements
Transformations of Functions ( Revisiting multiple modules) and Unit 5 Linear Systems ( con’t)
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k
I can transform a variety of functions including linear, quadratic and
f(x), f(kx), and f(x + k) for specific values of k (both positive and
logarithmic.
negative); find the value of k given the graphs. Experiment with cases
and illustrate an explanation of the effects on the graph using
I can use technology to experiment with the graphs of various
technology.
functions when transforming the equations using different values of k.
I can form conjectures based on my experiments with substituting
different values into the general (parent) functions.
A. REI.5 Prove that, given a system of two equations in two variables,
replacing one equation by the sum of that equation and a multiple of
the other produces a system with the same solutions.
I can solve pairs of linear equations in two variables using substitution
and elimination.
A.REI.6 Solve systems of linear equations exactly and approximately
(e.g. with graphs), focusing on pairs of linear equations in two
variables.
I can choose the best method for solving a linear system, and I can
justify my method.
I can graph a system of equations and determine its solution.
I can use technology to solve a linear system graphically.
I can solve a system of linear equations in two variables graphically
and symbolically.
I can determine the number of solutions to the system of equations.
A.REI.12 Graph the solutions to a linear inequality in two variables as a
half-plane (excluding the boundary in the case of a strict inequality),
and graph the solution set to a system of linear inequalities in two
variables as the intersection of the corresponding half-planes.
I can graph linear inequalities on the coordinate plane and describe
the meaning of the solution set.
I can graph the solutions to a linear inequality in two variables as a
half-plane, excluding the boundary for non-inclusive inequalities
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I can graph the solution set to a system of linear inequalities in two
variables as the intersection of their corresponding half-planes.
Unit 4 Statistical Models
S.ID.5 Summarize categorical data for two categories in two-way
I can create a two-way table from two categorical variables and read
frequency tables. Interpret relative frequencies in the context of the
values from a two-way table.
data (including joint, marginal, and conditional relative frequencies).
Recognize possible associations and trends in the data.
I can write clear summaries of data displayed in a two-way frequency
table.
I can interpret joint, marginal, and relative frequencies in context of
the problem.
I can recognize and describe associations and trends in data from a
two-way table.
S.ID.1 Represent data with plots on the real number line (dot plots,
histograms, and box plots).
I can construct dot plots, histograms, and box plots for data on a real
number line.
I can make predictions based on graphs and data sets.
I can construct and interpret various forms of data representations,
(including line graphs, bar graphs, circle graphs, histograms, scatterplots, box-and-whiskers, stem-and-leaf, and frequency tables). (*ACT)
( moved this up, but I think it is saying the same as statement #1)
S.ID.2 Use statistics appropriate to the shape of the data distribution
to compare center (median, mean) and spread (interquartile range,
standard deviation) of two or more different data sets.
I can describe a situation using center and spread.
I can use the correct measure of center and spread to describe a
distribution that is symmetric or skewed.
I can identify outliers (extreme data points) and their effects on data
sets.
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I can compare two or more different data sets using the center and
spread of each.
S.ID.3 Interpret differences in shape, center, and spread in the context
of the data sets, accounting for possible effects of extreme data points
(outliers).
I can interpret differences in different data sets in context.
S.ID.6 Represent data on two quantitative variables on a scatter plot,
and describe how the variables are related.
I can determine when linear, quadratic, and exponential models
should be used to represent a data set.
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.
I can determine whether linear and exponential models are increasing
or decreasing.
I can interpret differences due to possible effects of outliers.
I can determine the relationship shown in a scatterplot.
b. Informally assess the fit of a function by plotting and analyzing
residuals.
c. Fit a linear function for a scatter plot that suggests a linear
association on a scatter plot,
and describe how the variables are related.
I can sketch the function of best fit on the scatter plot.
I can use technology to find the function of best fit for a scatter plot.
I can find the equation for the line of best fit and use it to make
predictions.
I can compute the residuals (observed value minus predicted value) for
the set of data and the function of best fit.
I can construct a scatter plot of the residuals.
I can analyze the residual plot to determine whether the function is an
appropriate fit.
I can sketch a line of best fit on a scatter plot that appears linear.
I can write the equation of the line of best fit (𝑦 = 𝑚𝑥 + 𝑏) using
technology or by using two points on the best fit line.
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S.ID.8 Compute (using technology) and interpret the correlation
coefficient of a linear fit.
I can use a calculator or computer to find the correlation coefficient
for a linear association.
I can interpret the meaning of the correlation coefficient in the context
of the data.
S.ID.9 Distinguish between correlation and causation.
I can distinguish between correlation and causation.
Honors Addendum:
Note for Teachers of Honors: Do not teach this Honors Addendum at
the end of the quarter.
Embed the Honors Addendum within the regular Scope & Sequence.
A.APR.6 Rewrite simple rational expressions in different forms; write
a(x) b(x) in the form q(x)+r(x) b(x) , where a(x) , b(x) , q(x) , and r(x)
are polynomials with the degree of r(x) less than the degree of b(x) ,
using inspection, long division, or, for the more complicated examples,
a computer algebra system.
I can model with rational expressions.
7. (+) Understand that rational expressions form a system analogous
to the rational numbers, closed under addition, subtraction,
multiplication, and division by a nonzero rational expression; add,
subtract, multiply, and divide rational expressions.
I can simplify, multiply, divide, add, subtract with rational expressions.
AI.WCE.20 Operate (add, subtract, multiply, divide, simplify, powers)
with radicals and radical expressions including radicands involving
rational numbers and algebraic expressions.
I can rationalize the denominator.
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