Download algebra 1: njdoe model curriculum

ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
STUDENT LEARNING
OBJECTIVES
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1
Course:
Algebra 1
Write linear and exponential functions
(e.g. growth/decay and arithmetic and
geometric sequences) from graphs,
tables, or a description of the
relationship, recursively and with an
explicit formula, and describe how
quantities increase linearly and
exponentially over equal intervals.
UNIT #: 5
UNIT NAME: Functions and Descriptive Statistics
CCSS
NJCCCS
F.BF.2
F.LE.1
F.LE.2
Cherry Math: equations of exponential functions
http://wcherry.math.unt.edu/math1650/exponential.pdf
Regentsprep.org: Equations of Straight Lines
Lesson: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/EqLines.htm
Practice: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/pracEq.htm
RegentsPrep: exponential growth and decay
http://www.regentsprep.org/Regents/math/ALGEBRA/AE7/ExpDecayL.htm
2
Represent data on the real number line
(i.e. dot plots, histograms, and box
plots) and use statistics to compare and
interpret differences in shape, center,
and spread in the context of the data
(account for effects of outliers).
Page 1 of 4
S.ID.1
S.ID.2
S.ID.3
Laerd Statistics: measures of spread
https://statistics.laerd.com/statistical-guides/measures-of-spread-rangequartiles.php
Math is Fun: Dot Plots, Histograms
http://www.mathsisfun.com/data/dot-plots.html
http://www.mathsisfun.com/data/histograms.html
Algebra 1: Unit-5 Functions & Descriptive Statistics
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra 1
UNIT #: 5
UNIT NAME: Functions and Descriptive Statistics
Shodor: Box Plots (interactive)
http://www.shodor.org/interactivate/activities/BoxPlot/
3
4
Summarize and interpret categorical
data for two categories in two-way
frequency tables; recognize associations
and trends in the data.
S.ID.5
Represent and describe data for two
variables on a scatter plot, fit a function
to the data, analyze residuals (in order
to informally assess fit), and use the
function to solve problems.
S.ID.6
Math is Fun: Frequency Tables
http://www.mathsisfun.com/data/mean-frequency-table.html
Internet Retailer: Real-World application of data trends
http://www.internetretailer.com/trends/
Regentsprep.org: Scatter Plots and Lines of Best Fit (lessons, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AD4/indexAD4.htm
NLVM: Scatter Plot (interactive exploration)
Uses a given function or choose a
function suggested by the
context. Emphasize linear and
exponential models.
http://nlvm.usu.edu/en/nav/frames_asid_144_g_4_t_5.html?open=activities
Fitting Functions to Data
http://people.hofstra.edu/stefan_waner/realworld/calctopic1/regression.html
5
Interpret the slope, intercept and
correlation coefficient (compute using
technology) of a linear model.
Page 2 of 4
S.ID.7
S.ID.8
Interpreting Linear Models
http://www.math.montana.edu/frankw/ccp/modeling/discrete/linear/learn.htm
Algebra 1: Unit-5 Functions & Descriptive Statistics
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
6
Course:
Algebra 1
Distinguish between correlation and
causation in a data context.
UNIT #: 5
S.ID.9
UNIT NAME: Functions and Descriptive Statistics
Stats.org: difference between correlation and causation
http://www.stats.org/faq_vs.htm
Correlation vs Causation in a graph
http://chrisblattman.com/2013/05/24/correlation-versus-causation-in-a-singlegraph/
Major Content (identified by PARCC Model Content Frameworks)
Code
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S.ID.1
S.ID.2
S.ID.3
S.ID.5
S.ID.6
S.ID.7
Page 3 of 4
Common Core State Standards
Represent data with plots on the real number line (dot plots, histograms, and box plots).
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.
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points
(outliers).
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.
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 a scatter plot that suggests a linear association.
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Algebra 1: Unit-5 Functions & Descriptive Statistics
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
S.ID.8
S.ID.9
F.BF.2
F.LE.1
F.LE.2
Course:
Algebra 1
UNIT #: 5
UNIT NAME: Functions and Descriptive Statistics
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Distinguish between correlation and causation.
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate
between the two forms.★
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 another.
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).
Major Content (identified by PARCC Model Content Frameworks)
Page 4 of 4
Algebra 1: Unit-5 Functions & Descriptive Statistics
KK, EE July 2013