Last updated: 5/26/2015 ## Math - Algebra Quarter 4

Pythagorean Theorem

Define right triangle

Discovery of Pythagorean Theorem

Use of Pythagorean theorm to find missing side

Converse of Pythagorean theorem to prove triangle is a right triangle

Triples

Geometric Applications (area, perimeter, etc. after determining missing side)

Exponential Functions

Exponential Growth and Decay

Solving Exponential Equations

Graphing Exponential Functions

Transformations of Exponential Functions

Geometric Sequences

Recursive formulas for Arithmetic and Geometric Sequences

Discriptive Statistics

Statistics

Variables

Measures of  Central Tendency

Box and whisker plots

Distributions of Data

Comparing sets of data

Shapes of Distributions

Scatter Plots and lines/curves of best fit

Analyzing and predicting from lines and curves of fit

Two way tables (categorical data)

Choosing a data display

Quarter 4

Pythagorean Theorem

The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse

Using Pythagorean theorem can determine a missing side of a right triangl

The converse of the Pythagorean theoerem can determine if the sides of a triangle are those of a right triangle.

Determining a missing side of a right triangle reveals information that can be used in geometric concepts (area, perimeter,etc. )

Know the triples and their multiples

Exponential Functions

Graph exponential functions

Characteristics of exponential functions (including end behavior)

Common ratio determined from graph, table and list of points

Transformations of exponential functions

Solving exponential equations

Geometric Sequences (Explicit and recursive)

Pythagorean Theorem

How

Exponential Functions

What are the characteristics of an exponential function?

How can you determine the y-intercept from the equation?

How can you determine if an expontial graph models growth or decay?

Can we determine if the exponential graph is growth or decay from the equation?

Why does the exponential graph of the parent function, not intersect the x-axis?

How can we use exponential functions to solve real life problems?

Can you determine the percent of growth or decay from the common factor?

What are the siimilarities of the geometric sequences and the exponential functions?

Are geometric functions discrete or continuous?

How do recursive formulas help us determine numbers in a sequence (arithmetic or geoemetric)?

 (1) A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (1) A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (1) F-BF.1 Write a function that describes a relationship between two quantities. (1) F-BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context. (1) F-BF.1.b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. (1) F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (1) F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. (1) F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. (1) F-LE.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. (1) F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. (1) F-LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. (1) 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). (1) F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (1) F-LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. (1) F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context. (1) S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). (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. (1) 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). (1) 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. (1) S-ID.6.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, quadratic, and exponential models. (1) S-ID.6.b Informally assess the fit of a function by plotting and analyzing residuals. (1) S-ID.6.c Fit a linear function for a scatter plot that suggests a linear association. (1) S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (1) S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. (1) S-ID.9 Distinguish between correlation and causation.

Exponential Functions

Graph exponential functions

Understand the characteristics of the graphs

Understand the y-intercept

Recognize exponential growth and exponential decay

Write the domain and range of given exponential functions

Determine from the equation if the function is growth and decay

Describe the end behavior of the graph

Determine average rate of change of intervals of exponential functions

Solve exponential equations with technology and algebra

Solve real life problems using growth and decay

Recognize the geometric sequences

Write explicit formula for geometric sequences

Write recursive formulas for both arithmetic and geometric sequences

Examine transformations of exponential graphs, compared to the parent function.

Descriptive Statistics

Univariate Data

Describe different types of data (univariate, bivariate, categorical)

Calculate and interpret best centers

Examine the affect an outlier has on data

Measure the dispersion of data, range and interquartile range

Determine the MAD - Mean Average Deviation

Determine the Variance, Standard Deviation (Population)

Determine representation of dispersion (skewed, symmetric)

Determine if skewed left or right, clustered or not

Determine best centers and spreads for given data

Build Box- and Whisker Plots with and without graphing calculator

Determine the values of the Five Number Summary

Determine first, second and third quartile and percentiles of data

Determine spread of dispersion from Box and Whisker Plots

Comparing data based on centers, distribution (Spread)

Bivariate Data

Build scatter plot

Draw trend line or curve

Determine Positive, Negative or No relationship (strong or weak)

Write equations of line of best fit with and without the calcualtor (regressions)

Determine equations (regression) of curves of best fit using calculator

Determine if line/ curve is a best fit for data

List residuals

Graph resdiduals

Determine (summarize residuals)

Examine correlation coefficient - determine if line/curve is actually a good fit

Categorical Two - Way Display

Determine if data is qualitative or quantitative

Build a two way table

Determine each joint frequency

Determine marginal frequencies

Determine conditional frequencies

Exponential Functions

asymptote

common ratio

explicit

explicit formula

exponential decay

exponnential decay model

exponential function

exponential growth

exponential growth model

general rule

geometric sequences

recursive

explicit

compound interest

Descriptive Statistics

Univariate Data

Central Tendency

Mean, Median, Mode

Measure of Dispersion

Range

Interquartile Range

Variance

Standard Deviation

Box Plot

5 Number Summary

Box Plot

Frequency Histogram

Cumulative Frequency Histogram

Distribution Shapes

Skewed

Bivariate Data

Scatter Plot

Trend line

Possitive Relatonship (association)

Negative Relatoinship (association

No Relationships (Association)

Line of best fit (trend line/curve)

Linear Regression

Residuals

Correlation Coefficient

Causation

Two way tables

Joint frequeny

Marginal frequency

Conditional frequency

Joint relative frequency

Marginal relative frequency

Conditional relative frequency

Pass the paper

Pair share

Exit Notes

Classroom Assessments

Writing prompt

Dailly spiral review

Weekly spiral review

Benchmarks

Self-Correcting Lab Assessment

Algebra I Core Assessment

STARS Assessment

Algebra 1 - McGraw Hill Education

Algebra 1- Amsco School Publications

Big Ideas Algebra 1- Big Ideas Learning

NYS Modules 