Connected 3: Course Overview

Data Analysis

Inquiry Question: What story does your data tell? How do you know if your statistics tell the truth? How do you get the truth from your data?

Standard 3.1
Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge
a. Construct and interpret scatter plots for bicariate measurement data to investigate patterns of association between two quantities
b. Describe patterns such as clustering, outliers, positive or negative association, linear association and nonlinear association

Linear Models

Inquiry Questions: How can different representations of linear patterns present...

Standard 2.1
Linear functions model situations with a constant rate of change and can be represented numerically, algebraically and graphically
b. Graph proportional relationships, interpreting the unit rate as the slope of the graph
e. Derive the equations y=mx for a line through the origin and the equations y=mx+b for a line intercepting the vertical axis at "b"

Standard 2.3
Graph, tables and equations can be used to distinguish between linear and nonlinear functions
a. Define, evaluate and compare functions (linear and non-linear with context, equations, tables and graphs)
b. Use functions to model relationships between quantities including determining and interpreting rate of change and initial value in linear relationships and analyzing how credit and debt impact financial goals (PFL)

Standard 3.1
Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge
c. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line
d. Use the equations of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept

Pythagorean Theorem, Rational & Irrantional Numbers

Inquiry Questions: Why does the Pythagorean Theorem only apply to right triangles?

Standard 1.1
In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line
a. Define irrational numbers
c. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on the number line diagram, and estimate the value of the expressions

Standard 4.2
Direct and indirect measurement can be used to describe and make comparisons
a. Explain a proof of the Pythagorean Theorem and its converse
b. Apply the Pythagorean Theorem to determine unknown side lengths in right traingles in real-world and mathematical problems in two and three dimensions
c. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system

Algebraic Expressions & Equations

Inquiry Question: Do algebraic properties work with numbers or just symbols?

Standard 1.1
In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line
d. Apply the properties of integer exponents to generate equivalent numerical expressions
f. Evaluate square roots of small perfect numbers and cube roots of small perfect cubes
h. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used

Standard 2.2
Properties of algebra and equality are used to solve linear equations and systems of equations
a. Solve linear equations in one variable (rational number coefficients, variables on both sides, distributive property, and combining like terms)

Symmetry & Transformations

Inquiry Question:

Standard 4.1
Transformations of objects can be used to define the concepts of congruence and similarity
a. Verify experimentally the properties of rotations, reflections and translations
b. Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates

Algebraic Concepts

Inquiry Question: How does the context of the problem affect the reasonableness of a solution?

Standard 2.1
Linear functions model situations with a constant rate of chance and can be represented numerically, algebraically and graphically
c. Compare two different propertional relationships represented in different ways

Standard 2.2
Properties of algebra and equality are used to solve linear equations and systems of equations
b. Analyze and solve pairs of simulataneous line equations algebraically and graphically

Counting Principles & Probability Review

Inquiry Question: Why is it important to consider all of the possible outcomes of an...

Contact Information
Megan J Pule
970.488.5463
mpule@psdschools.org