Algebra 1: Course Overview
Numbers & Operations
Inquiry Question: Do algebraic properties work with numbers or just symbols? Why?
Standard 1.1
The complex number system includes real numbers and imaginary numbers
b. Use properties of rational and irrational numbersEquations
Inquiry Question: What are some similarities in solving all types of equations?
Standard 1.2
Quantitative reasoning is used to make sense of quantities and their relationships in problem situations
a. Reason quantitatively and use units to solve problemsStandard 2.4
Solutions to equations, inequalities and systems of equations are found using a variety of tools
a. Create equations and inequalities that describe numbers or relationships (including representing constraints)
b. Understand solving equations as a process of reasoning and explain the reasoning
c. Solve equations and inequalities in one variablePythagorean Theorem & Radicals
Inquiry Question: What is the difference between rational and irrational...
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 triangles in real-world and mathematical problems in two and three dimensions
Apply the Pythagorean Theorem to find the distance between two points in a coordinate systemInequalities
Inquiry Question: What is the difference between solving equations and solving inequalities? Why do we graph inequalities?
Standard 2.4
Solutions to equations, inequalities and systems of equations are found using a variety of tools
a. Create equations and inequalities that describe numbers or relationships (including representing constraints)
b. Understand solving equations as a process of reasoning and explain the reasoning
c. Solve equations and inequalities in one variableSymmetry & Transformations
Inquiry Question: Does anything really change when we make moves?
Standard 4.1
Transofrmations of objects can be used to define the concepts of congruence and similarity
a. Verify experimentally the properties of rotations, reflections and transitions
b. Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinatesLinear Functions
Inquiry Question: How can different representations of linear patterns present different perspectives of situations?
Standard 2.1
Functions model situations where one quantity determines another and can be represented algebraically, graphically and using tables
a. Formulate the concept of a function and use function notation including the concepts of domain and range
b. Interpret functions that arise in applications in terms of the context (average rate of change over an interval)
c. Analyze functions using different representations
d. Build a function that models a relationship between two quantitiesStandard 3.1
Visualize displays and summary statistics condense that information in data sets into usable knowledge
b. Summarize, represent and interpret data on two categorical and quantitative variables (display and interpret in scatter plots)
c. Interpret linear models (slope, correlation and coefficients)Data Analysis
Inquiry Questions: What are ways to lie with statistics?
Standard 3.1
Visualize displays and summary statsitics condense the information in data sets into usable knowledge
a. Summarize, represent and interpret data on a single count or measurement variable (represent data: dot plots, histograms, box plots; compare center and spread of two or more data sets; interpret differences in shape, center and spread accounting for outliers)
b. Summarize, represent and interpret data on two categorical and quantitiative variables (frequency tables, trends in data, displays and interpret in scatter plots)Exponents
Inquiry Questions: Can numbers ever be too big or too small to be useful?
Standard 1.1
The complex number system includes real numbers and imaginary numbers
a. Extend the properties of exponents to rational exponents including rewriting expressions involving radicals and rational exponents using properties of exponents
b. Use properties of rational and irrantional numbersIntro to Quadratics
Inquiry Qeustions: Do lines model all real-world situations?
Polynomials: Multiplying and Factoring
Inquiry Questions: How are multiplying and factoring polynomials related?
Standard 2.3
Expressions can be represented in multiple, equivalent forms
a. Interpret the structure of expressions (i.e. terms, factors, coefficients)
b. Write expressions in equivalent forms to solve problems
c. Perform arithmetic operations on polynomials (linear and quadratic)Quadratic Functions
Inquiry Questions: How are the components of a quadratic function related algebraically and graphically?
Standard 2.1
Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables
a. Formulate the concept of a function and use function notation including the concepts of domain and range
b. Interpret functions that arise in applications in terms of the context
c. Analyze functions using different representationsStandard 2.2
Quantitative relationships in the real world can be modeled and solved using functions
a. Construct and complare linear, quadratic, and exponential models and solve problems
b. Interpret expressions for a function in terms of the situation the modelSystems
Inquiry Questions: What makes a solution strategy both efficient and effective? Why?
Standard 2.4
Solutions to equations, inequalities and systems of equations are found using a variety of tools
a. Create equations and inequalities that describe numbers or relationships (including representing constraints)
b. Understand solving equations as a process of reasoning and explain the reasoning
c. Solve equations and inequalities in one variable
d. Solve systems of equations
e. Represent and solve (two variable) equations and inequalities graphically
Megan J Pule
970.488.5463
mpule@psdschools.org