Nine Week Overview for Algebra 1
State of Texas Assessments of Academic Readiness (STAAR™) Performance Level DescriptorsAlgebra 1
Mathematical process skills are not assessed in isolation but are incorporated into questions that assess Algebra 1 content. These process skills focus on applying mathematics to solve problems, communicating about mathematics, and using logical reasoning.
Students achieving Level III: Advanced Academic Performance can
• Evaluate the reasonableness of domains and ranges of linear and quadratic functions
• Apply the concept of slope as a rate of change in a variety of situations
• Generate representations of linear, quadratic, and other nonlinear functions
• Make predictions and critical judgments from functional relationships
Students achieving Level II: Satisfactory Academic Performance can
• Determine the domains and ranges of linear and quadratic functions
• Describe the concept of slope as a rate of change and use it to solve problems
• Determine solutions to linear and quadratic equations, linear inequalities, and systems of linear equations using a variety of methods
• Formulate linear and quadratic equations, linear inequalities, and systems of linear equations to solve problems
• Generate representations of linear and quadratic functions
• Analyze the effects of parameter changes on linear and quadratic functional relationships
• Interpret and draw conclusions from functional relationships
Students achieving Level I: Unsatisfactory Academic Performance can
• Identify slopes and y-intercepts of linear functions from tables, graphs, and equations given in slope-intercept form
• Simplify algebraic expressions and solve linear equations
• Formulate equations and systems of equations from simple linear situations
• Identify attributes of a quadratic function from its graph
Overall Performance 70% Passing
District / State
2012 / 2013 / 2012 / 2013
65% / 70% / 77% / 78%
2013 Blueprint Performance Snapshot
Category / Number of Questions / % Performance
2012 2013
1
Functional Relationships / 8 / 51% / 51%
2
Properties and Attributes of Functions / 12 / 46% / 45%
3
Linear Functions / 15 / 46% / 47%
4
Linear Equations and Inequalities / 10 / 44% / 47%
5
Quadratics and other Nonlinear Functions / 9 / 46% / 45%
Nine Week at A-Glance
Pacing / TEK / % Pass / Description / VocabularyWeek 1 / A.2B / 62%
34%
48% / identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete / Quadrants (1-IV)
Coordinate plane
Ordered Pair
Standard Form Linear Equation
Linear Function
x- intercept
y-intercept
A.5C / 57%
44%
69% / use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions
A.5B / 25% / determine the domain and range for linear functions in given situations
A.6B / 49%
34% / interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs
A.6E / 42% / determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations
A.7C / 36% / interpret and determine the reasonableness of solutions to linear equations and inequalities
Week 2 / A.2C / NA / interpret situations in terms of given graphs or creates situations that fit given graphs / Slope
Rate of change
Slope-intercept form
Parallel
Direct Variation
Constant of Variation
Function notation
Family of functions
Parent function
A.6A / NA / develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations
A.6B / 49%
34% / interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs
A.6C / 43%
47%
56% / investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b
A.6E / 42% / determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations
A.6F / 37%
57%
49% / interpret and predict the effects of changing slope and y-intercept in applied situations
A.6G / 44% / relate direct variation to linear functions and solve problems involving proportional change
A.2A / 31% / identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions
A.4C / 34% / Connect equation notation with function notation, such as y=x + 1 and f(x) = x + 1
Week 3 / A.2A / 31% / identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions / y-intercept
slope
slope-intercept form
A.4C / 34% / Connect equation notation with function notation, such as y=x + 1 and f(x) = x + 1
A.6C / 43%
47%
56% / investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b
A.6F / 37%
57%
49% / interpret and predict the effects of changing slope and y-intercept in applied situations
A.1C / 52% / describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations
A.5C / 57%
44%
69% / Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions
A.6D / 45% / graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and yintercept
A.7A / 64% / analyze situations involving linear functions and formulate linear equations or inequalities to solve problems
Week 4 / A.1C / 52% / describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations / y-intercept
slope
slope-intercept form
Point-slope form
Standard form
A.4C / 34% / Connect equation notation with function notation, such as y=x + 1 and f(x) = x + 1
A.6D / 45% / graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and yintercept
A.6F / 37%
57%
49% / interpret and predict the effects of changing slope and y-intercept in applied situations
A.7A / 64% / analyze situations involving linear functions and formulate linear equations or inequalities to solve problems
A.5A / NA / determine whether or not given situations can be represented by linear functions
A.5C / 57%
44%
69% / Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions
A.1D / 76%
60%
49% / represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities
A.1E / 46%
51% / interpret and make decisions, predictions, and critical judgments from functional relationships
Week 5 / A.6C / 43%
47%
56% / investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b / Parallel lines
Perpendicular lines
Converse
Scatter plot
Correlation
Line of fit
Positive correlation
Negative correlation
No correlation
Best fitting line
Linear regression
Zero of a function
A.6D / 45% / graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and yintercept
A.1E / 46%
51% / interpret and make decisions, predictions, and critical judgments from functional relationships
A.2B / 62%
34%
48% / identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete
A.2D / 67%
34% / collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.
A.5A / NA / determine whether or not given situations can be represented by linear functions
A.1B / 32% / gather and record data and use data sets to determine functional relationships between quantities
A.6E / 42% / determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations
Week 6 / A.7A / 64% / analyze situations involving linear functions and formulate linear equations or inequalities to solve problems / Inequality
One-Variable Inequalities
Solution of an inequality
Linear inequalities
A.7B / 75%
19%
44% / investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities
A.7C / 36% / interpret and determine the reasonableness of solutions to linear equations and inequalities
A.1C / 52% / describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations
A.1D / 76%
60%
49% / represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities
A.1E / 46%
51% / interpret and make decisions, predictions, and critical judgments from functional relationships
Week 7 / A.8A / 46% / analyze situations and formulate systems of linear equations in two unknowns to solve problems / Formulate
System of equations
Solution of a system of linear equations
Inconsistent system
Consistent Dependent system
A.8B / 50%
44%
37% / solve systems of linear equations using concrete models, graphs, tables, and algebraic methods
A.8C / 51% / interpret and determine the reasonableness of solutions to systems of linear equations
Week 8 / A.8A / 46% / analyze situations and formulate systems of linear equations in two unknowns to solve problems / Formulate
System of equations
Solution of a system of linear equations
Inconsistent system
Consistent Dependent system
A.8B / 50%
44%
37% / solve systems of linear equations using concrete models, graphs, tables, and algebraic methods
A.8C / 51% / interpret and determine the reasonableness of solutions to systems of linear equations
Week 9 / A.8A / 46% / analyze situations and formulate systems of linear equations in two unknowns to solve problems / Formulate
System of equations
Solution of a system of linear equations
Inconsistent system
Consistent Dependent system
System of linear inequalities
A.8B / 50%
44%
37% / solve systems of linear equations using concrete models, graphs, tables, and algebraic methods
A.8C / 51% / interpret and determine the reasonableness of solutions to systems of linear equations
A.1D / 76%
60%
49% / represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities
A.1E / 46%
51% / interpret and make decisions, predictions, and critical judgments from functional relationships
TEKS Deconstruction Algebra I Section 4.7 Graph Linear Functions Days 10-11
A Closer Look at the TEKS: STAAR 2013 Release Items by TEKS
IQ Analysis │ Investigating the Question / SE A.6F / RC 3TEK A.6(F) Interpret and predict the effects of changing slope and y-intercept in applied situations; / Units:
A.6F / Analysis
14. Students at a school will sell hats to raise money. There are some hats left over from last year, and 20 boxes of hats will be ordered this year. When the order arrives, the total number of hats the students will have can be determined using the function f(x) = 48x + 37, where
x represents the number of boxes ordered. If the number of hats per box changes so that the situation is modeled by the function h(x) = 24x + 37, then how many fewer hats will the students have available to sell if they still order 20 boxes?
Record your answer and fill in the bubbles on your answer document. / Type / Readiness Supporting
Data
Process Standard
% / Error Type
Procedural
Application
Conceptual
Guessing
A/F
B/G
C/H
D/J
Taught v. Learned / Similar to examples (taught)
Requires application (learned)
Question Level
(Depth of Knowledge) / Level 1
Level 2 / Level 3
Level 4
37% Correct (A) Mode is B
What do students need to know to be able to solve this problem?
A Closer Look at the TEKS: STAAR 2013 Release Items by TEKS
IQ Analysis │ Investigating the Question / SE A.6F / RC 3TEK A.6(F) Interpret and predict the effects of changing slope and y-intercept in applied situations; / Units:
A.6F / Analysis
24. An airplane’s altitude in feet during its descent for landing can be found using the function f(x) = −300x + 30,000, where x represents the horizontal distance in miles from where the plane begins its descent. After new government regulations become law, the airplane’s descent will be modeled by the function
g(x) = −300x + 30,500. Which statement describes this change?
F The airplane starts its descent from an altitude 500 feet higher.
G The airplane starts its descent from an altitude 500 feet lower.
H The airplane descends 500 feet per horizontal mile faster.
J The airplane descends 500 feet per horizontal mile slower. / Type / Readiness Supporting
Data
Process Standard
% / Error Type
Procedural
Application
Conceptual
Guessing
A/F
B/G
C/H
D/J
Taught v. Learned / Similar to examples (taught)
Requires application (learned)
Question Level
(Depth of Knowledge) / Level 1
Level 2 / Level 3
Level 4
57% answered correctly(H) Mode is F
What do students need to know to be able to solve this problem?
A Closer Look at the TEKS: STAAR 2013 Release Items by TEKS
IQ Analysis │ Investigating the Question / SE A.6F / RC 3TEK A.6(F) Interpret and predict the effects of changing slope and y-intercept in applied situations; / Units:
A.6F / Analysis
44 The graph below shows the water level in a tank being drained at a constant rate.
If the rate at which the tank is drained is changed to 3 inches per hour and the initial water level stays the same, how would the time it takes to empty the tank be affected?
F It would take 4 fewer hours.
G It would take 1.5 more hours.
H It would take 2 fewer hours.
J It would take 2 more hours. / Type / Readiness Supporting
Data
Process Standard
% / Error Type
Procedural
Application
Conceptual
Guessing
A/F
B/G
C/H
D/J
Taught v. Learned / Similar to examples (taught)
Requires application (learned)
Question Level
(Depth of Knowledge) / Level 1
Level 2 / Level 3
Level 4
49% answered correctly(H) Mode is J
What do students need to know to be able to solve this problem?