Big Ideas Algebra 1 Chapters 3-4
September – November (7 weeks); 1st Semester
Embedded Files
Chapter Title(s):
Graphing Linear Functions (Chapter 3)
Writing Linear Functions (Chapter 4)
Prepared Graduates:
MP1. Make sense of problems and persevere in solving them.
MP2. Reason abstractly and quantitatively.
MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
Standard(s):
2. Algebra and Functions
3. Data, Statistics, and Probability
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
Big Ideas Algebra 1 Chapters 3-4 focus on the family of linear functions. Consult Algebra 1 Families of Functions for additional evidence outcomes that apply to linear functions.
HS.F-IF.A. Interpreting Functions: Understand the concept of a function and use function notation.
Explain that a function is a correspondence from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). (CCSS: HS.F-IF.A.1)
HS.F-BF.A. Building Functions: Build a function that models a relationship between two quantities.
Write arithmetic sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.⭑ (CCSS: HS.F-BF.A.2)
HS.F-IF.C. Interpreting Functions: Analyze functions using different representations.
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.⭑ (CCSS: HS.F-IF.C.7)
Graph linear functions and show intercepts. (CCSS: HS.F-IF.C.7.a)
Graph piecewise-defined functions, including step functions and absolute value functions. (CCSS: HS.F-IF.C.7.b)
HS.F-LE.A. Linear, Quadratic & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems.⭑
Distinguish between situations that can be modeled with linear functions and with exponential functions. (CCSS: HS.F-LE.A.1)
Prove that linear functions grow by equal differences over equal intervals. (CCSS: HS.F-LE.A.1.a)
Identify situations in which one quantity changes at a constant rate per unit interval relative to another. (CCSS: HS.F-LE.A.1.b)
Construct linear functions, including arithmetic sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (CCSS: HS.F-LE.A.2)
HS.F-LE.B. Linear, Quadratic, & Exponential Models: Interpret expressions for functions in terms of the situation they model.⭑
Interpret the parameters in a linear function in terms of a context. (CCSS: HS.F-LE.B.5)
HS.S-ID.B. Interpreting Categorical & Quantitative Data: Summarize, represent, and interpret data on two categorical and quantitative variables.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (CCSS: HS.S-ID.B.6)
Informally assess the fit of a function by plotting and analyzing residuals. (CCSS: HS.S-ID.B.6.b)
Fit a linear function for a scatter plot that suggests a linear association. (CCSS: HS.S-ID.B.6.c)
Distinguish between correlation and causation. (CCSS: HS.S-ID.C.9)
HS.S-ID.C. Interpreting Categorical & Quantitative Data: Interpret linear models.
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (CCSS: HS.S-ID.C.7)
Using technology, compute and interpret the correlation coefficient of a linear fit. (CCSS: HS.S-ID.C.8)
A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.
Additional Colorado Academic Standards Resources:
Please visit the complete 2020 Colorado Academic Standards for High School Mathematics to view the following:
Colorado Essential Skills and Mathematical Practices connections
Inquiry Questions
Coherence Connections
Prior Knowledge Connections:
Defining and comparing functions (Grade 8)
Proportional relationships, slope, and y = mx + b (Grade 8)
Functions and linear functions (Grade 8)
Scatter plots and associations in bivariate data (Grade 8)
Academic Vocabulary & Language Expectations:
Relation, function, domain, range, independent variable, dependent variable, x-intercept, y-intercept, increasing, decreasing, end behavior, linear equation in two variables, linear function, nonlinear function, solution of a linear equation in two variables, discrete domain, continuous domain, function notation, standard form, slope, rise, run, slope-intercept form, constant function, family of functions, parent function, transformation, translation, reflection, horizontal shrink, horizontal stretch, vertical stretch, vertical shrink, absolute value function, vertex, vertex form, linear model, point-slope form, scatter plot, correlation, line of fit, residual, linear regression, line of best fit, correlation coefficient, interpolation, extrapolation, causation, sequence, term, arithmetic sequence, common difference, piecewise function, step function
Assessments:
SAT Suite Educator Question Bank (Content Domains: Algebra, Problem-Solving and Data Analysis)
Instructional Resources & Notes:
Big Ideas Algebra 1 Chapters 3-4 (skip Lesson 4.3)
Additional Modeling Tasks
Notes:
Lesson 4.3 (Writing Equations of Parallel and Perpendicular Lines) addresses evidence outcomes in Geometry. Lesson 4.3 should be skipped.
Page updated
Report abuse