LEARN NC

K–12 teaching and learning · from the UNC School of Education

Goal 5

Algebra - The learner will understand and use linear relations and functions.

Objective 5.01

Develop an understanding of function.

  • Translate among verbal, tabular, graphic, and algebraic representations of functions.
  • Identify relations and functions as linear or nonlinear.
  • Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
  • Interpret and compare properties of linear functions from tables, graphs, or equations.

Resources aligned to this objective

Walk the line
This lesson demonstrates the effects of changing the slope and y-intercept on the graph and equation of a line.
Format: lesson plan (grade 8–12 Mathematics)
By Carol Huss.
Mathematical translations
This lesson develops knowledge of algebraic expressions and their verbal equivalents. Students will establish a foundation for future Algebra I tasks by identifying mathematical symbols and expressions through group work and individual tasks. This lesson contains modifications for the novice high English Language Learner (ELL).
Format: lesson plan (grade 7–12 English Language Development and Mathematics)
By Seth Beale and Wendy Sumner.

Resources on the web

Which pocket?
In this lesson, one of a multi-part unit from Illuminations, students continue their investigation of the Paper Pool game by discovering a rule to predict the pocket in which the ball will land. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Taking its toll
In this Illuminations lesson, students compare the price of a toll to the distance traveled. Students investigate data numerically and graphically to determine the per-mile charge, and they predict the cost if a new tollbooth were added along the route. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Printing Books
Students explore the relationships among lines, slopes, and y-intercepts using the real-world situation of the printing of their textbook (Learn more)
Format: lesson plan (grade 8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Patterns and functions
In this lesson, students investigate properties of perimeter, area, and volume related to various geometric two- and three-dimensional shapes. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Learning about rate of change in linear functions using interactive graphs: Constant cost per minute
Students drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Learn the game
In this lesson, one of a multi-part unit from Illuminations, students learn the rules for and play an interactive game called Paper Pool. (Learn more)
Format: lesson plan (grade 7–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Investigating fire environments
In this lesson, one of a multi-part unit from Illuminations, students consider the meaning of the term variable, both in a mathematical and an everyday sense, by considering a text-based “equation.” (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Graphical representations for the number of hits
In this lesson, one of a multi-part unit from Illuminations, students continue their exploration of the Paper Pool game by graphically analyzing data collected during several games played. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Finding our top speed
This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. (Learn more)
Format: lesson plan (grade 8 Mathematics)
Provided by: National Council of Teachers of Mathematics
The Fibonacci series
Students explore the Fibonacci Series. They will identify the pattern among the Fibonacci numbers, look for applications of these numbers, and explore the ways that this pattern can be related to objects and shapes in both the natural and designed world. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: American Association for the Advancement of Science
Beyond handshakes
In this lesson, one of a multi-part unit from Illuminations, students explore triangular numbers. This exploration enhances students' ability to generalize a pattern with variables. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics
Barbie bungee
In this Illuminations lesson, students model a bungee jump using a Barbie doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions. (Learn more)
Format: lesson plan (grade 6–12 Mathematics)
Provided by: National Council of Teachers of Mathematics
Algebra in balance
In this lesson, one of a multi-part unit from Illuminations, students use an interactive pan balance tool to explore algebraic expressions. They determine if algebraic expressions are equal and balance pans to solve a system of equations. (Learn more)
Format: lesson plan (grade 6–8 Mathematics)
Provided by: National Council of Teachers of Mathematics