This unit of instruction is focused on the introduction of a precise definition of functions as students transition to the more formalized study of algebra. This task asks students to analyze graphs of functions and interpret rates of change, intersections, and points on the curves of different functions.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A penny is about $\frac{1}{16}$ of an inch thick. In 2011 there were approximately 5 billion pennies minted. If all of these pennies were placed in a s...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This 8th grade Math parent guide explains the content in straightforward terms so they can support their children’s learning at home and will encourage caretaker engagement with lessons.

Our Teacher Guides are meant to support the use of our online course and unit content. Please use these to accompany the use of our content and for ideas to support struggling learners, those needing extension and for additional resources.

Students will complete a Functions Choice Board they will have two options from each section. What is a function, graphing linear functions and Graphing Quadratic.

In CK-12 Middle School Math Concepts Grade 8, the learning content is divided into concepts. Each concept is complete and whole providing focused learning on an indicated objective. Theme-based concepts provide students with experiences that integrate the content of each concept. Students are given opportunities to practice the skills of each concept through real-world situations, examples, guided practice and explore more practice. There are also video links provided to give students an audio/visual way of connecting with the content.

There is a natural (and complicated!) predator-prey relationship between the fox and rabbit populations, since foxes thrive in the presence of rabbits, and rabbits thrive in the absence of foxes. However, this relationship, as shown in the given table of values, cannot possibly be used to present either population as a function of the other. This task emphasizes the importance of the "every input has exactly one output" clause in the definition of a function, which is violated in the table of values of the two populations.

Sample Learning Goals
Define a function as a rule relating each input to exactly one output and predictably acting on inputs
Predict outputs of a function using given inputs
Compose functions to create a new function
Determine which functions are geometric transformations

Sample Learning Goals
Define a function as a rule relating each input to exactly one output and predictably acting on inputs
Predict outputs of a function using given inputs
Compose functions to create a new function
Interpret, compare, and translate between multiple representations of an algebraic function

This task can be played as a game where students have to guess the rule and the instructor gives more and more input output pairs. Giving only three input output pairs might not be enough to clarify the rule.

In this lesson, students know that a function assigns to each input exactly one output. Students know that some functions can be expressed by a formula or rule, and when an input is used with the formula, the outcome is the output.

This resource is an informal assessment to determine student mastery of identifying functions through use of ordered pairs, a table, and graph. This activity culminates class discussions and assignments of NC.Math.8.F.1 and is based on student interest of basketball and softball.

This resource is an informal assessment to determine student mastery of identifying functions through use of ordered pairs, a table, and graph. This activity culminates class discussions and assignments of NC.Math.8.F.1 and is based on student interest of basketball and softball.

Students are provided with a scenario and asked to determine which amounts of postage is it impossible to make using only five-cent and seven-cent stamps? The mathematics task is intended to be a problem or question that encourages the use of mathematical practices. The dialogue is meant to show how students might engage in the mathematical practices as they work on the task.