Develop a model for a hanging chain. Pupils find a mathematical model for a hanging chain and then they compare their models to the precise function that models the curve. Scholars come up with a strategy to determine how close...

Critical thinking is an important aspect of mathematics — it's time to put your brain to work! Use this assessment to challenge pupils and test their skills. Concepts assessed include function notation, factoring, completing the square,...

Grab the wheel in learning about functions. A short performance task challenges young mathematicians to develop a function that describes the cars eight people drive. They consider whether the inverse of the function exists. If not, they...

Your knowledge of graphs is a function of how much you try. Young mathematicians work on a set of 12 questions that covers graphing functions, comparing functions, and rewriting functions in different forms to determine key features....

Viruses can spread like wildfire, and mathematics can model the speed of infection. Given a function, scholars analyze it to describe the spread of a disease within a stadium. Learners find the initial number infected and the maximum...

Build a patio from toothpicks and marshmallows to analyze functions! Learners look for patterns in the data as they create different size patios. As they discover patterns, they make connections between the different representations of...

Leaners investigate families of linear functions through dance. They choreograph dance moves to model nine unique linear functions of their choosing. Using their dance moves, teams create a video presentation complete with music and...

What will that cost in the future? The scenario provides pupils with a growth as a Consumer Price Index. Learners create functions for a given item to determine future prices and graph them. Class members then compare their functions to...

Four questions that get right to the polynomial point. High schoolers list all the attributes of a polynomial function, including finding all complex zeros. The last two questions prompt them to write a function based on the given...

Compose yourself! Learners first use given graphs of functions f and g to graph the composition function f(g(x)) and identify its value for a specific input. They then consider functions for which f(g(x)) = g(f(x)).

Time to put it all together! Building on the concepts learned in the previous lessons in this series, learners apply the Remainder Theorem to finding zeros of a polynomial function. They graph from a function and write a function from...

Building on knowledge from the previous lesson, the second lesson in this unit teaches scholars to identify and interpret rate of change and initial value of a linear function in context. They investigate how slope expresses the...

Functions model relationships between quantities. The Smarter Balanced sample items demonstrate the assessment strategies for eighth grade function modeling standards. Items range from constructing linear functions from a table and a...

Looking for higher-level thinking questions? This assessment provides questions that challenge young mathematicians to think and analyze rather than simply memorize. Topics include piecewise functions, linear modeling, exponential...

Mathematicians typically reference eight different types of functions. Scholars learn about the requirements for graphing a function and must decide how many different functions fit. To finish, they define each specific function meeting...

Don't lose the chance to use the task. Given three diagrams of curved pieces of wires, young mathematicians must explain whether it's possible to conclusively match the wires as representing cubic, exponential, or quadratic functions....

One of several presentations of eighth grade sample items looks at the basics of functions. Smarter Balanced sample items for Target E highlights the way function content shows up on the assessments. The presentation contains eight items...

Don't give your classes the third degree. Use radians instead! While working with degrees, learners find that they are not efficient and explore radians as an alternative. They convert between the two measures and use radians with the...

Writing and sketching functions—what more could you want to do? Learners write and sketch functions that meet certain conditions as they complete a short task. They find a parabola that encompasses three quadrants of the coordinate plane...

Take the road to a greater knowledge of functions. Young mathematicians graph an absolute value function representing a road connecting several towns. Given a description, they identify the locations of the towns on the graph.

You can learn to graph as well as a calculator using calculus. The lesson introduces using derivatives to find critical points needed to graph polynomials. Pupils learn to find local maximums and minimums and intervals of increase...

Having trouble finding performance task questions? Here is an assessment that uses all high-level thinking questions. It includes questions to assess sequences, linear functions, exponential functions, and increasing/decreasing intervals.

Create polynomials with specific values. The task consists of writing three polynomial functions that evaluate to specific values for any given number. Scholars first find a polynomial that evaluates to one for a given value, then a...

Let your classes show you what they know! Use this pre-test to assess the current knowledge of your learners. The assessment includes all pre-algebra concepts related to functions: writing and graphing linear relationships, comparing...