This problem is a quadratic function example. The other tasks in this set illustrate F.BF.1a in the context of linear (Kimi and Jordan), exponential (Rumors), and rational (Summer Intern) functions.
The purpose of this task is to give students experience modeling a real-world example of exponential growth, in a context that provides a vivid illustration of the power of exponential growth, for example the cost of inaction for a year.
Solar Cars STEM Kit. The Natural Sciences Education & Outreach Center collaborates with CSU faculty, National Parks and citizen science programs to translate their current scientific research into unique STEM experiences for students in the form of Educational Kits that can be checked out. Each kit contains just about all of the materials needed (minus common things like water and paper towels) to explore some really interesting scientific research topics.The kits are available for teachers and informal educators in Colorado to check out for a duration of a week by submitting either a local pickup form or a delivery form available at the linked website. This kit is provided free for educational use. This Kit is available in Spanish.
In this task students must figure out how much fresh water you must add to get a particular salt concentration in aquarium water.
The intent of this problem is to have students think about how function addition works on a fundamental level, so formulas have been omitted on purpose.
This task asks students to determine a recursive process from a context. Students who study computer programming will make regular use of recursive processes.
This simple conceptual problem does not require algebraic manipulation, but requires students to articulate the reasoning behind each statement.
In this task students are given graphs of quantities related to weather. The purpose of the task is to show that graphs are more than a collection of coordinate points, that they can tell a story about the variables that are involved and together they can paint a very complete picture of a situation, in this case the weather.
These unit conversion problems provide a rich source of examples both for composition of functions (when several successive conversions are required) and inverses (units can always be converted in either of two directions).
Temperature conversions provide a rich source of linear functions which are encountered not only in science but also in our every day lives when we travel abroad. The first part of this task provides an opportunity to construct a linear function given two input-output pairs. The second part investigates the inverse of a linear function while the third part requires reasoning about quantities and/or solving a linear equation.
Use a code to encode and decode secret messages. Colorado Americorp agents in Araphahoe, Denver, Garfield, Larimer, and Weld Counties. Work supported by the Corporation for National and Community Service under Americorps grant number 18AFHCO0010008. Opinions or points of view expressed in this lesson are those of the authors and do not necessarily represent the official position of or a position that is endorsed by the Corporation or the Americorps program. This resource is also available in Spanish in the linked file.
This task allows the students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, we are asking the students to determine which function has the greatest maximum and the greatest non-negative root.
This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.
This task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. The setting here is abstract as there is no formula for the function f. The focus is therefore on understanding the geometric impact of these three operations.
This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
This task presents an opportunity to explore a more general and non-algebraic view of functions.
The purpose of this task is to construct and use inverse functions to model a a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point.
This task focuses on the fact that exponential functions are characterized by equal successive quotients over equal intervals. This task can be used alongside F-LE Equal Factors over Equal Intervals.
This task focuses on the fact that linear functions are characterized by constant differences over equal intervals. It could be used alongside to F-LE Equal Differences over Equal Intervals I & II.