Cluster 1: Build a function that models a relationship between two quantities. (Algebra 1 - Supporting Cluster) (Algebra 2 - Major Cluster)Archived

Students are asked to write two explicit functions given verbal descriptions in a real-world context, compose the two functions, and explain the meaning in context.

Type: Formative Assessment

Students are asked to write and combine an exponential and a constant function from a verbal description to use when answering a related context question.

Type: Formative Assessment

Students are asked to write an explicit function rule given a verbal description of a functional relationship in a real-world context and are then asked to use the function rule to answer a question.

Type: Formative Assessment

Students are asked to write an explicit function rule given a verbal description of a functional relationship in a real-world context and are then asked to use the function rule to answer specific questions.

Type: Formative Assessment

This lesson unit is intended to help you assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables and develop experimental and analytical models of a physical situation.

Type: Lesson Plan

This lesson unit is intended to help you assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties with choosing an appropriate, systematic way to collect and organize data, examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile, generalizing using numerical, geometrical or algebraic structure and describing and explaining findings clearly and effectively.

Type: Lesson Plan

This is a great lab activity that allows students to develop a true understanding of slope as a rate of change. Students are active and involved and must use higher order thinking skills in order to answer questions. Students work through an activity, measuring heights of cups that are stacked. Students them determine a "rate of change - slope". Students are then asked to put this into slope-intercept form. The important part here is in their determining the y-intercept of the equation. Students then take this further and finally attempt to create a linear inequality to determine how many cups, stacked vertically, will fit under a table.

Type: Lesson Plan

In this Model Eliciting Activity, MEA, students create a plan for a movie theater to stay in business. Data is provided for students to determine the best film to show, and then based on that decision, create a model of ideal sales. Students will create equations and graph them to visually represent the relationships.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

The Plants versus Pollutants MEA provides students with an open-ended problem in which they must work as a team to design a procedure to select the best plants to clean up certain toxins. This MEA requires students to formulate a phytoremediation-based solution to a problem involving cleaning of a contaminated land site. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

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.

Type: Problem-Solving Task

This task provides an approximation, and definition, of e, in the context of more and more frequent compounding of interest in a bank account. The approach is computational.

Type: Problem-Solving Task

In this example, students are given the graph of two functions and are asked to sketch the graph of the function that is their sum. The intent is that students develop a conceptual understanding of function addition.

Type: Problem-Solving Task

This task addresses an important issue about inverse functions. In this case the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted.

Type: Problem-Solving Task

This task asks students to write expressions for various problems involving distance per units of volume.

Type: Problem-Solving Task

The context of this example is the spread of a flu virus on campus and the related sale of tissue boxes sold. Students interpret the composite function and determine values simply by using the tables of values.

Type: Problem-Solving Task

This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically address the standard (F-BF), building functions from a context, an auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (F-LE) domain of tasks.

Type: Problem-Solving Task

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).

Type: Problem-Solving Task

This task asks students to determine a recursive process from a context. Students who study computer programming will make regular use of recursive processes.

Type: Problem-Solving Task

This task asks students to use proportions of mass and volume to create ideal brine for saltwater fish tanks. It also asks students to compare graphs.

Type: Problem-Solving Task

This problem is a quadratic function example. The other tasks in this set illustrate MAFS.912.F.BF.1.1.a in the context of linear, exponential, and rational functions.

Type: Problem-Solving Task

The purpose of this task is to introduce students to exponential growth. While the context presents a classic example of exponential growth, it approaches it from a non-standard point of view.

Type: Problem-Solving Task

The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function.

Type: Problem-Solving Task

The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of the context. It can be used as either an assessment or a teaching task.

Type: Problem-Solving Task

Students design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Using the data they gather in a table, students graph and write an equation for a line of best fit. Students then use their derived equation to make predictions about the amount of water that would be wasted from one leak over a long period of time or the amount wasted by several leaks during a specific time period.

Type: Problem-Solving Task

This professional development resource provides a rich collection of information to help teachers engage students more effectively in mathematical modeling. It features videos of two complete lessons with commentary, background information on effective teaching, modeling, and lesson study, full lesson plans to teach both example lessons, examples of student work from the lessons, tips for effective teaching strategies, and list of helpful resources.

• In Lesson 1 students use mathematical models (tables and equations) to represent the relationship between the number of revolutions made by a "driver" and a "follower" (two connected gears in a system), and they will explain the significance of the radii of the gears in regard to this relationship.

• In Lesson 2 students mathematically model the growth of populations and use exponential functions to represent that growth.

Type: Professional Development

We will learn how to write a geometric sequence.

Type: Tutorial

Geometric series

Type: Tutorial

Finding the 4th term in recursively defined sequence

Type: Tutorial

Type: Unit/Lesson Sequence

This video demonstrates writing a function that represents a real-life scenario.

Type: Video/Audio/Animation

Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

In this activity, students enter inputs into a function machine. Then, by examining the outputs, they must determine what function the machine is performing. This activity allows students to explore functions and what inputs are most useful for determining the function rule. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

This applet allows users to set up various geometric series with a visual representation of the successive terms, and the corresponding sum of those terms.

Type: Virtual Manipulative