Although this task is quite straightforward, it has a couple of aspects designed to encourage students to attend to the structure of the equation and the meaning of the variables in it. It fosters flexibility in seeing the same equation in two different ways, and it requires students to attend to the meaning of the variables in the preamble and extract the values from the descriptions.
Material Type: Activity/Lab
The given solutions for this task involve the creation and solving of a system of two equations and two unknowns, with the caveat that the context of the problem implies that we are interested only in non-negative integer solutions. Indeed, in the first solution, we must also restrict our attention to the case that one of the variables is further even.
Material Type: Activity/Lab
This is a simple exercise in creating equations from a situation with many variables. By giving three different scenarios, the problem requires students to keep going back to the definitions of the variables, thus emphasizing the importance of defining variables when you write an equation. In order to reinforce this aspect of the problem, the variables have not been given names that remind the student of what they stand for. The emphasis here is on setting up equations, not solving them.
Material Type: Activity/Lab
This task asks students to consider the linear and quadratic functions appearing on a coordinate plane.
Material Type: Activity/Lab
This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4).
Material Type: Activity/Lab
The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.
Material Type: Activity/Lab
The purpose of the task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one. The reason for this is that it is possible to have two unequal numbers whose squares are equal.
Material Type: Activity/Lab
The purpose of this task is to continue a crucial strand of algebraic reasoning begun at the middle school level (e.g, 6.EE.5). By asking students to reason about solutions without explicily solving them, we get at the heart of understanding what an equation is and what it means for a number to be a solution to an equation. The equations are intentionally very simple; the point of the task is not to test technique in solving equations, but to encourage students to reason about them.
Material Type: Activity/Lab
The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing.
Material Type: Activity/Lab
Although this task is fairly straightforward, it is worth noticing that it does not explicitly tell students to look for intersection points when they graph the circle and the line. Thus, in addition to assessing whether they can solve the system of equations, it is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.
Material Type: Activity/Lab
Developing the Concept of a Determinant using DGS
Material Type: Simulation
The task is better suited for instruction than for assessment as it provides students with a non standard setting in which to interpret the meaning of functions. Students should carry out the process of flipping a coin and modeling this Random Walk in order to develop a sense of the process before analyzing it mathematically.
Material Type: Activity/Lab
The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions, or as an assessment tool with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.
Material Type: Activity/Lab
The primary purpose of this task is to illustrate that the domain of a function is a property of the function in a specific context and not a property of the formula that represents the function. Similarly, the range of a function arises from the domain by applying the function rule to the input values in the domain. A second purpose would be to illicit and clarify a common misconception, that the domain and range are properties of the formula that represent a function.
Material Type: Activity/Lab
In this real world problem students solve questions based on the relationship between production costs and price.
Material Type: Activity/Lab
This task requires students to use functions to calculate how to best benefit from a pizza promotion.
Material Type: Activity/Lab
This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is.
Material Type: Activity/Lab
The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.
Material Type: Activity/Lab
This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.
Material Type: Activity/Lab
The purpose of this task is to probe students' ability to correlate symbolic statements about a function using function notation with a graph of the function, and to interpret their answers in terms of the quantities between which the function describes a relationship
Material Type: Activity/Lab
