The first two parts of this task ask students to interpret the meaning of signed numbers and reason based on that meaning in a context where the meaning of zero is already given by convention.
In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.
The purpose of this task is to emphasize the use of the Remainder Theorem (a discussion of which should obviously be considered as a prerequisite for the task) as a method for determining structure in polynomial in equations, and in this particular instance, as a replacement for division of polynomials.
The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting.
This task assumes students are familiar with mixing problems. This approach brings out different issues than simply asking students to solve a mixing problem, which they can often set up using patterns rather than thinking about the meaning of each part of the equations.
In order to solve this problem, students must assume that if you mix a cubic foot of sand with a cubic foot of cement, you will have 2 cubic feet of mix.
The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.
The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.
This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions.
This task is designed to help students focus on the whole that a fraction refers to. It helps students to realize that two different fractions can describe the same situation depending on what you choose to be the whole.
This counting activity is done in pairs and helps reinforce the concepts of greater than, less than, and equal to.
This task presents a straight forward question that can be solved using an equation in one variable. The numbers are complicated enough so that it is natural to set up an equation rather than solve the problem in one's head.
The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation.
This task requires students to think about what makes a representative sample.
The purpose of this task is to engage students in an open-ended modeling task that uses similarity of right triangles, and also requires the use of technology.
This problem uses the same numbers and asks similar mathematical questions as "6.NS The Florist Shop," but that task requires students to apply the concepts of multiples and common multiples in a context.
This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not.
This real world word problem requires multiple steps.
In this group task students collect data and analyze from the class to answer the question "is there an association between whether a student plays a sport and whether he or she plays a musical instrument? "
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: Renee reasons as follows to solve the equation $x^2 + x + 1 = 0$. First I will rewrite this as a square plus some number. x^2 + x + 1 = \left(x+\frac{1...