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...
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: For this task, the letter $i$ denotes the imaginary unit, that is, $i=\sqrt{-1}$. For each integer $k$ from 0 to 8, write $i^k$ in the form $a+bi$. Des...
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: Let $z = 1 + i$ where $i^2 = -1$. Calculate $z^2, z^3,$ and $z^4$. Graph $z, z^2, z^3,$ and $z^4$ in the complex plane. What do you notice about the po...
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: A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine you are in charge of deciding how the rai...
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 aspects of the task and its potential use.
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: Three students disagree about what value to assign to the expression $0^0$. In each case, critically analyze the student's argument. Juan suggests that...