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.
This Illustrative Mathematics task 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.
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.
This task could serve as an introduction to periodic functions and as a lead-in to sinusoidal functions. By visualizing the height of a plane that is moving along the circumference of a circle several times, students get the idea that output values of the height functions will repeat themselves after each complete revolution. They also connect the situation with key features on the graph, for example they interpret the midline and amplitude of the function as the height of the center of the circle and its radius.
The purpose of this task is to model the population data for London with a variety of different functions. In addition to the linear, quadratic, and exponential models, this task introduces an additional model, namely the logistic model.
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.
The goal of this task is to construct and use an exponential model to approximate hard disk storage capacity on personal computers.
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.
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 (e.g., printed or electronic maps), thereby illustrating SMP 5 - Use Appropriate Tools Strategically.
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.
The basic idea is for students to demonstrate that they know what it means for two variables to be associated.
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? "