Students have the opportunity to create and interpret data from simple daily questions.
This real world problem is appropriate for mental mathematics and students should be encouraged to think through the solution mentally.
In this task students are asked to write an equation to solve a real-world problem. There are two natural approaches to this task. In the first approach, students have to notice that even though there is one variable, namely the number of firefighters, it is used in two different places. In the other approach, students can find the total cost per firefighter and then write the equation.
While not a full-blown modeling problem, this task does address some aspects of modeling as described in Standard for Mathematical Practice 4. Also, students often think that time must always be the independent variable, and so may need some help understanding that one chooses the independent and dependent variable based on the way one wants to view a situation.
This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. Students also have to pay attention to the scale on the vertical axis to find the correct match.
This real world task requires students to compare differing interest rates.
This problem provides an opportunity to experiment with modeling real data. Populations are often modeled with exponential functions and in this particular case we see that, over the last 200 years, the rate of population growth accelerated rapidly, reaching a peak a little after the middle of the 20th century and now it is slowing down.
The purpose of this task is for students to apply their knowledge of integers in a real-world context.
This word problem requires students to compute sales tax.
In this task students use linear equations to solve a real world problem.
This resource may be used as a primary source for a general education/quantitative reasoning (QR) math course delivered in the inquiry based learning style. It may also be used to supplement a QR course with occasional in-class active learning activities.
The purpose of this course is to expose you to the wider world of mathematical thinking. There are two reasons for this. First, for you to understand the power of quantitative thinking and the power of numbers in solving and dealing with real world scenarios. Secondly, for you to understand that there is more to mathematics then expressions and equations. The core course is a complete, ready to run, fully online course, featuring 9 topics: Problem solving, voting theory, graph theory, growth models, consumer finance, collecting data, describing data, probability, and historical counting. Additional optional topics are provided. The course materials can easily be used with a face-to-face course.
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.
This real world word problem requires multiple steps.
This tasks is an example of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are only told that there are two ingredients in the pasta and they have a picture of the box. It might even be better to just show the picture of the box, or to bring in the box and ask the students to pose the question themselves.
The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills.
In this task students use ratio and rate reasoning to solve the real-world problem of a runners rate and distance.
In this challenging instructional task students relate addition and subtraction problems to money and to situations and goals related to saving money.
There are a couple of ways to solve this real world word problem.
This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense.