This is the first of a series of tasks aiming at understanding the quadratic formula in a geometric way in terms of the graph of a quadratic function. Here the student works with an explicit function and studies the impact of scaling and linear change of variables.

This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.

This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.

This Illustrative Mathematics task operates at two levels. In part it is a simple exploration of the relationship between speed, distance, and time. Part (c) requires understanding of the idea of average speed, and gives an opportunity to address the common confusion between average speed and the average of the speeds for the two segments of the trip.

This Illustrative Mathematics task involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. An unexpected surprise awaits in this case, however, as no reasonable interpretation of the level of accuracy makes sense of the information reported on the bottles in parts (b) and (c). Either a miscalculation has been made or the numbers have been rounded in a very odd way.

The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of that context. It can be used as either an assessment or a teaching task.

The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.

Some people rent a car when they are going on a long trip. They are convinced they save money. Even if they do not save money, they feel that the knowledge that "if the car breaks down on the trip, the problem is the rental company's" makes the rental worth it. Analyze this situation and determine under what conditions renting a car is a more appropriate option. Determine mileage limits on one's own car and a break-even value of "ease of mind" for the driver and her family.

This exploratory task requires the student to use this property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

The purpose of this task is to gives students an opportunity to engage in Mathematical Practice #3 Construct viable arguments and critique the reasoning of others. This task gives a teacher the opportunity to ask students not only for a specific answer of whether the dollar came from in the cash box or not, but for students to construct an argument as to how they came to their solution.

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.

In our school and social lives we exist in a mobile electronic world. Each day we "plug in" and charge our electronic devices and equipment. These electronics may range from small items (cell phones) to large items (electric vehicles). While in our own home, our family is most likely responsible for purchasing the charging equipment, and then paying an electric company/provider for the electricity we use.

The proliferation of electronic buses (e-buses) in cities across the globe represents a significant stride toward sustainable urban transport. With the mounting concerns over air pollution and climate change, many cities have been prompted to reconsider their reliance on traditional diesel buses. According to a recent report by Bloomberg New Energy Finance[1], e-buses are set to dominate the public transit sector, becoming the majority of all buses on the road globally by 2032. China has been particularly noteworthy in this transition, as it is home to most of the world’s e-buses, driven in large part by government policies that prioritize electric vehicles and stringent emission standards. Cities throughout the world (e.g., Bogota, Colombia, New York, USA, and Berlin, Germany) are also making concerted efforts to incorporate e-buses into their fleets, albeit at a more gradual pace.

The goal of this task is to examine some population data from a modeling perspective. Because large urban centers and their growth are governed by many complex factors, we cannot expect a simple model (linear, quadratic, or exponential) to give accurate values or predictions over large stretches of time. Deciding on an appropriate model is a delicate process requiring careful analysis.

What can we make of the massive amount of crime statistics collected in major cities? Beyond just reporting numbers, how can we use these data to determine the safeness of a city?

TuvaLabs Data Stories provide resources for teachers to engage students in rich discourse about an interesting topic and then allows students to come to conclusions using mathematical reasoning and tools.

Premade number tents to use clothesline math with simple expressions, rational expressions, equations and sequences.

Find some pre-made number tents for integers and degrees, as well as a blank set of number tents to create your own number tents.

Premade number tents to use clothesline math with linear, exponential and trignometric functions.

Want to know how to set up clothesline math in your classroom? Read this post and find a few different methods. Then, choose which one works best for your classroom culture.