From the highest high to the lowest low here's a resource that won't fall flat. Given data on the area and the highest and lowest elevations of each of the 50 states, learners decide which states are the least flat and the most flat. Of...

We seem to keep missing each other. A short task provides pupils with a quadratic function, as well as a linear function with a missing coefficient. They must determine the value of the coefficient for which the graphs do not intersect.

How many ways can you slice dice distribution? A short performance task asks pupils to consider different types of distributions. Given histograms showing a triangular distribution and a bimodal distribution, they create pairs of dice...

Different equations, same solution. Scholars first find a system with equations y1 and y2 that have a given solution. They then find a different system with equations y3 and y4 that have the same solution. The ultimate goal is to...

Rumor has it exponential functions help solve problems! In a kingdom filled with rumors, young scholars must determine the speed a rumor spreads. The ultimate goal is to decide how many people must know the rumor for it to spread to the...

How many different types of triangles can your class name? A discovery lesson guides learners through an exploration of the different triangle types and the relationships between their angles and sides. Using coordinate geometry,...

One, two, or zero solutions—quadratic systems have a variety of solution possibilities. Using the parent function and the standard form of the function, learners describe the values of a, b, and c that produce each solution type. They...

What's in a triangle? Just 180 degrees worth of angles! Young learners use given angle relationships in a triangle to write an algebraic representation. Using a system of equations, they simplify the equation to a linear representation.

Some planes are just more efficient than others. Young mathematicians use data on the number of seats, airborne speed, flight length, fuel consumption, and operating cost for airplanes to analyze their efficiency. They select and use...

Divide and conquer the geometry problem. Young scholars consider how to subdivide triangles into smaller ones that have equal areas. They must apply their knowledge of medians to help accomplish the task.

The truth will always come out. A short performance task has learners considering a witness statement given to a detective. They apply special line segments in triangles and Ceva's Theorem to prove that the witness is actually lying.

Mathematics involves a study of patterns. The exploratory lesson has learners consider the addition pattern in different sets of numbers. Each set has a different pattern that pupils describe mathematically. The patterns involve...

How many intersections can two absolute value functions have? Young scholars consider the question and then develop a set of rules that describe the number of solutions a given system will have. Using the parent function and the standard...

Experiment with integer relationships. Young scholars consider integers that have a sum of 10. They begin with two integers, then three, four, and more. As they consider each situation, they discover patterns in the possible solutions.

How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...

You'd be surprised what you can do with a string! The constraint is the length of string, and the task is to maximize area. Given a series of composite shapes, learners must create a formula for the maximum area for a specified...

And round and round the park we go! Given a description of an amusement park with the locations of three attractions connected by walkways, learners consider what happens when additional attractions join the mix by doubling the length of...

Let the resource take center stage in a lesson on population density. Scholars use provided historical data on the center of the US population to see how it shifted over time. They plot the data on a spreadsheet to look the speed of its...

Take a dive into a three-dimensional task. Given a specific surface area, individuals must maximize the volume of a cylindrical swimming pool. They combine their understanding of surface area and volume to create a cubic function that...

From linear to quadratic with a simple operation. An exploratory lesson challenges learners to find two linear functions that, when multiplied, produce a given parabola. The task includes the graph of the sum of the functions as well as...

The task is simple, but the solution is a little more complex. Learners must find the smallest number that results in a perfect square when multiplied by two and a perfect cube when multiplied by three. The task requires an analysis...

Are there some rectangles that are more square than others? A thought-provoking task asks individuals to create a formula that objectifies the square-ness of a set of rectangles. They then use their formulas to rank a set of...

Height is dependent on weight—or is it the other way around? Given data from a physicians handbook, individuals compare the height and weight of males and females at different areas. They calculate differences and ratios to assist with...

How do you graph a sentence? Scholars do just that as they represent relationships between independent and dependent variables with a graphical representation. Given a sentence, they determine the pertinent relationship and create a...