Investigate the growth rates of alien animals. Pupils study fictional animals from another planet to determine how much they grow per year. The investigators plot the growth of their animals over a period of time and then compare...

How many ways can you make the number 9? Use a task that has pupils thinking about the many different ways a classroom of nine can be made up of boys and girls.

Sometimes the indirect path is best. Scholars determine whether the sum of a rational number and an irrational number is irrational. Reading a transcript of a conversation between classmates leads to an indirect proof of this concept.

Complex fractions and trigonometric expressions combine to create a challenging task ... as if they aren't challenging enough on their own! The task challenges individuals to consider the range of possible values when substituting in the...

Don't let a little challenge get between your pupils and their learning! Scholars compare two absolute value functions to recognize patterns and use them to build their own functions with outputs that are between the given. They then...

Young mathematicians have the hang of graphing with integer coefficients now. Can they generalize what they've learned to equations with variable coefficients? The task asks individuals to verify the solution to the system is (x,y) and...

Three angles in a triangle, three-dimensional space, it all seems connected somehow. Given several different triangles, pupils use the three angles of the triangle as coordinates to plot points in three-dimensional space. They explore...

Take a look at a star resource. Young mathematicians use a graphing calculator to draw intersecting lines that look like a star. They then apply translations to move the entire star and also consider what transformations must occur to...

Strive for gold with an informative resource. A short task challenges learners to investigate the thickness of a box made from a given volume of gold. The box must have specific dimensions, so setting up and solving a literal equation is...

Model a bicycle chain with circles and tangent lines. Given the dimensions of the sprocket wheels, young scholars calculate the length of the chain that surrounds them. A second task has learners write a function for the length of a...

Maximize a profit with an understanding of geometric dimension. A real-world task challenges learners to design a pattern using three different brick shapes. The bricks are dedicated with a different donation for each shape, so part of...

Is the gestation length of an animal a predictor of the average life expectancy of that animal? Learners analyze similar data for more than 50 different animals. They choose a data display and draw conclusions from their graphs.

Piece by piece ... dismantling a function can highlight interesting patterns. The task asks learners to slice functions in sections with the same vertical change. They then recreate the graph with these slices positioned horizontally....

Mathematicians typically reference eight different types of functions. Scholars learn about the requirements for graphing a function and must decide how many different functions fit. To finish, they define each specific function meeting...

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...

What came first, pedestrian one or pedestrian two? Scholars consider a problem scenario in which two people walk at different rates at different times. They must decide who reaches a checkpoint first. Their answers are likely to surprise...

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...

Let the class color. The video shows two different types of fraction of shapes problems. Pupils learn to shade a given fraction of a shape along with determining the fraction of a shape that is shaded. Learners practice the skill with...

Determine the cheapest way to the airport. Pupils read a scenario about trying to get 75 people to the airport using two different sizes of taxis. Learners calculate the number of smaller taxis needed given a number of large taxis and...

Sorting memories doesn't have to be difficult. Young mathematicians evaluate two different methods of sorting yearbook pictures. They answer a set of questions to explore each method, then develop their own sorting procedure based on...

Demonstrate the progression of operations with rational expressions through a multi-day lesson, equipped with worksheets for each day. High schoolers develop the concepts needed to perform operations with rational expressions. They learn...

Investigate the meaning of the Pythagorean Theorem through modeling. After comparing the area of the square of each side, individuals cut triangles and squares to facilitate the comparison.

Pupils build on previous experience with slope to investigate positive, negative, zero, and undefined slope. They complete a puzzle matching slope-intercept and standard forms of linear equations.

Counting is not all it adds up to be — sometimes it involves multiplying. The instructional activity introduces permutations and combinations as ways of counting, depending upon whether order is important. Pupils learn about factorials...