Illustrative Mathematics
Archimedes and the King's Crown
Learners will shout "Eureka!" in this quick but deep activity replicating the famous bathtub experiment of Archimedes. Given the scenario of a king with a suspected fake crown, young investigators develop formulas using density to...
Concord Consortium
All-in-All Problems
Graphs, functions, symbols, and more! Use these strategies to model everything from the flow of a river to the number of cars passing a toll booth. Presented differently but solved similarly, learners consider five different scenarios...
Curated OER
2001 U.S. National Chemistry Olympiad Part III
Here is a comprehensive method for assessing chemistry learners' knowledge; have them approach two laboratory problems, plan their methods of solving each, and then actually carry out the experiments to find the answers. Both the...
Mathed Up!
Compound Measures
Compounding is dividing units. Pupils practice using compound measures such as units for speed and density to solve problems that range from straightforward speed problems to those requiring conversions. The last few items challenge...
Mathematics Assessment Project
A Golden Crown?
For this assessment task, learners determine whether a crown with given information is composed of pure gold. The task expects algebraic and numerical solution methods, so unlike Archimedes, no bathtub is necessary.
Concord Consortium
School Bus Routes
Plan the way to school. Given a map of a school district, class members portray a transportation consultant hired to develop a bus transportation plan that will pick up the eligible riders and get them to school. The plan must contain...
Inside Mathematics
Population
Population density, it is not all that it is plotted to be. Pupils analyze a scatter plot of population versus area for some of the states in the US. The class members respond to eight questions about the graph, specific points and...
College Board
2016 AP® Biology Free-Response Questions
A remarkably high number of scholars passed the AP Biology exam in 2016 with over 61 percent earning college credit. The College Board released the entire free-response section for future scholars to study. After answering the eight...
Texas Education Agency
Texas Gateway: Ap Physics: Fluid Statics: Problems and Exercises
This is a list of 83 problems/exercises to solve based on the content in Chapter ll: Fluid Statics from the AP Physics online text.
Khan Academy
Khan Academy: Density Word Problems
Solve problems concerning real-world situations using your knowledge of volume, surface area, and density.