Given too much information about how many cows can graze on how many acres for how many weeks, determine how many cows can graze on 6 acres for 6 weeks. This problem is one of Stella's Stunners, a collection of challenging and entertaining mathematical problems to intrigue students in grades 6 - 12. The Stella problems are ideal for promoting inquiry, problem solving, and classroom discussion of key mathematical ideas. Sample solutions are provided for each problem, but students may find other solutions and may even compete with their classmates to find the most creative solution path. Stella problems can be printed out individually or in sets designed for Pre-Algebra, Algebra I, Geometry, Algebra II/Trigonometry, or Pre-Calculus. Problems can be printed with or without solutions and can be added to ORC Collections. The Stella website includes a wealth of teaching resource materials, including an essay on the value of problem solving, a list of 25 useful problem-solving heuristics, a biography of Stella, several tips for using Stella problems in the classroom, and listings of the Stella library by course, by title, and by Stella number. ORC hopes you enjoy the Stella problems, and we invite you to share with Stella's author any experiences you have using Stella problems with your students. (Stella number 2500.62)(author/sw)
Common Core State Standards for Mathematics
Standards for Mathematical Practice
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Expressions and Equations
Analyze and solve linear equations and pairs of simultaneous linear equations.
Analyze and solve pairs of simultaneous linear equations.
- Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
- Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
- Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
High School - Algebra
Create equations that describe numbers or relationships
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Reasoning with Equations and Inequalities
Solve systems of equations
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.