Find two different whole numbers, x and y, so that xy = yx. 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 2100.21)(author/sw)
Common Core State Standards for Mathematics
Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
Write and evaluate numerical expressions involving whole-number exponents.
Write, read, and evaluate expressions in which letters stand for numbers.
- Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.
- Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
- Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.