Student Explorations in Mathematics
Explorations in Mathematics is a resource available exclusively to NCTM members. To
access the extensive archive, please sign in. Not a member? Join now.
How many people are on the earth? How fast is the population growing? When will we run out of the resources needed to sustain life on our planet? Students explore these and other questions about growth in “7 Billion . . . and Growing.” They use data, measurement, unit analysis, percentages, and statistical analysis to investigate tasks about sharing earth’s resources, population growth, and growth models.
Do your students struggle with division? Many students have misunderstandings about division that relate to its definition. This exploration takes division from its definition and integer division through factoring and algebraic division using manipulatives and a variation on the standard division algorithm. It also links division, as well as factoring with integers, to algebra. This is an opportunity for students at all levels to strengthen their understanding of division and for upper-level students to explore polynomial division.
Why are we stuck in so much traffic? Can't we just build more roads? Data collected by the Texas A&M Transportation Institute shows driving time in urban areas appears to be increasing each year. In this activity, we will graph and analyze traffic data and learn about transportation issues in many of our metropolitan areas. How does your region compare to others? What options are available to ease traffic congestion in our urban areas?
This activity is a reworking of the Student Math Notes (SMN) activities "Egyptian Fractions" from March 2009 and "Egyptian Mathematics" from May 1983. A 2010-2011 user survey identified the original activity as one of the most popular SMN activities in the current collection of over seventy activities available. Give students an opportunity to explore fractions as the Egyptians used them as they are introduced to the Egyptian notations, answer questions of division using that notation, and then make connections to our modern representations. Students also explore a variety of methods for comparing fractions without needing common denominators. In this updated version, students work on developing their own methods for rewriting fractions.
Teachers and students explore various facets of health and nutrition while using mathematics in the investigations of data from government sources on nutrition. Mathematics and mathematical thinking include basic operations, reading and interpreting data from charts and tables, predicting outcomes based on data, and combinatorics.
Since their debut on 21 December 1913 in the New York World newspaper, crosswords have intrigued and delighted puzzle solvers. Much care is taken to edit these puzzles to present challenging clues as well as to produce grids that are consistent in their visual presentation.