Student Explorations in Mathematics
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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?
Multiplication is a mystery to many students. Their first experience with this basic arithmetic operation is as a table of facts to memorize. The purpose of this exploration is for students to understand the meaning behind multiplication, eliminating the mystery.
This activity begins with a brief formative assessment of student understanding of multiplication of two-digit numbers. It supports students' understanding of multiplication and its application. Constructivist pedagogy is used to move learning from the concrete (using manipulatives) to the representational (using pictures and diagrams) to the abstract (using algorithms). Students build models of the operation 27 x 15 and its result in a variety of ways. The activity promotes student reasoning and sense making by analyzing various multiplication algorithms (area models, partial products, lattice multiplication, and the traditional method).
This activity is a reworking of the
Student Math Notes
) activities "
" from March 2009 and "
" from May 1983. A 2010-2011 user survey identified the original activity as one of the most popular
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.
This activity is designed to help students understand which measure of central tendency-mean or median-is more appropriate when analyzing and reporting data. Students use estimation to gain an intuitive understanding of mean and then build on that knowledge through calculations. They discover some of the misconceptions about the mean and median of a data set and begin to understand the realities of how numbers can be used to inform readers in a persuasive manner.
The activity also gives students experience with using technology for the statistical calculations as they investigate relationships within scatterplots and lines of best fit. The activity concludes with students making conjectures-with supporting evidence-about which measure is more appropriate when reporting the data.