A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.
Joe Champion and Ann Wheeler
Robin S. O'Dell
Using a rule as a seesaw helps students steady their understanding of the mean.
Pamela Edwards Johnson, Melissa Campet, Kelsey Gaber, and Emma Zuidema
Three preservice teachers used virtual manipulatives during clinical interviews with students of elementary school age. The technology exposed students' problem-solving strategies and mathematical understanding, promoting just-in-time teaching about the target content. The process of completing and reflecting on the interviews contributed to growth of the preservice teachers' technological pedagogical content knowledge.
Trena L. Wilkerson, Tommy Bryan, and Jane Curry
Using candy bars as models gives students a taste for learning to represent fractions whose denominators are factors of twelve.
Katie L. Anderson
Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.
Terry L. Kurz and Jorge Garcia
An alternative method for teaching prime decomposition explores using tools rather than factor trees.
Aimee J. Ellington and Joy W. Whitenack
A mathematics specialist has great success using a pattern-block configuration to help a small group of fifth graders understand that fractional parts of a whole unit must be equal in size. That's just the way the funky cookie crumbles.