The two provided activities are geared for students in middle school to facilitate and deepen their understanding of the arithmetic mean. Through these activities, students analyze visual representations and use a special type of statistical thinking called transnumerative thinking.
Michael Daiga and Shannon Driskell
Juli K. Dixon, Treshonda Rutledge, Jennifer C. Caton, and Edward C. Nolan
Constraints for social distancing require teachers to find creative ways to engage students. Consider this fun strategy for exploring fraction equivalence, addition, and subtraction in a game environment where students use self-made or digital manipulatives.
Excerpts from discussion threads on the online MyNCTM community
Karl W. Kosko
Use Cuisenaire™ Rods to emphasize the column-and-row structure in arrays for meaningful multiplication.
A t a party that I attended, the hosts gave their guests the Tower of Hanoi puzzle with alternating dark and light discs and a challenge to move the 7 discs to a new post. (I disqualified myself because I knew how to solve the challenge.) However, the hosts' son and daughter-in-law misunderstood the directions and moved the dark discs to one side post and the light discs to the other side post. I immediately wondered, “How many moves did they take, assuming that they made the most efficient moves? How can their interpretation of the problem be generalized to n discs?”
This simple dice game supports students' development of flexibility with numbers, the properties of the four operations (+, −, ×, ÷), and the order of operations. It requires only dice and a game board for each player.
Joe Champion and Ann Wheeler
A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.
The mathematical concept of slope can be made real through a set of simple, inexpensive, and safe experiments that can be conducted in the classroom or at home. The experiments help connect the idea of slope with physical phenomena related to surface tension. In the experiments, changes in surface tension across the surface of the water, which correspond to greater slopes on the graph, lead to increased motion of the fluid. The mathematical content, targeted to middle school and high school students, can be used in a classroom or workshop setting and can be tailored to a single session of thirty to ninety minutes.
Kyle T. Schultz and Stephen F. Bismarck
A geometric approach using exact square manipulatives can promote an understanding of the algorithm to dismantle radical expressions.
Jessica F. Shumway
Three days of using building blocks significantly enriched second graders' thinking about multiple dimensions.