“Math is so boring!” How many times have we heard this statement from our students? As teachers, we are constantly looking for different activities to interest our students in mathematics and to convey the true richness and diversity of the subject.
Aesop's Fables are universally wellknown short tales. Although each tale teaches a moral lesson, some of these stories can also be settings for teaching mathematics lessons. Most students are familiar with the story of the tortoise and the hare, in which a tortoise challenges a hare to a race. In the race, we find that the tortoise plods along, slowly and surely, and beats the overconfident hare who decides to take a nap in the midst of the race. The hare awakens too late and realizes that it cannot catch up to the tortoise, which is way ahead and wins the race. The moral of the story is that the race is not always to the swift. CENTRAL OBJECTIVE Using this setting, we propose a mathematically rich activity that examines some of the "what ifs" that could have altered the outcome of the race between the quick but overconfident hare and the slow but persistent tortoise. For example, how long a Edited by Marilyn Howard,
Calculators are often efficient in finding the answer to an addition or subtraction problem, but they do not reveal the process by which the answer is obtained. Developing students' fluency in addition and subtraction using strategies and algorithms based on place value, composing and decomposing numbers in base 10, and reading and writing numerals in expanded form are important teaching and learning standards not only for the elementary grades but for middle school students as well (NCTM 2000; CCSSI 2010; TEA 2015). We introduced the Chinese abacus to our students as a hands-on tool to illuminate the meaning of a number in expanded form in terms of place values and to strengthen students' conceptual understanding of the standard algorithms of addition and subtraction. “Students' understanding of the base 10 number system is deepened as they come to understand its multiplicative structure” (NCTM 2000, p. 143). This activity will let students explore the mathematical properties of the base 10 system in a creative and interactive way. Students develop a deeper meaning of why the standard algorithms work and how they relate to a number in expanded form. This activity is best suited for elementary and middle grades.
This activity engages students in problem solving while exploring key concepts of number theory, such as divisibility and divisibility tests, place value, fractions, and scale factors.
As teachers, we are constantly looking for rich problem-solving tasks that connect different areas of mathematics, capture the interest of our students, and convey the true richness and diversity of the subject (Namakshi et al. 2015). Our activity focuses on exploring patterns in an n × n × n cube. Since most students are familiar with Rubik's® Cube and may have seen or played with one before, this activity ties in with an object familiar and interesting to them.
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