Illuminations: Classic Middle-Grades Problems for the Classroom

# Classic Middle-Grades Problems for the Classroom

 This lesson presents two classic problems (Mangoes Problem and Sailors and Coconuts) that can be represented and solved in several different ways. Middle-grades students work in groups on the problems to promote communication of mathematical ideas, and a variety of classroom solution attempts are described. This lesson plan was adapted from an article, written by Jerry Stonewater, which appeared in the November‑December 1994 issue of Mathematics Teaching in the Middle School.

### Learning Objectives

 Students will: apply and adapt a variety of appropriate strategies to solve problems monitor and reflect on the process of mathematical problem solving communicate their mathematical thinking coherently and clearly to others

### Extensions

 Suppose ten people take the "remaining" mangoes, just like in the original problem, that is, the first person takes one-tenth of the mangoes in the bowl, the second takes one-ninth of the remaining mangoes, the third takes one-eighth of the remaining ones, and so on, until only three are left. How many were in the original bowl? Work a number of mangolike problems starting with ten people, then nine people, then maybe only seven people. Figure out how many mangoes were originally involved in each problem. Then make a generalization that would enable you to tell how many mangoes were in the original bowl if three were left and you knew how many people removed mangoes.

### NCTM Standards and Expectations

 Algebra 6-8Develop an initial conceptual understanding of different uses of variables. Number & Operations 6-8Use factors, multiples, prime factorization, and relatively prime numbers to solve problems. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

1 period

### Web Sites

 More and Better Mathematics for All Students
 © 2000 National Council of Teachers of Mathematics Use of this Web site constitutes acceptance of the Terms of Use The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.