On student said this was true because it worked for every ex

On student said this was true because it worked for every example she had tried. The second student said it might not always be true because you can\'t prove something with examples. Write an explanation that begins with examples and then leads the students to understand that the sum of any three consecutive whole numbers is always divisible by 3. When Ms. Lopez asked her class to use their tiles and make rectangular arrays for the counting numbers 1 to 12, Robert made only one rectangle for 4 (1 by 4) and one for 9 (1 by 9). He did not form a 2-by-2 square and a 3-by-3 square for these numbers because he said they were not rectangles. What would you say to Robert? Sarah, a fifth-grade student, discovered that to test a

Solution

Robert is missing the idea that every square is also a rectangle . A square is a special form of a rectangle with all sides of same length. Now both the procedures are correct . But a 2-by-2 and 3-by-3 pattern looks nicer than the 1-by-4 and 1-by-9 one