1. Problem of the Day Problem of the Day Reasoning Length © Richard A. Medeiros 2005 next 148 -149

2. Selina must draw a six inch line on the chalkboard, but she has lost her ruler. The only tools she has are chalk and a sheet of paper. She knows that this type of paper is 8 ½ inches wide and 11 inches long. Selina must draw a six inch line on the chalkboard, but she has lost her ruler. The only tools she has are chalk and a sheet of paper. She knows that this type of paper is 8 ½ inches wide and 11 inches long. How can she use the paper to help draw the line she needs? How can she use the paper to help draw the line she needs? next

3. I have to figure out how to draw a six inch line on the board without a ruler. I can use a piece of paper 8½ x 11 inches and a piece of chalk. After thinking about my options and testing several ideas, I have decided to place the paper vertically (11inches) on the board Solution

4. and place a mark at both ends of the paper. Then I will move the paper to the right lining it up with my chalk mark and will place another mark on the end. Finally, I will line the paper up horizontally (8½ inches) at my first mark. Then, I will erase the 11 inches, and 6 inches will remain. next

5. Mathematically, my equation would be… 8½ + 8½ - 11= m Logically, my answer makes sense both mathematically and manually.

6. 8½ x 11 8½ + = 17 - 11 = m m = 6 8½ x 11 6 17 My solution 8½ x 11 next 11 next

7. 11 - 8½ = 2½ 8½ - 2½ = m m = 6 8½ x 11 62½ 8½ x 11 Student’s solution next

8. 11 ÷ 2 = 5½ 8½ - 5½ = 3 3 x 2 = m 3 8½ x 11 Math Coach solution m = 6 3 next