Problem

of the

Day

Problem

of the

Day

Reasoning LengthReasoning Length© Richard A. Medeiros 2005

next 148 -149

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?

nextnext

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

next

Solution

and place a mark at both ends ofthe 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

Mathematically, my equation would be…

8½ + 8½ - 11= m Logically, my answer makes sense both mathematically and manually.

next

8½ x 11 8½ x 11

8½ + 8½ = 17

17 - 11 = m m = 6

8½ x 116

17 My solution

8½ x 11

nextnext

11

nextnextnextnext

11 - 8½ = 2½

8½ - 2½ = mm = 6

8½ x 11

62½

8 ½ x 11

Student’s solutionnextnextnextnextnext

11 ÷ 2 = 5½

8½ - 5½ = 33 x 2 = m

35½

8½ x 11

Math Coachsolution

m = 6

8 ½ x 11

3nextnextnextnextnextnext