Dana Saragaglia Math 608 Project

 Bill and Marcus wanted to make a rectangular box out of plywood. At the lumber yard, they realized that they had forgotten the dimensions of the box. Bill remembered that one of the sides had an area of 96 square centimeters. Marcus remembered that the other sides had areas of 252 and 168 square centimeters. What are the dimensions of the box? Muller, G. (1999). Menu of problems. Mathematics Teaching in the Middle School, 4(7), 460.

Bill and Marcus’s mom has had enough of them leaving their video games all on the floor. Mom: Boys you need to go and pick up all your video games and store them in a box. She quickly gave them the dimensions for a rectangular box and sent them on their way to purchase plywood to build it. At the lumber yard, Bill and Marcus discovered a problem. Bill: I can’t remember the dimensions mom said. All I can remember is one of the sides had an area of 96 square centimeters. Marcus: Well I remember that the other sides had areas of 252 and 168 square centimeters. Apply your knowledge to help Bill and Marcus figure out the dimensions.

 Finding area of a rectangle  Finding surface area and volume of rectangular prisms  Solving equations  Key Vocabulary-dimensions, rectangular, area

 Are we finding the surface area or volume?  What type of shape (prism, cylinder, etc) is the box?  What is the formula or area, surface area, and/or volume?

 96 = 4 ∙ 24, 24 doesn't divide 252 or 162  96 = 6 ∙ 18, 18 divides 252 to get 14 but 6 ∙ 14 ≠ 162  96 = 8 ∙ 12, 12 divides 252 and ÷ 12 = 21 and 162 ÷ 12 = ∙ 12 = 162 and 8 ∙ 14 ≠ 252 Therefore, my dimensions are 8, 12, and 21

lw = 96 lh = 252 wh = 168 Multiple the first two: (lw)(lh) = 96 ∙ 252 whl ² = 24,192 -Substitute 168 for wh (168)l² = 24,192 -Divide by 168 l² = 144 l = 12 12w = 96; w = 8 and 12h = 252; h = 21

Solve for w Substitute lw = 96 l = 96/w lh = 252 (96/w)(168/w) = 252 Wh = 168 h = 168/w

(96/w)(168/w) = 252 -Multiply the left side 16,128/w ² = Find the cross-product 16,128 = 252w² - Divide both sides by = w² - Take the square root 8 = w

 If each video game takes up 15 inches cubed. At most how many video games will fit into the box? (Games Galore I) V = 2016 cm ³ -Need to convert from centimeters to inches 2016 cm 1 cm x ≈ in³ x in in /15 ≈ 52.8 Therefore, 52 games will fit into the box =

Bill and Marcus’s mom has had enough of them leaving their video games all on the floor. Mom: Boys you need to go and pick up all your video games and store them in a box. She quickly gave them the dimensions for a rectangular box and sent them on their way to purchase plywood to build it. At the lumber yard, Bill and Marcus discovered a problem. Bill: I can’t remember the dimensions mom said. All I can remember is one of the sides had an area of 96 square centimeters. Marcus: Well I remember that the another side had an area of 168 square centimeters. Apply your knowledge to help Bill and Marcus figure out all the possible the dimensions.

 If you have 34 video games and each take up 15 inches cubed. What are the smallest dimensions possible to store all the games. (Games Galore II)