1. PRE-ALGEBRA

2. Reasoning Strategy: Make a Model (10-8) How can you use a model to help solve a problem? Example: A box company makes boxes to hold popcorn for a movie theater. Each box is made from a piece of cardboard that is 8½ in. by 11 in. (the size of a piece of copy paper). If the boxes are made by cutting out a square from the corner and folding the sides up, then what are the dimensions of the box that will hold the most popcorn? Step 1: Understand the problem. 1. Goal: Find the dimensions of the box that will hold the most popcorn = greatest volume 2. Given Information: The size of the cardboard is is 8½ in. by 11 in. Step 2: Make a plan. 1. Build boxes using sheets of paper. 2. Cut squares from the corners of increasing sizes starting with whole numbers 1 in., 2 in., 3 in. and so on. 3. Find the dimensions and volumes of each box until the values start to decrease. Then, go by halves.

3. PRE-ALGEBRA Reasoning Strategy: Make a Model (10-8) Size of CutLengthWidthHeightVolume 1 in.9 in.6.5 in.1 in. 9  6.5  1 = 58.5 in. 3 2 in.7 in.4.5 in.2 in. 7  4.5  2 = 63 in. 3 3 in.5 in.2.5 in.3 in. 5  2.5  3 = 37.5 in. 3 1½ in.8 in.5.5 in.1.5 in. 8  5.5  1.5 = 66 in. 3 2½ in.6 in.3.5 in.2.5 in. 6  3.5  2.5 = 52.5 in. 3 Step 3: Organize your information into a table or chart. So, the box that would hold the most popcorn would be 8 in. (length) by 5½ in. (width) by 1½ in. (height) and hold 66 cubic in. (in. 3 )

4. PRE-ALGEBRA A can company rolls rectangular pieces of metal that measure 8 in. by 10 in. to make the sides of cans. Which height, 8 in. or 10 in., will make the can with the greater volume? Build two cans using 8 in.-by-10 in. pieces of paper. You do not need to make the bases, just the sides. LESSON 10-8 Additional Examples Reasoning Strategy: Make a Model

5. PRE-ALGEBRA (continued) The volume of the can with height 8 in. is greater. not to scale Measure your models to find approximate radii. Radius of 10-in. high can 1.3 in. Radius of 8-in. high can 1.6 in. Find the volumes. V = r 2 h = (1.3) 2 (10) = 16.9 53.1 in. 3 V = r 2 h = (1.6) 2 (8) = 20.48 64.3 in. 3 LESSON 10-8 Additional Examples Reasoning Strategy: Make a Model

6. PRE-ALGEBRA Solve. 1.You cut square corners from a piece of cardboard that has dimensions 32 cm by 40 cm. You then fold the cardboard to create a box with no lid. To the nearest centimeter, what are the dimensions of the box that will have the greatest volume? 20 cm by 28 cm by 6 cm LESSON 10-8 Reasoning Strategy: Make a Model Lesson Quiz