CONSTRUCTING RECTANGULAR PRISMS
OBJECTIVES:
1. To construct a rectangular prism.
2. To determine the volume and total surface area of said prism.
3. To find patterns in the changes in volume and total surface area when the dimensions are doubled, and tripled.
MATERIALS: Paper, Pencil, Ruler, Scissors, Calculator
PROCEDURE:
STEP 1: Construct rectangular prisms using paper.
Student 1: Construct a 2 ¼ in. by 3 ½ in. by 4 3/8 in. rectangular prism.
Student 2: Construct a second rectangular prism. Double the dimensions
used by Student 1. Are your dimensions correct?
Student 3: Construct a third rectangular prism. Triple the dimensions
used by Student 1. Are your dimensions correct?
STEP 2: Determine the different ways one may find the volume of your rectangular prism. Show complete work. Did the volume of the same rectangular prism change? Explain why each solution is different from the other/s.
STEP 3: Determine the different ways one may find the total surface area of your rectangular prism. Show complete work. Did the total surface area change? Why so?
STEP 4: Discuss the following with all other members of the group:
1. What do you think happens to the volume of a rectangular prism when the dimensions are doubled? Tripled?
2. What do you think happens to the total surface area of a rectangular prism when the dimensions are doubled? Tripled?
STEP 5: As a group, make a poster that reflects your group’s answers to the questions in Step 4.
STEP 6 (Final step): Gallery Walk & Classroom Talk. Compare your group’s findings to the findings of the other groups. Any similarity?
EXTENSION: Write a proof for each of the two cases: doubled dimensions and tripled dimensions.
(Lesson designed by R.E. Jope, Achieve Early College High School, McAllen, TX USA)
