Covering and Surrounding, Investigation 2, Problem 2.2 Completed
Stretching the Perimeter
Mathematical Goals National Standards State Standards
NAEP 6NJ 4.2.E.2,
• Understand that the perimeters of rectangles with a fixed
G1d, G2d, M2f 6NJ 4.2.E.4
area can vary considerably. CAT6
• Explore questions of maximum and minimum in the context LV16.13, LV16.14
of finding the largest and smallest perimeter for rectangles of CTBS
fixed area. LV16.55,LV16.56
• Continue to develop facility using formulas for finding ITBS
perimeter and area of rectangles. LV12.G, LV12.M
• Continue to develop a conceptual understanding of area and
Technology: ExamView CD-ROM, TeacherEXPRESS CD-ROM,
Student Activity CD-ROM, www.PHSchool.com
Materials: Student notebooks, Overhead projector, String,
Scissors, Inch grid paper, 4 by 6 rectangle cut from
inch grid paper or transparency
Pacing: 45 minutes
1. LAUNCH (10 minutes) Targeted Resources
Use the Getting Ready to model the procedure with a 4 in.-by-6 in. Transparency 2.2 Getting
rectangle, cutting it as described in the Student Edition. Ready
MM of Representation—model the procedure using the smartboard
• What is the area of this new shape? How do you know?
• How can we find the perimeter of this shape?
• How do the area and perimeter of this new shape compare with the
area and perimeter of the 4 in.-by-6 in. rectangle?
Once students understand the problem, let them work individually using
inch grid paper.
MM of Representation,Engagement—show individual students shapes on
2. EXPLORE (20 minutes) Targeted Resources
As students work, make sure they take time to measure accurately
enough to see the differences in perimeters. Suggest that students who
finish early try to make another figure with an even greater perimeter than
the one they just made.
MM of Engagement—Have students check each other’s work for accuracy
Have students cut string the length of the perimeter of their figures, which
makes it easier to compare perimeters.
3. SUMMARIZE (15 minutes) Targeted Resources
Have groups share their findings for each question. Focus on the fact that
every new figure has an area of 24 square units, yet the perimeters vary.
• Look at the area and perimeter of the shapes we made. How are
they the same and how are they different?
• Why are the areas always the same? Why is the perimeter of this
figure longer than the perimeter of this one?
Use the conversation on the changing perimeter to lead into Question E.
MM of Expression—Students share their findings with a partner, form
conjectures, then share these with the class
Turn the conversation toward discussing the smallest perimeter. The goal
is for students to see how shorter cuts will reduce the perimeter and
longer cuts increase the perimeter.
Have the class present their reactions to Talecia’s statement in
Question D. If necessary, refer the class to the figures they have just
made. Wrap up by referring back to Problem 2.1.
• Are there other rectangular shapes with an area of 24 square
units that would have a perimeter less than 20 units?
4. ASSIGNMENT GUIDE Targeted Resources
Core 7 Labsheet 2ACE Exercises 3–
Other Connections 18, 19; unassigned choices from previous problems
Labsheet 2ACE Exercises
Adapted For suggestions about adapting ACE exercises, see the CMP 10–12
Special Needs Handbook.
Answers to ACE and