Lesson #1 title: PART 1 = SAME AREA but DIFFERENT PERIMETER (‘bowling alley’ and ‘gardens’)
Date:
THROUGH-LINE: Beauty – creating
Beauty is observed by creating different rectangles (the largest or the smallest) depending on the given P (outside) or the given A (inside).
OUTCOMES:
1. Draw two or more rectangles for a given area in a problem-solving context.
2. Conclude that for a fixed area, the GREATEST PERIMETER occurs with the rectangle that looks
most like a ‘bowling alley’ and has w = 1cm.
3. Conclude that for a fixed area, the SMALLEST PERIMETER occurs with the rectangle that is
most like a square (sides are all equal or nearly all equal).
MATERIAL NEEDED: highlighters, pencil, blue pen, grid paper, RULER
2
NOTE: For each rectangle use whole-centimetre sides. Assume each square is 1 cm . LABEL length, width, Area, Perimeter on the diagram.
2
Example #1: Draw AS MANY rectangles as possible with an area of 12 cm .
BF:
CONCLUSIONS:
What is the AREA of all
these rectangles?
Which rectangle has the
LARGEST perimeter?
Why?
Which rectangle has the
SMALLEST perimeter?
Why?
PERIMETER is
MEASURED IN
AREA is
MEASURED IN
Example #2: (Obtained from Eduguide5, p.220)
Draw AS MANY different rectangles with an area of 18 cm2.
BF:
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
CONCLUSIONS:
1.SAME AREA THEN GREATEST PERIMETER when rectangle
2. SAME AREA THEN SMALLEST PERIMETER when rectangle
L1(3)
YOUR TURN  or continue together with MsT
#1: Draw AS MANY different rectangles with an area of 10 cm2.
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
#2: Draw AS MANY different rectangles with an area of 15 cm2.
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
L1(4)
#3: Draw AS MANY different rectangles with an area of 20 cm2.
BF:
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.