Lesson #2 title: PART 2 = SAME AREA but DIFFERENT PERIMETER (‘SQUARES’, ‘bowling alley’, ‘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.
2.
3.
Draw two or more rectangles for a given area in a problem-solving context.
Conclude that for a fixed area, the GREATEST PERIMETER occurs with the rectangle that looks most like a
‘bowling alley’ and has w = 1cm.
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
NOTE: For each rectangle use whole-centimetre sides. Assume each square is 1 cm2 . LABEL length, width, Area, Perimeter on the diagram.
2
Example #1: Draw AS MANY different rectangles with an area of 16 cm .
BF:
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
WHEN
SAME
AREA,
GREATEST
PERIMETER
when
rectangle
WHEN
SAME
AREA,
THEN
SMALLEST
PERIMETER
when
rectangle
L2(2)
YOUR TURN  or continue together with MsT
#1: Draw AS MANY different rectangles with an area of 11 cm2.
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
#2: Draw AS MANY different rectangles with an area of 28 cm2.
BF:
BF:
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
L2(3)
#3: Draw AS MANY different rectangles with an area of 24 cm2.
BF:
BF:
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
#4: Draw AS MANY different rectangles with an area of 25 cm2.
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
L2(4)
#5: Draw AS MANY different rectangles with an area of 21 cm2.
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.
#6: Draw AS MANY different rectangles with an area of 30 cm2.
BF:
BF:
BF:
OUTLINE greatest perimeter in GREEN. OUTLINE smallest perimeter in YELLOW.