Scaling a rectangular prism

1
Scaling a rectangular prism

• Need notebook, centimeter ruler, paper, tape
• Warm up order of ops problem with fractions
• Agenda
• Build a rectangular prism from a net drawing
• Have students make it 3 ½ times bigger, not
  specifying how, or what measure to make bigger
  (linear dimension, surface area or volume)
• Construct a net
• Fold the net
• Show how you know it is 3 ½ times bigger.
• Extension do a scale model for a pyramid.
• Goals
• Review net diagrams
• Use multiplication of a mired number to scale.
• See this as a ratio
• Compare different kinds of measure, linear,
  surface area, volume.
• Standards
• 7.P.6, 7.N.2, 7.N.8, 7.G.7

2
Warm up
3
With your partner make a box from a net

• On a sheet of paper (graph paper is easier to use
  if you have it.) Draw the net diagram to the
  left, be careful be accurate in your measurements
  and drawing
• Cut out the outline.
• Fold along the dotted lines
• Tape closed to form a rectangular prism.

3 ½ cm
3 ½ cm
1 cm
3 ½ cm
1 cm
2 ½ cm
4
Now with your partner make a bigger box

• Make a box that is 3 ½ times bigger than the box
  you just made.
• Start by drawing a new net diagram with
  dimensions that will make the box 3 ½ times
  bigger. (You may need to tape some sheets of
  paper together.)
• When you are done show me your box and explain
  to me how you made it 3 ½ times larger.

5
3 ½ times bigger net
12 ¼ cm
12 ¼ cm
3 ½ cm
12 1/4 cm
3 ½ cm
8 3/4 cm
6
Bonus This is a net for a pyramid
185 m
145m

• Make a model of the Great Pyramid of Giza that is
  1/1000 scale (Remember that 1cm is 1/100 of a
  meter.)

230 m
7
Homework

• Calculate the volume and surface area of both
  rectangular prisms. (The one that is 3 ½ times
  larger and the one we started with that is 2 ½cm
  by 3 ½cm by 1cm.)
• You may need to do some research to find out how
  to calculate these measures.

8
Original Size Volume and surface area

• Original Size
• V lwh (2 ½)(3 ½)(1) 8.75 cm3
• SA 2lw 2wh 2lh 2(2 ½)(3 ½)
• 2(3 ½)(1)
• 2(2 ½)(1)
• ____________
• 29.5 cm2

9
3 1/2 Size Volume and surface area

• 3 ½ Size
• V lwh (8 ¾)(12 ¼)(3 ½) 375 cm3
• SA 2lw 2wh 2lh 2(8 ¾ )(12 ¼ )
• 2(12 ¼)(3 ½)
• 2(8 ¾ )(3 ½
  )
• ____________
• 360 cm2

10
Homework (day 2)

• Create a rectangular prism that has ½ the volume
  of the larger prism we created in class
• Optional create a rectangular prism that has ½
  the surface area of the larger prism we created
  in class.

11
1/2 volume net
6 1/8 cm
6 1/8 cm
3 ½ cm
6 1/8 cm
3 ½ cm
8 3/4 cm
12
1/2 Surface Area net
8 cm
8 cm
4 cm
8 cm
4 cm
5 cm
13
½ Surface Area net

• ½ of the Original Surface Area is ½ 360 180
• 180 2lw 2wh 2lh
• 180 2(lw wh lh)
• 90 lw wh lh assume l5, w4
• 90 (5)(4) 4h 5h
• 90 20 4h 5h
• 90 20 9h
• 70 9h
• 8 ? h