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13Unit Scale Down, Scale Up
jOb ective Use proportions to find the measurements of similar figures.
1. Textbook Instructions 13 Scale Down, Scale Up
In this unit students learn the principles of Ryan, Ricky, and Jessica were looking at the map to see the road to the
proportion and scale. Treasure Castle. Ryan wanted to know how far the Treasure Castle is,
so he asked Panda, “How many miles is the Treasure Castle from here?”
The student adventurers in the textbook have
a map of the way to Treasure Castle and Panda said, “The length of the bridge that goes across the mud pool is
want to know how far it actually is. The panda 30 m. This map scales down the real length. You figure it out on your
offers two pieces of information: the bridge on own.” Then Panda walked away. Have students review what a proportion is. Is the bridge
the map is actually 30 meters long and the
map itself is correctly drawn to scale. actually drawn as 30 m? (No, it is drawn as 2 cm.)
Can distances on the map be converted to
real distances? Yes, because while the map
is much smaller than the territory it
represents, the proportions are the same.
How much smaller is the map than the
territory it represents? We know that the
bridge is actually 30 meters long. If we
measure how long the bridge is on the map,
we know that this distance is equivalent to 30
meters on the ground.
108
2. Build Understanding
Few real maps are drawn precisely to scale in all respects, due to practical considerations.
Example: on a highway map of the US, the lines that mark highways on the map are much wider than real
highways, up to several kilometers wide. If a highway about 100 meters wide were shown to scale on a
nationwide map, it would be too narrow to be visible.
Road maps may also exaggerate the size of highway interchanges so that motorists looking at the map can
get a sense of the layout of on-ramps and off-ramps without requiring insets drawn to a different scale. In an
earlier era, sea charts exaggerated the size of harbor entrances for the same reason.
182 NUMINO Teacher s Guide
13Unit Scale Down, Scale Up
jOb ective Use proportions to find the measurements of similar figures.
1. Textbook Instructions 13 Scale Down, Scale Up
In this unit students learn the principles of Ryan, Ricky, and Jessica were looking at the map to see the road to the
proportion and scale. Treasure Castle. Ryan wanted to know how far the Treasure Castle is,
so he asked Panda, “How many miles is the Treasure Castle from here?”
The student adventurers in the textbook have
a map of the way to Treasure Castle and Panda said, “The length of the bridge that goes across the mud pool is
want to know how far it actually is. The panda 30 m. This map scales down the real length. You figure it out on your
offers two pieces of information: the bridge on own.” Then Panda walked away. Have students review what a proportion is. Is the bridge
the map is actually 30 meters long and the
map itself is correctly drawn to scale. actually drawn as 30 m? (No, it is drawn as 2 cm.)
Can distances on the map be converted to
real distances? Yes, because while the map
is much smaller than the territory it
represents, the proportions are the same.
How much smaller is the map than the
territory it represents? We know that the
bridge is actually 30 meters long. If we
measure how long the bridge is on the map,
we know that this distance is equivalent to 30
meters on the ground.
108
2. Build Understanding
Few real maps are drawn precisely to scale in all respects, due to practical considerations.
Example: on a highway map of the US, the lines that mark highways on the map are much wider than real
highways, up to several kilometers wide. If a highway about 100 meters wide were shown to scale on a
nationwide map, it would be too narrow to be visible.
Road maps may also exaggerate the size of highway interchanges so that motorists looking at the map can
get a sense of the layout of on-ramps and off-ramps without requiring insets drawn to a different scale. In an
earlier era, sea charts exaggerated the size of harbor entrances for the same reason.
182 NUMINO Teacher s Guide
