#### Math - 2019-20

# G.14 - Proportional Reasoning

G.14The student willapplythe concepts of similarity to two- or three-dimensional geometric figures. This will includea)

comparingratios between lengths, perimeters, areas, and volumes of similar figures;b)

determininghow changes in one or more dimensions of a figure affect area and/or volume of the figure;c)

determininghow changes in area and/or volume of a figure affect one or more dimensions of the figure;d)

solvingproblems, including practical problems, about similar geometric figures.

*Adopted: 2016*

### BIG IDEAS

- I can decide fair prices for two different sizes of popcorn
containers at the movie theater, determine how much packing material is
required to ship 100 boxes of Earth globes, and calculate which diameter pipe
will carry enough water for all the homes in Miller Park area.

- I will be
able to define, describe,
and analyze 2- and 3-dimensional figures, their properties and relationships,
including how a change in one measurement will affect other measurements of
that figure.

### UNDERSTANDING THE STANDARD

· A change in one dimension of a figure results in predictable changes in area and/or volume. The resulting figure may or may not be similar to the original figure.

· A constant ratio, the scale factor, exists between corresponding dimensions of similar figures.

· If the ratio between dimensions of similar figures is a:b then:

The ratio of their areas is a^{2}:b^{2}.

The ratio of their volumes is a^{3}:b^{3}.

### ESSENTIALS

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

·
G.14a_{1} **Compare**
ratios between side lengths, perimeters, areas, and volumes, given two similar
figures.

·
G.14b_{1} **Describe**
how changes in one or more dimensions affect other derived measures (perimeter,
area, surface area, and volume) of a figure.

·
G.14c_{1} **Describe**
how changes in one or more measures (perimeter, area, surface area, and volume)
affect other measures of a figure.

·
G.14d_{1} **Solve**
real-world problems involving measured attributes of similar figures.

### KEY VOCABULARY

geometric
object, two-dimension, three-dimension, compare, ratio, side, lengths,
perimeters, area, volume, dimension, change, similar, compare, total surface
area, measured attributes, predictable, constant, ratio, corresponding,
proportional, integral/necessary, compare

*Updated: Jul 30, 2019*