# G.14 - Proportional Reasoning

G.14  The student will apply the concepts of similarity to two- or three-dimensional geometric figures.  This will include

a)  comparing ratios between lengths, perimeters, areas, and volumes of similar figures;

b)  determining how changes in one or more dimensions of a figure affect area and/or volume of the figure;

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

d)  solving problems, including practical problems, about similar geometric figures.

### 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

2016 VDOE Curriculum Framework - G.14 Understanding

·  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 a2:b2.

­  The ratio of their volumes is a3:b3.

·  Proportional reasoning is important when comparing attribute measures in similar figures.

### ESSENTIALS

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

·  G.14a1  Compare ratios between side lengths, perimeters, areas, and volumes, given two similar figures.

·  G.14b1  Describe how changes in one or more dimensions affect other derived measures (perimeter, area, surface area, and volume) of a figure.

·  G.14c1  Describe how changes in one or more measures (perimeter, area, surface area, and volume) affect other measures of a figure.

·  G.14d1  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