options: Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
problem_activity: Problem 1
Pentagon
$${FGHIJ}$$
is a scale image of pentagon
$${ABCDE}$$
.
[IMG]
a.   Complete the table below with the measurements of each pentagon.
| **                Original line segment               ** | **                Original length               ** | **                Corresponding line segment               ** | **                Scale length               ** |
|----------------------------------------------------------|----------------------------------------------------|---------------------------------------------------------------|-------------------------------------------------|
|                          $$AB$$                          |                                                    |                            $$FG$$                             |                                                 |
|                          $$BC$$                          |                                                    |                            $$GH$$                             |                                                 |
|                          $$CD$$                          |                                                    |                            $$HI$$                             |                                                 |
|                          $$AE$$                          |                                                    |                            $$FJ$$                             |                                                 |
b.   Is there a proportional relationship between the side lengths of the original pentagon and the scaled pentagon? Explain using the measurements in the table.
c.   What is the constant of proportionality?
d.   What is the scale factor?
Problem 2
Melissa orders business cards to promote her new website. She previews the cards online before placing her order. The scale image she sees online and the actual size of the cards are shown below.
[IMG]
What scale factor was used to create the online image from the actual size of the business card?
Problem 3
For each situation described below, sketch and label the scale image using the scale factor.
a.   Your family recently had a family portrait taken. Your aunt asks you to take a picture of the portrait using your phone and send it to her. The original portrait is 3 feet by 3 feet and the scale factor from the original picture to the picture on your phone is
$${1 \over18}$$
. Draw the scale drawing, in inches, that would be the size of the portrait on your phone.
b.   Create a scale drawing of the arrow below using a scale factor of 150%.
[IMG]


correct_option_index: 2

3