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

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

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.

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.

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

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.

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.

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.

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

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
Julia, Keller, and Isreal are volunteer firefighters. On Saturday, the volunteer fire department held its annual coin drop fundraiser at a streetlight. After one hour, Keller had collected $42.50 more than Julia, and Isreal had collected $15 less than Keller. The three firefighters collected $125.95 in total. How much did each person collect?
Problem 2
Your parents are redecorating the dining room and want to place two rectangular pictures, each measuring 25 inches across, on the wall, which measures
$${10 {2\over3}}$$
feet long. They want to place the pictures so that the distance between the pictures and the distances from each picture to the end of the wall are the same, as shown in the diagram below.
[IMG]
Determine the distance each picture should be placed from the ends of the wall. Explain the strategy that you used.
Problem 3
Three toothpick configurations are shown in the chart below.
[IMG]
a.   Extend the pattern to complete the chart.
b.   How many toothpicks will be in the 10th design?
c.   Write an expression to represent the number of toothpicks in the
$$n$$
th design.
d.   Which design will have 175 toothpicks? Write and solve an equation.


correct_option_index: 8