options: 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.

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.

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

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.

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

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.

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.

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

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
problem_activity: Problem 1
At the store, you see oranges on sale at 1 pound for $3. At a different store, your brother sees oranges on sale at 3 pounds for $8.
Do the oranges cost the same at both stores? Which store offers the better deal? Justify your answer.
Problem 2
Callie biked 12 miles in 3 hours. Carter biked 10 miles in 2 hours.
Represent each person's trip with a double number line. Explain how you can see that they are not going the same speed.
Problem 3
Density is the relationship between the mass of an object and its volume, or amount of space it takes up. A scientist finds a rock and determines its mass to be 18 grams and its volume to be 4 cm
$$^{3}$$
. Another rock is found with a mass of 63 grams and a volume of 14 cm
$$^{3}$$
.
Draw two double number lines to compare the two rocks. Do the rocks have equivalent ratios of mass and volume? Do they have the same density?


correct_option_index: 1