options: 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.

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 & 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.

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

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

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.

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

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
problem_activity: Problem 1
The grocery store sells beans in bulk. The grocer's sign above the beans says, “5 pounds for $4.”
At this store, you can buy any number of pounds of beans at this same rate, and all prices include tax.
Alberto said, “The ratio of the number of dollars to the number of pounds is 4:5. That's $0.80 per pound.”
Beth said, "The sign says the ratio of the number of pounds to the number of dollars is 5:4. That's 1.25 pounds per dollar."
Are Alberto and Beth both correct? Explain.
Problem 2
Claude and Dora go shopping at the same grocery store as Alberto and Beth.
Claude needs two pounds of beans to make soup. Show Claude how much money he will need.
Dora has $10 and wants to stock up on beans. Show Dora how many pounds of beans she can buy.
Whose rate of change, Alberto’s or Beth’s, do you prefer to use to solve Claude’s problem? Dora’s problem? Explain.
Problem 3
Sanyukta can type 2 pages in 8 minutes.
a.   What are two rates associated with this ratio?
b.   Sanyukta has a deadline in 22 minutes, at which point she needs to be done typing an article. What is the greatest number of pages that Sanyukta can type before her deadline?
c.   Sanyukta has to type a 9-page article. How much time will it take her?
Problem 4
Solve each problem involving distance, speed, and time.
a.   Melanie drives at a constant speed of 35 miles per hour. How far does she travel in 2 hours?
b.   Nathan drives at a constant speed of 40 miles per hour. How long it take him to travel 60 miles?
c.   Oscar drives at a constant speed of 50 miles per hour. How far does he travel in 90 minutes?
d.   Penelope travels 14 miles in 30 minutes. At what constant speed is she driving?


correct_option_index: 7