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.

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

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.

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

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

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

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

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.

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

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: Activity
Students use scientific notation as a tool to understand the relative scale of different units (MP2). They practice modeling skills by identifying essential elements of the problems and gathering relevant information before computing (MP4).
Launch
Arrange students in groups of 2. Instruct students to first read through the problems and decide on what information they need to solve each problem. Record relevant information for all students to see. Only record information when students have asked for it. Possible information students will ask for include:
Mai’s dad’s computer holds 500 gigabytes of storage space.
A kilobyte is 1,000 bytes, a megabyte is 1,000,000 bytes, and a gigabyte is 1,000,000,000 bytes.
1 character is roughly 1 byte.
An emoji is roughly 4 bytes.
A full-length, high-definition film is around 8 gigabytes and runs 2 hours.
A person sleeps about 8 hours in a night.
Give 15–20 minutes of work time before a brief whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge of working with very large numbers. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
For each question, think about what information you would need to figure out an answer. Your teacher may provide some of the information you ask for. Give your answers using scientific notation.
Mai found an 80’s computer magazine with an advertisement for a machine with hundreds of kilobytes of storage! Mai was curious and asked, “How many kilobytes would my dad’s new 2016 computer hold?”
The old magazine showed another ad for a 750-kilobyte floppy disk, a device used in the past to store data. How many gigabytes is this?
Mai and her friends are actively involved on a social media service that limits each message to 140 characters. She wonders about how the size of a message compares to other media.
Estimate how many messages it would take for Mai to fill up a floppy disk with her 140-character messages. Explain or show your reasoning.
Estimate how many messages it would take for Mai to fill a floppy disk with messages that only use emojis (each message being 140 emojis). Explain or show your reasoning.
Mai likes to go to the movies with her friends and knows that a high-definition film takes up a lot of storage space on a computer.
Estimate how many floppy disks it would take to store a high-definition movie. Explain or show your reasoning.
How many seconds of a high-definition movie would one floppy disk be able to hold?
If you fall asleep watching a movie streaming service and it streams movies all night while you sleep, how many floppy disks of information would that be?
Student Response
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Student Facing
Are you ready for more?
Humans tend to work with numbers using powers of 10, but computers work with numbers using powers of 2. A “binary kilobyte” is 1,024 bytes instead of 1,000, because
\(1,\!024 = 2^{10}\)
. Similarly, a “binary megabyte” is 1,024 binary kilobytes, and a “binary gigabyte” is 1,024 binary megabytes.
Which is bigger, a binary gigabyte or a regular gigabyte? How many more bytes is it?
Which is bigger, a binary terabyte or a regular terabyte? How many more bytes is it?
Student Response
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for free access to Extension Student Response.
Activity Synthesis
In a whole-class discussion, ask students what they might have found surprising or interesting when comparing different digital media and different hardware. If time permits, discuss how scientific notation helps to make those comparisons.
Speaking: MLR8 Discussion Supports.
As students explain what they noticed about the differences in digital media and hardware, press for details in students’ ideas by requesting that students challenge an idea, elaborate on an idea, or make explicit their process for calculating or comparing the values. Revoice student ideas to model mathematical language use in order to clarify, apply appropriate language, and involve more students. This will help students produce and make sense of the language needed to communicate their own ideas.
Design Principle(s): Support sense-making; Optimize output (for explanation)


correct_option_index: 8