# Lesson 16

Is a Smartphone Smart Enough to Go to the Moon?

## 16.1: Old Hardware, New Hardware (20 minutes)

### Activity

Students perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Students use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.

As students work, look for those who use scientific notation to make their calculations and estimations easier. Consider asking them to share their work later.

### Launch

Arrange students in groups of 2. Display or distribute the included blackline master containing computer hardware specifications over time for all to see throughout the activity. Give students 15–20 minutes to work before a brief whole-class discussion.

### Student Facing

In 1966, the Apollo Guidance Computer was developed to make the calculations that would put humans on the Moon.

Your teacher will give you advertisements for different devices from 1966 to 2016. Choose one device and compare that device with the Apollo Guidance Computer. If you get stuck, consider using scientific notation to help you do your calculations.

For reference, storage is measured in bytes, processor speed is measured in hertz, and memory is measured in bytes. Kilo stands for 1,000, mega stands for 1,000,000, giga stands for 1,000,000,000, and tera stands for 1,000,000,000,000.

2. Which one has a faster processor? How many times faster?
3. Which one has more memory? How many times more memory?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

Select students who chose various devices to share their results. A key insight to take away would be how rapidly technology improves and how modern smartphones are much, much more sophisticated than the computer that put people on the Moon.

Speaking, Listening: MLR7 Compare and Connect. Ask students to create a visual display of their strategy and result for comparing the Apollo Guidance Computer and the device they selected. Invite students to take a tour of the displays and identify “what is the same and what is different about each approach”. Draw students’ attention to the ways the values were compared using different strategies (e.g., using estimation, calculating differences using scientific notation versus expanded form). In this discussion, emphasize the mathematical language used to make sense of the different strategies to compare the values. These exchanges strengthen students’ mathematical language use and reasoning when comparing large and small quantities.
Design Principle(s): Maximize meta-awareness

## 16.2: A Bit More on Bytes (25 minutes)

### 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

1. 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?”
2. 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?
3. 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.

4. 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.

5. 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.

6. How many seconds of a high-definition movie would one floppy disk be able to hold?
7. 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

For access, consult one of our IM Certified Partners.

### 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.

1. Which is bigger, a binary gigabyte or a regular gigabyte? How many more bytes is it?
2. Which is bigger, a binary terabyte or a regular terabyte? How many more bytes is it?

### Student Response

For access, consult one of our IM Certified Partners.

### 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)