Students count in binary with cards they can hold, read a hex color as three bytes, and use real spec sheets to work out how long a game takes to download on two internet plans.
Objectives
Students will be able to:
- Convert numbers between binary and decimal, up to eight bits (0 to 255).
- Read a hexadecimal color code as three bytes: red, green and blue.
- Use units of storage (bit, byte, KB, MB, GB, TB), speed (GHz) and throughput (Mbps, Gbps) to compare two real devices or plans, without mixing up bits and bytes.
Board question
- If each of your ten fingers can only be up or down, how many different patterns can you make? Make a guess and give one reason.
- Which is bigger, 1 TB or 1,000 GB? Answer in one sentence.
Students answer in the notebook at the start, and revisit the answer on the exit ticket.
The 90-minute block
| Minutes | Segment | Teacher | Students |
|---|---|---|---|
| 0–8 | Do Now | Board question. Collect a few guesses for the fingers question; most will say 10 or 20. | Answer both board asks. |
| 8–25 | I Do | Place value in decimal first (ones, tens, hundreds), then the same idea with twos. Show why ten fingers make 1,024 patterns. Introduce hex as shorthand: one hex digit is four bits, so a byte is two hex digits. | Notes; copy the place-value chart. |
| 25–35 | We Do | Pairs hold the eight binary cards. Call out numbers (5, 13, 100, 255) and have pairs flip cards face up to make them. Then flip a pattern and have the room read it. | Make and read numbers with the cards. |
| 35–78 | Lab: Bits You Can Hold | Circulate through Parts A–C. In Part C, watch for the bits-and-bytes trap: a 6 GB game is 48 gigabits. | Lab sheet Parts A–C. |
| 78–84 | Debrief | The 931 GB mystery. Show the drive. Drive makers count 1 TB as 1,000,000,000,000 bytes; the operating system counts in powers of 2, so it shows about 931 GB. | Revisit the second board ask. |
| 84–90 | Exit Ticket | Board question returns. Two Tech+-style items. | Revisit, then answer. |
The 50-minute period
| Minutes | Segment | Teacher | Students |
|---|---|---|---|
| 0–5 | Do Now | The fingers question only. | Answer the first ask. |
| 5–15 | I Do | Place value in decimal and binary; the 1,024 answer. | Notes. |
| 15–42 | Lab: Bits You Can Hold | Parts A and C. Part B (hex colors) becomes tomorrow's warm-up. | Lab sheet Parts A and C. |
| 42–50 | Exit Ticket | Both board asks and the two items. Mention the 931 GB mystery as a hook for tomorrow. | Revisit, then answer. |
What moves to tomorrow: Part B (hex colors) opens tomorrow as a 15-minute warm-up, followed by the 931 GB debrief.
Materials
- Binary card sets: eight cards per pair, showing 1, 2, 4, 8, 16, 32, 64 and 128 dots.
- Spec sheets (printed): two laptops and two home internet plans.
- Chromebooks with a color picker open (any search engine has one).
- Lab sheet (printed), one per student. Calculators stay put away until Part C.
Before class
- Print and cut the binary cards. Card stock lasts all year.
- Pick two real laptops from a store listing and two plans from a local provider. Black out prices if you want the focus on specs.
- Check a 1 TB drive's properties in Windows or ChromeOS so you can show the class the "931 GB" it reports.
Vocabulary
- Bit
- One binary digit: a 0 or a 1. The smallest piece of data.
- Byte
- Eight bits. Enough to store one letter or a number from 0 to 255.
- Binary
- Base 2. Each place is worth twice the place to its right.
- Hexadecimal
- Base 16. Uses 0–9 and A–F; one hex digit stands for four bits.
- Throughput
- How much data moves per second, measured in bits: Mbps, Gbps.
- Clock speed
- How many cycles a processor runs per second, measured in GHz.
Exit ticket
Item 1 is always the board question, revisited. Then:
What is the binary number 0010 1101 in decimal?
- 44
- 45 (key)
- 90
- 101
A home internet plan is 300 Mbps. About how long does it take to download a 1 GB file?
- About 3 seconds
- About 27 seconds (key)
- About 3 minutes
- About 5 minutes
Support
- A place-value strip (128 down to 1) is printed at the top of Part A.
- Hex letters and their values are printed beside Part B.
- Part C can be done with a partner reading the spec sheet aloud.
Stretch
- Store your first initial as a byte. Capital A is 65, B is 66, and so on.
- Explain the 931 GB mystery in writing, with the math.
Where this leads
Help desk and sales calls turn on these numbers: why a new drive "looks smaller," whether a plan is fast enough, which laptop fits a budget. Students practice explaining a spec to someone who does not know what it means.