Binary Numbers - Count the Dots Activity

Substitute Teacher Lesson Plan (Grade 2, ~45 minutes)

Objective

Students will learn that computers store information using only two symbols — zero and one — and will practice representing numbers using a set of "dot cards" that double in value (1, 2, 4, 8, 16), building an understanding of the binary number system.

Materials

• Photocopy Master: Binary Numbers (page 6) — pre-cut into sets of five cards per student (each card shows dots on one side, blank on the other)
• Worksheet Activity: Binary Numbers (page 5) — one per student
• A set of five large demonstration cards (dots on one side) for the teacher/five student volunteers to hold at the front

(No other materials needed — this activity is self-contained.)

Warm-up (~5 min)

1. Tell students: "Computers only understand two numbers — 0 and 1. Today we're going to learn a secret code computers use called binary numbers."
2. Choose five children to come to the front and each hold one of the five demonstration cards, arranged in order from most dots to least dots (16, 8, 4, 2, 1).
3. Ask the class: "What do you notice about the number of dots on each card?" (Each card has twice as many dots as the card to its right.)
4. Ask: "If we kept going, how many dots would the next card have?" (32)

Main Activity (~25 min)

1. With the five volunteers still holding their cards, explain: "We can make numbers by turning some cards face down (hiding the dots) and adding up the dots that are still showing."
2. Practice as a whole class:
3. Ask the five volunteers to show the number 6 (they should show the 4-dot and 2-dot cards, turn the rest face down).
4. Try 15 (8, 4, 2, and 1 dot cards showing).
5. Try 21 (16, 4, and 1 dot cards showing).
6. Explain the code: When a card is face down (hidden), it is written as a 0. When it is showing, it is written as a 1. This string of 0s and 1s is a binary number.
7. Ask the class to figure out what number 01001 represents in normal counting (decimal). (Answer: 9)
8. Ask what 17 would look like in binary. (Answer: 10001)
9. Try a couple more examples together until most students seem comfortable with the idea.
10. Hand out each student's own set of five cut-out cards (from the Photocopy Master) and the Binary Numbers worksheet (page 5).
11. Have students work individually or in pairs to:
12. Lay their cards out in order with the 16-dot card on the left.
13. Flip cards to show exactly 5 dots.
14. Find ways to make 3, 12, and 19 using their cards.
15. Discuss with a partner: Is there more than one way to make any number? What is the biggest number they can make? What is the smallest?

Wrap-up / Exit Ticket (~10 min)

1. Bring the class back together. Ask a few students to share what numbers they made and how they flipped their cards.
2. Ask the class as a whole:
3. "What is the biggest number you can make with five cards?" (31)
4. "What is the smallest?" (0)
5. "Is there any number between 0 and 31 that you couldn't make?" (No — every number in between can be made.)
6. Exit Ticket: On a small piece of paper, have each student write down how they would make the number 9 using their cards (which cards would show dots: 8 and 1). Collect these as they leave or place them in a basket.

If Time Remains

Have students attempt the "Extra for Experts" challenge from the worksheet: try making the numbers 1, 2, 3, and 4 in order using their cards, flipping as few cards as possible each time. Ask if they can describe a reliable method or pattern for increasing any number by one using the cards.