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Technologies K–10 · Years 5–6

Binary cards: counting with on and off

Digital Technologies (NSW Science and Technology K–6, 2017); Digital Technologies: Knowledge and understanding, Data representation (ACARA v9)

Practical, model not builtLow risk

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The idea

Five cards showing 1, 2, 4, 8 and 16 dots, each either face up (1) or face down (0), make every whole number from 0 to 31 in exactly one way, which is how digital systems store numbers as off and on states.

What you need

  • 5 binary cards per group showing 1, 2, 4, 8 and 16 dots on one side and blank on the back
  • 3 extra cards showing 32, 64 and 128 dots
  • Mini whiteboard and marker

How to do it

  1. Lay the 5 cards in a row, dots up, with 16 on the left and 1 on the right. Notice each card has twice the dots of the card to its right.
  2. Turn cards face down so the dots showing add up to 5. Write the pattern as 1 for face up and 0 for face down.
  3. Make 13, 21 and 31 the same way and write each pattern.
  4. Count from 0 to 31 by adding one dot each time. Watch how often each card flips.
  5. Find the largest number the 5 cards can make, then add the 32, 64 and 128 cards and find the new largest number.
  6. Give a partner a 5-digit pattern of 0s and 1s to turn into a number, and check each other's answers.

What you should see

5 = 00101, 13 = 01101 (8 + 4 + 1), 21 = 10101 and 31 = 11111, the largest number 5 cards can make. Every number from 0 to 31 has exactly one pattern, 32 patterns in all. When counting, the 1-card flips every step, the 2-card every second step, the 4-card every fourth. With 8 cards the largest number is 255, so one byte (8 bits) holds 256 different values. The learner knows it worked when every number they make can be checked by adding the dots showing.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

  • Binary numbers are a code that computers translate into 'real' numbers (they are the same numbers written in base 2).
  • More cards make each card worth more (each new card doubles the largest number but the existing cards keep their values).
  • 1 and 0 mean yes and no only (they are digits in a place-value system).

Safety card

Low riskLearners carry it out

Hazards

  • None beyond normal classroom activity

Controls

  • Not applicable

Note

No chemicals or heat.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

  • Science and Technology K–6 Syllabus (2017), NESA. The syllabus taught in 2026; the 2024 syllabus replaces it from 2027. Code read from the official syllabus document (DOCX) on 2026-09-22.ST3-11DI-T
  • Science and Technology K–6 Syllabus (2024), NESA. Implementation from 2027, so this code describes the future syllabus. Code read from the outcomes page on 2026-09-22.ST3-DDT-02
  • Australian Curriculum v9AC9TDI6K04AC9TDI6K03

Sources

The pages the author read to write this activity.

  1. www.nsw.gov.au/education-and-training/nesa/curriculum/science/science-and-technology-k-6-2017
  2. curriculum.nsw.edu.au/learning-areas/science/science-and-technology-k-6-2024/outcomes
  3. www.csunplugged.org/en/topics/binary-numbers
  4. classic.csunplugged.org/activities/binary-numbers
  5. www.digitaltechnologieshub.edu.au/teach-and-assess/classroom-resources/lesson-ideas/introduction-to-binary
  6. digitaltechnologieshub.edu.au/plan-and-prepare/scope-and-sequence-f-10/5-6-binary-numbers

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