Flip, Fold, Represent

Overview

Students create a paper “flippy do” using eight folding sections to represent the binary place values 1, 2, 4, 8, 16, 32, 64 and 128. They use it to investigate how digital systems represent numbers with two states, then participate in a short binary showcase by decoding and explaining examples.

Learning intentions

Students will:

• Explain that binary uses only two states: 0 and 1.
• Identify the powers of 2 from (2^0) to (2^7), representing values up to 128.
• Construct and use a physical binary representation.
• Connect a practical model to how digital technologies store and communicate information.

Success criteria

• I can describe what the two sides of a binary flap represent.
• I can label the eight place values correctly: 1, 2, 4, 8, 16, 32, 64 and 128.
• I can represent a decimal number using open and closed flaps.
• I can explain how adding selected place values gives the represented number.

Curriculum links

• Digital Technologies — understanding how digital systems represent and process information.
• Digital Technologies — developing computational thinking through decomposition, pattern recognition and representation.
• Technology — planning, making and evaluating a practical outcome for a specified purpose.
• Key competencies — thinking; managing self; participating and contributing; using language, symbols and texts.

Lesson structure (55 minutes)

1. 0–6 min · Retrieval: Flippy Do learning. Teacher asks students to recall how the Flippy Do represented values using two states and prompts: “What did 1 mean?” “What did 0 mean?” and “How did the place values change?” Students sketch or explain one Flippy Do example, then retrieve the place-value sequence 1, 2, 4, 8. Formative checkpoint: listen for the idea that a 1 includes a value and a 0 excludes it. Address the misconception that 0 means “nothing is represented” rather than “this value is not included.”

2. 6–14 min · Model binary place values. Teacher introduces the CS Unplugged binary-card investigation and models four cards labelled 8, 4, 2 and 1, linking them to 1, 2, 4 and 8 bit values. Demonstrate that each card can be face up/on or face down/off and that four cards can represent denary numbers from 0 to 15. Model 13 as 8 + 4 + 1, giving 1101 when read from largest to smallest value. Students predict the values for selected card patterns and explain the difference between a bit’s value and the number of bits. Formative checkpoint: students show thumbs up/down for whether each card is included. Address misconceptions about reversing bit order and confusing “an 8 bit” with “eight bits.”

3. 14–25 min · Pair investigation: represent denary numbers. In pairs, students use four binary cards marked 8, 4, 2 and 1. One student names or draws a denary number from 0–15; the other represents it with the cards and records the 4-bit pattern from 8 to 1. Partners check the total, then swap roles. Include 0, numbers requiring a zero in the middle, and numbers such as 5, 10 and 15. Teacher circulates and asks, “Which values are switched on?” and “How do you know every position is accounted for?” Formative checkpoint: check that students always record four bits, including leading zeroes, and read in the agreed order.

4. 25–36 min · Conversion practice. Teacher models both directions: binary-to-denary by adding values where the bit is 1, and denary-to-binary by selecting the largest available value and filling unused positions with 0. Students complete a short paired practice set, such as 0101, 1010, 0111, 1001 and denary values 3, 6, 12 and 14. Partners explain one answer to another pair or the teacher. Formative checkpoint: pause after one example to diagnose whether students are adding bit positions, reading the pattern backwards, or omitting zero positions.

5. 36–45 min · Apply the idea to digital devices. Teacher connects the investigation to digital systems: devices use bits and groups of bits to represent numbers and can use agreed patterns to represent text, images, sound or instructions. Students discuss and record one example of information a device could represent with binary, explaining that the pattern is a representation interpreted using rules. Briefly compare the four-card model with larger groups of bits, including 8-bit values from 0 to 255. Formative checkpoint: students complete the sentence, “A bit is ___, while the value of a bit position is ___.”

6. 45–55 min · Consolidation and exit ticket. Students complete an individual exit ticket: (a) write the 4-bit binary pattern for denary 11; (b) convert 1001 to denary; (c) explain why the answer for denary 2 is 0010 rather than 10; and (d) state one way digital devices use binary to represent information. Teacher collects responses and notes students needing further practice with bit order, zeroes, or place values. If time allows, students explain conceptually how 8-bit patterns could support ASCII characters or how hexadecimal provides a shorter way to write binary patterns.

Resources

• the binary hook, teaching, challenge and plenary deck
• the binary flippy-do construction and practice sheet
• A4 paper or thin card, one sheet per student
• Pens or fine felt-tip pens
• Scissors, shared between pairs
• Teacher-prepared model flippy do
• Board or projected display
• Optional timer for construction and challenge phases

Assessment

• Retrieval checkpoint (0–6 min): Listen for accurate explanations of the Flippy Do model, including that 1 means a value is included and 0 means it is excluded. Record students who cannot recall the place-value pattern 1, 2, 4, 8.
• Modelling checkpoint (6–14 min): Check that students can identify the value of each 4-bit card, explain that each position has a different value, and distinguish the value of a bit position from the number of bits in a group. Watch for reversed bit order.
• Investigation checkpoint (14–25 min): Check paired representations for correct use of all four positions, including leading and internal zeroes. Question students about how their selected values total the target denary number.
• Conversion checkpoint (25–36 min): Review paired practice for accurate binary-to-denary addition and denary-to-binary selection. Identify whether errors result from reading the cards in the wrong order, treating 0 as an absent position, or adding positions rather than their values.
• Application checkpoint (36–45 min): Assess whether students understand binary as a representation system used by digital devices and can give a relevant example of represented information.
• Exit ticket (45–55 min): Assess 4-bit denary-to-binary conversion, binary-to-denary conversion, the need to retain zeroes, and the connection between binary and digital information. Use responses to plan a follow-up mini-lesson or targeted practice.
• Support and extension evidence: Provide a completed value strip or partially completed pattern for students who need support. Extend students with 8-bit values, a conceptual introduction to ASCII character codes, or the idea that hexadecimal compactly represents groups of binary bits.

Differentiation

• Provide a completed place-value strip or partially labelled model for students who need construction support. Keep the values visible: 128, 64, 32, 16, 8, 4, 2, 1.
• Pair students strategically, with roles such as maker/checker or setter/decoder. Use oral rehearsal before students write explanations.
• For EAL learners, use the visual terms “on/off”, “1/0”, “include/not include” and sentence starters: “The number is ___ because I added ___.”
• Extend confident students by asking them to find two different binary patterns whose values differ by one, or to explain why eight binary positions can represent numbers from 0 to 255, even though this lesson focuses on values up to 128.