📚 OpenKernel EDU3D3D

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Teaching the visible machine

Arithmetic and Input

Build integer calculations with saved inputs and test cases.

Total classroom time: 135 minutes · 3 × 45 minutes

Learning outcomes

  • Translate an ordered expression into accumulator operations.
  • Save input before destructive operations.
  • Distinguish negative floor division and signed remainder.
  • Test a two-input calculator with zero/negative cases.

Before class

queue demonstration integers 3 and 4; supply number lines for negatives. Explicitly note that this machine's floor DIV and JavaScript signed MOD are separate rules: for negative operands, their returned pair is not the usual quotient/remainder identity. Never teach −9 = (−3×4)+(−1).

Three-session plan

Session 1: Emoji Math · 45 minutes

Focus: calculate (x+5)×2−4

Checkpoint: x=−3 yields 0 without a fixed answer.

Session 2: Division and Remainders · 45 minutes

Focus: save/restore the original for DIV 4 and MOD 4

Checkpoint: −9 gives −3 then −1, zero divisor produces an actionable error.

Session 3: A Two-input Calculator · 45 minutes

Focus: preserve a and b

Checkpoint: (−2,5) yields 3 then −10.

Support and differentiation

show R0/R1 as separate paper boxes and write one operation per line.

Extend the thinking

devise a new zero/negative test and explain why reloading a is required before multiplication.

Assessment evidence

working variable-input calculator and a short explanation of accumulator overwrite; assess correct machine rules, not an invented division convention.

Print student worksheetView answer key

Curriculum mapping notes

OpenKernel EDU aligns with concepts in the following frameworks. These connections support teacher planning. Check your current local grade or course expectations and assessment requirements when selecting activities.

Ontario

Coding and computational thinking in elementary mathematics; algorithms, programming, data representation and computer systems in secondary computer studies/digital technology contexts.

Units 1–3 address state/data/computers, 4–8 sequence/control/algorithm/debugging/representation, and 9–10 decomposition/systems/projects. Select actual grade/course expectations locally. This model does not establish coverage of all mathematical, digital citizenship, hardware-building or networking outcomes.

British Columbia

Applied Design, Skills and Technologies learning through designing, testing and refining solutions; secondary computer studies/programming concepts involving algorithms, data and computer systems.

Units 4–10 support iterative program design and explanation; units 1–3, 8 and 9 support data/state/system representation. Paper design, trace evidence and reflection make the process visible. Check current grade/course wording; not every ADST competency is covered.

Alberta

Computing science in applicable science/programming contexts; senior-high Career and Technology Studies Computing Science (CSE) concepts in algorithms, structured programs, data and systems.

Units 1–8 develop state, control and abstraction; units 9–10 apply decomposition and testing. Check the current program of studies and course requirements when deciding which activities suit your class.

Selected CSTA 2017 connections

These concept references use the CSTA 2017 framework. Check the current adopted edition and the full standard’s grade-level scope before using an identifier in a formal school mapping.

  • 1B-AP-10 — Sequences, events, loops and conditionals in programs. Aligns with units 1, 4, 5, 9 and 10. Simulated events are distinguished from a physical-device event system.
  • 2-AP-12 — Combinations of control structures in programs. Aligns with units 4–7 and 10 through decisions, loops and calls. Use the complete standard when planning work on compound conditionals or other nested control structures.
  • 2-AP-13 — Decomposing problems and subproblems into manageable parts. Aligns with units 6, 7, 9 and 10 through algorithm roles, reusable services and partitioned work.
  • 2-AP-14 — Reusable procedures and parameters for organizing code. Aligns with units 7 and 10. The VM uses register-passed input/result conventions, rather than high-level parameter declarations.
  • 2-AP-17 — Systematic testing and refining with a range of test cases. Aligns with checked challenges when paired with prediction, debugging explanations and varied cases. A pass alone does not demonstrate the complete standard.

Units 1–3, 8 and 9 also connect to the Computing Systems concept. Algorithm, state, debugging, abstraction and control describe the ideas taught in this resource; consult the local framework for its expectation names and scope.

Official source landing links

Use these official landing pages to check the current adopted edition and local grade or course expectations.