Teacher answer key

Arithmetic and Input

Gather four kinds of evidence: prediction of relevant state; behavior across varied cases including boundaries; explanation using trace/state evidence; and a reasoned correction of one mismatch. Mark each as emerging, with support or independent using paper or your school’s existing approved process. A challenge pass is machine-behavior evidence, not proof of authorship or complete mastery. Accept equivalent correct programs; the public key is a model, not the only possible answer.

Public teaching material. Solutions are examples; equivalent correct programs may also pass the actual checks.

4. Emoji Math

Combine addition, subtraction, and multiplication as ordered steps.

Open this lesson →

1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

LOAD 10
ADD 5
PRINT
MUL 2
SUB 4
PRINT
HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 15, 26

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	10	`{"registers":[10,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
ADD	1	2	10	15	`{"registers":[15,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
PRINT	2	3	15	15	`{"registers":[15,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	15

2. Build and check

Read one integer x and print (x + 5) × 2 − 4. Your program must work for every supplied input, including negative numbers.

Required instruction types: INPUT, ADD, MUL, SUB

Example challenge solution

INPUT
ADD 5
MUL 2
SUB 4
PRINT
HALT

Actual checker fixtures

Case 1

Input: 0
Initial memory: All bytes initially zero
Expected output: 6

Case 2

Input: -3
Initial memory: All bytes initially zero
Expected output: 0

Case 3

Input: 12
Initial memory: All bytes initially zero
Expected output: 30

3. Explain the machine

Why is MUL after ADD necessary for (x+5)×2−4?

Reasoning and teaching note

Each operation modifies the accumulated result; reversing ADD/MUL changes the expression for most x.

5. Division and Remainders

Explain floor division and signed remainder, including negatives.

Open this lesson →

1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

LOAD -9 R1
LOAD R1
DIV 4
PRINT
LOAD R1
MOD 4
PRINT
HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: -3, -1

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	0	`{"registers":[0,-9,0,0,0,0,0,0],"flags":{"zero":false,"negative":true,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
LOAD	1	2	0	-9	`{"registers":[-9,-9,0,0,0,0,0,0],"flags":{"zero":false,"negative":true,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
DIV	2	3	-9	-3	`{"registers":[-3,-9,0,0,0,0,0,0],"flags":{"zero":false,"negative":true,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None

2. Build and check

Read an integer. Print its floor quotient by 4, then its signed remainder by 4. Keep the original long enough to calculate both.

Required instruction types: INPUT, DIV, MOD, COPY

Example challenge solution

INPUT
COPY R0 R1
DIV 4
PRINT
LOAD R1
MOD 4
PRINT
HALT

Actual checker fixtures

Case 1

Input: 18
Initial memory: All bytes initially zero
Expected output: 4, 2

Case 2

Input: -9
Initial memory: All bytes initially zero
Expected output: -3, -1

Case 3

Input: 0
Initial memory: All bytes initially zero
Expected output: 0, 0

3. Explain the machine

Why save the original input before calculating the quotient?

Reasoning and teaching note

DIV overwrites R0; reload original before MOD. For−9, documented floor quotient−3 and signed remainder−1 are distinct rules.

6. A Two-input Calculator

Build a reusable calculator instead of a fixed answer.

Open this lesson →

1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

INPUT
COPY R0 R1
INPUT
COPY R0 R2
LOAD R1
ADD R2
PRINT
LOAD R1
MUL R2
PRINT
HALT

Queue input: 3, 4

Initialize memory: All bytes initially zero

Try prediction key

Output: 7, 12

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
INPUT	0	1	0	3	`{"registers":[3,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
COPY	1	2	3	3	`{"registers":[3,3,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
INPUT	2	3	3	4	`{"registers":[4,3,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None

2. Build and check

Read integers a and b. Print their sum and then their product. Use the supplied values rather than fixed answers.

Required instruction types: INPUT, ADD, MUL

Example challenge solution

INPUT
COPY R0 R1
INPUT
COPY R0 R2
LOAD R1
ADD R2
PRINT
LOAD R1
MUL R2
PRINT
HALT

Actual checker fixtures

Case 1

Input: 3, 4
Initial memory: All bytes initially zero
Expected output: 7, 12

Case 2

Input: -2, 5
Initial memory: All bytes initially zero
Expected output: 3, -10

Case 3

Input: 0, 8
Initial memory: All bytes initially zero
Expected output: 8, 0

3. Explain the machine

What mistake occurs if you multiply immediately after printing the sum?

Reasoning and teaching note

PRINT leaves R0 at a+b; multiplying by b then gives(a+b)b. Reload a for ab.