The shape of the lesson
By the end of the lesson, learners can
- Filling in a trace table: Load a program in the lab, enter the test data and step through it line by line.
- Loops and selection: With a FOR loop, the loop counter gets its own column.
- Post-condition loops and DIV/MOD: This algorithm adds up the digits of a whole number.
- Columns: one per variable, plus OUTPUT (prompts too).
- Rows: move down as the algorithm moves on; record a value only when it changes.
- Conditions: test each one with the current values, every time.
- Loops: WHILE tests first (may run 0 times); REPEAT tests last (runs at least once).
One picture every idea returns to
A dry run is working through an algorithm by hand with given test data. A trace table has a column for each variable and one for OUTPUT (including user prompts). Work line by line: write a new value in the column only when it changes, move down a row as the algorithm moves on, and follow every condition and loop exactly as written, not as you think the programmer meant.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Be the computer.. A dry run means working through an algorithm by hand, one line at a time, exactly as the computer would. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Filling in a trace table | Load a program in the lab, enter the test data and step through it line by line. Project tab 1 of the lab (Programs with a live trace table) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Loops and selection | With a FOR loop, the loop counter gets its own column. Model the worked example Trace with input 6 on the board, one line at a time. Your turn: Dry-run the same algorithm with the input 7. What are the four outputs? | Pairs |
| 21 to 30 min | Teach and check: Post-condition loops and DIV/MOD | This algorithm adds up the digits of a whole number. Model the worked example Input 4071 on the board, one line at a time. Your turn: What is output for the input 9005, and how many times does the loop run? | Round Table |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 18 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Post-condition loops and DIV/MOD, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Round Table
One sheet travels round the team. Each student adds one line of working or one idea and passes it on, so the solution is built four hands at a time and every contribution is visible.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| The rogue value -1 is input and recorded in the trace table, but the loop ends before it is processed. | Do not add it to the total. |
| Use the new value of a variable on the next line. | After Number becomes 3, the OUTPUT on the same pass shows 3, not 6. |
| A REPEAT loop always runs at least once, because the condition is tested at the end. | With input 0 this algorithm still runs once and outputs 0. |
Dry-running algorithms with trace tables: worksheet
6 questions, 18 marks. Written in the style of the papers; no past paper question is reproduced.
Complete a trace table for this algorithm.
A ← 1
B ← 1
FOR I ← 1 TO 4
C ← A + B
A ← B
B ← C
OUTPUT C
NEXT IDry-run the digit-sum algorithm from this lesson with the input 608. Give the values of Digit, Sum and Number after each pass, and the output.
Complete a trace table for this algorithm with the inputs 15, 40, 25, 0.
Max ← 0
Total ← 0
INPUT Value
WHILE Value <> 0 DO
Total ← Total + Value
IF Value > Max
THEN
Max ← Value
ENDIF
INPUT Value
ENDWHILE
OUTPUT Total, " ", MaxState the values of DIV(29, 4) and MOD(29, 4).
Dry-run this algorithm and state each output.
Count ← 10
REPEAT
IF Count > 5
THEN
Count ← Count - 3
ELSE
Count ← Count - 1
ENDIF
OUTPUT Count
UNTIL Count <= 2Explain why a trace table is useful when testing an algorithm.
Answer key and marking notes
- I = 1: C = 2, A = 1, B = 2, output 2.
- I = 2: C = 3, A = 2, B = 3, output 3.
- I = 3: C = 5, A = 3, B = 5, output 5.
- I = 4: C = 8, A = 5, B = 8, output 8.
- Pass 1: Digit 8, Sum 8, Number 60.
- Pass 2: Digit 0, Sum 8, Number 6; Pass 3: Digit 6, Sum 14, Number 0.
- Output 14.
- Value 15: Total 15, Max 15.
- Value 40: Total 55, Max 40.
- Value 25: Total 80 (Max stays 40).
- Value 0 ends the loop; output 80 40.
- DIV(29, 4) = 7.
- MOD(29, 4) = 1.
- 10 > 5: Count 7, output 7. 7 > 5: Count 4, output 4.
- 4 is not > 5: Count 3, output 3.
- 3 is not > 5: Count 2, output 2; 2 <= 2 so the loop stops. Outputs: 7, 4, 3, 2.
- It shows the value of each variable (and each output) at every step of the algorithm.
- So the actual results can be compared with the expected results, and the line where an error happens can be found.
6 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
What are the values of DIV(58, 8) and MOD(58, 8)?
- A7 and 2
- B2 and 7
- C7.25 and 2
- D7 and 0.25
What is output by this algorithm?
X ← 3
Y ← 0
FOR I ← 1 TO 4
Y ← Y + X
X ← X - 1
NEXT I
OUTPUT X, " ", Y- A-1 6
- B0 6
- C-1 10
- D-1 2
The inputs are 60, 50, 75, 0, 90. What is output?
Count ← 0
INPUT Number
WHILE Number > 0 DO
IF Number > 50
THEN
Count ← Count + 1
ENDIF
INPUT Number
ENDWHILE
OUTPUT Count- A2
- B3
- C4
- D1
What is output by this algorithm?
N ← 20
REPEAT
N ← N - 7
OUTPUT N
UNTIL N < 5- A13, 6, -1
- B13, 6
- C20, 13, 6
- D13, 6, -1, -8
The input is 3070. What is output?
INPUT Number
Result ← 0
WHILE Number > 0 DO
Result ← Result * 10 + MOD(Number, 10)
Number ← DIV(Number, 10)
ENDWHILE
OUTPUT Result- A703
- B3070
- C7030
- D73
What is output by this algorithm?
A ← 0
B ← 1
FOR I ← 1 TO 5
IF MOD(I, 2) = 0
THEN
A ← A + I
ELSE
B ← B * I
ENDIF
NEXT I
OUTPUT A, " ", B- A6 15
- B9 8
- C15 6
- D6 0
Quiz key
58 = 7 × 8 + 2, so DIV(58, 8) = 7 and MOD(58, 8) = 2. Swapping the two mixes up quotient and remainder. 7.25 is the ordinary division 58 / 8, which DIV does not give. The remainder is a whole number, 2, not the decimal part 0.25.
Y gains 3, 2, 1 and 0 (Y = 3, 5, 6, 6) while X goes 2, 1, 0, -1, so the output is -1 6. "0 6" stops reducing X one pass too early. "-1 10" adds 4 + 3 + 2 + 1, as if X started at 4. "-1 2" reduces X before adding it to Y, the reverse of the order of the two lines.
60 and 75 are greater than 50; 50 is not (the test is > 50, not >= 50). The input 0 makes Number > 0 false, so the loop ends and 90 is never read: Count = 2. 3 counts either 50 or 90. 4 counts both. 1 stops after the first input.
Pass 1: N = 13, output 13, 13 < 5 false. Pass 2: N = 6, output 6, false. Pass 3: N = -1, output -1, -1 < 5 true, so the loop stops. Stopping at 6 tests the condition before the output, as if it were a WHILE loop. 20 is never output because N is reduced first. -8 would need a fourth pass after the condition was already true.
Pass 1: digit 0, Result 0, Number 307. Pass 2: digit 7, Result 7, Number 30. Pass 3: digit 0, Result 70, Number 3. Pass 4: digit 3, Result 703, Number 0, so the loop ends. The algorithm reverses the digits, and the leading zero of 0703 is not kept in an integer, so 703 is output. 3070 is the input unchanged. 7030 swaps pairs of digits instead of reversing. 73 ignores the 0 digits, but Result is still multiplied by 10 on the pass where the digit is 0.
Even I (2 and 4) are added to A: A = 6. Odd I (1, 3, 5) multiply B: B = 1 × 1 × 3 × 5 = 15. Output 6 15. "9 8" sends odd values to A and even to B, reversing the condition. "15 6" outputs the values in the wrong order. "6 0" assumes B starts at 0, but it starts at 1, so the products are not wiped out.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.