Two-dimensional arrays and nested loops pack

At a glance

The shape of the lesson

Topic

Programming

Syllabus reference

Cambridge IGCSE Computer Science 0478, 8.2

Level

IGCSE

Duration

45 minutes, lab-led; stretches to a 60 minute block (see the contingency notes)

Position in topic

Lesson 10 of 11 in Programming; follows One-dimensional arrays; leads into Reading from and writing to files

Central model

Fig. 1: a 2D array of sales for 3 shops (rows) over 4 weeks (columns)

Cooperative structure

Mix-Pair-Share

Assessment

Stage 1 check and the exam-style plenary from the student lesson, plus the worksheet as the exit task

Learning objectives

By the end of the lesson, learners can

Section by section

Declaring a 2D array: The two bounds in the declaration give the number of rows and the number of columns.
Nested loops: In the lab, choose 2D array with nested loops.
Column totals and grand totals: Swap the loops to work down each column instead of across each row.

Key points to leave on the board

Declare: ARRAY[1:rows, 1:columns] OF type.
Access: Name[Row, Column]; elements = rows × columns.
Nested loops: the inner loop completes for each pass of the outer loop.
Totals: reset a row total inside the outer loop, before the inner loop.

The core visual model

One picture every idea returns to

A two-dimensional (2D) array is a table of elements of the same data type, with two indexes: one for the row and one for the column. Declare it with two sets of bounds: DECLARE Sales : ARRAY[1:3, 1:4] OF INTEGER (3 rows, 4 columns, 12 elements). Access an element with Sales[Row, Column]. To process every element, use nested loops: the inner loop runs completely for every pass of the outer loop.

Fig. 1: a 2D array of sales for 3 shops (rows) over 4 weeks (columns)

Lesson sequence

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, Rows and columns.. Some data comes as a table: sales for each shop in each week, a noughts and crosses board, marks for each student in each test. 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: Declaring a 2D array	The two bounds in the declaration give the number of rows and the number of columns. Your turn: Using the table, what are Sales[3, 1] and Sales[1, 4], and how many elements does Sales have?	Whole class, then pairs
13 to 21 min	Teach and check: Nested loops	In the lab, choose 2D array with nested loops. Project tab 6 of the lab (2D arrays with nested loops) and let a student drive it while the class predicts. Model the worked example Row totals on the board, one line at a time.	Pairs
21 to 30 min	Teach and check: Column totals and grand totals	Swap the loops to work down each column instead of across each row. Model the worked example Column totals on the board, one line at a time. Your turn: A 2D array is declared ARRAY[1:5, 1:6]. How many times does the statement inside a pair of nested loops over every element run?	Mix-Pair-Share
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, 17 marks). Learners self-assess against the objectives before they leave.	Individual

Timing and contingency

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 Column totals and grand totals, 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.

Running the cooperative task

Mix-Pair-Share

Students mix around the room until you call pair; they pair with the nearest classmate, discuss the prompt, then mix again. Three prompts of rising difficulty, three different partners.

The full structure, with its variations and the other twelve, is on the cooperative-learning page.

Examiner traps to pre-empt

What to head off, and how

Trap learners fall into	Teaching move that pre-empts it
Do not swap the indexes.	Sales[3, 2] is row 3, column 2 (the value 1), but Sales[2, 3] is row 2, column 3 (the value 4).
RowTotal ← 0 must be inside the outer loop but before the inner loop.	Outside both loops, each row's total would include the rows before it.

Worksheet

Two-dimensional arrays and nested loops: worksheet

6 questions, 17 marks. Written in the style of the papers; no past paper question is reproduced.

NameClassDate

Q1 · explain[2 marks]

Describe a two-dimensional array.

Q2 · write[2 marks]

Write a declaration for a 2D array Seats that stores a CHAR for each seat in a cinema with 12 rows of 20 seats.

Q3 · trace[3 marks]

State the values stored and the output.

FOR R ← 1 TO 2
    FOR C ← 1 TO 3
        Grid[R, C] ← R * C
    NEXT C
NEXT R
OUTPUT Grid[2, 3], " ", Grid[1, 2]

Q4 · write[5 marks]

Marks[1:30, 1:4] stores 4 test marks for each of 30 students (one row per student). Write pseudocode that outputs each student's total mark.

Q5 · analysis[2 marks]

A student puts RowTotal ← 0 before both loops in a row-total program. Explain the effect on the output.

Q6 · apply[3 marks]

Using the Sales table in this lesson (3 shops by 4 weeks), state (a) Sales[1, 2] (b) the total for week 4 (c) the total for shop 2.

Answer key and marking notes

Q1 · 2 marks

A table-like data structure with rows and columns, under one identifier, all elements the same data type.
Each element is accessed with two indexes: row and column.

Q2 · 2 marks

DECLARE Seats : ARRAY[1:12, 1:20]
OF CHAR

Q3 · 3 marks

Row 1: 1, 2, 3.
Row 2: 2, 4, 6.
Output: 6 2

Q4 · 5 marks

FOR Student ← 1 TO 30
Total ← 0 inside the outer loop, before the inner loop
FOR Test ← 1 TO 4 ... NEXT Test
Total ← Total + Marks[Student, Test] inside the inner loop
OUTPUT Student, Total after the inner loop, then NEXT Student

Q5 · 2 marks

RowTotal is never reset between rows.
So each row's output is a running total that includes all previous rows; only the first row's total is correct.

Q6 · 3 marks

(a) 8
(b) 6 + 7 + 8 = 21
(c) 3 + 9 + 4 + 7 = 23

Quiz

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.

Assign in the app Run as a class game Topic question bank

Q11 mark

How many elements are in the array declared by DECLARE Seats : ARRAY[1:4, 1:6] OF CHAR?

Q21 mark

The 2D array Sales holds these values.

Sales	Column 1	Column 2	Column 3	Column 4
Row 1	14	9	12	7
Row 2	11	16	8	13
Row 3	5	10	15	6

What is output by OUTPUT Sales[2, 3]?

Q31 mark

How many times is OUTPUT "*" run?

FOR Row ← 1 TO 3
    FOR Column ← 1 TO 4
        OUTPUT "*"
    NEXT Column
NEXT Row

Q41 mark

Sales holds the values in the table.

Sales	Column 1	Column 2	Column 3	Column 4
Row 1	14	9	12	7
Row 2	11	16	8	13
Row 3	5	10	15	6

What is the second line output by this program?

FOR Row ← 1 TO 3
    RowTotal ← 0
    FOR Column ← 1 TO 4
        RowTotal ← RowTotal + Sales[Row, Column]
    NEXT Column
    OUTPUT "Shop ", Row, " total: ", RowTotal
NEXT Row

AShop 2 total: 48
BShop 2 total: 35
CShop 2 total: 90
DShop 2 total: 42

Q51 mark

Sales holds the values in the table.

Sales	Column 1	Column 2	Column 3	Column 4
Row 1	14	9	12	7
Row 2	11	16	8	13
Row 3	5	10	15	6

A student moves RowTotal ← 0 to before the outer loop.

RowTotal ← 0
FOR Row ← 1 TO 3
    FOR Column ← 1 TO 4
        RowTotal ← RowTotal + Sales[Row, Column]
    NEXT Column
    OUTPUT "Shop ", Row, " total: ", RowTotal
NEXT Row

What is the third line output?

AShop 3 total: 126
BShop 3 total: 36
CShop 3 total: 90
DShop 3 total: 48

Q61 mark

Grid holds the values in the table.

Grid	Column 1	Column 2	Column 3
Row 1	4	1	2
Row 2	9	5	8
Row 3	6	3	7

What is output?

Total ← 0
FOR Index ← 1 TO 3
    Total ← Total + Grid[Index, 4 - Index]
NEXT Index
OUTPUT Total

Quiz key

Q1: A

There are 4 rows and 6 columns, so 4 × 6 = 24 elements. 10 adds the bounds instead of multiplying. 6 is only the number of columns. 35 treats the bounds as running from 0 (5 × 7).

Q2: A

Sales[2, 3] is row 2, column 3, which holds 8. 10 is Sales[3, 2], with the indexes swapped. 16 is row 2, column 2. 12 is row 1, column 3.

Q3: A

The outer loop makes 3 passes and the inner loop runs 4 times in each, so the OUTPUT runs 3 × 4 = 12 times. 7 adds the loop counts. 4 counts only one pass of the outer loop. 3 counts only the outer loop.

Q4: A

On the second pass Row = 2 and the inner loop adds 11 + 16 + 8 + 13 = 48. 35 is the total of column 2, with rows and columns confused. 90 would be the running total of rows 1 and 2, which happens only if RowTotal is not reset. 42 is the total of row 1.

Q5: A

Because RowTotal is only set to 0 once, each output includes all rows so far: 42, then 42 + 48 = 90, then 90 + 36 = 126. 36 is the correct row 3 total from the original program. 90 is the second line. 48 is the row 2 total.

Q6: A

The elements used are Grid[1, 3] = 2, Grid[2, 2] = 5 and Grid[3, 1] = 6: the diagonal from top right to bottom left, total 13. 16 is the other diagonal, Grid[Index, Index] (4 + 5 + 7). 19 is the total of column 1. 7 is the total of row 1.

Lab and demo

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.

Tab 62D arrays with nested loops

Slides

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.

Also for this topic

Everything else you can use

Student lessonTwo-dimensional arrays and nested loops Practice pageWorked solutions, reveal one at a time Topic question bankEvery MCQ for Programming Revision notesOne page per lesson, with the traps Notes PDFPrint the topic notes Topic planProgramming: every lesson in order

Original work by the TheLucidSTEM team. The worksheet items are written in the style of the papers; no past paper question is reproduced.