Column Multiplication: 42 × 13

Overview

This animation demonstrates the standard long multiplication algorithm for $42 \times 13$. It shows step-by-step multiplication of the multiplicand by each digit of the multiplier, including explicit carry digits, a zero placeholder in the second partial product, and the final addition to yield $546$. The key takeaway is a clear visual breakdown of the column method with attention to place value and carrying.

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Phases

#	Phase Name	Duration	Description
1	Setup	~3s	Display the problem $42 \times 13$ in a vertical column format with a multiplication line. Numbers are right-aligned. A caption reads "42 × 13".
2	Multiply by Units (3)	~8s	Highlight the units digit 3 of the multiplier and the units digit 2 of the multiplicand. Show $2 \times 3 = 6$ and write 6 in the units column of the first partial product row. Then highlight the tens digit 4 (multiplicand) and the 3 again. Show $4 \times 3 = 12$. Write 2 in the tens column and display a small carry digit 1 above the hundreds column. The partial product $126$ is now fully written. Caption updates: "2 × 3 = 6", then "4 × 3 = 12, carry 1".
3	Multiply by Tens (1)	~8s	Draw a zero placeholder in the units column of the second partial product row (to show alignment for tens multiplication). Highlight the tens digit 1 of the multiplier and the units digit 2 of the multiplicand. Show $2 \times 1 = 2$ and write 2 in the tens column. Then highlight the tens digit 4 and the 1. Show $4 \times 1 = 4$ and write 4 in the hundreds column. The second partial product $420$ is complete (with the trailing zero). Caption updates: "Add zero placeholder", "2 × 1 = 2", "4 × 1 = 4".
4	Add Partial Products	~5s	Underline the two rows and show the addition of $126 + 420$. Step-by-step: highlight units $6+0=6$, then tens $2+2=4$, then hundreds $1+4=5$. Reveal the final sum $546$ below the line. Caption: "126 + 420 = 546".

Total duration: ~24 seconds

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Layout

┌─────────────────────────────────────────────┐
│                                             │
│              MAIN (column multiplication)    │
│                                             │
├─────────────────────────────────────────────┤
│  Caption / step label (bottom strip)        │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Main	The full column layout: multiplicand 42 on top, multiplier 13 below, multiplication line, first partial product row (126), second partial product row (420 with zero placeholder), automatic alignment of digits by place value. Carry digits appear as small numbers above the appropriate column (e.g., a "1" above the hundreds column). Highlighting (color change or bounding box) focuses on digits currently being operated on.	This area occupies about 80% of the frame vertically. All numbers are right-aligned. Use a monospaced or clear font.
Caption	A single line of text at the bottom that describes the current step, e.g., "2 × 3 = 6", "Carry 1", "Add zero placeholder", "126 + 420 = 546".	The caption changes with each sub-step. It is always visible and centered.

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Notes

• Carry digits: When $4 \times 3 = 12$, a small "1" appears above the hundreds column (above the empty space to the left of the tens digit of 42). It is placed close to the column and disappears once the partial product is fully written.
• Zero placeholder: The zero in the units column of the second row (420) is shown explicitly by writing a "0" after the multiplication by the tens digit begins. Alternatively, the second row can be shown as "42" shifted left, but the zero placeholder makes the alignment clear.
• Highlighting: Each digit involved in a multiplication or addition step is briefly highlighted (e.g., with a colored box or a glow). The highlight moves sequentially.
• Transitions: All digit appearances are instantaneous (written in) or fade-in; no complex transformations. The carry digit fades in and out.
• No code or audio is specified; focus purely on visual animation steps.
• Timekeeping: The durations per phase are estimates and can be adjusted slightly to maintain a comfortable pace. The total animation stays well under 30 seconds.