Design a page grid with ratios, margins and gutters
Subtract margins and gutters before sharing width · Allocate remaining space in a stated column ratio · Distinguish linear print scaling from area scaling
Section Paper 2 · Historical Extended · non-calculator
Exam scope and assessment notes
Extended content; not a Core requirement. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Ratios
- Length units and similar-area scales
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Subtract margins and gutters before sharing width
- Allocate remaining space in a stated column ratio
- Distinguish linear print scaling from area scaling
Budget the whole width
A page grid includes content columns, margins and gutters between columns. For three columns there are two internal gutters, not three. Subtract all fixed spaces from the overall width, then divide the remaining width into the ratio parts. Check by adding columns and spaces back to recover the page width. If the remaining width is zero or negative, the proposed layout cannot have positive-width columns.
Scale the complete layout
On a 200 mm card with no outer margins, two 10 mm gutters leave 180 mm for columns in ratio 1:2:1. One part is 45 mm, so columns are 45, 90 and 45 mm. If the whole design is scaled by factor k, every length including gutters and margins scales by k, while rectangular area scales by k². Scaling only the columns would not preserve the full layout proportions.
Sources for this lesson
Pause and explain
How many internal gutters separate three adjacent columns?
Worked example
A 200 mm card with no margins has three columns in ratio 1:2:1 and two 10 mm gutters. Find the column widths.
Show the worked solution
- Usable column width=200−20=180 mm.
- Four ratio parts give 45 mm per part.
Answer 45 mm, 90 mm, 45 mm.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find the widths of the three 1:2:1 columns on the 200 mm card with two 10 mm gutters and no margins.
Give me a hint
Share 180 mm in four parts.
Compare my reasoning
- One part=180/4=45 mm.
- The widths sum to 180 mm; gutters restore 200 mm.
45 mm, 90 mm, 45 mm.
Look for these in your work
- Budget gutters first
- Check the full width
A 300 mm poster has 20 mm left and right margins and two equal columns separated by a 20 mm gutter. Find each column width.
Give me a hint
Subtract both margins and the one gutter.
Compare my reasoning
- Usable width=300−40−20=240 mm.
- Each equal column is 120 mm.
120 mm each.
Look for these in your work
- Count fixed spaces correctly
- Verify the total
A 210 mm by 100 mm card has 15 mm left and right margins, two 10 mm gutters, and three columns in ratio 2:3:3. Find column widths, then their widths and total card area when the entire card is printed at scale 0.8.
Give me a hint
First share 160 mm; then scale all lengths.
Compare my reasoning
- Eight parts give original columns 40, 60, 60 mm; scaled columns are 32, 48, 48 mm.
- Scaled card dimensions are 168 by 80 mm; area=13 440 mm², or 0.64 of 21 000 mm².
Columns 40, 60, 60 mm; scaled 32, 48, 48 mm; scaled card area 13 440 mm².
Look for these in your work
- Scale margins and gutters too
- Square the factor for area
Common mistakes
- Subtract all fixed spaces before applying the ratio.
- A linear scale is not the area scale.
What can you explain now?
How many internal gutters separate three adjacent columns?
Compare with the explanation
Two.
There is one gap between each adjacent pair.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
How many internal gutters separate three adjacent columns?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.