Constructions and Tilings - Class 7 Mathematics (CBSE)
Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.
1. Why this chapter matters
Geometry becomes hands-on in this chapter. Students use ruler and compass to create accurate figures, then study tilings to see how shapes cover a plane without gaps or overlaps. It combines precision, pattern, and spatial reasoning.
In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.
2. Core ideas
Construction versus drawing
A drawing can be approximate. A construction uses geometric tools and rules to make a figure with required measurements or properties.
Compass and straightedge
A ruler draws straight lines and measures lengths. A compass transfers equal lengths and draws circles/arcs.
Tiling
A tiling covers a surface using repeated shapes without gaps or overlaps. Squares, equilateral triangles, and regular hexagons tile easily.
3. Rules and formulas to remember
- Full angle around a point: 360 degrees. Tile angles around a point must fill 360 degrees.
- Straight angle: 180 degrees. Used in line constructions.
- Square angle: 90 degrees. Four squares meet around a point.
- Equilateral triangle angle: 60 degrees. Six equilateral triangles meet around a point.
4. Worked examples
Example 1: Why do squares tile a floor?
Each square corner is 90 degrees. Four corners meet to make 360 degrees with no gap.
Example 2: Why do regular pentagons not tile by themselves easily?
A regular pentagon angle is 108 degrees, and 108 does not fit exactly into 360.
Example 3: Construct a circle of radius 4 cm.
Set compass opening to 4 cm, place needle at centre, rotate once.
Example 4: What tool transfers equal length without measuring repeatedly?
A compass.
5. Activity corner
Create paper cut-outs of squares, equilateral triangles, pentagons, and hexagons. Try covering a sheet without gaps. Record which shapes tile and explain using angles around a point.
When writing an activity answer, include three things:
- What you did.
- What you observed.
- What mathematical rule or pattern the activity shows.
6. Common mistakes and how to avoid them
- Mistake: Using a ruler when a compass is needed for equal lengths Fix: Use compass arcs to preserve equality.
- Mistake: Leaving tiny gaps in tiling and calling it valid Fix: A tiling must have no gaps and no overlaps.
- Mistake: Not labelling construction steps Fix: Write clear steps for marks and reproducibility.
7. How to write high-scoring answers
- State the given information in mathematical form.
- Write the rule, formula, diagram, table, or operation you are using.
- Show every step clearly.
- Keep units such as cm, m, rupees, degrees, or minutes where needed.
- Check whether the answer is reasonable.
8. Practice set
- What is the angle around a point?
- How many square corners meet at a tiling point?
- How many equilateral triangle corners meet at a point?
- Name two construction tools.
- Can a regular hexagon tile a plane?
- Why are construction steps important?
9. Answer key
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What is the angle around a point? Answer: 360 degrees.
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How many square corners meet at a tiling point? Answer: 4.
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How many equilateral triangle corners meet at a point? Answer: 6.
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Name two construction tools. Answer: Ruler and compass.
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Can a regular hexagon tile a plane? Answer: Yes.
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Why are construction steps important? Answer: They show how the figure can be accurately reproduced.
10. Quick revision
- Main themes: geometric construction, compass, straightedge, tiling, symmetry.
- Redo the worked examples without looking at the solutions.
- Explain the activity in your own words.
- Correct the common mistakes once before the test.
- Create one new word problem from daily life and solve it step by step.
