CBSE Class 6 · Mathematics
Playing with Constructions
Official NCERT chapter from Ganita Prakash (book code fegp1). ExamMaster notes are original teaching at CBSE Class 6 depth.
This lesson follows the official chapter “Playing with Constructions” in Ganita Prakash. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.
- CBSE Class 6
- Easy level
- 8 concepts
1Artwork
Artwork in this chapter still hides squares, rectangles, and equal lengths you can test. A decoration is allowed; the test is the figure’s properties.
A pretty pattern with no equal-side test is only artwork, not a construction yet.
Figure. Class 6 artwork here is a tiling of squares, not a freehand picture. Each small square is drawn equal; the four make one larger square.
How it works
- See a motifThe picture.
- Name a property to testEqual sides, right angle.
- Run the testThe maths under the art.
2Squares and Rectangles
A rectangle has four right angles (and opposite sides equal). A square is a rectangle with all sides equal.
A rhombus that is not right-angled is not this chapter’s square.
Figure. A square has four equal sides. A rectangle has opposite sides equal. Both need four right angles. The square is drawn as a visual square; the rectangle is longer than it is tall.
How it works
- Check right anglesFour of them for a rectangle.
- Check side lengthsOpposite equal; all equal → square.
- Keep both testsAngle and side.
3Constructing Squares and Rectangles
A construction is a sequence of allowed steps: ruler for straight, compass for equal lengths, set-square or perpendicular method for right angles. Freehand is a sketch.
Calling a sketch “constructed” is a miss.
Figure. A constructed rectangle is a sequence: draw a base of measured length, raise a right angle with a set-square, copy the opposite length, and close. Dashed ticks mark the right-angle corners.
How it works
- List the allowed toolsThe ones the task names.
- Copy equal lengths with compass, not by eyeA step.
- Record the orderA construction has a sequence.
4An Exploration in Rectangles
You may change length and breadth while keeping right angles. Perimeter and area can move differently. That is an exploration, not a new definition.
A skinny rectangle is still a rectangle if the angle-and-opposite-side tests pass.
Figure. Two rectangles share perimeter 20. The 8-by-2 has area 16; the 6-by-4 has area 24. Same fence, different floor. The drawn sides keep those ratios.
How it works
- Keep four right anglesThe rectangle test.
- Change one sideA new rectangle.
- Recompute P and A if askedThey need not move together.
5A square is a rectangle with equal sides
Every square passes the rectangle tests and the all-sides-equal test. Not every rectangle is a square.
Saying “square or rectangle” as if they never overlap is a miss.
Figure. Every square is a rectangle: four right angles, opposite sides equal. A square adds one test — all four sides equal. A long rectangle fails that extra test and is still a rectangle.
How it works
- Run rectangle testsRight angles, opposite sides.
- Ask all sides equal?Yes → also a square.
- A long rectangle fails the equal-side testRectangle only.
6A construction is a sequence of allowed steps
Step 1, step 2, step 3 — each uses a named tool. Skipping “copy this length” and drawing by eye breaks the sequence.
The order can matter: a perpendicular before a length-copy, if the task says so.
Figure. A construction is an ordered list of allowed moves: measure a base, raise a right angle, copy a length, close the figure. A skipped step is not a construction, even if the picture looks close.
How it works
- Write the stepsNumbered.
- Name the tool in eachAllowed only.
- Refuse an eye-balled length as a constructed lengthA miss.
7Rotate the paper to test equal sides
A turn of the page can sit one side on another. If they land, those sides match. That is a test, not a new square.
A turn that needs a stretch is a fail.
Figure. Rotate the page by a right angle and the long side of a rectangle still matches the long side. That is a test for equal opposite sides, not a new drawing.
How it works
- Pick two sidesCandidates.
- Rotate so one lies on the otherOr use compass measure.
- Pass only if they land without a stretchEqual.
8A miss: drawing freehand and calling it constructed
Freehand can look tidy. Constructed means the allowed tools did the equal-length and right-angle jobs.
The miss is the word “constructed” on a sketch.
Figure. A freehand four-side can look like a rectangle and still fail the tests. A constructed rectangle has measured sides and raised right angles. The miss is calling the sketch constructed.
How it works
- Ask which tool copied the lengthCompass, or eye?
- If eye, call it a sketchNot constructed.
- Redo with the allowed sequenceThen the name is earned.
A square is
- A rectangle with all sides equal
- Never a rectangle
- Any tidy four-sided sketch
Rectangle tests plus equal sides.
Notes
- The official chapter title is “Playing with Constructions”. Teach the school test for that title, not a contest shortcut.
- If a step needs a later class, stop. The next official chapter will pick it up.
Recap
Hold these pegs from the official chapter “Playing with Constructions”. The wording is ExamMaster’s teaching, not a textbook recap.
- Artwork
- Artwork in this chapter still hides squares, rectangles, and equal lengths you can test.
- Squares and Rectangles
- A rectangle has four right angles (and opposite sides equal).
- Constructing Squares and Rectangles
- A construction is a sequence of allowed steps: ruler for straight, compass for equal lengths, set-square or perpendicular method for right angles.
- An Exploration in Rectangles
- You may change length and breadth while keeping right angles.
- A square is a rectangle with equal sides
- Every square passes the rectangle tests and the all-sides-equal test.
- A construction is a sequence of allowed steps
- Step 1, step 2, step 3 — each uses a named tool.
Practise Playing with Constructions
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device