8. Playing with Constructions

10 topics2 h

Chapter 8 of NCERT Mathematics for Class 6: Playing with Constructions. Four sections — Drawing with a compass, What makes a square a square, Constructing and exploring rectangles and Diagonals, and points equidistant from two points. Ten videos, 2 h in all.

Worked answers to the 6 exercise questions in this chapter →

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Part 1

Drawing with a compass

9 minEvery curve in these figures is part of a circleEvery curve in these figures is part of a circle — and here a straight line counts as one too.9 min · 12 partsहिंदी9 minWorking out the order in which a figure has to be drawnThe hard part of a construction is the order, not the hand. Start with whatever needs nothing.9 min · 12 partsहिंदी

Part 2

What makes a square a square

10 minThe two properties that define a rectangle, and the one more a square needsA figure earns a name by passing a test, not by looking right. Two conditions make a rectangle; a square needs one more.10 min · 12 partsहिंदी9 minNaming corners in order, and why a rotated square is still a squareABCD is a walk round the boundary, not four labels — which is why a rotated square is still a square.9 min · 12 partsहिंदी

Part 3

Constructing and exploring rectangles

9 minConstructing a square or rectangle from its side lengthsA square built from its side length, with a reason given for every step before it is drawn.9 min · 12 partsहिंदी9 minThe shortest and longest crossing inside a rectangleThe first quantity in this chapter that is not a number but a range. Slide two points along a rectangle and watch the crossing change.9 min · 12 partsहिंदी9 minWhich rectangles break into identical squares, and which do notA construction problem with no measurements in it at all, and that is exactly the point.9 min · 12 partsहिंदी

Part 4

Diagonals, and points equidistant from two points

9 minWhy a rectangle's diagonals are equal, and when they split the corners evenlyA rectangle's diagonals cut its corners into eight angles. Measuring seven of them tells you nothing about the eighth.9 min · 12 partsहिंदी10 minConstructing a rectangle from one side and a diagonalConstructing a rectangle when nobody gives you two sides — only one side and a diagonal.10 min · 12 partsहिंदी10 minThe points that are the same distance from two given pointsFind a point a known distance from each of two known points. Almost every construction worth doing is built on that one move.10 min · 12 partsहिंदी

What you will be able to do

  • State what the book counts as a curve, and give an example that is not bent
  • Break a given figure into components and say what each one needs
  • Name the corners, sides and angles of a four-sided figure, and identify which sides are opposite each other
  • Explain what makes an ordering of four corner labels a legitimate name
  • Construct a square of a given side using a ruler and a right angle
  • Set up the exploration: build the rectangle and identify the two sliding points
  • Simplify a hard construction to an easier one and then build the hard one back up
  • Draw both diagonals of a rectangle and name them correctly
  • Draw a rough diagram for a construction whose data are an angle and a side
  • Identify, in a figure to be recreated, which point cannot be drawn immediately and why

What this chapter assumes you already know

  • Measuring and marking a length in centimetres and millimetres with a ruler
  • The idea that two things can be the same distance apart without being in the same place
  • Measuring and marking a stated length with a ruler
  • The idea that a drawing can be broken into parts that are drawn separately
  • Measuring a length in centimetres and comparing two lengths
  • The idea of a four-sided closed figure with straight sides
  • Reading a position off a grid of dots
  • Measuring a length in centimetres and millimetres and recording it

It builds directly on A point fixes a location; a segment is the shortest route between two points, Straight and right angles as the landmarks of a full turn and Reading and drawing an angle with a protractor.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "A curve is the bendy sort of line."
  • "An arc is a different kind of object from a circle."
  • "The compass draws the circle; the ruler is a separate exercise."
  • "The centre is somewhere on the curve."
  • "Freehand is good enough if you are careful."
  • "Both halves of an eye come from one compass position."
  • "Drawing is a skill; either your hand is steady or it isn't."
  • "You should start at the top left and work across."