Estimation was a key part of the First Class Test for Guides pre-1968. There were various sorts of estimation to master, along with various ways of calculating it.
Hints on Girl Guide Badges - 1933 edition advises:
"To Measure a Height -
Method A (in sunlight). To measure a tree, etc. Stand a pole upright on the ground, and measure both the pole, and its shadow. Next measure the shadow of the tree. As the shadow of the pole is to the pole, so will the shadow of the tree be to the tree.
Example: A shadow of 8ft is cast by a pole of 4ft. Therefore a shadow of 24ft is case by a tree of 4 x 24 over 8 = 12ft.
Method B (to measure a telegraph pole, etc.) Plant a pole upright in the ground at A, a convenient measured distance from the base B of the telegraph pole. Walk on past the ole, until, when lying on the ground, at C, the top of the pole can be seen, with the eye nearest the ground, in line with the top of the telegraph pole D. What CA is to the pole, then CB will be to the telegraph pole.
Example: Let 20 feet be the measured distance BA and 4 feet the distance AC to where the angle DCB was obtained. Let 5 feet be the height of the pole. Then what CA 4 feet is to the pole 5 feet (A), CB 24 feet is to the telegraph pole (BD). =524 over 4 = 30 feet."
For estimating weight, a good starting point is to become familiar with certain regular weights. For instance, if you are familiar with how much a standard bag of sugar weighs (1 kilogram, or 2.2lbs), then you can hold a weight in your hands and estimate whether the weight you are holding is similar to that known weight, half as much, twice as much . . .
"To Measure the Width of a River - Select a prominent object on the other bank of the river, and mark a spot directly opposite it on your side. Net, pace along the bank at right angles to the imaginary line across the river and when you have taken a convenient number of paces (say 20), plant a pole upright in the bank. Continue in the same direction, until you have doubled the number of paces you originally took. Mark the spot, turn and proceed inland at right angles to your previous course, until you bring the central pole into line with the prominent object on the other side of the river.
Should it be impossible to walk along the actual edge of the bank, a line further inland may be taken and the distance from this line to the nearer bank being subtracted from the width of the river is the final calculation."
"To Measure the distance apart of two objects a known distance away and unapproachable, the same method is employed in a different form.
Let A and B be the two objects. Erect a pole at point C immediately opposite object B and at right angles to the line AB. Proceed away from C in a straight line with BC until you have covered a distance equal to BC. Mark the spot at D. From thence turn to the left and continue at right angles to CD until at E the pole at C comes into line with object A, then the distance DE = the distance apart of A and B.
If the distance from B to C and from C to D = 20 yards and the distance measured from D to E before E came into line with A = 30 yards.
Then A is distant from B 30 yards."