Why measurement units are built in tens

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What the video covers, what to say before it, where a class usually goes wrong, and what to set afterwards. An account is free, and it opens every chapter of every book.

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What to assume they know

Extending Indian place value to the right of the point — the chain of places and the decimal point (Part I, §3.4)
A hundredth part, and continuing the split — hundredths, and moving between counts of parts (Part I, §3.3)
The relations 1 cm = 10 mm, 1 m = 100 cm, 1 kg = 1000 g from earlier classes
Reading a price written with rupees and paise
Writing a fraction whose denominator is 10, 100 or 1000 in decimal form

What they should be able to do

State each of the chapter's unit relations and, from it, say what one small unit is worth as a fraction of the larger one
Convert between mm and cm, cm and m, g and kg, and paise and rupees, in both directions
Justify a conversion by naming the place each digit lands in, rather than by quoting a rule about moving the point
Split a three-digit count of small units into tenths, hundredths and thousandths of the large unit, as the chapter does for 254 g
Say why a quantity written with a trailing zero, such as 0.010 kg, is the same quantity as one written without it
Read the sizes of very small things off a list and place them on a common scale
Read an amount of money written in decimal form and say what the digits after the point count

Where it usually goes wrong

"Each conversion is a separate fact to learn." There are three relations in this section and every conversion in it follows from one of them. Present them as three, not as twenty.
"Converting means multiplying or dividing by 10, 100 or 1000." That description is true but hides the reason, and it is the reason that makes the answer checkable. The chapter's route — this many thousandths, regrouped into tenths, hundredths and thousandths — is longer on the page and shorter in the head.
"0.010 kg has an error in it." It is the same weight as 0.01 kg. The extra zero records that the count started in thousandths, and the chapter prints both forms for 10 g on the same line.
"A bigger number means more stuff." 254 g and 0.254 kg are one weight; 250 p and ₹2.50 are one amount. Numbers only compare once the unit is the same.
"Small units exist because small things are hard to measure." They exist because the unit was split. A millimetre is a tenth of a centimetre, which is the same object §3.1 produced with a finer ruler.
"Paise are gone, so 0.01 rupee means nothing." Coins of 25 paise and below were withdrawn; the unit was not. The old café bill, and any modern bank statement, still carries two digits after the point.
"The rice picture just shows five bags." It shows one number, 11.111 kg, with each digit standing beside the heap it counts. That is the argument, and an explanation that treats it as decoration wastes it.

Questions to check understanding

Convert a length between mm, cm and m, and a weight between g and kg, in both directions
Fill a two-way conversion table of the kind printed on pp.65, 66, 67 and 69
Given a price in paise, write it in rupees with the point, and the reverse
Given a decimal quantity, say what the digit in a named place counts
Order a set of small measurements given in mixed units
Add several quantities given in different units of the same kind, converting first
Explain, for one conversion, why the digits land where they do

Examples worth working on the board

Length relations (Part I, §3.5, pp.64–66). 1 cm = 10 mm. 1 mm = 0.1 cm. 5 mm = 0.5 cm. 12 mm = 1.2 cm, worked as 10 mm plus 2 mm. 5.6 cm = 56 mm. 1 m = 100 cm, which makes one centimetre 0.01 m; ten of them come to 0.1 m, and fifteen to 0.15 m, worked as 10 hundredths plus 5 hundredths and then as 1 tenth plus 5 hundredths. The page also asks how many millimetres a metre holds and whether 1 mm may be written as a thousandth of a metre.
The two blank tables (Part I, §3.5, pp.65–66). Millimetre to centimetre: two worked entries and four blanks, the blanks being 70 mm, an entry equal to 0.9 cm, 134 mm, and an entry equal to 203.6 cm. Centimetre to metre: six blanks — 36 cm, 50 cm, an entry equal to 0.89 m, 4 cm, 325 cm, and an entry equal to 2.07 m.
The very small things illustration (Part I, §3.5, p.65). Checked; every label in it is artwork. Mustard seeds, a snail shell, an ant, a single hair and three broad blue stripes are drawn against one another, and the stripes carry the labels 0.5 mm, 1 mm and 1.5 mm with the words Actual size beside them. The bullet list beneath supplies: pen strokes of those three widths, taken as fine, medium and bold; a human hair, roughly 0.1 mm across; newsprint, from 0.05 mm to 0.08 mm thick; mustard seed, 1 mm to 2 mm; the ant named as Carabera Bruni, 0.8 mm to 1 mm long, reported from Sri Lanka and China; the land snail named as Acmella Nana, its shell 0.7 mm across, reported from Malaysia.
More small things (Part I, §3.5, pp.66–67). Checked p.66: a fish, a jellyfish and an octopus drawn inside a square whose sides are marked 1 cm. Hummingbird egg, 1.3 cm by 0.9 cm. Philippine Goby, about 0.9 cm. Irukandji jellyfish, belly 0.5 cm to 2.5 cm, tentacles reaching 1 m. Wolfi octopus, 1 cm to 2.5 cm, under 1 gm.
Weight relations (Part I, §3.5, pp.67–68). 1 kg = 1000 g, which makes one gram 0.001 kg; five grams come to 0.005 kg, and ten to 0.010 kg, printed with the trailing zero and also as a hundredth. 254 g = 0.254 kg, worked by splitting 254 thousandths into 200, 50 and 4 thousandths and then rewriting those as 2 tenths, 5 hundredths and 4 thousandths. 1 g = 1000 mg, so 1 mg = 0.001 g. Six blanks follow: 465 g, 68 g, 1560 g, 704 g, an entry equal to 0.56 kg, and an entry equal to 2.5 kg.
The rice photograph (Part I, §3.5, p.68). Checked; the labels are inside the photograph and extract only as a stray line. Five heaps on one shelf, each captioned twice, in kilograms above and grams below: 10 kg with 10000 g, 1 kg with 1000 g, 0.1 kg with 100 g, 0.01 kg with 10 g, 0.001 kg with 1 g. The text states that each heap is ten times the one before and gives the combined weight as 11.111 kg. Every digit of that total is one of the heaps, which is the whole point of the picture.
Money relations (Part I, §3.5, pp.68–69). 1 rupee = 100 paise. 1 paisa = 0.01 rupee. 75 paise = 0.75 rupee, worked as 70 hundredths plus 5 hundredths and then as 7 tenths plus 5 hundredths. Six blanks: 10 p, an entry equal to ₹0.05, an entry equal to ₹0.36, an entry equal to ₹0.50, 99 p, and 250 p.
The coins and the bill (Part I, §3.5, pp.68–69). Down the outer margin of p.68 runs a column of eight photographed coins for the eight paise denominations the text lists: 1, 2, 3, 5, 10, 20, 25 and 50. The text says all denominations of 25 paise and below went out of use in 2011, and that paise are still seen on bills and statements. On p.69 a handwritten café bill is photographed, dated 3/3/1970, with two money columns headed for rupees and paise: three dosas at 1 and 50, two teas at 0 and 12, one cake at 0 and 15, and a total of 1.77. The bill is entirely artwork and extracts as nothing.
Prices remembered (Part I, §3.5, p.69). From the 1970s: a masala dosa at 50 paise, a banana between 20 and 25 paise, peppermints at 2 or 3 paise each, and rice at ₹2.45 a kilogram. Students are asked to collect more from adults.

Figures to have open

A magnified centimetre showing ten millimetre divisions. Standard schematic, and the single graphic the first half of the topic rests on.
A true-scale strip carrying the small things from p.65. It must be drawn at honest relative sizes or it teaches nothing; the printed illustration does this and says so with its own Actual size label.
The five rice heaps with their paired captions and the total. Redraw rather than lift — the printed labels sit inside a photograph and will not survive rescaling, and the leader lines from the digits of 11.111 to the heaps are the addition this figure is really making.
A column of the eight paise coins, or a plain set of labelled discs. The textbook's photographs are not required.
The old café bill with two money columns. Redraw; a handwritten prop is fine, and the rupee-and-paise column heads must be legible.
No table from the textbook is required.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 3 "A Peek Beyond the Point", §3.5 Units of Measurement, pp.64–69. The section carries three unnumbered subheadings: Length Conversion, opening on p.64; Weight Conversion, opening on p.67; and Rupee — Paise conversion, opening on p.68. The very small things illustration is on p.65, the second set of small creatures on pp.66–67, the rice photograph on p.68, and the coins, the old bill and the remembered prices on pp.68–69.
Backward pointer: Part I, §3.4, pp.58–64, for the chain of places these units are riding on.
Forward pointer inside the same chapter: Part I, §3.8, pp.76–77, where two of the recorded disasters are unit errors rather than point errors.