A tenth part — teaching notes

These teaching notes are for members

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.

Create a free account Sign in

What to assume they know

Why whole units are not enough to measure with — why the unit is cut up at all, and reading a length off a tenth-marked scale (Part I, §3.1)
Column addition and subtraction of whole numbers, including carrying and borrowing
Adding fractions that share a denominator
Reading a mixed number such as 3 and 4 tenths
The Land of Tens: each place is ten of the one before — each place in the Indian system holds ten of the one to its right (Part I, Chapter 1)

What they should be able to do

Write one length in both available forms: as units and tenths, and as a plain count of tenths
Convert between those two forms in either direction and justify the conversion by the ten-to-one relation
Read aloud, and tell apart, four numbers that use the same digits differently
Put a list of lengths written in tenths into increasing order
Add two such lengths by combining units with units and tenths with tenths, and trade ten tenths for a unit when the tenths overflow
Subtract by breaking one unit into ten tenths when there are not enough tenths to take from
Carry out the same addition or subtraction by first turning both numbers into a count of tenths, and check that the two routes agree
Find the constant step in a sequence written in tenths and continue it

Where it usually goes wrong

"41 tenths and 41 and 1 tenth are near enough the same." They differ by more than 36 units. The four look-alikes on p.49 exist precisely to be told apart, and an explanation that races past them wastes the best item in the section.
"You can compare counts of tenths across pictures." The page says outright that the unit length differs from picture to picture. A count of tenths is a length only once the unit is fixed.
"Thirteen tenths is an illegal number." It is a perfectly good count; it simply is not the tidiest way to leave an answer. The whole of the carry step is turning it into one unit and three tenths.
"There is a correct method." The chapter gives three routes to Sonu's arm length and two to Shylaja's finger, and asks the student to try a further one. The agreement between the routes is the lesson, not any single route.
"You may write this as 3.4." Not yet. The decimal point has not been introduced at this stage of the chapter — it arrives at Part I, §3.4, p.62. Everything in this topic is written as units and tenths or as a count of tenths, and an explanation that reaches for the point early destroys the argument §3.4 is about to make.
"Subtraction always goes left to right." The page states that starting from the tenths is convenient, exactly as with whole numbers. Starting from the units and then discovering you cannot finish is the common error.

Questions to check understanding

Write a given length both as units-and-tenths and as a count of tenths
Order a mixed list of lengths written in the two forms
Add or subtract two lengths in tenths, showing the trade explicitly
Do the same computation by a second route and confirm the answers agree
Read aloud a number written in tenths, and write down one read aloud to you
Continue a sequence in tenths, including a decreasing one, and state the step
Given a picture of an object on a scale, say what one part of that scale is worth before reading any length off it

Examples worth working on the board

The pencil (Part I, §3.2, p.48). 3 and 4 tenths units long, read also as three units plus four one-tenths, and written out as (3 × 1) + (4 × one-tenth). Checked p.48: a pencil above a tenth-marked ruler, with a second copy below it carrying ten small arrows across one unit and the sum of ten one-tenths written under them.
The trade rate (Part I, §3.2, p.48). Ten one-tenths added together make one unit, so the pencil is also 34 tenths.
Splitting 34 tenths back apart (Part I, §3.2, p.49). 34 × one-tenth is written as 10 + 10 + 10 + 4 tenths, then as 1 + 1 + 1 and 4 tenths.
The four look-alikes (Part I, §3.2, p.49). 4 and 1 tenth; 4 tenths; 41 tenths; 41 and 1 tenth. The page prints how each is said aloud. This is the single most useful item on the page for an explanation.
The USB cable (Part I, §3.2, p.49). 4 and 8 tenths units, equally 48 tenths. Checked p.49: alongside it are a pencil box against a vertical scale, a closed fist against a short scale, and a leaf against a scale running to 11, all with the measurements left blank. The page warns that the unit length is not the same in each picture.
Eight lengths to order (Part I, §3.2, p.49). 9 tenths; 1 and 7 tenths; 130 tenths; 13 and 1 tenth; 10 and 5 tenths; 7 and 6 tenths; 6 and 7 tenths; 4 tenths.
Four more to order (Part I, §3.2, p.50). 4 and 1 tenth; 4 tenths; 41 tenths; 41 and 1 tenth. Two of these four are the same number, which is the point of the item.
Sonu's arm (Part I, §3.2, p.50). Lower arm 2 and 7 tenths units, upper arm 3 and 6 tenths units. The page works this three ways: by parts, in a stacked column, and by converting both to tenths (27 tenths and 36 tenths).
The honeybee (Part I, §3.2, p.51). Head 2 and 3 tenths units, thorax 5 and 4 tenths units, abdomen 7 and 5 tenths units. Checked p.51: a photograph of a bee with three brackets across the top labelled head, thorax and abdomen. The labels are artwork.
Shylaja's hand (Part I, §3.2, p.51). Hand 12 and 4 tenths units, palm 6 and 7 tenths units, middle finger unknown. Checked p.51: a drawn hand with two bracketing rectangles, the taller carrying the hand length and the shorter the palm length. Two methods are printed; the second is the stacked one, and the page states in words that a unit is split from 12 to make ten tenths, leaving 11 units and 14 tenths.
The two fish (Part I, §3.2, p.52). Celestial Pearl Danio 2 and 4 tenths cm; Philippine Goby 9 tenths cm. Checked p.52: two painted fish with their names set beneath as captions.
Six sequences (Part I, §3.2, p.52). Their opening terms, all in tenths: (a) 4, 4 and 3 tenths, 4 and 6 tenths; (b) 8 and 2 tenths, 8 and 7 tenths, 9 and 2 tenths; (c) 7 and 6 tenths, 8 and 7 tenths; (d) 5 and 7 tenths, 5 and 3 tenths; (e) 13 and 5 tenths, 13, 12 and 5 tenths; (f) 11 and 5 tenths, 10 and 4 tenths, 9 and 3 tenths. Three of the six run downwards.

Figures to have open

A pencil, or any straight object, above a ruler whose single unit is visibly cut into ten equal parts. Standard schematic. It must be possible to count the ten parts.
Ten one-tenth tiles that assemble into one unit tile. Standard schematic, and the single most reusable graphic in the chapter.
The bee with its three body sections bracketed. The textbook's photograph is not needed; a labelled schematic is clearer and the labels must be legible.
A hand with the whole-hand length and the palm length bracketed, so the finger is visibly the difference. Redraw from the p.51 layout.
Two small fish drawn to scale against a tenth-marked centimetre ruler, so the size difference is visible rather than asserted.
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", §3.2 A Tenth Part, pp.48–52. The pencil and the ten-arrow figure are on p.48; the four look-alikes and the objects with unequal units on p.49; Sonu's arm on p.50; the bee and Shylaja's hand on p.51; the two fish and the six sequences on p.52.
Backward pointer: Part I, Chapter 1, for the ten-to-one relation between neighbouring places in the Indian system.
Forward pointers inside the same chapter: Part I, §3.3, pp.52–58, which splits the tenth again; Part I, §3.4, p.62, where the decimal point finally appears; Part I, §3.7, pp.74–75, where these same sums are redone in decimal notation.