A fraction as a part of one whole

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What to assume they know

A fraction as an equal share, and why one-ninth is less than one-fifth: a fractional unit is one of the equal parts a whole is cut into, and the number underneath counts those parts
The idea of "the same amount" applied to a solid object, from primary school
Recognising a rectangle and a right-angled triangle by sight
Counting the parts of a shape sequence produces a number sequence: counting the parts of a drawn shape

What they should be able to do

Identify the whole in a picture before naming any piece of it
Name a piece as a fractional unit by counting how many identical copies of it rebuild the whole
Measure a larger piece by counting fractional units inside it, and write the result as a fraction
Judge whether two differently shaped pieces of the same whole are the same size
Explain why an unequal two-way cut does not produce halves
Read a piece back to the cut that made it — from the piece to its denominator
State what stays fixed and what may vary when the same whole is cut into a given number of equal parts

Where it usually goes wrong

"Different shape means different fraction." This is exactly what the two six-way cuts on p.154 exist to break. Run them side by side and count the pieces in each, out loud.
"Any four pieces make quarters." Only equal ones do. A student who has broken a real chikki knows the pieces come out ragged; say so, and say that the mathematics assumes the idealised equal cut.
"The bigger piece needs its own new name." It does not — it is counted in the units already available. This is the move the whole chapter runs on and it first appears here, on p.154.
"The whole is whatever is on the page." The whole has to be chosen and stated. When the drawn-out piece sits next to the slab, a student can read the piece as its own whole. Name the whole aloud in every frame.
"Fractions are about circles." §7.1 used rotis and §7.2 uses a rectangular slab on purpose. Show at least one non-circular whole before any circle appears.
"A fraction with a bigger denominator is a bigger piece." Carried over from the previous topic and worth one sentence here, because the sixths on p.154 look substantial next to the quarters on the same page.

Questions to check understanding

Given a drawn piece and the whole it came from, write the fraction it represents
Given a fractional unit, say how many copies rebuild the whole
Decide whether two differently shaped pieces of one whole are the same size, and justify it
Shade a stated fraction of a given grid or slab in two visibly different ways
Say why a picture of an unequally split object does not show halves
Given a piece that is several fractional units, write its fraction by counting
The solutions appendix bound with this chapter answers the §7.2 Math Talk question and the eight-piece Figure it Out on its §7.2 page

Examples worth working on the board

The intact chikki (§7.2, p.154). Checked against the printed page. A rectangular slab is printed at the top right with the caption naming it as one whole. The scoring on the drawn slab is part of the artwork, not part of the mathematics.
The two-piece break (§7.2, p.154). Checked against the printed page. The slab is shown broken into two pieces of unequal size. The smaller piece is labelled by the book with a boxed fraction; the text then measures the larger piece by counting how many copies of the small piece sit inside it, and reports the count as 3.
Six pieces, two different cuts (§7.2, p.154). Checked against the printed page. On the left, the slab is cut by straight horizontal and vertical dashed lines and one rectangular piece is drawn out beside it. On the right, the same slab is cut by slanting dashed lines and the piece drawn out beside it is a right-angled triangle. Both drawn-out pieces carry the same boxed label. This side-by-side pair is the argument of the section — reproduce the contrast, not the drawing.
The Math Talk question (§7.2, p.154). Printed as a question to the class: cutting one whole into six equal parts in different ways gives pieces of different shapes, so are those pieces the same size? The solutions appendix bound with this chapter answers it in the affirmative on its §7.2 page.
The one-third piece (§7.2, p.155). Checked against the printed page. A whole slab is shown with two dashed cuts, and a single tall piece is drawn out beside it with a curved arrow and a note saying it came from breaking the slab into three equal pieces. This is the reverse direction — piece first, denominator recovered from it.
Eight pieces to name (§7.2, p.155). Checked against the printed page. The whole chikki drawn above the set is scored into a grid of twenty-four equal blocks — six across by four down, counted off the printed page — and each lettered piece covers a whole number of those blocks. The Figure it Out set then prints eight pieces labelled a to h with an empty answer box under each: a small upright rectangle two blocks tall, a large right triangle, a smaller right triangle, a tall thin rectangle four blocks tall, an L-shaped piece of three blocks (two side by side with a third sitting on the right-hand one), a triangle pointing right, a single square block, and a narrow right triangle. The pieces are drawn art and do not extract; every one of these descriptions comes from the printed page. The solutions appendix records answers of one twelfth, one quarter, one eighth, one sixth, one eighth, one sixth, one twenty-fourth and one twenty-fourth in that order. Each of those is a whole number of twenty-fourths, which is what makes the block count the way to check them: the three-block L is three twenty-fourths, that is one eighth.
The counter-example the section needs but does not print. The chapter does print an unequal break — the two-piece slab above, on p.154 — and it names both pieces. What it never does is take an unequal two-way split and say in so many words that neither piece may be called one half. P.154 already prints an unequal split.

Figures to have open

A plain rectangular slab that can be cut in several different ways and reassembled. This is the workhorse figure; everything from section 2 to section 9 runs on it. Standard schematic, redrawn — do not reproduce the printed chikki artwork on pp.154–155.
A single frame holding a rectangular sixth and a triangular sixth of the same slab, with an overlay or dissection showing they match. The textbook prints the two cuts but does not print the overlay; the overlay is added here and should be labelled as such.
Eight lettered pieces with empty naming boxes, matching the eight printed on p.155 in shape. Must follow the textbook's set, since a student will be holding that page.
No photograph, table or data figure from the textbook is required.

Where this sits in the book

NCERT Ganita Prakash, Class 6, Chapter 7 "Fractions", §7.2 "Fractional Units as Parts of a Whole", pp.154–155 — the intact slab, the two-piece break and the two six-way cuts (p.154); the one-third piece and the eight-piece Figure it Out (p.155)
§7.1, p.152, for the sharing reading this topic converts, and for the printed definition of fractional unit
§7.3, p.156, which is where the same move is applied to a length
Summary, p.186, for the printed one-line statement of fractional units
Solutions appendix bound with this chapter file, §7.2 pages