Brackets decide which operation happens first

What to assume they know

• Writing a situation as an expression before computing it — an expression names a number
• Multiplication and subtraction of two- and three-digit numbers
• Reading a word problem and identifying which quantities combine
• Comfort with rupee amounts and giving change

What they should be able to do

• Explain why an expression carrying more than one operation can be read in more than one way once its context is removed
• State the rule the chapter gives for a bracketed expression: settle what is inside first
• Given a situation, write a bracketed expression that describes it, and say which grouping the situation forces
• Evaluate a bracketed expression in the order the brackets require
• Detect a wrong reading by testing its answer against the situation, not by re-checking the arithmetic
• Recognise that this chapter reaches order of operations through brackets and through terms, rather than through a memorised acronym

Where it usually goes wrong

• "Multiplication before addition is a rule called BODMAS that you memorise." This chapter never prints that acronym, or any other — all twenty-two printed pages (Part I, pp.24–45) were checked. It reaches the same outcome by two routes a student can reconstruct: brackets, and then the notion of terms. An explanation that reaches for the acronym as a shortcut is teaching a different book.
• "Purna made an arithmetic mistake." He did not. 30 + 5 = 35 and 35 × 4 = 140 are both correct. He evaluated a different expression from the one the marbles describe, which is a modelling error, not a computation error.
• "Brackets change the value of an expression." They select which value the written symbols name. Nothing about the marbles changed when the brackets went in.
• "Once brackets exist, every expression needs them." The chapter goes straight on to show that an expression with no brackets is still readable, by way of terms. Brackets are for the cases where the ordering must be forced.
• "100 – 15 + 56 is a wrong expression." It is a perfectly good expression; it is the wrong expression for Irfan's shopping. The distinction is the chapter's whole method.
• "If the arithmetic checks out, the answer is right." Section 8 exists to break this. The ₹141 answer survives every arithmetic check and is still wrong.

Questions to check understanding

• Given a situation, write the expression that describes it and bracket it correctly (the shape of Examples 4 and 5)
• Evaluate a bracketed expression, showing the inner value first
• Given two candidate expressions for one situation, say which one describes it and why the other does not
• Insert brackets into an unbracketed expression so that it takes a stated value — the chapter asks this directly later in the chapter (Part I, p.38)
• Explain, in words, why a stated answer cannot be right, arguing from the situation rather than from the arithmetic

Examples worth working on the board

Two of them are deliberately wrong readings.

• The Shalini sentence pair (Part I, §2.2, p.26). One sentence about sitting next to a friend, printed twice — once without a comma and once with one — and each printing is given its own meaning: in one the friend has the toys, in the other Shalini does. Two illustrations accompany them. This is the chapter's bridge into brackets and should open the explanation, not be dropped as decoration.
• Example 4 — the playground marbles (pp.26–27). Mallesh brought 30 marbles; Arun brought 5 bags with 4 marbles in each. The expression written down is 30 + 5 × 4. Two routes are then printed:
  • add first: 30 + 5 is 35, and 35 multiplied by 4 gives 140
  • multiply first: 5 × 4 is 20, and 20 added to 30 gives 50. The chapter names the second as correct for this situation and asks why the first went wrong. Note: both routes are arithmetically flawless; what is wrong with the first is that it does not describe the bags.
• The bracketed form (p.27): 30 + (5 × 4), which the chapter evaluates in two printed steps, the inner product first.
• Example 5 — Irfan's change (p.27). A biscuit pack at ₹15, a packet of toor dal at ₹56, a ₹100 note handed over. The chapter first offers the unbracketed 100 – 15 + 56, reads it left to right, and gets 141 — then rejects it on the ground that a customer cannot receive more than he paid. The bracketed form is 100 – (15 + 56); the inside comes to 71, and the change is ₹29.
• Two useful numbers to have in view: 141 (the absurd one) and 29 (the right one). The gap between them is what makes the section land.
• No table, grid or number line appears on pp.26–27. Both pages were looked at; the only artwork is the pair of Shalini illustrations on p.26.

Figures to have open

• The Shalini illustration pair (Part I, p.26). Two drawings of children with toys, matching the two readings of one sentence. Redraw rather than reproduce; what matters is that the two pictures differ only in who is holding the toys.
• The playground: 30 loose marbles beside 5 bags of 4. The textbook prints no such picture — this is added here, and it should be drawn so that the count 5 × 4 is visibly separate from the 30.
• Two evaluation ladders for section 3, laid out in parallel so the branching point is visible. An added device.
• No textbook table or diagram is needed from pp.26–27 beyond the illustration pair; this was checked against page renderings of both pages.

Where this sits in the book

• NCERT Ganita Prakash, Class 7, Part I, printed Chapter 2 "Arithmetic Expressions", §2.2 "Reading and Evaluating Complex Expressions" — the section opens on p.26; Example 4 begins on p.26 and is resolved at the top of p.27; the unnumbered subheading "Brackets in Expressions" and Example 5 are on p.27.
• Chapter SUMMARY, Part I, p.44 — the third bullet names brackets and terms together as the chapter's two devices.
• Return visit: Part I, printed Chapter 2, pp.35–36 and pp.38–40, where brackets are taken back out again — Removing a bracket after a minus sign flips every term inside and The distributive property, and using it to compute faster.