Every expression can be rewritten as a sum of terms

What to assume they know

• Writing a situation as an expression before computing it — an expression names a number
• Brackets decide which operation happens first — brackets force one part to be settled first
• Class 6 integers: negative numbers, and the inverse of a number
• Class 6 token model of integers, which the chapter asks students to reach back to
• Division written as a fraction bar as well as with ÷

What they should be able to do

• Identify the terms of an expression by locating the plus signs
• Rewrite any subtraction as the addition of an inverse, and state that the value is unaffected
• Give the terms of an expression that mixes addition, subtraction and multiplication, keeping the sign with the term it belongs to
• Explain why a product or a quotient counts as a single term
• Evaluate an unbracketed expression by settling each term and then adding
• Write the expression for a described situation and list its terms
• Decide, for a pictured arrangement, whether it is described by a sum of terms or needs a bracket

Where it usually goes wrong

• "6 × 5 + 3 has three terms." The multiplication sign does not cut. Counting numbers instead of counting plus signs is the commonest error here.
• "The terms of 83 – 14 are 83 and 14." The second term is −14. Dropping the sign is what makes every later exercise go wrong, because the whole point of the rewriting is that the sign travels with the term.
• "You can only swap a subtraction for an addition when the numbers work out nicely." The chapter asks the student to test it on several examples precisely so this doubt is settled by evidence rather than by assertion.
• "The rings round the terms are official notation." The chapter says on p.28 that this marking is a temporary aid, not usual practice. A student who draws them in a board answer has misread the book.
• "Terms must be added left to right." Once the expression is a sum of terms the order is free — that is the next topic, Commutative and associative: why order and grouping are free, and it is what the term rewriting buys you.
• "An expression with a division cannot be split into terms." 4 + 100/2 has two terms, one of which is a quotient.
• "Any pictured arrangement splits into a sum of terms." Example 11 is built to break this: the right-hand arrangement is a bracket case, and the chapter has to reach back for brackets to describe it.

Questions to check understanding

• Identify the terms of a given expression (asked repeatedly from p.28 onward)
• Complete a terms table: expression, sum of terms, list of terms (Part I, p.29)
• Find an expression's value by writing out its terms first (Part I, p.34)
• Write a story or situation that a given expression describes (Part I, p.34)
• Write the expression for a situation, list its terms, and find its value (Part I, p.34)
• Match a pictured arrangement to one of several candidate expressions (Part I, pp.33–34, and again p.43)

Examples worth working on the board

The terms are the answer in most of these, so state the expression.

• The starting split (Part I, §2.2, p.28): 12 + 7, whose terms are 12 and 7. Trivial on purpose — it establishes that the plus sign is the only cut.
• The inverse move (p.28): 83 – 14, rewritten so that its terms are 83 and −14. The chapter states the inverse of 14 and the inverse of −14 explicitly before doing this.
• Three further splits (p.28): –18 – 3 splits into −18 and −3; 6 × 5 + 3 splits into 6 × 5 and 3; 2 – 10 + 4 × 6 splits into 2, −10 and 4 × 6. The chapter says outright that a product carries no plus inside it and so is not cut.
• The terms table (p.29). Three columns — the expression, that expression re-set as a sum of terms, and the list of terms. Five rows: 13 – 2 + 6 (fully worked, terms 13, −2, 6); 5 + 6 × 3 (part worked, the sum-of-terms column filled in but the list left blank); then 4 + 15 – 9, 23 – 2 × 4 + 16 and 28 + 19 – 8, all blank. Note that the printed layout offers three empty rings on the blank rows, which is itself a hint about how many terms to expect.
• Evaluating by terms (p.31): 30 + 5 × 4 becomes 30 and 20, which add to 50 — the same number the brackets forced in the previous topic, now reached without brackets.
• A term with a bracket in it (p.31): 5 × (3 + 2) + 7 × 8 + 3. Three terms. The chapter states the value of the first term as 25 and of the second as 56, leaving 3 as it stands, and totals them.
• Example 7 — four dosas (p.32). Each dosa ₹23, a ₹5 tip for the waiter. Expression 4 × 23 + 5; terms 4 × 23 and 5, valued at 92 and 5. Follow-up printed alongside: the same tip but seven friends.
• Example 8 — the group game (p.32). Ruby sits out; 33 children are playing; the teacher calls out 5. Ruby writes 6 × 5 + 3. Follow-ups printed on p.33: what she would write if 4 were called, and if 7 were called, and then the same for the student's own class size. Check available to the explanation: the terms must still account for all 33 children.
• Example 9 — rice packets (p.33). 100 kg packed into 2 kg packets, on top of four such packets already held. Expression 4 + 100/2, printed with the division as a fraction bar. Terms 4 and 100/2. This is the chapter's one worked case of a quotient sitting inside a term.
• Example 10 — paying ₹432 (p.33). The permitted money is coins worth ₹1 or ₹5, together with notes worth ₹10, ₹20, ₹50 or ₹100. Two printed splits: 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1 and 8 × 50 + 1 × 10 + 4 × 5 + 2 × 1. Each is a four-term expression, and the chapter asks for more such splits.
• Example 11 — two block arrangements (pp.33–34). Left: five columns of two green squares, with a column of three pink squares at the end — described by 5 × 2 + 3, whose terms are 5 × 2 and 3. Right: two columns, each five yellow squares above three blue ones — this one needs a bracket, 2 × (5 + 3), and the chapter also offers 5 + 3 + 5 + 3 and 5 × 2 + 3 × 2 for it. Counts taken from the printed p.33.

Figures to have open

• The ringed-term device (Part I, pp.28–29). Each term drawn inside its own loop with plus signs between the loops. Redraw it; it is the chapter's central visual idea. Confirmed against page renderings of pp.28 and 29 — the loops are ovals, and the sign of a negative term sits inside the oval with the number.
• The three-column terms table (Part I, p.29). Reproduce the structure, not the printed styling: the expression, its terms shown added together, and the terms listed out.
• The group-game picture (Part I, p.32). Stick-figure children clustered into six groups of five with three left over, plus signs drawn between the clusters. Redraw. It is what makes 6 × 5 + 3 obvious rather than asserted.
• The two block arrangements (Part I, p.33). Exact counts, checked against the printed page: left is five two-square green columns plus one three-square pink column; right is two columns of five yellow squares over three blue.
• The rice-packet and ₹432 examples need no figure.

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". Two unnumbered subheadings carry this topic: "Terms in Expressions", pp.28–29, and "More Expressions and Their Terms", pp.32–35. The evaluate-the-terms rule and the two worked evaluations are on p.31.
• Chapter SUMMARY, Part I, p.44 — the third bullet pairs terms with brackets.
• Backward pointer: Class 6 Ganita Prakash, the token model of integers, which this section names twice as the place to argue from.
• Forward pointer: Part I, printed Chapter 4 "Expressions using Letter-Numbers", §4.4, where terms return as like and unlike terms in algebra.