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Chapter 2 · Arithmetic Expressions

Writing a situation as an expression before computing it

Teaching notesNCERT9 min

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9 min.

What to assume they know

  • The four operations on whole numbers, and the signs +, –, ×, ÷
  • Reading a two-operand calculation aloud ("five times twenty-five")
  • Class 6 place value and comfort with three- and four-digit numbers
  • What it actually takes to make one lakh — reading and writing large numbers, for the later worked amounts

What they should be able to do

  • Recognise a written arithmetic phrase as an arithmetic expression, and state that it has exactly one value
  • Use = to link an expression to its value, and read that link as a statement about two names for one number
  • Read a single expression aloud in more than one way (as an operation, and as a noun such as a sum or a product)
  • Given a short situation, write an expression describing it before working the number out, and say what part of the situation each piece records
  • Produce several different expressions with the same value, and explain why that does not make the value ambiguous
  • Explain what information is lost when an expression is replaced by its value

Where it usually goes wrong

  • **"= means and the answer is."** It is a claim that both sides name one number, which is why 13 + 4 = ___ + 6 (Part I, §2.1, p.25) is a sensible thing to write at all. A student who reads = as a one-directional command cannot make sense of an expression on the right-hand side.
  • "Writing 5 × 25 is leaving the job half done." The question asked for the expression. The unevaluated form still shows the daily cost and the number of days; ₹125 shows neither. Both are correct answers to different questions.
  • "Every number has one proper expression." Twelve is printed with four, and the chapter then asks for more. Many names, one value.
  • "13 + 2 and 15 are different numbers." They are two names for the same number, in the way that a person's name and nickname pick out one person.
  • "An expression must contain an operation." A bare numeral names a number too; the chapter's own list of ways to write twelve simply happens to restrict itself to two numbers and one operation, and says so.

Questions to check understanding

  • Given a short everyday situation, write the expression that describes it (the chapter's own Example 1 shape; recurs throughout §2.2)
  • Fill a blank so that two expressions have equal value, e.g. 13 + 4 = ___ + 6 (Part I, §2.1, p.25)
  • Arrange a list of expressions in increasing order of value (Part I, §2.1, p.25)
  • Write as many expressions as possible for a stated value, with a restriction on how many numbers or which operations may be used — the chapter reopens this at the end of the chapter as a puzzle (Part I, p.45)
  • Read a given expression aloud in words, and identify which operation it names

Examples worth working on the board

  • The four opening phrases (Part I, §2.1, p.24): 13 + 2, 20 – 4, 12 × 5, 18 ÷ 3. The chapter works only the first one, stating that 13 + 2 has the value 15 and writing 13 + 2 = 15.
  • Reading aloud (p.24). The same expression 13 + 2 is offered twice: once as an addition being carried out, once as a noun phrase naming a sum. Both readings are printed.
  • Example 1 — Mallika (p.24). ₹25 spent on lunch each day, Monday to Friday. The answer the chapter wants is the expression 5 × 25, and it then offers two ways of saying that expression aloud. Note: the chapter does not compute ₹125 here. Leaving it unevaluated is the point of the example.
  • Twelve, four ways (p.24): 10 + 2, 15 – 3, 3 × 4, 24 ÷ 2. All four use exactly two numbers and one of the four operations. Good raw material for a fan-out visual: one value at the centre, four names around it.
  • The open task (p.24): choose a number of your own and write as many expressions for it as you can. Worth running live in the explanation with a small number, because it is where a student first feels that the naming is not unique.
  • Comparison between two expressions (p.24, carried into p.25): the chapter writes 10 + 2 > 7 + 1, which puts a relation sign between two expressions with no numeral in sight. Use it here only to show that =, < and > relate values, and hand the argument on to Comparing two expressions by reasoning, not by evaluating.
  • No figure is needed for this topic. Printed p.24 was looked at: apart from the chapter banner and a QR code in the top corner, the page carries no diagram, table or number line.

Figures to have open

  • No textbook figure is required. Printed p.24 (Part I) was inspected; the section carries running text and centred display lines only.
  • The "one value, many names" fan-out in section 7 is a standard schematic.
  • The ₹25 × 5 lunch strip in sections 5–6 is also not in the book; the textbook prints no picture with Example 1.

Where this sits in the book

  • NCERT Ganita Prakash, Class 7, Part I, printed Chapter 2 "Arithmetic Expressions", §2.1 "Simple Expressions" — pp.24–25; the material for this topic sits on p.24, with the comparison signs spilling onto p.25.
  • Chapter SUMMARY, Part I, p.44 — the first bullet frames §2.1 as a revision of what an expression and its value mean.
  • Closing puzzle page, Part I, p.45 — reopens "many expressions, one value" as an extended task.
  • Forward pointer: Part I, printed Chapter 4 "Expressions using Letter-Numbers" (§4.1–§4.2), where the same idea is redone with letters standing in for numbers.

The book

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