PrepShorts · Teaching notes · Class 7 Mathematics · Chapter 2, Arithmetic Expressions
Chapter 2 · Arithmetic Expressions
Writing a situation as an expression before computing it
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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 why13 + 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 × 25is 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 + 2and15are 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 that13 + 2has the value 15 and writing13 + 2 = 15. - Reading aloud (p.24). The same expression
13 + 2is 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.