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Chapter 4 · Period 1 of 9 · 40 min

What Does a Letter Stand For? Building the First Expressions

The Notion of Letter-Numbers · Inductive

Students often confuse '4 less than n' with 'n less than 4', writing n – 4 when 4 – n is meant — make the word-order explicit during the Q5 share. Example 3 (Example 3, section 4.1 p.82) extends the idea to two variables and is a useful self-study pointer for students who finish early.

0–8Open with a question: if a friend is always 3 years older than you, how would you write their age without knowing yours? Students share guesses. Introduce the idea that a letter can hold any number — a 'letter-number'. Walk through Example 1, section 4.1 p.81 ("Shabnam is 3 years older than Aftab. Derive the expression s = a + 3…"), reading the table together and naming the expression s = a + 3.
8–20Move to Example 2, section 4.1 p.82 ("Parthiv's L-shaped matchstick pattern: derive the expression 2n…."). Students count matchsticks for 1, 2, 3 L-shapes on rough paper, record in a table, and spot the doubling. Class agrees on 2n as the general formula; establish vocabulary: letter-number, algebraic expression.
20–33Students attempt Figure it Out Q5, section 4.1 p.84 ("Write algebraic expressions for: (a) 5 more than a number; (b) 4 less than a number; (c) 2 less than 13 times a number; (d) 13 less than 2 times a number.") individually, then compare with a partner. Discuss how 'less than' reverses the order students expect.
33–40Quick whole-class share: three students read their expressions aloud. Clarify any confusion between 'a less than b' and 'a minus b'. Preview that letter-numbers can also describe costs and shapes — introduce Example 3 briefly as a teaser for the follow-up unit.

Homework

Munirathna joins a pipe of unknown length k metres to a 20 m pipe. Write the expression for the combined length. (**Figure it Out Q2, section 4.1 p.84**)

Assessment

Figure it Out Q5, section 4.1 p.84 — Write algebraic expressions for: (a) 5 more than a number; (b) 4 less than a number; (c) 2 less than 13 times a number; (d) 13 less than 2 times a number.

Which algebraic expression correctly represents '7 less than 4 times a number n'?

  • A 4n – 7
  • B 4 + n – 7
  • C 4(n – 7)
  • D 7 – 4n

A. 4n – 7

What each wrong option reveals

  • B The student did not apply the multiplication correctly, treating '4 times n' as simply adding 4 and n before subtracting 7.
  • C The student grouped the subtraction inside a bracket with 4 as a factor, confusing '4 times a number, then subtract 7' with '4 times (number minus 7)'.
  • D The student reversed the subtraction order, writing 7 – 4n instead of 4n – 7, misreading 'less than' as 'minus from the left'.
Chapter 4 · 9 periods of 40 min

Also saved as 5 periods or 7 periods.

  • 2Formulas for Shapes, Costs, and Calendars
    The Notion of Letter-Numbers
  • 3Order, Brackets, and the Bridge to Algebra
    Revisiting Arithmetic Expressions
  • 4The Silent Times Sign: Reading and Writing 4n
    Omission of the Multiplication Symbol in Algebraic Expressions
  • 5From Convention to Simplification: Like Terms at Work
    Omission of the Multiplication Symbol in Algebraic Expressions
  • 6Why Are Two Expressions Equal? Bracket Removal and Proof
    Simplification of Algebraic Expressions
  • 7Simplify, Verify, Correct: Multi-Step Expression Practice
    Simplification of Algebraic Expressions
  • 8Detective Work: Formulas Behind Patterns and Grids
    Pick Patterns and Reveal Relationships
  • 9Four Problems, One Chapter: Expressions at Work
    Synthesis
Ganita Prakash · Class 7 · 15 chapters

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