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New NCERT textbook · Class 8 Maths

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Chapter 12 · Period 1 of 16 · 45 min

Mean as a Balance Point on the Number Line

The Balancing Act · Inductive

Watch for students who compute the mean numerically rather than reading distances from the dot plot — the goal here is the geometric reasoning, not the formula. Students who conflate 'closest to the middle' with 'balance point' benefit from a counter-example using a highly skewed small dataset.

0–10Open by asking students to place the numbers 2, 4, and 9 on a hand-drawn number line and guess where the 'balancing point' might sit — a quick mental estimation before any formula is named. Collect three or four guesses and note them on the board.
10–25Introduce the balance-point model: the mean is the point where total left-distance equals total right-distance. Students verify this for their three numbers by computing distances from candidate points, then articulate in pairs why shifting the candidate left or right immediately breaks equality. Establish the uniqueness argument through discussion.
25–38Figure it Out Q2, section 5.1 p.113 ("A dot plot shows a collection with its mean of 9 but one dot is missing....") — students mark the missing value using the balance-property rather than the average formula, explaining their reasoning aloud. Move to Figure it Out Q4, section 5.1 p.114 ("Three dot plots show song lengths for different albums...."), where students identify the target album and argue why the others fail the balance test.
38–45Pairs share one sentence each: 'The mean must be unique because…'. Consolidate with a class statement connecting the verbal argument to the arithmetic definition of mean.
Assessment

Figure it Out Q2, section 5.1 p.113 — A dot plot shows a collection with its mean of 9 but one dot is missing; mark the missing value to restore the balance.

A set of five values has a mean of 12. A student claims that if the value 12 is removed from the set, the mean of the remaining four values will still be 12. Is the student correct? Justify your answer using the balance-point model of the mean.

The student is correct. The mean is the balance point where total left-distance equals total right-distance. The value 12 sits exactly at the balance point, contributing zero to either side's distance total. Removing it does not disturb the equality of distances, so the balance point — and hence the mean — of the remaining four values is still 12. Algebraically: original sum = 5 × 12 = 60; removing 12 gives a new sum of 48 and a new count of 4; new mean = 48 ÷ 4 = 12.

Chapter 12 · 16 periods of 45 min

Also saved as 10 periods or 13 periods.

  • 2How Adding or Removing Values Shifts the Mean
    The Balancing Act
  • 3Proving What Happens When Every Value Shifts or Scales
    The Balancing Act
  • 4Finding the Unknown Using the Mean Formula
    The Balancing Act
  • 5Mean and Median from Frequency Tables
    The Balancing Act
  • 6Spreadsheets: Cell References and AVERAGE Formulae
    The Balancing Act
  • 7Extended Practice: Mean, Median, and Mixed Problems
    The Balancing Act
  • 8Introducing Line Graphs: Temperature and Launches
    Visualising and Interpreting Data
  • 9Rainfall Line Graphs and Monthly-Average Data
    Visualising and Interpreting Data
  • 10Reading a Choropleth Infographic: Rice and Wheat Consumption
    Visualising and Interpreting Data
  • 11Activity Strips: Decoding and Creating Time-Use Representations
    Visualising and Interpreting Data
  • 12Sleep-Duration Curve and Smooth-Curve Line Graphs
    Visualising and Interpreting Data
  • 13Plotting and Comparing Multi-Series Line Graphs
    Visualising and Interpreting Data
  • 14Mean Grids, Median Constraints, and Algebraic Mean Puzzles
    Visualising and Interpreting Data
  • 15Validity Statements, Algebraic Properties, and Moonrise Patterns
    Visualising and Interpreting Data
  • 16Putting the Chapter to Work: Balance, Unknowns, Frequencies, and Graphs
    Synthesis
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