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Themed maths

Estimation station and class survey for IGCSE and GCSE

A start-of-term lesson that sets the tone: estimate first, then measure, and treat being wrong as part of maths. Then collect some anonymous class data and summarise it with averages, a grouped frequency table and a scatter graph.

Level
IGCSE and GCSE (Higher and Extended)
Time
40 minutes, plus a 10-minute extension
Topics
Number: estimation, percentage error and bounds; Statistics: averages and range; Statistics: grouped data and scatter graphs
Equipment
The starter is non-calculator. A calculator is allowed in the main activity.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A10 minEstimation station
Main: task B15 minClass survey: hand spans and travel times
Main: task C10 minSpot the link
Extension10 minFast finishers or homework

Starter (5 minutes)

Estimate, don’t calculate: round first.

  1. Estimate 49.8 × 20.3 by rounding each number first.
  2. Estimate (612 + 389) ÷ 4.9.
  3. A student estimates that a corridor is 30 m long. It is really 24 m. By what percentage of the true length was the estimate out?

Main activity (35 minutes)

Task A: Estimation station (10 min)

At each station, write your estimate first, then measure. These are one group’s results.

  1. A student estimated that a desk is 90 cm long. It measured 120 cm. Find the percentage error of the estimate.
  2. Five estimates of the number of counters in a jar were 150, 210, 180, 260 and 200. There are 196. Find the mean of the estimates, and its percentage error to 1 decimal place.
  3. A book is 7.4 cm thick, measured to the nearest millimetre. Write down the error interval for its thickness T cm.

Task B: Class survey: hand spans and travel times (15 min)

Made-up data from a class of 10 (hand spans in cm): 18, 20, 19, 22, 21, 17, 20, 23, 19, 21. A class of 25 recorded how long their journey to school takes:

Time, t minutesFrequency
0 < t ≤ 106
10 < t ≤ 209
20 < t ≤ 307
30 < t ≤ 403

  1. Find the mean, the median and the range of the hand spans.
  2. Estimate the mean journey time.
  3. Which class interval contains the median journey time?
  4. For a pie chart of the journey times, find the angle of the 10 < t ≤ 20 sector.

Task C: Spot the link (10 min)

A line of best fit on a scatter graph of hand span (cm) against height (cm) passes through (150, 17) and (180, 23).

  1. Find the gradient of the line, and use the line to estimate the hand span of a student who is 165 cm tall.
  2. The heights in the survey were from 150 cm to 185 cm. Would the line give a reliable estimate for a height of 120 cm? Explain.

Extension (10 minutes)

For fast finishers.

  1. Two more students join the hand-span survey, with spans of 16 cm and 24 cm. Find the new mean and the new range.

For teachers

Teacher notes and full worked answers
  • Estimation station: set up four or five stations (a desk to measure, a jar of counters, a corridor, a book’s thickness, a minute with eyes closed). Students write an estimate first, then measure. Being wrong is the point: celebrate the closest estimate and the best reasoning, not just the right answer, and agree a class norm that a reasoned wrong answer is a good start.
  • Class survey: the data in the tasks are made up, so the answers can be checked. Then collect your own class’s anonymous data on the board (a show of hands for travel-time groups, hand spans written on sticky notes with no names) and repeat the calculations. Nothing is stored on the site.
  • Ask each group which estimate surprised them most, and why: it is a good way to learn names as well as reasoning.

Starter

  1. About 1000
    • 50 × 20 = 1000
  2. About 200
    • (600 + 400) ÷ 5 = 200
  3. 25%
    • 30 − 24 = 6
    • 6/24 × 100 = 25%

Task A: Estimation station

  1. 25%
    • Error = 120 − 90 = 30 cm
    • 30/120 × 100 = 25%
  2. Mean 200; 2.0%
    • Mean = 1000 ÷ 5 = 200
    • (200 − 196)/196 × 100 = 2.04…% = 2.0%
  3. 7.35 ≤ T < 7.45
    • Half of 0.1 cm is 0.05 cm either side.

Task B: Class survey: hand spans and travel times

  1. Mean 20 cm, median 20 cm, range 6 cm
    • Total = 200, so mean = 200 ÷ 10 = 20
    • In order: 17, 18, 19, 19, 20, 20, 21, 21, 22, 23; median = (20 + 20) ÷ 2 = 20
    • Range = 23 − 17 = 6
  2. 17.8 minutes
    • Midpoints 5, 15, 25, 35
    • (6 × 5 + 9 × 15 + 7 × 25 + 3 × 35) ÷ 25 = 445 ÷ 25 = 17.8
  3. 10 < t ≤ 20
    • The median is the 13th of 25 values.
    • Running totals: 6, then 15, so the 13th value is in 10 < t ≤ 20.
  4. 129.6°
    • 9/25 × 360 = 129.6

Task C: Spot the link

  1. Gradient 0.2; about 20 cm
    • Gradient = (23 − 17) ÷ (180 − 150) = 6/30 = 0.2
    • 165 cm is 15 cm past 150 cm: 17 + 0.2 × 15 = 20
  2. No
    • 120 cm is outside the range of the data (extrapolation), so the pattern may not hold there.

Extension

  1. Mean 20 cm; range 8 cm
    • (200 + 16 + 24) ÷ 12 = 240 ÷ 12 = 20
    • 24 − 16 = 8

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

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