Estimating the area of Antarctica

Estimating the area of Antarctica

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Further Resources

Continent area
Here is a map of Antarctica.

Estimate the area of Antarctica using the map scale. Show your working out and explain how you made your estimate.
(You can draw over the map if it helps you with your estimation).
 
 
 
 
 
 
 
 
 
 
 
 
 
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
pisa, estimation, area
Description of task: 
Students use a scale map to estimate the area of Antarctica and explain their method.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 7-8
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
Scoring:   Y11 (09/2000)
2 marks
or

These scores are for answers that use the correct method AND give the correct result. The second digit indicates the different approaches. 

Any 1 of:

  • Answers which are estimated by drawing a square or rectangle – between 12 000 000 sq kms and 18 000 000 sq kms (units not required).
  • Answers which are estimated by drawing a circle – between 12 000 000 sq kms and 18 000 000 sq kms.
  • Answers which are estimated by adding areas of several regular geometric figures – between 12 000 000 and 18 000 000 sq kms.
  • Answers which are estimated by other correct methods - between 12 000 000 sq kms and 18 000 000 sq kms.
  • Answers which are correct (between 12 000 000 sq kms and 18 000 000 sq kms) but no working out is shown.

These scores are for answers that use the correct method BUT give an incorrect or incomplete result. The second digit in parentheses indicates the different approaches, matching the second digit in parentheses of the Full credit Scores.

 16%
 
 
1 mark
or
Any 1 of:
  • Answers which are estimated by drawing a square or rectangle – correct method but incorrect or incomplete answer. For example:

    • Draws a rectangle and multiplies width by length, but the answer is an overestimate or an underestimate (e.g., 18 200 000).
    • Draws a rectangle and multiplies width by length, but the number of zeros is incorrect (e.g., 4 000 × 3 500 = 140 000).
    • Draws a rectangle and multiplies width by length, but forgets to use the scale to convert to square kilometres (e.g., 12 cm × 15 cm = 180).
    • Draws a rectangle and states the area is 4 000 km × 3 500 km. No further working out.
  • Answers which are estimated by drawing a circle - correct method but incorrect or incomplete result.
  • Answers which are estimated by adding areas of several regular geometric figures - correct method but incorrect or incomplete result.
  • Answers which are estimated by other correct methods - but incorrect or incomplete result.
 44%
0 marks Any 1 of:

  • Answers which show the perimeter instead of area. For example: 16 000 km as the scale of 1 000 km would go around the map 16 times.
  • Incorrect answers. For example: 16 000 km (no working out is shown, and the result in incorrect).
  

NOTE: © OECD (2002). Reproduced with permission of the OECD.