Measuring the park

Measuring the park

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working out the area of a park.
[NOT DRAWN TO SCALE]
 
The diagram above shows the measurements of a park.
 
What is the area of the park, in hectares? __________ ha
 (NOTE: 1 ha = 10 000 m2)

Show all your working, with the formulas you use, in the box below.
 
 
 
 
 
 
 
 
 
 
 
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, composite shapes, rectangles, triangles, hectares
Description of task: 
Students calculate the area of a composite shape.
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: 
  Y10 (12/97)
Area of rectangle correct i.e., a = b × h,
or Correct formula given i.e., 350 × 300 m2 = 105 000 m2		 moderate
Area of triangle(s) correct i.e., a = b × h, or  
Correct formula given i.e., 
(75 × 100) m2 = 3750 m2, or  
75 x 100 = 7500m2 (they have automatically added the two areas of the triangles together in one step)		 difficult
Addition of the first 2 parts (above) and the correct conversion i.e., divide answer(s) by 10 000 (even if errors in area answers above). difficult
 
NOTE: If students record correct answer, 11.25 ha, they automatically gain 1 mark for each part, regardless of working.
Diagnostic and formative information: 
Student response Likely calculation Likely reason
1600 (or 1.6)   Confuses area and perimeter.
1.75 50 × 500 ÷ 10 000 Doesn't use composite shapes correctly.
12 10.5 + 2 × .75 Calculates area of triangle as base × height
13 10.5 + 2 × 1.25 Calculates area of triangle as base × hypotenuse.