How big is the dressing table?

How big is the dressing table?

Pencil and paper
Overview
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about calculating width, height, perimeter, area and volume.

  drawers.png

The dressing table above has three rows, and each row has three drawers. The drawers have the following measurements:

  • all drawers are 30 cm wide
  • row 1 drawers are 12 cm high
  • row 2 and row 3 drawers are 20 cm high
  • all spaces around the drawers are 3 cm
 
a)
 
i)
 
ii)
 
What is the width of the dressing table? __________ cm
 
What is the height of the dressing table? __________ cm
 
b) What is the perimeter of the front face of the dressing table? __________ cm
 
c) What is the area of the front face of the dressing table? __________ cm2
 
The diagram below shows the measurements of one of the bottom drawers of the dressing table.

d) What is the volume of the drawer? __________ cm3
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, perimeter, volume, rectangles, cuboids
Description of task: 
Students calculate the width, height, perimeter and area of a dressing table, and the volume of a drawer from given measurements.
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 (12/1997)
a) i)
ii)		 102
64		 easy
easy
b)   332 [Accept if = 2 × {a) i) + a) ii)}.] moderate
c)   6 528 [Accept if = a) i) × a) ii).] moderate
d)   18 000 moderate
Diagnostic and formative information: 
  Student response Likely calculation Likely reason
a) i)
    ii)		 99
61		   Ignores one 3 cm strip.
b) 166 102 + 64 Calculates half of true perimeter.
c) 166 102 + 64 Confuses area and perimeter.
d) 80
 
320
 
18, 180, 1800		 30 + 30 + 20
 
4 × 3 + 4 × 30 + 4 × 20		 Adds rather than multiplies
dimensions to get volume.
Confuses volume and length
of all edges of the cuboid.
Wrong order of magnitude of answer.