Volume and surface area II

Volume and surface area II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about volume and surface area.
This shape is made up of four cubes, all the same size, glued together.
Each cube has sides of 5 cm.
a) If calculated correctly, which expression gives the volume of one cube?
  (A)   4 × 4 × 4    
(B)   5 × 5 × 5    
(C)   6 × 6 × 6    
(D)   4 × 5 × 6

(E)   None of these. The correct expression is __________
 
b) What is the total volume of the four cubes?
  (A)   256 cm3    
(B)   480 cm3    
(C)   500 cm3    
(D)   864 cm3

(E)   None of these. The volume is __________  cm3
 
c) If calculated correctly, which expression gives the area of one face of one cube?
  (A)   1 × 3 × 5    
(B)   1 × 6 × 5    
(C)   1 × 5 × 5    
(D)   6 × 5 × 5

(E)   None of these. The correct expression is __________
 
d) What is the surface area of the six faces of one cube?
  (A)   90 cm2    
(B)   150 cm2    
(C)   180 cm2    
(D)   900 cm2

(E)   None of these. The surface area is __________ cm2
Task administration: 
This task can be completed with pencil and paper.
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, surface area, volume, cuboids
Description of task: 
Students answer four multiple-choice questions about volume and surface area.
Curriculum Links: 
This resource can help to identify students' understanding of voulme and surface area and multiplicative strategies.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 6-7
Multiplicative thinking, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   

Y8 (10/1997)
a) B (5 × 5 × 5) easy
b) C (500 cm3) easy
c) C (1 × 5 × 5) [Accept E and 5 × 5.] easy
d) B (150 cm2) easy
Diagnostic and formative information: 
  Student response Likely calculation Likely reason
a) E – 5 × 5 × 5 × 5
E – 5 × 5 × 6

 

 Expression for volume of four cubes.
Surface area for one cube.
b) E – 125
E – 375		 5 × 5 × 5
3 × 125		 Volume of one cube.
Volume of three cubes.
c) E – 1 × 4 × 5

 

  
d) E – 120 4 × 5 × 6