Using cubes

Using cubes

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working out perimeter and volume.

Question 1Change answer

     A Soma cube is made from 27 small cubes. Each small cube has a side measurement of 3 cm.
soma-cube.png
a)  What is the length of one side of the Soma cube? cm
b)  What is the volume of the cube? cm3

Question 1Change answer

     Jack made a cross from 5 cubes. Each small cube has a side of 4 cm.
cross-of-cubes.png
c)  What is the perimeter of the front face of the cross?  cm

d)  What is the volume of the cross? cm3
Task administration: 
This task can be completed with pencil and paper or online (with SOME auto marking).
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
length, perimeter, volume, cuboids, 3-dimensional shapes
Description of task: 
Students calculate the volume of 3-dimensional shapes made up from cubes.
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 (07/1997)
a) 9 easy
b) 729 (9 × 9 × 9)
[Accept if = a)3.]		 difficult
c) 48 difficult
d) 320 very difficult
Diagnostic and formative information: 
  Common errors Likely calculation Likely misconception
a)
b)		 3
27		 3
3 × 3 × 3		 Ignores that each cube is 3 cm.
a) 27 3 × 3 × 3 Confuses length with area and volume.
b) 81 9 × 9 Confuses area and volume.
c) 16
12
20		 4 × 4
4 × 3
5 × 4		 Counts only some of the perimeter.
Counts only some of the perimeter.
Assumes each of the 5 cubes contributes 4 cm to the perimeter.
d) 20
80		 5 × 4
5 × 4 × 4		 Confuses length and volume.
Confuses area and volume.