Constructing different shaped boxes

Constructing different shaped boxes

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
This task requires is about making boxes from grid paper and calculating the volumes.
For this task you are going to construct 3 different sized boxes (without lids) and calculate their volumes.
 
a)
Make three boxes, of different sizes, each from a piece of 12 cm× 12 cm square grid paper you have been given.
Label the boxes A, B, and C. Each box can only be made by cutting out a square or squares from each corner of your grid paper (an example is shown in the diagram below), and then folding up and cellotaping each side.
 
 i.e.,
 
b)
Calculate the volume of each open box you have made.
 
Volume of Box A = ______________
 
Volume of Box B = ______________
 
Volume of Box C = ______________
 
c)
If you were now asked to make a box without a lid from a piece of 8 cm × 8 cm square grid paper (by cutting out squares from each corner), what dimensions would you construct to give it:
 
  i)
 
ii)		 maximum volume? _______________
 
minimum volume? _______________
 
Square Grid Template: 12 cm × 12 cm 
Task administration: 
Equipment:
Three 12 cm x 12 cm squares cut out of grid paper per student; scissors; cellotape.
  • This task assesses the students' ability to construct open boxes from grid paper and calculate their volumes.
  • Students could do part a) individually, in pairs, or as a group. Parts b) and c) should be done individually.
  • The students should work with whole squares in the grid, rather than part squares.
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
volume, model construction, nets
Description of task: 
This practical task requires students to construct open boxes from grid paper and calculate their volumes.
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: 

 

  

3 marks
(1 mark each)

 a)  

Constructs and labels three boxes without lids, with any 3 of the following dimensions:
 

  • 10 × 10 × 1
  • 8 × 8 × 2
  • 6 × 6 × 3
  • 4 × 4 × 4
  • 5 × 5 × 2

3 marks
(1 mark each)
1 mark

 b)  

Calculates the correct volume for the boxes they have constructed
in part a).
Records units of cm3 for all volumes calculated.

1 mark
1 mark
1 mark

 c)

i)
ii)

6 × 6 × 1 (also accept 36)
2 × 2 × 3 (also accept 12)
Records units of cmfor all lengths noted, or cm3 for all volumes.