Net of an open box II

Net of an open box II

Auto-markingPencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about identifying nets for an open box shape.

Question

Here is a box without a top.      Open-box.png
 
Select ALL the nets below that can be folded to make this box.
 
Here is an example of a net that can be folded:      
Open-box-net-H.png
 
 

    • Open-box-net-A.png

    • Open-box-net-B.png

    • Open-box-net-C.png

    • Open-box-net-D.png

    • Open-box-net-E.png

    • Open-box-net-F.png

    • Open-box-net-G.png

Task administration: 
This task can be completed with pencil and paper or online (with auto-marking displayed to students).
Level:
3
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
nets, cubes, 3-dimensional shapes
Description of task: 
Students identify which nets can be folded to make an open box shape.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, sets 3-4
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y7 (03/2010)

No    

 very easy
No      easy
Yes     difficult
Yes      moderate
No     easy
Yes    

difficult
Yes    moderate
Based on a representative sample of 209 Year 7 students.  

NOTE:
All 7 shapes correct (including 4 correct nets) – very difficult;
6 shapes correct (including 3 correct nets) – difficult;
5 shapes correct (including 2 correct nets) – moderate.

Teaching and learning: 
The assessment focus of this resource is on student's ability to visualise and identify nets for a 3-dimensional open top cube.
The questions that really discern students' understanding are those where the students correctly identify the nets that do fold to make the open box cube,
i.e.  Open-box-net-C.png ,  Open-box-net-D.png,  Open-box-net-F.png and Open-box-net-G.png
Diagnostic and formative information: 
Percentage of students who did not identify specific shapes of nets that can fold into the open box shape
67% of students did not show that  could be folded into an open top cube.
43% of students did not show that   could be folded into an open top cube.
51% of students did not show that   could be folded into an open top cube.
43% of students did not show that   could be folded into an open top cube.
The above errors relate to students' ability to translate a 2-dimensional net into a three dimensional shape. 
Many nets tend to have the base at the centre of the shape.
and had the base off centre of a long shape which made it more difficult and could require some visual turning before identifying the folds.
The nets and were more "centrally structured" about the base and were notably easier.
Next steps: 
No correctly identified net
Students who could not identify one correct net may need some time exploring the making and folding of nets to develop and understand how they work. The nets in this resource can be enlarged and cut out for students to explore how they fold. Then they can start to visualise nets that fold to shapes.

Correctly identified one net
A small number of students only identified one net. This may relate to a reading error and have been because they were only looking for one.  For these students ask them if there are any more shapes that can be folded into an open cube.  The nets in this resource can be enlarged and cut out for students to explore how they fold – remind them that the top is open (it is not a total cube).

Correctly identified some of the nets
For students who identified some (but not all the shapes), working in small groups, ask them how many shapes they (as a group) think there are that can fold into the shape.  Get them to justify how each can or cannot fold.  If appropriate, let them know there are four shapes that can fold. Get students to design several similar nets and have them ask the group to identify whether they can or cannot fold into the shape (or another shape).

Correctly identified all the nets
For students who identified all the nets correctly have them share their findings in a small group and discuss how they can check whether the net folds.  Have students describe how the net is folded and then discuss an easy way to identify how they fold (be able to explain to a peer). Showing an X on the base can provide a reference point that illustrates how the net folds not just whether it folds into the shape. Have students design their own nets for other prisms and have them ask others to identify whether the nets can or cannot fold into the prisms, or what shape they fold into.

To explore orientation of nets see Cubes and faces