View from a different angle

View from a different angle

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 recognising a 3-D shape from different angles.

Question

Jared's 3-D shape
Jarrod had four cubes that were glued together.  The shape is shown above.
 
Select all the shapes below which show Jarrod's shape from a different angle. 
The shape may have been turned sideways or upside down, or rotated.

    • 3-D shape option 1

    • 3-D shape option 2

    • 3-D shape option 3

    • 3-D shape option 4

    • 3-D shape option 5

    • 3-D shape option 6

    • 3-D shape option 7

    • 3-D shape option 8

    • 3-D shape option 9

Task administration: 
This task can be completed with pencil and paper or online (with auto-marking displayed to students).
Copyright: 
Graphics copyright (c) NZCER
Level:
4
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
views, 3-dimensional shapes, visualising
Description of task: 
Students identify shapes after they have been rotated in 3 dimensions.
Curriculum Links: 
This resource can help to identify students' ability to sort 3-dimensional shapes into classes.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Geometric thinking, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y8 (10/2015)
Each individual shape correctly identified as identical or different
 
All 9 shapes correct (i.e., 3 correct identical options identified)
8 or more shapes correct, with none incorrect
Correct answers shown: option 2, 3 and 8
very easy
 
easy
very easy
Based on a representative sample of 102 Y8 students.
Teaching and learning: 
  • This resource is about being able to visualise in three dimensions by recognising which objects are identical to a given one.
  • Students need to be able to visualise the effects of rotating the given 3-D shape.
  • Students in the trial found each individual shape very easy, but only about two-thirds of them could get all nine shapes correct.
Diagnostic and formative information: 
Common error  
  • About a fifth of students in the trial did not identify this shape as being correct.
  • This shape required a more complex rotation.
 option 8 shape
  • A smaller number of students did not identify this shape as being correct.
  • This shape required a more complex rotation.
 option 2 shape
  • These were the most commonly identified shapes that were not identical to the target shape.
  • These are more complex shapes as they had a height and a width of two blocks. The other three shapes that are not identical have all the blocks lying in a 2-D plane.
 option 1 shape  or    option 7 shape
Next steps: 
Visualising more complex rotation
These students may need more practice drawing 2-D representations of 3-D shapes (Click on views for examples). They may then need practice on visualising 2-D representations of 3-D shapes.
 
Visualising more complex shapes
Students could use explore the different shapes in the soma cube, especially the three that have a height and a width of two cubes. Two of these are mirror images, and the third is the initial shape given in this resource. Students may also need more practice on visualising 2-D representations of 3-D shapes. Students could use digital technology and take their own photos of 3-D shapes, and make this type of problem to give their peers to solve.
 
The resource View from a different angle II is very similar, but focusses on reflection as well as rotation. This makes it a harder option for students.