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Shapes and Transformations progression


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Last updated 10 January 2013 11:10 by NZTecAdmin

Adults are able to sort, describe, define and create representations of shapes and the ways in which they can be transformed in space. They use strategies to apply their knowledge of shapes to tasks in their everyday lives.

Most adults will be able to:
Activities
1.
  • sort and describe objects by their shape attributes.

Learners can:

  • sort objects by shape attributes into groupings, such as cylinders and boxes
  • describe the shape attributes of objects, for example, a box has 6 rectangles as faces.
 
  • sort and describe objects by their shape attributes.
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2.
  • identify and describe plane shapes in objects
  • record the result of transformations (flips, turns and slides) on plane shapes.

Learners can:

  • identify plane shapes, including triangles, rectangles and circles in everyday objects
  • record the result of flipping, sliding or turning plane shapes.
 
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3.
  • create mental images of plane shapes
  • recognise and represent plane shapes in objects from different perspectives
  • predict and communicate the results of transformation (flips, turns, slides and/or scaling) on plane shapes.

Learners can:

  • identify and sketch (from observation involving different points of view and perspectives) plane shapes
  • predict the result of flipping, sliding, turning and/or scaling plane shapes.
 
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4.
  • define plane shapes and prisms by their spatial features
  • create and describe mental images of prisms, including cylinders
  • make two-dimensional representations of prisms (and vice versa)
  • describe the transformations (flips, turns, slides and/or scaling) that are used to map one object onto another.

Learners define plane shapes and prisms by their spatial features. For example, a learner can make, state, draw and describe:

  • a triangle as a plane shape that has 3 straight sides and 3 corners (vertices)
  • a rectangle as a plane shape that has 4 straight sides (quadrilateral) and 4 right-angled vertices
  • a parallelogram as a quadrilateral with parallel opposite sides.
 
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5.
  • define classes of plane shapes by their geometric properties and classes of solid shapes by their surfaces
  • use spatial visualisation to solve problems that involve surface area and volumes of prisms
  • describe sizes, positions and orientations of shapes under transformation (flips, turns, slides and/or scaling).

Learners can define classes of plane shapes by their geometrical properties and classes of solid shapes (such as cuboids and spheres) by their surfaces. For example, a learner can describe the relationships among types of parallelograms, such as a rhombus, square and rectangle.

Parallelogram Rectangle Rhombus Square

 
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6.
  • visualise three-dimensional objects and spaces from different perspectives and analyse their cross-sections
  • examine the congruence, similarity and line or rotational symmetry of objects, using transformations.

Learners can visualise and describe three-dimensional objects and spaces from different perspectives and know the congruence, similarity and line or rotational symmetry of objects. For example, a learner knows that:

  • all squares have rotational symmetry of order 4 and therefore all squares have 4 right-angled vertices and 4 congruent sides with parallel opposite sides
  • all squares have 4 congruent sides with parallel opposite sides, 2 axes of symmetry that are perpendicular bisectors of adjacent sides of the square and 2 axes of symmetry that bisect the vertices to make angles of 45 degrees.
 
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