Math // Geometry

Recognising and drawing shapes by attributes

Recognise and draw shapes having specified attributes (e.g. a given number of angles or equal faces); identify triangles, quadrilaterals, pentagons, hexagons, and cubes

Ages
7 to 8
Type
Method
Builds on
2 topics
Leads to
1 topic
Standards
1 code

Quick check

If the learner is given instructions like "draw a shape with 5 sides" or "draw a shape with all equal angles," can they draw it correctly?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Draw a shape with exactly 5 sides (pentagon)
  • Identify all quadrilaterals in a set of mixed shapes
  • Name and draw a hexagon, explaining it has 6 sides and 6 angles

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • 2-D shapes (age 6+)Required

    Geometry // Ages 6 to 7

    Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties

  • Defining attributes of shapesRequired

    Geometry // Ages 6 to 7

    Drawing shapes by attributes extends understanding defining vs non-defining attributes

You are here

Recognising and drawing shapes by attributes

Ages 7 to 8 // Method

Leads to

1 topic
  • Classifying quadrilateralsRequired

    Geometry // Ages 8 to 9

    Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Children learn to draw and identify polygons by their defining attribute — a pentagon is ANY closed figure with five straight sides whose sides do not cross each other, not one memorised 'textbook' shape. The core obstacle is the prototype effect: learners draw and accept only the regular, symmetrical, horizontal-base version and miss irregular, tilted or rotated members of a class. Guidance centres on generating many varied and irregular examples, defining each class by its attribute (side/vertex count, closed, straight-sided, sides not crossing), and hunting for ALL members in mixed sets that include non-prototypical and near-miss shapes. Accurate side/vertex counting is scaffolded by marking each once.

Common misconceptions

  • Draws or accepts only the prototypical regular, symmetrical, horizontal-base example and misses irregular or rotated members of a class.
  • Miscounts sides or vertices when drawing or identifying (draws six sides when asked for five; loses track counting an irregular shape).
  • Draws a non-closed figure or one with curved sides, not attending to 'closed' and 'straight-sided'.
  • Judges class membership by the name/look ('that's not a quadrilateral, it's a diamond') rather than by counting the sides.

Useful representations

  • Geoboard / pegboard and dotted paper for constructing polygons to a target side-count
  • Mixed shape sets containing regular, irregular, tilted and near-miss examples plus non-examples
  • Side/vertex tally marks made while counting
  • Side-by-side regular vs irregular pentagon/hexagon to show both satisfy the attribute

Teaching practices

  • Define each shape class by its attribute (a hexagon is ANY closed shape with 6 straight sides / 6 vertices) and check drawn shapes against it.
  • Demand and celebrate IRREGULAR and rotated examples — 'draw a different pentagon that doesn't look like that one' — to break the single-prototype image.
  • Give mixed 'find them all' sets that include irregular, tilted and near-miss shapes so identifying a class means applying the attribute, not matching a picture.
  • Model counting and marking each side/vertex once when drawing or checking, so the side-count is accurate.
  • Use dotted paper, geoboards or a peg grid to support accurate drawing of straight-sided closed figures.

Activities to try

  1. 1

    Build a polygon to a target side-count

    Why it works: A polygon class is defined by its attribute (number of straight sides meeting at vertices, closed figure with sides that do not cross), invariant to size, orientation and regularity — not by matching a single remembered prototype.

    1. Given an instruction such as 'build a shape with exactly five straight sides', construct the figure on dotted paper, a geoboard, or a peg/rubber-band grid.
    2. Count and mark each side (and vertex) once as it is drawn, so the total is checked rather than guessed.
    3. Ensure the figure CLOSES and that every side is straight before declaring it finished.
    4. When one valid shape is made, draw 'a different pentagon that does NOT look like the first one' — a long, spiky, or irregular one.
    5. Compare a regular and an irregular example of the same class side by side and state why both satisfy the attribute.
  2. 2

    Find them all in a mixed set

    Why it works: Identifying a class means applying its attribute to every candidate, including irregular and rotated ones, rather than recognising a familiar picture.

    1. From a mixed set that includes regular, irregular, tilted, rotated and near-miss shapes plus non-examples, mark EVERY member of a named class (e.g. 'circle all the quadrilaterals').
    2. For each shape marked or skipped, justify by counting sides/vertices and checking closed + straight-sided, not by its name or look.
    3. Deliberately inspect the awkward shapes — a long thin tilted four-sided shape, a dented pentagon — and decide membership by the attribute.
    4. Explain why a square is a quadrilateral, and why a 'diamond' is also a quadrilateral regardless of its orientation.
  3. 3

    Name, draw and justify by attribute

    Why it works: Justifying class membership by the attribute count — and producing a non-prototypical second example — demonstrates the definition is understood, not just a remembered shape.

    1. Draw a named polygon (e.g. a hexagon) and explain how you know it is one by counting its six straight sides and six vertices/angles.
    2. Produce a second example of the same name that looks clearly different from the first.
    3. State the defining attributes in your own words ('a hexagon is any closed shape with six straight sides that do not cross each other').

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
2.G.1

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