# Sorting shapes II

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Overview

Using this Resource

Connecting to the Curriculum

Marking Student Responses

Working with Students

Further Resources

**This task is about putting shapes into groups, then describing the groups you have made.**

Task administration:

This task can be completed with pen and paper or online (with NO auto marking).

Level:

2

Curriculum info:

Keywords:

Description of task:

This task is about sorting shapes into different groups.

Curriculum Links:

This resource can help to identify students' understanding of the

*properties of shapes*.Learning Progression Frameworks

This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.

Read more about the Learning Progressions Frameworks.Answers/responses:

This student has sorted the shapes with a clear justification,

e.g.,

**Question a)**

**Question b)**
Sorting the shapes into groups based on being

*open*or*closed*was the most common justification that students gave for their decision.
Some students used phrases such as finish ones/not finish, They all have gaps, joined/not joined or they're not cinicting

*(sic)*to describe the shapes being*open*or*closed*.
Most students sorted the shapes into two groups. Triangles and right angles were two other commonly used classifications, e.g.,

- the shapes in the box is some kind of triangle
- because one group is a open shape group and one group is right angle

Students could also sort by other attirebutes AND into three (or more) groups,.e.g, number of sides/corners, or for question b) colour.

*Based on an online sample of 25 students.*

Teaching and learning:

The aim of this resource is to encourage students to justify their reasons for sorting shapes into groups. These justifications should ideally be based on geometric properties such as open/closed, right angle, number of sides, number of corners, parallel lines, etc.

Diagnostic and formative information:

Common error |
Likely reason |

Students are unable to sort the shapes into discrete groups. | Students may not have enough experience of shapes and their properties to be able to group a set of shapes. |

Students sort the shapes into groups but provide no justification. | Students may not have the necessary geometric vocabulary to explain their groups. |

Students give an insufficient justification such as because they look the same. | Students may not have the necessary geometric vocabulary to explain what it is about their groups that is the same or different. |

Students give a clear justification for their classification but one or more shapes do not fit in the group described. | Students may have a misunderstanding of one or more geometric terms, e.g., right angle |

Next steps:

**Students are unable to sort the shapes into discrete groups**

These students may need more practice with grouping and sorting more familiar shapes before moving on to irregular shapes or shapes with open sides.

Using materials such as attribute blocks or 2-D shapes, have students sort the shapes into groups and explain their reasoning.

The following Level 2 ARB resources could be used to help students build up their capacity to describe and sort shapes. They use vocabulary such as curved, straight, corners and sides.

**Students sort the shapes into groups but provide no justification.**

Building up precise geometric vocabulary with students is important so they can explain or justify their ideas or provide definitions.

Some of the key vocabulary that students may need to develop in the early years of geometry might be: sides, corners, open/closed shapes, right-angle, straight, curved, parallel and perpendicular.

This skill can be developed by providing students with a shape and having them describe it with as much detail as they can. The following Level 2 ARB resources provide models for the use of this type of vocabulary:

**Students give an insufficient justification such as because they look the same.**

Students whose explanation was insufficient could be asked probing questions such as "What is the same about these shapes?" or "What do you notice about this group of shapes you have put together?"

Some students may not have the necessary vocabulary to explain their reasoning. Refer to the ideas above for ways to help students develop their geometric vocabulary.

**Students give a clear justification for their classification but one or more shapes do not fit in the group described.**

If students have given a justification such as because they all have right angles but then have included an equilateral triangle in the group, ask the student what their understanding of right angle is and then identify shapes in and around the classroom which have right angles. The Level 3 ARB resource Right angled triangles could be used to check this understanding further.

Similarly, some students may have included the arrow shape in the group 'triangles' because it has a triangular quality to it. This could open up a discussion on the properties of a triangle (three sides, three angles, three corners) against which they could check the arrow shape and other similar-looking shapes.

For more information about shape properties and geometric thinking refer to the Geometric Thinking Concept Map.