Rich tasks
- This is an open-ended activity that requires students to identify and sort 3D shapes into groups and justify their decisions. The task can be given at the start of a topic, done as the students gain enough knowledge to complete them, inserted into a topic at an appropriate place, or given as a homework task.
- Treasure!
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1. Treasure!
- Encourage students to find simple 3-D objects from their everyday experience (e.g. a shoe box, high-bounce ball or small can). They may need to find out the names of shapes they do not know as part of the task.
- Whether the activity is done in class or for homework, it is worthwhile giving students opportunity to share their ‘treasures’ in groups or class. Objects might also provide a useful resource for the “Guess what I have” game on page 253 of the Student Resource Book.
- The pictures / objects and description cards students make in this task could form a ‘museum’ display, providing students with objects they could group and re-group later in different ways. Students could make a record by photographing the different groupings they have made.
- If done as a homework project, you could ask students to contribute a page for a ‘class book’ about some of the groups they made. If your students have access to appropriate digital tools they could write or record these descriptions in a digital book or presentation.
Naming and describing 3D shapes page 248
- Understand the difference between 2-D and 3D shapes.
- Describe 3D shapes using mathematical language, for example faces, corners and edges
- Know the names of 3D shapes, for example prisms, cones, pyramids, cylinders and spheres
- Develop mental images of 3D shapes from attributes described by others.
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Teacher notes
- Encourage students to look closely and discuss similarities and differences between 3-D shapes when describing them. Students at this level do not need to see all the differences or create precise mathematical definitions, but they should be encouraged to ‘notice’. For example, a student may observe that both cones and pyramids meet at a single point or apex, and that they differ because the cone has a curved rather than flat face.
- If possible students should have access to actual 3-D shapes to manipulate, name, describe and sort throughout the chapter. If commercial shapes are not available, students could make their own with plasticine or playdough and straws, use real objects, containers or packaging, or students working at Level 3 or 4 could construct 3-D shapes from nets for use in junior classes.
- Making shapes, for example with playdough or plasticine as in ‘Look what I made!’ on page 249 of the Student Resource Book is helpful for students who need further experience of flat and curved faces or to support counting and description of the number of sides, corners or edges since the material can be marked as it is counted.
- Encourage students to notice shapes in the real world. Discussion about how the properties of a shape affect the purpose for which they are chosen is important in the curriculum at this level. Students could take photographs of 3-D shapes if they have digital devices. The properties (edges, faces, corners) could be identified/labelled on each image using appropriate software such as ‘Skitch’.
- Model mathematical vocabulary and encourage students to use it themselves when talking about shapes and their properties. Ensure students realise an edge is the line where two faces meet, and a corner or vertex is a point where at least 3 edges meet. Ask students to touch the corner point or run their finger along the edge if they seem unsure.
- It is important students use the words “edges” and “faces”, rather than “sides” to describe 3-D shapes. When counting these features, it is helpful if students are able to mark the shape or drawing in some way (e.g. with colours, stickers), to keep track of what has already been counted.
- A corner may also be referred to as a vertex (plural - vertices). Similarly, cuboids are called rectangular prisms, and triangular pyramids (composed of equilateral triangles) may be called tetrahedrons.
You will need to explain these and other terms when they arise. There are many mathematical dictionaries available online which you can refer to. NZmaths have a helpful glossary which relates specifically to the NZ curriculum at https://nzmaths.co.nz/nzc-glossary-mathematics-terms
Sorting 3D shapes page 254
- Sort 3D shapes according to categories they and others have created.
- Justify why shapes have been grouped the way they have.
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Teacher notes
- At level 2 students should know the names and be able to describe and sort these 3-D shapes.
cylinders, spheres, cubes and cuboids, triangular and other prisms, cones, pyramids with different shaped bases
- Students need opportunities to describe and sort 3-D shapes in groups that make sense to them, before they are introduced to categories such as pyramids and prisms.
- Students should be encouraged to look closely at each item in the groups they create to check they all share the attribute(s) they are being sorted by.
- Provide opportunity for students to resort the same set of objects in a different way or independently of each other and justify their groupings, as this will support understanding that shapes may fit into more than one group, and therefore can legitimately be grouped in several ways. For example, a square can fit into a quadrilateral group and into a group of regular polygons.
Nets page 256
- Investigate the way 3D shapes create a 2D net.
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Teacher notes
- In this activity students deconstruct and then reconstruct a box. Try to provide a range of different sized and shaped boxes (preferably only cuboids at this point as this makes the various faces easier to discriminate between).
- If possible, provide students with boxes that have 6 complete faces rather than bases or lids made of parts. Students may also notice and therefore need to discuss the purpose of “flaps” in the construction of some boxes.
- Looking at the plain sides of packaging (rather than the coloured side), encourages students to attend to the shapes within the net and how they relate to specific edges, faces, or corners.
