# Dear Family, your Operation Maths guide to 3-D Objects

## Dear Family, your Operation Maths guide to 3-D Objects

Category : Uncategorized

Dear Family, listed below are some practical suggestions as to how you might support your children’s understanding of the maths topic of 3-D objects. Also below, are a series of links to digital resources that will help both the children, and you, learn more about 3-D objects. The digital resources are organised according to approximate class level.

#### Practical Suggestions for all Children

• Naming shapes: 3-D is short for three dimensional, i.e objects with length, width and depth/height. In Operation Maths we refer to them as 3-D objects, so as to distinguish them from their flat, 2-D relations. 3-D objects can also be referred to as solid shapes and they include cubes, cuboids, spheres, cones, cylinders, pyramids, etc. Distinguishing between 2-D shapes and 3-D objects can be a bit confusing for both adults and children; for example, the shape of a real ball may be referred to as a circle, since, if a ball is drawn, or shown in a picture, then the flat, 2-D shape of the ball in the image is now a circle! But in reality, it is a 3-D object called a sphere. And a box is not a 2-D shape, it is a 3-D object called a cuboid, but the flat surface of a box is usually the 2-D shape of a rectangle or, sometimes, a square. So, if looking for 3-D objects at home, ask the children to examine and if possible pick up, actual objects, as opposed to flat representations of the shapes in a picture book or magazine.
• 3-D Shape hunts: Play games like “I spy, with my little eye, something the shape of a cube, cuboid, sphere” etc. Again, be careful that you affirm with your child that it is the entire object that you are looking at, as opposed to just a surface or a flat face of the object.

• Sweet! A great place to find 3-D shapes is in treats and their wrappings or containers. Next treat time, look carefully at your Maltesers (spheres), Toblerone box (triangular prism), Smarties container and Lindor chocolates box (both hexagonal prisms), tub of Quality Street (octagonal prism) Starburst/Opal Fruits (cuboid), mini-rolls and hot chocolate powder (both cylinders) and wafer cones (cone, of course!)
• Properties: Each family of 3-D objects also has properties or characteristics that make them different from other 3-D objects. In the younger classes, the children will be exploring whether a 3-D object can roll, stack, slide etc. When out and about or helping around the house, children can be asked to name the 3-D objects that are easier to stack on shelves in the shop, in the cupboard etc? What 3-D objects might roll off a shelf? As the children get older, they will be exploring properties such as the number of corners (also called vertices), the number and type of edges (straight or curved), and the number and type of surfaces (flat faces or curved surfaces). Through developing a better understanding of what makes an object that 3-D object, the children can start to group 3-D objects with similar properties or characteristics together.
• Take it apart! 3-D objects and 2-D shapes, as mentioned earlier, are very connected. Another way that children can explore this relationship is to take apart examples of 3-D objects. Boxes are ideal for this, so, before you put your boxes in the recycling bin, ask your child to tear it open along an edge so as to open it out flat and identify the 2-D shapes that make it. This is referred to as the 2-D net of a 3-D object. Did they see the 2-D shapes they expected to see?
• Play, play, play! Encourage your child to play and explore with 3-D objects as much as possible:
• Lots of the toys that are aimed at preschool age children focus on 3-D shapes: wooden building blocks, shape sorter toys etc. Even older children can return to these toys and look at them in a new way to see what they can now discover and say about these shapes.
• Magformers , Geomag and 3-D puzzles are examples of toys specifically geared towards the construction of 3-D structures. Other toys that can be used to create 3-D structures include Lego, K’nex, Mega Bloks, Plus-Plus and Stickle Bricks/Bristle Blocks.
• Build anything! Use boxes and any objects from around the home to build, stack, etc. Without even realising it, the children will be exploring and learning about the properties of these shapes.
• Solve 3-D puzzles. Perhaps you have a Rubik’s Cube somewhere around the house? Or look out for other 3-D puzzles like Rubik’s Cage, Soma cube or Tetris Shake. Any of these these type of puzzles are a very worthwhile way to spend time!

#### Digital Resources for Infants

The Number Jacks have quite a number of 3-D shape-based episodes including Sphere today, Gone tomorrow, a Circle at both ends (cylinder) and Boxing Day.

3-D Shapes Song: Introduces cone, cylinder, cube and sphere.

3-D Solids: A video lesson from Matholia introducing common solid (3D) shapes, including cubes, cuboids, cones, cylinders, spheres and pyramids.

I know it – Geometry & Shapes Try the solid shapes interactive quizzes for Kindergarten

Solid Shapes: A selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. Activity L1-L7 are all about solid, 3-D objects.

Math Games: a whole suit of geometry games, for all class levels; choose the skill you want to practice.

#### Digital Resources for First and Second Classes

NB: Children in first and second may also enjoy the links for infant classes, above

Describing and Naming Solids: A video lesson from Matholia describing the properties of common solid (3D) shapes, including cube, cuboid, cylinder, cone and sphere.

White Rose Geometry: a series of lessons on 2-D and 3-D shapes. These lessons could be followed up with other geometry lessons in year 2

What Shape am I? Use the clues to identify the name of the 3-D object. Guess the name before you click on to see the answer.

Drawing 3-D Objects: Video to show how to draw 3-D objects. Drawing is a great way to understand these shapes better.

I know it – Geometry & Shapes Scroll down to the interactive quizzes for Grade 1 and for Grade 2

3-D Shapes: A selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. Activity N1-N10 are all about 3-D shapes.

Math Games: a whole suit of geometry games, for all class levels; choose the skill you want to practice.

#### Digital Resources for Third to Sixth Classes

NB: Children in these classes may also enjoy the links for first and second classes, above

Maths is Fun: Background information on 3-D solids as a part of geometry.

Describing and Naming Solids: A video lesson from Matholia describing the the characteristics (e.g. faces, edges, corners) of common solid (3D) shapes, including cube, cuboid, cylinder, cone and sphere.

Khan Academy – Solid Shapes: Watch this series of videos on geometric solids and answer the practice questions.

3-D Shapes: Lots of useful information about 3-D shapes from BBC Skillswise, including a video highlighting 3-D shapes in the real world.

Drawing 3-D Objects: Video to show how to draw 3-D objects. Drawing is a great way to understand these shapes better.

Cube Nets: Can you predict which of these nets will form a cube? Make your prediction and then watch the animation to see if you were correct.

IXL: A selection of geometry games from ixl.com. You can do a number of free quizzes each day without having a subscription.

I know it – Solid Shapes: Interactive quiz for Grade 3 and another one for Grade 4

Kangaroo Hop: Get your kangaroo to the finish line first by choosing the correct 2-D or 3-D shapes.

Math Games: a whole suit of geometry games, for all class levels; choose the skill you want to practice.

3-D shape quiz: For 5th or 6th class or those looking for a challenge!

## Digging Deeper into … 2-D Shapes and 3-D Objects (infants to second class)

Category : Uncategorized

For practical suggestions for families, and helpful links to digital resources, to support children learning about the topic of 2-D shapes and 3-D objects, please check out the following posts:

Dear Family, your Operation Maths Guide to 2-D Shapes

Dear Family, your Operation Maths Guide to 3-D Objects

### 3-D shapes or 3-D objects?

In the PDST Shape and Space manual, it is suggested that “using the word ‘shape’ to describe both 2-D shapes and 3-D shapes can cause confusion for pupils”. For example, asking pupils to ‘describe the shape of this shape’ highlights one problem. Another problem is that pupils must be able to think of all cuboids as being ‘the same shape’, while mathematically speaking all cuboids are not the same shape.

The manual goes on to suggest that it would be more helpful to refer to 3-D things as ‘objects’. Using ‘objects’ also reinforces the notion that if it can be physically handled/picked up, it must be a 3-D object, as opposed to a 2-D shape which should always only have length and width, not depth/height.

So, throughout the Operation Maths books, this topic is titled 3-D objects to avoid confusion and to provide clarity for the pupils. However, wherever there is reference to “strand unit”, the term 3-D shapes is used, as this is the term used in the 1999 Primary Maths curriculum.

### So what first? 2-D or 3-D?

2-D and 3-D objects are very inter-related, to the point that there is often much debate about which of the topic should be taught first; 2-D shapes, 3-D objects or teach them both concurrently.

Since 2-D shapes are lacking the third dimension of depth or height that their 3-D relations possess, this makes them quite abstract as only flat, drawn/printed shapes are truly 2-D. Whereas, 3-D objects can be picked up, manipulated, used for constructions etc., making them much more suited to the concrete learning experiences that are essential in the early years. They are the objects that we find in the real-world. Thus, since 2-D shapes are only flat representations of the faces of 3-D objects, it could be argued that it would be more logical, and more in line with the concrete-pictorial-abstract (CPA) approach, to teach about 3-D objects before 2-D shapes.

On the other-hand, it could be argued that 2-D shapes should be taught first as it is likely than young children would be more familiar with them. For example, the vocabulary of 2-D shapes features more regularly in common speak than the vocabulary of 3-D objects. Many children will likely have encountered many 2-D shapes from picture books and patterns around their homes, etc. And so, it remains inconclusive as to which order of progression is most beneficial!

In the Operation Maths books, the children meet the specific topic of 2-D shapes prior to that of 3-D objects each school year. However, it is envisaged that by the time the children in the junior classes are formally engaging with 2-D shapes, they have already encountered and informally explored both 2-D shapes and 3-D objects via the monthly themes (laid out in the long-term and short-term plans of each TRB) and in the suggested Aistear play activities (detailed also in the TRB) of which, the Aistear theme of construction is particularly relevant.

### Infant classes

Whether considering 2-D shapes or 3-D objects, the suggested progression within each topic is very similar:

• Undirected play
• Sorting and ordering activities
• Building and making (including making patterns)
• Identifying

Undirected play may include sand and water play, use of formal construction toys, constructing using “junk” or found materials; any activities that allow the children to handle and manipulate shapes and objects.
In the Operation Maths TRBs for junior and senior infants there are ample suggestions for suitable activities, under the headings of various themes. “Undirected play” does not imply that the teacher is superfluous to the process; rather while the children are the instigators, the teacher can play a vital role, observing the way in which the children interact with the materials, and asking the children to explain what they did, how they did it and why they did it that way. This can be a great way to assess the prior knowledge and language that the children may already have.

Sorting and ordering activities include the Early Mathematical Activities (EMA) used early on in the infant classes; thus it is likely that shapes and/or objects have already been used as part of these activities, for example sorting and matching according to colour, size etc; ordering according to length/height etc.

At this point, the children should also be prompted to sort the shapes and objects according to their respective properties as relevant and appropriate:

• Sort 2-D shapes according to the number of corners and the number and type of sides (straight, curved or both; sides that are different or the same).
• Sort 3-D objects according to those that roll/do not roll, slide/do not slide, build/do not build, are hollow/solid; as a development, according to the number of corners and the number and type of faces and edges (please see end of post for more information on faces and edges).
• The teacher can also isolate shapes/objects to create sets and then ask the children to identify the rule of the set: “What’s my rule?” (see image above). The children can also be encouraged to play the “What’s my rule?” game in groups.
• Isolate a particular shape/object in the room and ask the children to locate others that are the same/similar and make a set of like objects/shapes.
• The children may also be naming the shapes as part of these explorations; however this is not necessary as it is more important that they appreciate the similarities and difference between shapes, rather than identifying them.

Building and making with shapes/objects may have already been explored informally as part of the undirected play phase. The purpose now is to develop this into more formal teacher-directed tasks and activities:

• Build the tallest building/castle that you can. What objects did you use/not use and why?
• Dip a face of a 3-D object in paint and use it to print. Make a pattern using the prints. What do you notice?
• Try printing with different faces of the same 3-D object. Are the resulting prints the same or different?
• Push 3-D objects into sand/plasticine to make imprints. Or (if able) trace around the 3-D objects on paper to make designs.
• Use cut-out shapes, gummed shapes, tangrams and/or pattern blocks to make pictures and patterns.
• Use the shapes to cover surface of your book/mini-white board; which shapes did you use/not use and why?
• Combine two shapes/objects to make a new shape/object.

As part of the building and making activities the children may begin to realise how certain shapes/objects can be combined to become other shapes/objects. Similarly, through the reverse of these activities, and other shape cutting activities, the children should begin to realise that shapes can also be separated (partitioned) to reveal new shapes. This can include deconstructing 3-D objects to reveal their net. These activities can be revisited once the children can also name the shapes/objects, so as to arrive at certain understandings and become more accurate with mathematical language eg that two squares can make a rectangle; that, when using tangrams, two of the same size triangles can be rearranged to make a square, a larger triangle etc.

Identifying the specific shapes/objects evolves from the previous activities as the children begin to realise that it is the specific properties and attributes of a shape/object that defines it, eg all shapes with three corners (and three sides) are triangles, irrespective of their size or colour and irrespective of the measure of sides and corners (later to be referred to as angles). Activities which will serve to reinforce this include “Guess the shape/object” using descriptions (see below), guessing unseen shapes/objects from touch (eg in a feely bag), locating a specific shape from a collection using touch alone.
Through the experiences of printing and imprinting with the 3-D objects, it is also hoped that the children realise that the flat faces of 3-D objects are in fact 2-D shapes.

### First and Second classes

The children in these classes will continue to sort, describe, compare and name shapes as done in infants, but to now also include new shapes and objects i.e. semi-circle (1st), oval and cone (2nd). They will continue to construct and make shapes, extending this to creating and drawing the shapes themselves.

They will further explore the combining and partitioning of 2-D shapes, and this understanding will extend to include the fractions of halves (1st) and quarters (2nd). The properties of 2-D shapes will be further explored
in second class via the stand units of symmetry, angles and area (i.e. tessellating 2-D shapes)

Q: How many faces on a cylinder? Three or two?
Traditionally, in Ireland, and in Irish textbooks, a cylinder was recorded as having three faces. However, this is not mathematically correct, as strictly speaking a face is flat, and a 2D shape (figure), so therefore a cylinder has in fact only two faces, (both circles), and one curved surface. And while it may be argued that a cylinder has a third face i.e. the rectangular shape you see when you disassemble the net of the 3-D object, in this disassembled state it is no longer a cylinder, since it can no longer roll, a specific property of all cylinders.
Another way to think about the faces of 3-D objects is to consider the number and shape of the resulting outlines of tracing around, or printing, each surface of the 3-D object. It is only possible to trace around the opposite ends/bases of the cylinder, since only these are flat, thus it has only two faces, both of which are circular in shape. Similarly, it is only possible to trace around one surface on a cone, which therefore means it has only one face (a circle) and one curved surface.
And how many edges on a cylinder? Officially none, as an edge is where two flat faces meet and the faces on a cylinder are on opposite sides and do not touch/meet. However, that leaves the problem of how to describe the place where each face meets the curved surface.  So in Operation Maths, as occurs typically in other primary texts in other countries, there is a distinction made between straight edges (which are in fact true edges) and curved edges (which strictly speaking are not edges).

## Digging Deeper into … 3-D Objects

Category : Uncategorized

For practical suggestions for families, and helpful links to digital resources, to support children learning about the topic of 3-D objects, please check out the following post: Dear Family, your Operation Maths Guide to 3-D Objects

The first obvious question to be addressed is why this topic is called 3-D objects in Operation Maths, when most other textbooks, and even the curriculum refer to this topic as 3-D shapes?

In the PDST Shape and Space manual, it is suggested that “using the word ‘shape’ to describe 2-D shapes and 3-D shapes can cause confusion for pupils”. For example, asking pupils to ‘describe the shape of this shape’ highlights one problem. Another problem is that pupils must be able to think of all cuboids as being ‘the same shape’, while mathematically speaking all cuboids are not the same shape.

The manual goes on to suggest that it would be more helpful to refer to 3-D things as ‘objects’. Using ‘objects’ also reinforces the notion that if it can be physically handled/picked up, it must be a 3-D object, as opposed to a 2-D shape which should always only have length and width, not depth/height.

So, throughout the Operation Maths books, this topic is called 3-D objects to avoid confusion and to provide clarity for the pupils. However, wherever there is reference to “strand unit”, the term 3-D shapes is used, as this is the term used in the curriculum.

### CPA

As usual, this topic is explored using a CPA approach, where the initial focus is on the exploration of 3-D objects and the identification of similarly shapes objects from the child’s environments. And, in a similar way to the teaching of 2D shapes, while the 3-D objects will be identified by name, the greater focus should be on their properties, as appropriate to each class level e.g.

• identifying whether the objects roll, stack, or slide
• relating the properties of each object to its purpose and use in the environment
• recording, sorting and comparing according to the number and shape of faces and curved surfaces
• recording, sorting and comparing according to the number of edges and vertices (corners)

It is important that the children discover the properties of the 3-D objects by hands-on investigations and by classifying and sorting. Sorting activities help develop the children’s communication, observation, reasoning and categorising skills, and thus will help to develop a conceptual understanding of the objects. In the senior classes using online interactive sorting activities based on Venn diagrams or Carroll diagrams can be very useful. Asking children to bring in examples of 3-D objects from home will help them to become aware of 3-D objects in their environment.

### Faces, curved surfaces and edges

How many faces on a cylinder? Three or two?

Traditionally, in Ireland, and in Irish textbooks, a cylinder was recorded as having three faces. However, this is not mathematically correct, as strictly speaking a face is flat, and a 2D shape (figure), so therefore a cylinder has in fact only two faces, (both circles), and one curved surface. And while some may argue that a cylinder has a third face i.e. the rectangular shape you see when you disassemble the net of the 3-D object, in this disassembled state it is no longer a cylinder, since it can no longer roll, a specific property of all cylinders.

Another way to think about the faces of 3-D objects is to consider the number and shape of the resulting outlines of tracing around each surface of the 3-D object. It is only possible to trace around the opposite ends/bases of the cylinder, since only these are flat, thus it has only two faces, both of which are circular in shape. Similarly, it is only possible to trace around one surface on a cone, which therefore means it has only one face (a circle) and one curved surface.

And how many edges on a cylinder? Officially none, as an edge is where two flat faces meet and the faces on a cylinder are on opposite sides and do not touch/meet. However, that leaves the problem of how to describe the place where each face meets the curved surface.  So in Operation Maths, as occurs typically in other primary texts in other countries, there is a distinction made between straight edges (which are in fact true edges) and curved edges (which strictly speaking are not edges).

In 5th and 6th class, it is important that the children realise that only some of the 3D objects are also polyhedra, and that only five of these are categorised as platonic solids.