Foil fun

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Purpose

In this unit students investigate and describe the features of solid shapes, learn the names for common solid shapes, and are introduced to the construction of nets for these shapes.

Achievement Objectives
GM2-4: Identify and describe the plane shapes found in objects.
Specific Learning Outcomes
• Explore and describe the faces, edges, and corners of 2D and 3D objects.
• Make, name, and describe polygons and other plane shapes.
Description of Mathematics

This unit explores basic solid objects by allowing the students to play with them in a structured way. The end product of the exploration is the construction of nets. All of the activities here will strengthen the students' concepts of 3D objects and their attributes, as well as their understanding and use of geometrical terms and language. This knowledge is foundational for work at Levels 3 and 4, where more sophisticated definitions of shape are used (Te Whanau Taparau - The Polygon Family). The experiences explored in this unit provide an opportunity for teachers to assess students' competency in identifying, describing, and constructing describe 3-D shapes.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing supports to students, and by varying the task requirements. Ways to support students include:

• painting the faces of shapes in different colours (or labelling them with coloured dots) to support children in identifying the different faces, and therefore the total number of faces
• allowing a variety of nets to be explored. Students can estimate, either independently or with a partner, what shape they think the nets will form
• varying the complexity of the nets used
• emphasising key vocabulary (e.g. edges, net, faces, vertex) through the display of students' annotated work and the display of collaboratively created exemplars
• grouping students strategically to encourage tuakana-teina (peer learning), scaffolding, and extension
• extending students by allocating different parcels to pairs of children and asking them, without disassembling the shapes, to draw the nets they envisage for their parcels.

The context for this unit can be adapted to suit the interests and experiences of your students by, for example:

• introducing Māori kupu for 3-D shapes. For example, rango (cylinder), poro-tapawha hangai (cuboid), koeko (pyramid). More examples can be found in Paekupu. You could also encourage students, who speak a language other than English at home, to share the words related to shapes that they use at home.
• providing some photos of local buildings with interesting shapes, such as wharekai (eating place) and challenge the children to make an appropriate net.
Required Resource Materials
• Resources to use in the creation of a class chart
• A variety of cardboard packages (e.g. cereal boxes)
• Grid paper (to support students in drawing 3D shapes - optional)
• Models of solid shapes (cubes, rectangular prisms, triangular prisms, and cylinders)
• Paper
• Card
• Foil
• Scissors
Activity

Session 1: Packages

In this activity we investigate the features of 3D shapes using packaging. If you have time, cover your packages in old wrapping paper or plain paper and address them to pairs or groups of three students.

1. Put a your packages variety of packages into a pillowcase (this could be a pretend mailbag.) Gather the students on the mat and tell them that you have a variety of parcels in your bag. Ask a student to select a parcel from the pillowcase. As a class, ask the students to describe the parcel to you. Record their responses in a mind map or table, focusing on key words that they give you. For example, the packet has 8 corners, it has a square face, and it has straight edges. Differentiate between words like 'side' and 'edge' if students use them to describe the same attribute of a shape. Clarify the meaning of important terms: face, edge, vertex (corner). Look also for students to differentiate between 2D and 3D (although all of the packages will be 3D, students might identify that the face of a 3D shape is 2D).
2. Put the students into pairs and get one person from each pair to select a parcel from the pillowcase.
3. Have the student pairs choose a parcel and describe the features, using the vocabulary generated in discussion. Have them draw the package (perhaps using grid paper), name the shape(s) they can see have been used in the construction of the package, and describe the features of the overall shape. They should record these descriptions in an appropriate manner (e.g. a mind map, list, using a graphic organiser). Ask students to also use any new/different vocabulary that they know of, and that was not mentioned in discussion, to describe their parcel. You could use a poster of shapes or a 3D tool (search online for 3D shape viewer) to support students in naming the shape.  Roam and support students to refer back to the vocabulary generated in class discussion.
4. Provide time for this work to be shared with another pair, and then with the class.
5. Draw attention to any new terms that students used to describe their parcel, and add these to the class chart created at the start of the session.
6. If the packages were wrapped ask the students to guess what might be in their package. Wrapped parcels could then be unwrapped.

Session 2: Solids

In this activity we investigate the faces of 3D shapes.

1. Revise the vocabulary used in Session 1 by describing a shape for the class. You could play this as a game of "guess the shape". Show students three different packages or shape blocks. Give students time to draw and describe the shapes on mini whiteboards. Hide the shapes under a cloth, behind a screen etc. Have the students ask you a series a questions that can be answered with 'yes' or 'no' and guess what the shape is.
2. Introduce the solid shapes e.g. the cubes, rectangular prisms, triangular prisms etc. Hand these out for students to feel and explore. Get students to describe their 3D shape to a buddy, encouraging them to use the vocabulary on the chart.
3. Give each student a 3D shape and ask them to trace around the faces and write a description of the shape and its faces. Have them share their drawing and description with a partner.
4. Students could then create their own designs, e.g. Robots, schools, villages, animals by drawing around the faces of the 3D solid shapes. You might display some tangram pictures to help students see how 2D shapes can be arranged and manipulated to represent a recognisable object. This could be linked to learning in another curriculum area or students' interests (e.g. use the shapes to create your favourite place, a waka, a native New Zealand bird).
5. As a class, develop a chart with a picture of the 3D solid, name of the 3D solid, and a description of its number of edges, corners, and faces.

Session 3: Solids’ Faces

In this activity students play a game that involves identifying 3D solid shapes from drawings of the faces of these solids. Model this game for students.

1. Hand out a collection of solid shapes to each pair (i.e. of cubes, rectangular prisms, triangular prisms, and cylinders).
2. In pairs, students are to trace all of the faces of one solid shape onto a single sheet of paper.
3. Partners swap sheets with another pair. The other pair has to match the solids with the drawings of the faces. Pairs then check guesses.

Session 4: Netting

In this activity students explore making a net for a solid shape by taking a solid shape, rolling it along paper, and tracing around the shape of each face. Model this process for students.

1. Have students select a solid shape to "unwrap" (either individually or in pairs).
2. Direct students to "unwrap" the solid by rolling the shape and tracing each face (including the sides) as they roll.  Students could then investigate how many different nets they can make with their shape by rolling the shape in different ways. The result should resemble a net for the shape. You could come up with a system as a class to ensure that you don't accidentally trace the same side multiple times (e.g. using a pencil to mark a dash on each side as it is traced). Ensure you model drawing the same shape multiple different ways. Set an expectation for the number of nets your students are to draw (e.g. at least 3). Students ready for extension could i) create a net without tracing (i.e. with imaging), or ii) create a net for a more complex shape. You could also provide complex shape nets for students to cut out and fold.
3. Have students cut out their nets and fold them together to establish which design correctly makes their solid shape. They may need support to fold along the lines that they have made.
4. Conclude the session by giving the students a package from Session 1 to carefully unpack and form a net. Look at the similarities and differences between the packages and the drawn nets.
5. Display the packages that have been unpacked as nets. You might arrange the nets by the type of shape they construct (i.e. rectangular prism, cubes, triangular prisms, cylinders).

Session 5: Foil covers

In this session students make a cover for their solid shape.

1. Begin this session by sharing the nets drawn in the previous session. Discuss the similarities and differences between the net designs. Use the vocabulary chart to support the discussion. Encourage students to use these words in discussion.
2. Give students a piece of foil to wrap around their shape. Model pressing the foil tightly around the shape, putting pressure onto the foil to ensure it tightly wraps around the shape, and then carefully cutting along the edges of one of the faces of the shape. Cut only as many edges as you need to, to be able to remove the solid from the inside of its foil cover. Reassemble the foil to make the original shape.
3. Have students repeat this process. They may want to make more than one solid shape. You could stuff foil shapes with something to give them more structure.
4. Make a display of the foil solids. Make sure the names of the solids are clearly labelled

Session 6: A Collection of Solids

In this session students will find practical examples of 3D shapes by making a display that categorises 3D shapes.

1. Provide time for students to collect pictures of examples of 3D shapes from magazines, junk mail, or websites.
2. Create either individual charts, or a large, shared chart categorising the different types of solids.
3. Display the chart(s) with the foil models.