Week+7+-+3-Dimensional+Objects

__**Learning Activity 7.1: Munching mathematics again**__ If anyone is looking for the examples of nets that is supposed to be on pg 420 (a 2004 edition) of Booker, it is on page 444 if you have the 2010 edition of the book.

Achor 15/07/2011 //Mathematics Challenge:// How many different nets can you find for the 3-dimensional object that is a Toblerone box? You could go back to the shop and buy some more Toblerones to do this investigation, or you could make drawings (nets) and cut them out an fold them up to try to make a Toblerone box. 3 different nets

__**Learning Activity 7.2: Exploring 3-dimensional objects**__

**__Geometric Solids (dodecahedron)__** **Positives:** The manipulatives brings the shape to 3d life. Can colour sides, faces, edges etc which makes coutningeasier. Can rotate object to examine it. **Weaknesses:** requires prior knowledge of computer, and functions (shift key). The instructions could be too advanced for younger studen. Is easy to miscolour a face instead of colouring an edge or corner. Therefore, it is easy to lose concentration when going back to correct mistake. **__Cube Nets__**

**Positives:** is interactive, and shows which nets can be folded into cubes. Reasons are provided if nets cannot be folded into cubes.

**Weaknesses:** explanations are written and not visual. Students may not understand language or comprehend what it means. The activity is quite boring. It would be better of it showed or gave a visual of how it works or doesn’t work. Vicki 12/7/11.

**Geometric Solids** Strengths: Colourful and interactive. Has two stages one uses the solids diagram to play and learn about faces, sides and edges. The second stage allows you to record your findings from working on the geometric shape. Weaknesses: Difficult to access and hard to follow directions - especially for children. This activity was hard to navigateas the exploration tool kept defaulting to the record sheet. **Cube Nets** Strengths: A great tool to get students to visually think 3D as they try to visualise 2D cubes flat patterns to create 3D. If you select the correct 2D folds then it turns into a colour indicating that the selection is correct. Weakness: It would be great if there could be more interaction for the students as it can be a little simplistic Adam 12.07

**__Geometric Solids__** Positives: Students are able to manipulate the shape with ease and see the shape from all possible angles. Weaknesses: The activity asks “For any polyhedron, what is the relationship between the number of faces, vertices, and edges?” questions like these need to be answered with the help of someone who is more cognitively developed to assist the student due to the fact it is quite advanced for grades 3 to 5. Achor 15/07/2011

__ **//Learning Activity 7.3 Record Chart: Supporting children’s learning of 3D objects//** __ Creating geometric shapes from folding paper (face models) || Three-dimensional objects can be classiﬁed in three general categories: • those with all their surfaces or faces ﬂat, for example prisms and other polyhedrons • those with curved surfaces only, for example spheres • those with a combination of ﬂat and curved surfaces, for example cylinders and cones. Newer construction materials in geometry such as Polydron, Clixi and geoshapes that are made from plastic and have interlocking edges 3D representation - using isometric sketches to help interpret figural information || Adam T. 12.07
 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * Colouring and shading in geometric shapes
 * **Questions I have and related things I do not understand from my reading**(See if any of your //Maths Mates Group// have any ideas for you in answering one of these questions.) ||

**//Learning Activity 7.3 Record Chart: Supporting children’s learning of 3D objects//**
 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * Use of models / mainpulatives to help students make sense of maths. Live in a 3d world with geometry – models can be collected or made. 3d objects often called solids. Prisms have 2 parallel faces joined to one another by rectangles. Pyramid named after the shape of the base. || Build on knowledge of 3d objects – relate to 2d in books and text. 3d object with all faces or surfaces flat is a polyhedron. Platonic solid = all faces, edges, angles, vertices etc are identical. Children confuse pyramids and prisms due to limited exposure. Can be seen in net form. Important for students to be able to represent 3d objects in 2d. The use of nets can help this. ||
 * **Questions I have and related things I do not understand from my reading** (See if any of your //Maths Mates Group// have any ideas for you in answering one of these questions.) ||
 * Maths Mate Contribution **


 * Hi everyone, if you could help submit your contributions by Saturday, I will collate and post this weeks topic on Saturday night ** - ** thanks :) **


 * Week 7 Contribution **
 * Supporting Children’s Learning of 3D shapes. What ideas and examples did your group gain from this week. Try to come up with 5 ideas. **

Idea 1: Obtain a series of circles made from thin card or paper with a similar diameter. Cut a thin, pizza-like section from one of the circles and bend the remaining circle to ﬁt the two cut edges together. The resulting shape will be a cone. 2 Repeat the action on the other circles but each time make the pizza section larger. Compare the resulting cones and make a general statement about the cones and the pizza sections (Booker, p.458, 2010).

References: Booker, G. (2010). Teaching Primary Maths, 4th Edition. Pearson: Australia

I found the "Cube Nets" (National Council of Teachers of Mathematics, 2011) task particularly interesting. However, I would adapt the exercise if teaching it from ICT to a hands on task. In a classroom setting I would place students into groups of 3 or 4, with each group receiving an A4 sheet with each of the nets as shown on the Cube Nets exercise. Students could then cut these out, and in groups work out which are nets for the cube. Students would be asked how it was that they reached that conclusion, and what similarities were found with all the nets (ie, all have six smaller squares, whereas some nets that weren't successful only had four). This would allow students the use of a hands on manipulative while making their own three dimensional models (Reys, Lindquist, Lambdin & Smith, 2009). Working in groups will encouraging discussion between group members in order for students to construct their own knowledge (Booker, Bond, Sparrow & Swan, 2010)

References:

Booker, G., Bond, D., Sparrow, L. & Swan, P. (2010). //Teaching Primary Mathematics,// (4th Ed.). Frenchs Forest, New South Wales : Pearson Australia

National Council of Teachers of Mathematics, (2011). //Cube Nets.// Retrieved from http://illuminations.nctm.org/ActivityDetail.aspx?ID=84

Reys, R., Lindquist, M., Lambdin, D. & Smith, N. (2009)//. Helping Children Learn Mathematics,// (9th Ed.). Hoboken, New Jersey : John Wiley and Sons

Supporting Children’s Learning of 3D shapes. What ideas and examples did your group gain from this week. Try to come up with 5 ideas.

It is important for children to visualise what a 2D representation of a 3D object looks like and vice versa (Booker, Bond, Sparrow and Swan, 2010). One way to understand these connections is with the use of nets. A net has all the features of its corresponding 3D object including faces, edges and vertices. Children can learn about the net of a rectangular prism with a simple activity using a toothpaste box. Prior to cutting the box, children can be asked to visualise and draw what they think the net would look like if the box was cut along one of the long edges and folded flat. They can then cut along one of the long edges to make the net and compare their drawing to the net. This activity can be extended by placing the children in groups and asking them to discover other net combinations that will also form the rectangular prism or box.

**__References: __**

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). Teaching primary mathematics. Frenchs Forest, NSW: Pearson Australia.

Kerrie Wyer - 14/7/11.

There are many three-dimensional shapes in real-life which can be used to support children’s learning (Reys, Lindquist, Lambdin, & Smith, 2009). Some examples include: tennis balls, tissue boxes, drink cans, and ice-cream cones. There are two key benefits of using everyday objects when learning about three-dimensional objects. Firstly, the ability to relate learnings to real-life, provides a greater opportunity for students’ understanding (Booker, Bond, Sparrow, & Swan, 2010). Secondly, the use of models can help students to make sense of new mathematical learnings (Booker et al., 2010).

References  Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching primary mathematics// (4th ed.). Frenchs Forest, NSW: Pearson Australia. Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //Helping children learn mathematics// (9th ed.). Hoboken, New Jersey: John Wiley & Sons. Vicki 15/7/11

Learning Geometry can be quite daunting for students if they do not quite understand the concept of shape and space. It is important for teachers to check the students prior knowledge through class discussions or group activities (Booker, et al, 2010). An example of this is learning about nets; students will not be able to learn about nets if their knowledge on prisms and their properties are limited. In order for students to grasp the concept of geometry they need to create their own learning experiences through carefully planned activities that allow students to manipulate and investigate different shapes as oppose to just learning from a book. Another way student's can be in par with the other students is to use the scaffolding or mentoring method where the more cognitivly developed demonstrate or teach the students who do not grasp the concept yet.

__ Reference __ Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching primary mathematics// (4th ed.). Frenchs Forest, NSW: Pearson Australia.

Achor 15/07/2011