Week+6+-+2-Dimensional+shapes+and+spatial+reasoning

__**Learning Activity 6.1: A deeper exploration into how children learn shape and space concepts**__


 * **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** ||
 * - Allowing use of children’s language is important in explanations and reflections. - Teachers should be familiar with the language used within their classroom by students.- Constructivism underpins new maths teaching style.- Children should be exposed to a variety of activities. Teachers should plan for same aspect of learning several times.- A wide range of materials should be used.- Vocab is not the main priority when learning geometry. || -Van Hiele theory. Based on learning, not age. Many primary students on Van Hiele level 1.- attention to similarities and differences are vital to working mathematically.- predicting adds anticipation and fun for many children. ||
 * **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 6.1 Record Chart: A deeper exploration into how children learn shape and space concepts//** understandings and knowledge embedded in the activity || Adam T 08.07
 * **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** ||
 * Vocabulary of shape is important but is not the main purpose of geometry.Teachers should ask students and use "what if" theories to encourage reflection and discussion.Constructivsm is the preferred method of teaching in order for students to understand meaning.Using practical based methods is important when teaching geometry eg: cardboard, play doh etc. || Van Hiele's theory stemmed from Piaget's teaching methods. That it focuses of teaching levels which are not age related. A teacher can not rely soley on conducting activities. Reﬂection and discussion with a teacher is vitally important in developing
 * **Questions I have and related things I do not understand from my reading**None ||

Are the teaching approaches offered by Van Hiels strictly for each level, or would you be allowed to offer free orientation to Level 2, for example? || ‍Sarah Wright 9.7.11 ‍ Achor 11/07/2011
 * ** 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 ** ||
 * * The level at which children operate cannot be related strictly to age as they progress at different rates.
 * A variety of materials needs to be used to support learning
 * The best way to find out what children already know is to ask them. || * Language of communication needs to be at students level, not just from a teachers perspective.
 * There are misconceptions that constructivism is ‘unguided discovery’ for students
 * Concept Maps ||
 * ** Questions I have and related things I do not understand from my reading **
 * **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** ||
 * * Geometry in primary school incorporates a lot of hand on activities where students can control their learning outcomes
 * Children build new connections to existing knowledge.
 * To find out about the children’s prior knowledge the best method is to ask them. Perhaps through class discussion
 * Recognition of shapes allows students to compare the differences between other shapes. || * The Van Hiele (Booker. Et al, 2010). Theory, how it describes the characteristics of each cognitive development.
 * Encouraging students to predict the consequence of actions.
 * A parallelogram is a quadrilateral with two pairs of parallel lines. ||
 * **Questions I have and related things I do not understand from my reading** ||

__**Learning Activity 6.2: Further exploration of 2-dimensional figures**__


 * **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** ||
 * -Young children can explore factors using materialsFactor = number that divides with no remainderMultiple = product of a number and any other whole number.Prime number = greater than 1 that has 2 factors, 1 and itself. (opp = composite numbers)Divisibility = divides with no remainder.Fibonacci sequence = first two terms are 1, then the sum of the previous two terms. || - Square representation of factors can link to area.- Factor me out game = finding factors of numbers 2-36.- Often confusion between multiples & factors – keep language to finding factors and finding multiples.- Greatest common factor and least common multiple. Good source of problem solving.- Relatively prime = numbers with no common factors other than 1 (p. 424)- Polygonal figures = related to geometrical shapes.- Pascals triangle associated with probability- Pythagorean triple = tripe of numbers (abc)- Our hands, tip of finger to first knuckle and so forth = Fibonacci sequence. ||
 * **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 6.2 Record Chart: Further exploration of 2-dimensional figures//** rectangle. This is diﬃcult for children (and adults) to grasp. Cutting out the corners of a triangle then piecing the corners together as way for students to understand protractors and angles. ||
 * **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** ||
 * Investigating 2D shapes using cutting and folding methods. Begin by naming those polygons that are consistent with a number pattern angle (such as 8-gon) before teaching quadrilaterals || A square is included as a special case of the group ‘rectangles’. So a square is a

Adam T. 08.07

**// Learning Activity 6.2 Record Chart: Further exploration of 2-dimensional figures //**
 * ** 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 geoboards || * <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif; font-size: 10pt;">Concave – having an interior angle of greater than 180 degrees.
 * <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif; font-size: 10pt;">To develop children’s concepts we need to offer a range of orientations, sizes, contexts and materials.
 * <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif; font-size: 10pt;">Arrowhead – Chevron ‘French for arrowhead’
 * <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif; font-size: 10pt;">Confusion between oval and eclipse due to use in sporting contexts. ||
 * <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif;">** Questions I have and related things I do not understand from my reading ** <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif; font-size: 10pt;">(See if any of your //Maths Mates Group// have any ideas for you in answering one of these questions.)  ||

> **//Achor 11/07/2011//** > || > |||| **Questions I have and related things I do not understand from my reading**  ||
 * L earning Activity - A lesson on paving **
 * What misconceptions are evident? The students counted the paving stones instead of the length of the pond.
 * What other misconceptions could be possible? That students were becoming increasingly confused as to how the calculation should be solved.
 * How are the misconceptions addressed? The teacher thought it would have been better if he had a chance to reherse the lesson before presenting the lesson to the class.
 * What other mathematics content or proficiency strands were or could be addressed? How could this be achieved? Using practical materials to recreate the task. This way the students could calculate the problem by measuring the length or by adding thetotal number of sides to calculate the area of the pond. Adam T 08.07
 * **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**  ||
 * Children recognise common shapes very early.
 * Students need to become familiar with the properties of a circle before they can learn the pi.
 * ** Analog clocks can be used to explore angle sides.
 * The use of greek words in mathematics can be confusing to students
 * In greek isos means equal ||

__**Learning Activity 6.3: A lesson on paving**__

Students counted the number of pavers down the side instead of measuring the length. Teacher explained in a different way. Group discussion about ways to solve problem. Comparison of problem to an earlier example – engages prior knowledge.
 * What misconceptions are evident? What other misconceptions could be possible?
 * How are the misconceptions addressed?

Area – calculating total number of pavers needed to pave around pool Measurement – measuring pavers, and indirect measurement of pool / pond. Geometry – looking at shapes within pavers. Different ways that pavers could be layed. Vicki 6/7/11 <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif; margin-left: 36pt;">** Learning Activity 6.3: A lesson on paving **
 * What other mathematics content or proficiency strands were or could be addressed? How could this be achieved?


 * <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif;">What misconceptions are evident? What other misconceptions could be possible? **

<span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif;">The first student seemed to have a misconception regarding multiplication; his line of thought was hard to follow considering you could not see the whiteboard in the classroom. The second video showed a whole classroom with the misconception of length of the side of the pond, some students were using the pavers to measure the length of the pond.


 * <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif;">How are the misconceptions addressed? **

<span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif;">In the first video, the teacher could see the student had confused himself and made him feel comfortable by suggesting that he write down what he is thinking and discuss it at the end of the class because he ‘understood’ what it was like to have the answer but then when you try to explain it you completely forget

In the second video, after walking around observing the students during their work the teacher realises the mistake he has made in his instruction which has led to the class confusion. To rectify this he tried explaining the task in different ways to the students and clarifying their understanding by asking questions.


 * <span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif;">What other mathematics content or proficiency strands were or could be addressed? How could this be achieved? **

<span style="color: #ff8200; font-family: Arial,Helvetica,sans-serif;">This could address measurement in particular area and perimeter. It could also look at geometry, using irregular shapes.

This could be achieved by asking students to find the perimeter of the pond or the area of the pond for example.

Achor 11/07/2011
 * What misconceptions are evident? What other misconceptions could be possible? The first student had idea on multiplication that to reach the answer you can use a different formula to get the same answer. The students concept may be correct but his explanation lacks depth thus making him seem lost in his train of thought.
 * How are the misconceptions addressed? The teacher asked him to work it out in his book to reflect on what he proposed and then pitch the idea again once he is on the right train of thought again.
 * What other mathematics content or proficiency strands were or could be addressed? How could this be achieved? This could have been achieved through the mentoring method. Teacher or a student who is more cognitively developed demonstrating the formula and show the problem is solved.


 * __Week Six Mathsmates__**

// Spatial learning experiences // Consider what knowledge you have gained so far about **how** children learn mathematics and brainstorm with your MathMates some lesson **ideas** in the area of Space/Geometry. Decide on 5 lesson ideas to submit. Each must be from a different year level and explore a different concept. Make sure you acknowledge the appropriate year level, spatial concept and how it is delivered. Keep it brief E.g. 1. Year 1 2. Exploring Directional knowledge <span style="background-color: #ffff00; font-family: 'Calibri','sans-serif'; font-size: 14px;">Active participation: Listening to verbal instructions from peers and moving themselves in appropriate directions on a people sized chalk grid. E.g. //2 forward, 1 left.//

**Year 2** Area of space/geometry: 2D - 4 Triangles Active participation: Students work in pairs ﬁtting shapes together. This activity is related to tangram however it is tailored to younger children. Present children with four card triangles produced from a square. Show them how the original square may be re configured by placing the tips of triangles toward the centre of the square. Students will create a variety of hexagons, different-sized quadrilaterals and different ways to construct triangles. These are recorded in silhouette form for checking new combinations and later reflective discussion. (Booker, Bond, Sparrow, Swan, pp. 424-425, 2010). . **References:** <span style="color: #008000; font-size: 10pt; line-height: 150%; margin-left: 42.55pt; text-indent: -42.55pt;">Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching primary mathematics// (4th ed.). Frenchs Forest, NSW: Pearson Australia. Adam T. 08.07.11 Year 4 Area of space/geometry: Tessellation Active participation: Students use two 2D shapes of choice to create a pattern or picture on a piece of A4 paper. This can be done in in groups of two students.

This lesson idea is set around the Australian Curriculum measurement and geometry strand for year four students. The substrand being that students "Create symmetrical patterns, pictures and shapes with and without digital technologies" (Australian Curriculum and Assessment Authority, n.d.). The idea behind the lesson is that students in their group of two will create discussion about how shapes can be rotated to create patterns, furthering students knowledge of shapes to form patterns.

Ref: Australian Curriculum and Assessment Reporting Authority (ACARA), (n.d.), //The Australian Curriculum: Mathematics.// Retrieved from []

**__Spatial learning experiences__** Consider what knowledge you have gained so far about how children learn mathematics and brainstorm with your MathMates some lesson ideas in the area of Space/Geometry. Decide on 5 lesson ideas to submit. Each must be from a different year level and explore a different concept. Make sure you acknowledge the appropriate year level, spatial concept and how it is delivered.

**Year 2** **Measurement and Geometry/Shape/ACCMMG043** **Learning outcome**– Describe and draw two-dimensional shapes, with and without digital technologies (ACARA, 2010). This activity focuses on geometric features and describing shapes and objects using everyday words such corners, edges and faces. Active participation – Children are placed in groups of 4. Each group is given a brown paper bag with a ball, a box, a cone and a triangle shaped Toblerone box. Each student takes it in turns to put their hand in the bag and select an object which they must not take out of the bag. The other students take it in turns asking questions and guessing the shape. The person that guesses the object or the shape wins. At the end of the activity children draw up a table and list all the features of the shapes they can think of. Children then return to the floor and as a group construct a table on the whiteboard for each shape listing all the features. They are asked to look around the room for further examples of each shape. . **Year 3** **Measure and Geometry/Shape/ACMMG063** **Learning outcome** – Make models of three dimensional objects and describe their key features. Active participation – this activity allows children to create a three-dimensional cube using origami. The students watch the teacher fold and make the cube. If the children appear unsure the teacher can make a second one. The children are given two square pieces of coloured paper. The teacher takes them step by step as they make their own cube. When the cubes are completed the teacher asks the students what they notice about the cubes. This question leads into a discussion about the features of the cube such as 12 sides, 8 corners and 6 faces.

**Year 4** **Measure and Geometry/Location and Transformation/ACMMG090).** **Learning outcome** – Use simple scales, legends and directions to interpret information contained in basic maps (ACARA, 2010).  Students are placed in groups of 4 and are given a map of the school. Each group is asked to write down a set of mathematical directions for a new student of the school to follow. Each group will have one of the following destinations - the canteen, library, school hall, basketball court, art room or bike shed. For example, students will write from the classroom door turn right and walk 53 steps to the front door of the building. Walk down the steps and walk 22 steps directly ahead until you reach a large green building. When groups have finished this task they will give their directions to another group to follow. The teacher will give the groups a peer assessment sheet to complete. When completed students will return to the classroom to present their peer assessments to the class and reflect on the lesson. **Year 5** **Measure and Geometry/Location and transformation/ACMMG114** **Learning outcome** – identify line and rotational symmetries (ACARA, 2010) The teacher demonstrates to the class line and rotational symmetry with pictures from nature, for example a flower or a crab. Children are placed in pairs and each given a square, circle and an equilateral triangle and are asked to fold the shapes to determine how many lines of symmetry they have. They are asked to draw the shape and the lines of symmetry in their work books. When they have completed this task they are asked to choose 2 more shapes from a hexagon, rhombus, trapezium and parallelogram. At the end of the lesson the students share their answers with the class. **Grade 6** **Measure and Geometry/Shape/ACMMG140** **Learning outcome** – Construct prisms and pyramids from nets. Students are placed in pairs for this activity. The teacher gives the students the nets for a triangular prism and a triangular pyramid which have been copied onto a piece of cardboard. Students cut out and assemble their 3d shapes using glue or sticky tape to keep them together. The students are asked to answer the following questions: What features does the pyramid net have? What features does the triangular prism have? What do they both have in common? At the end of the activity the class share their answers and reflect on the lesson.

**__References__** Australian Curriculum, Assessment and Reporting Authority (ACARA). (2010). Retrieved from [|http://www.australiancurriculum.edu.au]

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

Ehow. 2011 Properties of a cube retrieved from []

Reys, R., Lindquist, M., Lambdin, D., & Smith, N (2009). Helping children learn mathematics. New York: John Wiley & Sons.

Kerrie 9/7/11.

Hi everyone,

Proposed studymates 3 contribution is below. Thanks Adam and Suzanne. I have used your contrubtions plus my 3 lesson plans to make up the five. I will tidy the setting out and references up before I post. If there are to be any changes let me know. I will incorporate any late positngs today if they appear. There is a note on the DB saying we can have less than 500 words this week. Hope everyone is going well with their essays. Kerrie.

Kerrie, this is good, you certainly got a tough week to do. The only think I've noticed is that you have referenced Reys, but I didn't see it as an intext reference. (I may have just simply missed it).

Particularly tough week as there weren't many contributors this week and I'm sure you are just as busy as the rest of us finishing off your assignment!! I'm just about ready to cut off my big toe over this assignment - it is driving me bonkers! Getting there though, very slowly though, but it'll be done. :)

Thanks Suzanne. You are right there is no Reys reference. Thanks for reading the weekly contribution. I'm also getting their slowly with the essay. Hoping to have it finished tomorrow night.

**__Spatial learning experiences__** Consider what knowledge you have gained so far about how children learn mathematics and brainstorm with your MathMates some lesson ideas in the area of Space/Geometry. Decide on 5 lesson ideas to submit. Each must be from a different year level and explore a different concept. Make sure you acknowledge the appropriate year level, spatial concept and how it is delivered.

**Year 2**

Area of space/geometry: 2D - 4 Triangles

Active participation: Students work in pairs ﬁtting shapes together. This activity is related to tangram however it is tailored to younger children.

Present children with four card triangles produced from a square. Show them how the original square may be re configured by placing the tips of triangles toward the centre of the square. Students will create a variety of hexagons, different-sized quadrilaterals and different ways to construct triangles (Booker, Bond, Sparrow, Swan. 2010. p. 424-425). These are recorded in silhouette form for checking new combinations and later reflective discussion.

**Year 3**

**Measure and Geometry/Shape/ACMMG063**

**Learning outcome** – Make models of three dimensional objects and describe their key features.

Active participation – this activity allows children to create a three-dimensional cube using origami. The students watch the teacher fold and make the cube. If the children appear unsure the teacher can make a second one. The children are given two square pieces of coloured paper. The teacher takes them step by step as they make their own cube. When the cubes are completed the teacher asks the students what they notice about the cubes. This question leads into a discussion about the features of the cube such as 12 sides, 8 corners and 6 faces.

Year 4

Area of space/geometry: Tessellation

Active participation: Students use two 2D shapes of choice to create a pattern or picture on a piece of A4 paper. This can be done in in groups of two students.

This lesson idea is set around the Australian Curriculum measurement and geometry strand for year four students. The substrand being that students "Create symmetrical patterns, pictures and shapes with and without digital technologies" (Australian Curriculum and Assessment Authority, n.d.). The idea behind the lesson is that students in their group of two will create discussion about how shapes can be rotated to create patterns, furthering students knowledge of shapes to form patterns.

**Year 5** **Measure and Geometry/Location and transformation/ACMMG114** **Learning outcome** – identify line and rotational symmetries (ACARA, 2010) The teacher demonstrates to the class line and rotational symmetry with pictures from nature, for example a flower or a crab. Children are placed in pairs and each given a square, circle and an equilateral triangle and are asked to fold the shapes to determine how many lines of symmetry they have. They are asked to draw the shape and the lines of symmetry in their work books. When they have completed this task they are asked to choose 2 more shapes from a hexagon, rhombus, trapezium and parallelogram. At the end of the lesson the students share their answers with the class.

**Grade 6** **Measure and Geometry/Shape/ACMMG140** **Learning outcome** – Construct prisms and pyramids from nets. Students are placed in pairs for this activity. The teacher gives the students the nets for a triangular prism and a triangular pyramid which have been copied onto a piece of cardboard. Students cut out and assemble their 3d shapes using glue or sticky tape to keep them together. The students are asked to answer the following questions: What features does the pyramid net have? What features does the triangular prism have? What do they both have in common? At the end of the activity the class share their answers and reflect on the lesson.

**__References__**

Australian Curriculum, Assessment and Reporting Authority (ACARA). (2010). Retrieved from [|http://www.australiancurriculum.edu.au]

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

Ehow. 2011 Properties of a cube retrieved from []

Reys, R., Lindquist, M., Lambdin, D., & Smith, N (2009). Helping children learn mathematics. New York: John Wiley & Sons.

Fractions Achor 11/07/2011 Grade 1 Pi Fractions Active participation Students work in small groups of 3 or 2 on a drawn pizza cut into 8 pieces. Every time one team member takes a slice or two from the pizza while the other team member close their eyes. When the team members open their eyes they are to write down what is the fraction of the pizza according to the missing slices. The slices are returned and the activity is repeated till they reach an understanding.

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

Hey guys,

Sorry for the late submission been having a few problems with my web browser. I hope i am not too late. =(

Achor