Theory
Common Student Misconceptions
Two-dimensional shapes
Transformations
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Three-dimensional shapes
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Mathematics Language for Geometry
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Activities
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Word Problems |
Early years
Shapes Learning the concept of geometry through matching objects according to attributes such as size and shape. Children find shapes in their environments and describe them in their own words and later learn names for these shape. Objective: Students will learn shape names and match them with objects through storytelling. (Adapted from First-School.ws, n.d.)
Video used with recording: https://www.youtube.com/watch?v=1h1HcChju_0 Year 1 Walking with a difference Give and follow directions to familiar locations (ACMMG023) Objective: Students will use instructional language to direct their partner to their destination. Key mathematical vocabulary: turn, left, right, clockwise, anti-clockwise, forward, backward, sideways, over, under, paces, steps, footsteps Activity:
Assessment: Listen for students’ instructional language and observe their movement toward the destination, followed by a conversation that reflects on their learning. Record observations as anecdotal notes. (Adapted from Victoria Walks, n.d.) |
If we cut a cube using its lines of symmetry. How many pieces will I have?
From the entry I walk straight ahead 3 paces, I turn left and walk 15 paces. What room am I in? What room is to my left? Is there a room behind me? Which rooms are furthest from where I am standing?
Activities Year 5 Three-dimensional nets Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111) Objective: Students will explore the two-dimensional shapes that make up three-dimensional objects and connect them with their name. |
Resources
Curriculum Map
In the Early Years Learning Framework (Document 16, outcome 5, p. 6) children will learn the key learning concept of geometry through comparing processes that include sorting, matching, ordering and classifying objects according to attributes such as size and shape, along with communicating mathematical thinking and strategies to others through representations that use three-dimensional shapes. They will also develop awareness of two- and three-dimensional shapes. Children find shapes in their environments and describe them in their own words and later learn names for these shape. Children will demonstrate their ability to create, copy and extend repeating designs using shapes.
(Charles Sturt University Early Years Learning Framework Consortium, 2009)
Geometry can be found in the Australian Curriculum across Foundation to Year 6.
FOUNDATION
YEAR 1
YEAR 2
YEAR 3
YEAR 4
YEAR 5
YEAR 6
(Charles Sturt University Early Years Learning Framework Consortium, 2009)
Geometry can be found in the Australian Curriculum across Foundation to Year 6.
FOUNDATION
- Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment (ACMMG009)
- Describe position and movement (ACMMG010)
YEAR 1
- Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features (ACMMG022)
- Give and follow directions to familiar locations (ACMMG023)
YEAR 2
- Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042)
- Describe the features of three-dimensional objects (ACMMG043)
- Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044)
- Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045)
- Identify and describe half and quarter turns (ACMMG046)
YEAR 3
- Make models of three-dimensional objects and describe key features (ACMMG063)
- Create and interpret simple grid maps to show position and pathways (ACMMG065)
- Identify symmetry in the environment (ACMMG066)
YEAR 4
- Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)
- Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)
- Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)
YEAR 5
- Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)
- Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)
- Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114)
- Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)
YEAR 6
- Construct simple prisms and pyramids (ACMMG140)
- Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)
- Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)
References
Charles Sturt University Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective communicators. Retrieved
from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Hansen, A. (2011). Shape and space. In S. Hansen (Ed.), Children’s errors in mathematics (2nd ed.) (pp. 76-98). Exeter, England: Learning Matters.
Haylock, D. (2014). Mathematics explained for primary teachers. London, England: SAGE Publications.
Koester, B. (2003). Prisms and pyramids: Constructing three-dimensional models to build understanding. Teaching Children Mathematics, 9(8), 436-442.
Retrieved from http://go.galegroup.com.ezproxy1.acu.edu.au/ps/retrieve.dosgHitCount&sort=RELEVANCE&doc&prodId=AONE&tabID=T002
&searchId=R1&resultList&search&contentSegment=¤tPosition=1&searchResults&inPS=true&userGroupName=acuni&docId=GALE%
7CA99618625&contentSet=GALE%7CA99618625
McKay, E. (2013). The shape of things [Video file]. Retrieved from https://www.youtube.com/watch?v=1h1HcChju_0
TES Australia Senior Secondary Team. (2013). 3D shapes and nets matching activity. Retrieved from
http://www.tesaustralia.com/ResourceDetail.aspx?storyCode=6331025
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex,
England: Pearson Education.
Victoria Walks. (n.d.). Lesson plan level 1: Mathematics following directions. Retrieved from http://www.victoriawalks.org.au/Assets/Files/5641%20VWI%20
Smart%20Steps%20Lesson%20Plan%20Maths%20L1%20FINAL%5B2%5D.pdf
from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1
Hansen, A. (2011). Shape and space. In S. Hansen (Ed.), Children’s errors in mathematics (2nd ed.) (pp. 76-98). Exeter, England: Learning Matters.
Haylock, D. (2014). Mathematics explained for primary teachers. London, England: SAGE Publications.
Koester, B. (2003). Prisms and pyramids: Constructing three-dimensional models to build understanding. Teaching Children Mathematics, 9(8), 436-442.
Retrieved from http://go.galegroup.com.ezproxy1.acu.edu.au/ps/retrieve.dosgHitCount&sort=RELEVANCE&doc&prodId=AONE&tabID=T002
&searchId=R1&resultList&search&contentSegment=¤tPosition=1&searchResults&inPS=true&userGroupName=acuni&docId=GALE%
7CA99618625&contentSet=GALE%7CA99618625
McKay, E. (2013). The shape of things [Video file]. Retrieved from https://www.youtube.com/watch?v=1h1HcChju_0
TES Australia Senior Secondary Team. (2013). 3D shapes and nets matching activity. Retrieved from
http://www.tesaustralia.com/ResourceDetail.aspx?storyCode=6331025
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex,
England: Pearson Education.
Victoria Walks. (n.d.). Lesson plan level 1: Mathematics following directions. Retrieved from http://www.victoriawalks.org.au/Assets/Files/5641%20VWI%20
Smart%20Steps%20Lesson%20Plan%20Maths%20L1%20FINAL%5B2%5D.pdf