In my 25-day placement in a Year 3/4 class I was fortunate enough to be given a fairly free-reign on the creation of the term’s curriculum. I taught a Numeracy unit on Geometric Reasoning and Space (angles, location, shape and symmetry), with the aim of meaningfully linking the content descriptors of Art, HASS Celebrations, Dance and Mathematics through the theme: ‘Patterns in Nature, Maths and Art’.
|Lesson||Teaching strategy (5e model, HITS)||Math Capabilities (BitL), learning intention.||Curriculum||Assessment|
|1 – Geometry||ENGAGE Questioning Feedback||Place name on SOLO chart.||Diagnostic (what do you know?)|
|2 – Fibonacci sequence||ENGAGE, EXPLORE, EXPLAIN, EVALUATE.||Understand connection between the number sequence and spiral shape||ACNA081 (explore and describe patterns resulting from performing multiplication).||Summative (artwork).|
|3 – 2D shapes||EXPLORE AND EXPLAIN Multiple exposures Collaborative learning||Fluency Identify 2D shapes from verbal instructions.||ACMMG088 (Compare and describe 2D shapes that result from combining and splitting common shapes, create 2D shapes from written or verbal instructions).||Formative (chatterbox, verbal – 2D shape bingo, create table of 2D shape properties).|
|4 – 3D shapes||EXPLAIN, EXPLORE, EVALUATE Metacognitive strategies||Fluency Reasoning Problem-solving Identify features of 3D shapes (edges, faces, vertices). Name shape using 2D base shape.||ACMMG063 (make models of 3D objects and describe key features). Describe number patterns resulting from multiplication.||Formative (table of 3D properties, discussion of number patterns).|
|5 – Perspective drawing||ENGAGE, EXPLORE AND EVALUATE||Create realistic and proportionate 3D world (shape and perspective).||ACMMG063, ACAVAM111 (Use materials, techniques, and processes to explore visual connections when making artworks)||Summative (artwork).|
|6 – Symmetry||ENGAGE Questioning Collaborative learning||Fluency Draws symmetrical objects and simple transformations from verbal instructions.||ACMMG066 (identify symmetry in the environment).||Diagnostic (dialogic, whiteboards)|
|5 – Symmetry||EXPLAIN Explicit teaching Questioning||Fluency Understanding Understand that there is more than one type of symmetry, identify number of symmetries.||ACMMG091 (create symmetrical patterns, pictures and shapes with and without digital technologies).||Formative (using manipulatives to identify rotational and reflective symmetry).|
|6 – Rangoli Artwork||ELABORATE Worked example Structuring lessons||Problem solving Apply knowledge of symmetry to creating pattern.||ACMMG091 and HASS (Celebrations).||Summative (Rangoli artwork).|
|7 – Math Games||EVALUATE Metacognitive strategies Multiple exposures||Fluency Understanding Recall mathematical names/concepts in new context. Ext.: define quadrilaterals using relational properties||All curriculum content descriptors relating to geometry and spatial thinking.||Summative (observation of games: LEGO, Rangoli pattern challenge, Swamp hunt, measuring angles, ext.: properties of quadrilaterals).|
In composing the geometry sequence I was guided not only by the content descriptors of the Australian Curriculum, but by research into the development of geometrical thinking through the Van Hiele Levels which I was exposed to in the Deakin Primary Numeracy unit. van Hiele argued that children need to be exposed to five scaffolded levels of geometric understanding through deliberate instruction appropriate for their development. Students move from a visual-based system (they are the same shape because they look the same) to a property-based system (a square is a four-sided shape) through to a relational system (if shape has property X it also has property Y).
It was through the integration of maths and art especially where I was able to help the students see connections between shape and form and move into the higher van Hiele levels. This was especially evident in the link between the ‘Fibbonici Number Sequence’ and the relational properties of 2D and 3D shapes.