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Shapes, angles and transformations in Years 3 to 6 at home
What the Australian Curriculum expects in shapes, angles and transformations from Year 3 to Year 6, where children get stuck, and how to help at home.
Read the guideKey points
Shapes, objects, position and transformations sit in the Space strand of the Australian Curriculum; angles sit in Measurement.
Angles begin in Year 3 as measures of turn, gain their names in Year 4, and are measured in degrees with a protractor in Year 5.
Symmetry appears in Year 4, translations, reflections and rotations in Year 5, and combinations of transformations in Year 6.
Most of this strand can be practised with paper, a ruler and things already in the house.
What has your child already done?
This is the part of primary maths parents most often say they cannot help with, usually because the vocabulary has changed since they were at school. The content is more familiar than it sounds. Below is what the curriculum expects year by year, from the Queensland Curriculum and Assessment Authority's alignment documents for version 9.0, and what tends to cause trouble.
Before Year 3, the Space strand is about naming and placing. In the Foundation year children "sort, name and create familiar shapes" and describe where things are in relation to other people and objects [1]. Year 1 adds comparing and classifying familiar shapes, and giving and following directions to move people and objects within a space [2]. By Year 2 children classify shapes by "the number of sides and using spatial terms such as 'opposite', 'parallel', 'curved' and 'straight'", and locate positions in two-dimensional representations of a familiar space [3]. The words angle, symmetry, reflection and rotation do not appear in those three years.
What happens in Years 3 and 4?
Year 3 keeps the focus on objects and maps. Children "make, compare and classify objects, identifying key features and explaining why these features make them suited to their uses", and they "interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other" [4]. Angles arrive this year, but in the Measurement strand: children "identify angles as measures of turn and compare angles with right angles in everyday situations" [4].
Year 4 is busier. Children represent composite shapes using combinations of familiar shapes, and "create and interpret grid reference systems using grid references and directions to locate and describe positions and pathways" [5]. This is also where transformations begin: Year 4 students "recognise line and rotational symmetry of shapes and create symmetrical patterns and pictures" [5]. In Measurement, the angle names appear: children estimate and compare angles using "acute, obtuse, straight angle, reflex and revolution" [5].
What happens in Years 5 and 6?
Year 5 moves to three dimensions and the coordinate plane. Children "connect objects to their nets and build objects from their nets", and construct a grid coordinate system to describe position and movement [6]. The three transformations are named here: students "describe and perform translations, reflections and rotations of shapes" and "recognise what changes and what remains the same" [6]. The protractor appears in Measurement, where children "estimate, construct and measure angles in degrees" [6].
Year 6 pulls the strand together. Children compare the parallel cross-sections of objects and relate them to right prisms, locate points in all four quadrants of the Cartesian plane, and "recognise and use combinations of transformations to create tessellations and other geometric patterns" [7]. Angle work becomes reasoning rather than measuring: students identify relationships between angles on a straight line, angles at a point and vertically opposite angles, and use them to find unknown angles [7].
Where do children usually get stuck?
The most common difficulty is that children learn a shape from one typical picture rather than its properties. A Slovakian study published in the European Journal of Contemporary Education in 2017 tested 80 fourth-grade pupils, at about age 10, at one school. Only 35 per cent correctly identified a square that had been rotated through 45 degrees, 32 per cent called a cube a square, and 68.75 per cent correctly rejected a rhombus as a square [8]. The same pattern appears earlier: in a Turkish study of 82 five and six year olds, 93 to 96 per cent recognised the standard equilateral triangle on a horizontal base, but 48.5 per cent missed an isosceles triangle and 51.2 per cent a right-angled one [9]. Both are small overseas samples, not Australian figures, but the effect is easy to spot at home.
Angles have their own sticking point. A French study of 90 pupils in Years 3 and 4, published in The Journal of Mathematical Behavior in 2013, set out to overcome the known obstacle of side length, where children judge an angle by the length of its arms. It reports that side length "is not the only difficulty faced by pupils" and that "the salience of the prototypical right angle constitutes a real learning obstacle" [10]. In practice, treating every corner as a right angle.
How can you help at home?
The Mathematics Hub, funded by the Australian Government Department of Education and managed by Education Services Australia, keeps its advice to families simple: "Travelling, shopping, cooking and making are all great times to talk about numbers, measurements, shapes" [11]. A few things work well for this strand.
Turn things around. When you name a shape, turn it onto a corner and ask whether it is still the same shape and why. Asking what has changed and what has stayed the same is the exact language of the Year 5 content.
Fold paper. Folding a shape to test whether the halves match is line symmetry, and the quickest way to make the Year 4 content concrete. Cutting a shape out and sliding, flipping and turning it on the table covers translations, reflections and rotations with no special equipment.
Use maps. Grid references on a park map, a shopping centre directory or a street map cover the Year 4 and Year 5 position content directly, and giving directions aloud, including turns, builds the language of angle as turn.
Unfold a box. A flattened cereal box is a net, and predicting the shape before you unfold it is the Year 5 content almost exactly.
Look for repeating patterns. Tiled floors, brick walls and paving are tessellations, where Year 6 ends up.
Our free printable worksheets cover shapes and objects (/worksheets/maths/topic/shapes-and-objects), angles (/worksheets/maths/topic/angles), transformations (/worksheets/maths/topic/transformations) and position and mapping (/worksheets/maths/topic/position-and-mapping), with answers included. If you are unsure which year level to work at, our guide to what the curriculum expects in each year (/learn/is-my-child-on-track) sets it out, and the measurement guide for Years 3 to 6 (/learn/measurement-years-3-to-6-how-to-help-at-home) covers the strand angles belong to.
How Noooli can help
Noooli offers short daily maths practice, about ten minutes a day, for Kindergarten to Year 6, aligned to the Australian Curriculum, with free printable maths worksheets (/worksheets/maths) and answer keys and no sign-up. Parents can see their child's progress. Noooli is also on the App Store and Google Play: get the app (/free/app).
References
1. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 Mathematics Prep: achievement standard aligned to content descriptions", 2023. https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_prep_as_cd_alignment.pdf
2. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 Mathematics Year 1: achievement standard aligned to content descriptions", 2023. https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr1_as_cd_alignment.pdf
3. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 Mathematics Year 2: achievement standard aligned to content descriptions", 2023. https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr2_as_cd_alignment.pdf
4. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 Mathematics Year 3: achievement standard aligned to content descriptions", 2023. https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr3_as_cd_alignment.pdf
5. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 Mathematics Year 4: achievement standard aligned to content descriptions", 2023. https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr4_as_cd_alignment.pdf
6. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 Mathematics Year 5: achievement standard aligned to content descriptions", 2023. https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr5_as_cd_alignment.pdf
7. Queensland Curriculum and Assessment Authority, "Australian Curriculum v9.0 Mathematics Year 6: achievement standard aligned to content descriptions", 2023. https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr6_as_cd_alignment.pdf
8. Gunčaga, J., Tkačik, Š. and Žilková, K., "Understanding of Selected Geometric Concepts by Pupils of Pre-Primary and Primary Level Education", European Journal of Contemporary Education, 6(3), 2017, pages 497 to 515. https://files.eric.ed.gov/fulltext/EJ1154716.pdf
9. Yeşil Dağlı, Ü. and Halat, E., "Young Children's Conceptual Understanding of Triangle", Eurasia Journal of Mathematics, Science and Technology Education, 12(2), 2016, pages 189 to 202. https://www.ejmste.com/download/young-childrens-conceptual-understanding-of-triangle-4480.pdf
10. Devichi, C. and Munier, V., "About the concept of angle in elementary school: Misconceptions and teaching sequences", The Journal of Mathematical Behavior, 32(1), March 2013, pages 1 to 19. https://www.sciencedirect.com/science/article/abs/pii/S0732312312000491
11. Mathematics Hub, "Families", Education Services Australia for the Australian Government Department of Education. https://www.mathematicshub.edu.au/families/
Common questions
When do children start learning about angles?
Angles first appear in Year 3 of the Australian Curriculum, where children identify angles as measures of turn and compare them with a right angle. Year 4 adds the angle names, and Year 5 is where children measure angles in degrees with a protractor.
What is the difference between shapes and transformations?
Shapes work is about naming, classifying and building two-dimensional shapes and three-dimensional objects. Transformations are about moving them: sliding, flipping and turning a shape and noticing what stays the same. Line and rotational symmetry come first, in Year 4, and the three movements follow in Year 5.
Why does my child say a rotated square is a diamond?
Children often learn shapes from a single typical picture, so a square tilted on its corner no longer matches the image they hold. Turning shapes around, and asking what has actually changed about the sides and corners, helps separate the name from the picture.
