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1. sort 2-D and 3-D objects using two attributes

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1. sort 2-D and 3-D objects using two attributes

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3. identify 2-D shapes as part of 3-D shapes

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3. identify 2-D shapes as part of 3-D shapes

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5. make simple tiling from regular 2-D shapes shapes. 

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5. make simple tiling from regular 2-D shapes shapes. 

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describe positions and movement of shapes on the tilings

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1. let children make sets of shapes with two and then three attributes differences.

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1. let children make sets of shapes with two and then three attributes differences.

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(begin with 2-D shapes followed by 3-D shapes

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2. let students compare and contrast 2-D shapes.

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2. let students compare and contrast 2-D shapes.

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1. quadrilaterals
2. triangles

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Examples of attributes for activity 1 are:

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Examples of attributes for activity 1 are:

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1. have 2 sides and 2 angles equal
2. have two opposite sides equal and parallel, and all angles equal
3. have all sides and angles equal

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rectangles and trapeziums, rectangles and squares, squares and parallelograms, kite and rhombus, the equilateral triangle and the isosceles triangle etc.
questions like those below may help:
a. which triangles has 2 sides and angles equal?
b. select the triangle with a right-angle
c. which quadrilateral has two opposite sites equal and parallel?
d. how different is the kite from the rhombus?

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3. show children some 3-D shapes and ask them to form the shapes from 2-D knex.

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3. show children some 3-D shapes and ask them to form the shapes from 2-D knex.

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or let children dismantle a 3-D shape formed using knex and identify all the 2-D shapes that made the 3-D shape.

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4. let children compare and contrast the rectangular prism and the triangular prism

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4. let children compare and contrast the rectangular prism and the triangular prism

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Questions like those below may enhance the discussion in activity 4.

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Questions like those below may enhance the discussion in activity 4.

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1. which attributes do all
a. rectangular prisms have
b. triangular prisms have
2. which prisms have
a. congruent faces
b. all rectangular faces
3. how are the square and the rectangular prism
a. alike?
b. different
4. how are the triangular prism and the rectangular prism alike or different.

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5. let children form 4-point, 5-point 6-point and 8-point stars using a 2-D shapes they think is convenient to use.

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5. let children form 4-point, 5-point 6-point and 8-point stars using a 2-D shapes they think is convenient to use.

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b. let children make tessellations with two chosen 2-D shapes

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the formation of stars is important for the construction of Islamic tilings.

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the formation of stars is important for the construction of Islamic tilings.

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the important thing to discuss under activity 5 is how the shapes were moved and placed in order create the stars or the tilings

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6. let children identify the 2-shapes that can be divided in two equal halves such that one half looks exactly the same as the other half. 

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6. let children identify the 2-shapes that can be divided in two equal halves such that one half looks exactly the same as the other half. 

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let children make copies of those shapes on the paper grid and draw the lines that divide the shapes into two identical parts (when the shape is folded along that line, the two halves match exactly onto each other.

continue the investigation of lines symmetry with regular polygons. let children predict the number of lines of symmetry for a regular polygon with 8, 9,10 sides

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6. symmetry is when two or more parts looks identical. a line that divides a symmetrical shape into 2 identical parts is called a'line of symmetry'

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6. symmetry is when two or more parts looks identical. a line that divides a symmetrical shape into 2 identical parts is called a'line of symmetry'

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a. let children identify shapes with horizontal and vertical lines of symmetry.
b. on a paper grid draw one-half of a symmetrical shape and ask children to complete the shape.
c. let children revisit 'making stars' and let them identify the symmetrical lines of the stars.

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Howse,  D. T., & Howse, M. E.  (2015). Linking the Van Hiele Theory to Instruction. Teaching Children Mathematics, 21(5), 304-313. doi:10.5951/teacchilmath.21.5.0304

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Howse,  D. T., & Howse, M. E.  (2015). Linking the Van Hiele Theory to Instruction. Teaching Children Mathematics, 21(5), 304-313. doi:10.5951/teacchilmath.21.5.0304

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Alberta Education (2016). Mathematics Kindergarten to Grade 9. Alberta, Canada

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Alberta Education (2016). Mathematics Kindergarten to Grade 9. Alberta, Canada

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Arabi/Islamic geometry 01: A background to two dimensional design-geometry and pattern. http://catnaps.org/islamic/geometry.html

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Arabi/Islamic geometry 01: A background to two dimensional design-geometry and pattern. http://catnaps.org/islamic/geometry.html