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1. Distinguish 2-D shapes by their properties.

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1. Distinguish 2-D shapes by their properties.

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Teacher guides students to perform the following activities:

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Teacher guides students to perform the following activities:

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The main ideas to be developed in each activity are:

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The main ideas to be developed in each activity are:

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Materials needed for the activities include:

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Materials needed for the activities include:

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1. 2-D shapes (attribute blocks)

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2. Distinguish 3-D shapes by their properties

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2. Distinguish 3-D shapes by their properties

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 3. Describe relationship among 2-D and 3-D shapes.

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 3. Describe relationship among 2-D and 3-D shapes.

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4. Form tessellations using 2-D or 3-D shapes.

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4. Form tessellations using 2-D or 3-D shapes.

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 5. Describe positions and motions of shapes on a given tililing

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 5. Describe positions and motions of shapes on a given tililing

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1. students sort 2-D shapes with one attribute, two attributes, and/or three attributes differences. Examples of attributes/properties:               a. have equal sides                   b. have a right (90⸰ ) angle      c. have opposite sides parallel. etc

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1. students sort 2-D shapes with one attribute, two attributes, and/or three attributes differences. Examples of attributes/properties:               a. have equal sides                   b. have a right (90⸰ ) angle      c. have opposite sides parallel. etc

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2. students sort 3-D shapes using attributes. Example:      a. have triangular faces           b. have a circular base             c. have rectangular faces.

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2. students sort 3-D shapes using attributes. Example:      a. have triangular faces           b. have a circular base             c. have rectangular faces.

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3. students talk about the relationship between 2-D and 3-D shapes. a question like the one below may serve as a clue for the discussion;                    a. which attribute do all triangular or  rectangular prisms have?                             b. what 2-D shapes make up the rectangular prism or the triangular prism?

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3. students talk about the relationship between 2-D and 3-D shapes. a question like the one below may serve as a clue for the discussion;                    a. which attribute do all triangular or  rectangular prisms have?                             b. what 2-D shapes make up the rectangular prism or the triangular prism?

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3. let students make tessellation with 2-D shapes with the following rules:           a. no gaps between the shapes.                                       b. shapes do not overlap.        c. pattern can go on forever in all directions. 

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3. let students make tessellation with 2-D shapes with the following rules:           a. no gaps between the shapes.                                       b. shapes do not overlap.        c. pattern can go on forever in all directions. 

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4. let students extend activity 3 with stars

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4. let students extend activity 3 with stars

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Tile using stars and other polygons (at least up to 6-point stars)

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5. Let students talk about motions and positions of shapes in their various tessellations.

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5. Let students talk about motions and positions of shapes in their various tessellations.

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1. students should not just sort polygons by their shapes but by their properties to establish the differences between them. What make the square different from the rectangle? what is the difference between the rectangle and the trapezium? The emphasis of this activity is to establish the differences among properties of shapes.

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1. students should not just sort polygons by their shapes but by their properties to establish the differences between them. What make the square different from the rectangle? what is the difference between the rectangle and the trapezium? The emphasis of this activity is to establish the differences among properties of shapes.

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2. Emphasis on the characteristics of the triangular and the rectangular prism.

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2. Emphasis on the characteristics of the triangular and the rectangular prism.

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A prism is named base on the shape of its base. if the base is a square it is called a square prism and so on.

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3. The prisms are made up of the simple polygons. the faces and the bases are all polygons.

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3. The prisms are made up of the simple polygons. the faces and the bases are all polygons.

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4. Students make tessellations from one or more simple polygons.

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4. Students make tessellations from one or more simple polygons.

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you can begin with one type of shape and when students become more familiar with tessellation, then they can move on to combine different types of shapes.

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5. discuss the various motions on students tessellations: translation, reflection and rotation.

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5. discuss the various motions on students tessellations: translation, reflection and rotation.

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Also, discuss the various congruent shapes on the students tessellations. [position or orientation of a shape does not change the size and area of the shape]
Talk about translation and rotation

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6. on the dotted or grid paper let students draw their tessellations and continue to discuss the motions and positions of the various shapes.

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6. on the dotted or grid paper let students draw their tessellations and continue to discuss the motions and positions of the various shapes.

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Example of the drawing of tessellation made with squares and equilateral triangles is shown below

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Example of the drawing of tessellation made with squares and equilateral triangles is shown below

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(this can also be viewed as a tiling with 4-point star

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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

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Howse, T. D., & 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, T. D., & 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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Eberle, R. S. (2015).  “I Don't Really Know How I Did That!”. Teaching Children Mathematics, 21(7),  402-411. doi:10.5951/teacchilmath.21.7.0402

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Eberle, R. S. (2015).  “I Don't Really Know How I Did That!”. Teaching Children Mathematics, 21(7),  402-411. doi:10.5951/teacchilmath.21.7.0402

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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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6. Identify reflection symmetry on a tessellation 

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6. Identify reflection symmetry on a tessellation 

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7. guide students to identify various symmetrical lines (mirror lines) that can be found on their drawn tessellations. 

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7. guide students to identify various symmetrical lines (mirror lines) that can be found on their drawn tessellations. 

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8. on a dotted paper, make a piece of tessellation and indicate various mirror lines and ask children to make images of the tessellation using the mirror lines as lines of reflection.

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8. on a dotted paper, make a piece of tessellation and indicate various mirror lines and ask children to make images of the tessellation using the mirror lines as lines of reflection.