3.19 Tesselations

Mathematics

Space and shape

Educator section

Memorandum

24.2 No, pentagons do not tesselate

26

(a) 50

(b) 105

(c) 993

(d) 995

(e) 12

(f) 12

(g) 12

(h) 7

(i) 100

(j) 100 000

(k) 5 r. 3

(l) 9 r. 5

(m) 8 r. 6

(n) 9 r. 5

(o) 7 r. 4

Leaner section

Content

Activity: tesselations [lo 1.8]

24. TESSELLATIONS

24.1 Did you know?

When a surface is covered by tiles so that there are no gaps left between the tiles, and no tiles overlap, the pattern that is made is called a tessellation, e.g.

We say the form tessellates.

24.2 Do you think ALL polygons will tessellate? __________ Motivate your answer.

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24.3 Use a combination of polygons, e.g. a triangle and a square and design a floor covering for a kitchen or bathroom. It must tessellate! Colour it in neatly.

25. Time for self-assessment

Colour in the face that shows your ability:
I was able to group different triangles according to their characteristics.
I can explain the following concepts:
acute-angled triangle
equilateral triangle
obtuse-angled triangle
isosceles triangle
right-angles triangle
scalene triangle
symmetry
tessellations
I can indicate the axes of symmetry of figures.
I can draw a pattern with shapes that tessellate.

26. Can you improve the mark you got in the previous mental test? Try to complete this one in 2 minutes.

a) 16 + 19 + 15 = ____________

b) 28 + 36 + 41 = ____________

c) 1 009 – 16 = ____________

d) 1 012 – 17 = ____________

e) ____________ x 8 = 96

f) 9 x ____________ = 108

g) 84 ÷ 7 = ____________

h) 63 ÷ ____________= 9

i) 10 ⁵ ÷ 103 = ____________

j) 10³ x 102 = ____________

k) 43 ÷ 8 = ____________

l) 59 ÷ 6 = ____________

m) 78 ÷ 9 = ____________

n) 86 ÷ 9 = ____________

o) 53 ÷ 7 = ____________

27. CHALLENGE!

• See if you can get the following correct

27.1 Arrange 20 toothpicks to form seven squares (see sketch). Move three toothpicks so that only five squares of the same size are left.

27.2 Arrange your toothpicks as shown in the example below. Move only two so that you form a parallelogram and three rhombuses.

27.3 Trace the following pieces of a tangram onto a folio sheet and cut them out neatly. (You may use a tangram if you have one in the class.)

Use all the pieces and build a cat in as many different ways as possible!

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.8: We know this when the learner performs mental calculations involving squares of natural numbers to at least 10 ² and cubes of natural numbers to at least 5 ³ .