# 4.1 Investigate and approximate the area of polygons  (Page 3/3)

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6.2 Add all the numbers from 1 to 20 inclusive. Look for a pattern and a short way. Write down what you did and your answer on the dotted line below. Then check your answer the long way. You may use a calculator to do so.

7. Another interesting pattern can be seen in the answers if you add:

• 1 to 10 inclusive = _____
• 11 to 20 inclusive = _____
• 21 to 30 inclusive = _____
• 31 to 40 inclusive = _____
• 41 to 50 inclusive, and so on to 100. Write down the answers, study them and try to explain why this pattern occurs.

8. More patterns with shapes. The following pattern may be made with toothpicks, one for each straight line.

• Pattern: Each time we add one triangle, we need ______more toothpicks.
• We could put our information into a table. Please complete it.
 Number of triangles 1 2 3 4 5 6 17 25 Number of toothpicks
• How are the last two answers calculated? There are at least two different ways (without a calculator) and it is important that you should discuss these with your friends.

Hint: Maybe you could look at the toothpicks needed for six triangles and use them to calculate how many toothpicks are needed for 17 triangles, or you could think that you know the general pattern and just apply it to find out how many toothpicks are needed for 17 triangles. Your discussion is important, so the answers are not being given to you.The same applies to the 25 triangles.

8.4 Write down how you calculated the answers for

1. 17 triangles
2. 25 triangles

9. Complete the table:

 In 1 2 3 4 5 6 10 20 50 Out 8 15 22 29 36

1. Do the following show tessellation? Write “yes” or “no” for each one.

 Using the trapezium and diamond ________ Using just the trapezium ________ Using circles _______

2. Write down one way in which the sides of a trapezium differ from the sides of a

parallelogram .

3. Why is the triangle used in the building of the framework of the roofs of houses?

4. On a floor there are 10 tiles in a row and there are 17 rows of tiles. How many tiles are there altogether?

5. Dad uses 135 tiles to tile a stoep. He places 9 tiles across the width of the stoep. How many tiles are there in the length of the stoep?

6. Make a diagram to show what a square tiled area would look like if 16 square tiles were used to cover it. Use your ruler to draw in the tiles.

7. Complete the table:

 1 2 3 4 5 6 10 12 20 4 7 10 13 16

8. Complete this table:

 1 2 3 4 7 8 1 4 9 16 100

9. Thirty squares are made with toothpicks as shown in the diagram (one toothpick for each straight line). How many toothpicks are needed?

1. Find a pattern and write down the missing numbers: 5; 13; 21; 29; ___;___

## Assessment

 Learning outcomes(LOs) LO 2 Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. Assessment standards(ASs) We know this when the learner: 2.1 investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns: represented in physical or diagrammatic form; 2.1.2 not limited to sequences involving constant difference or ratio. 2.2 describes observed relationships or rules in own words. LO 4 measurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts. We know this when the learner: 4.8 investigates and approximates (alone and /or as a member of a group or team): 4.8.2 area of polygons (using square grids and tiling) in order to develop an understanding of square units; volume/capacity of three-dimensional objects (by packing or filling them) in order to develop an understanding of cubic units.

## Memorandum

ACTIVITY 1area of polygons

1.1 to 1.3 Practical own work and recording of it.

2. 4 whole blocks and 5 and a bit blocks = about 9 blocks

3.1 6

3.2 12

• 7 square cm
• counted the length on the long side and the number of tiles on the short side.
• 5 x 2 = 10 tiles or 10 square cm
• Drawing
• 4m x 3m = 12 square metres
• Drawing
• 6 rows
• Drawing

8.1 Yes

8.2 Drawing

9. 23 x ? =736

32 tiles

10. 75 x 54 = 4 050 tiles!

ACTIVITY 2 Patterns

1.4

4 shapes

2. Multiples of 9 – the digits forming each multiple of 9 add up to 9, so 54 is a multiple of 9; 72 is a multiple of 9. This is useful for checking answers.

• Missing output numbers: 35; 42; 49; 70; 91
• Flow diagram: input numbers: 1; 2; 3; 4; 5; 6; 7; 8; 9; 10 Operator: x 7

Output numbers: 7; 14; 21; 28; 35; 42; 49; 56; 63; 70

• multiplied by 7

4.1

 1 2 3 4 7 8 9 10 20 50 7 12 17 22 37 42 47 52 102 252

4.2 Flow diagram:

Input numbers: 1; 2; 3; 4; 7; 8; 9; 10; 20; 50

Operators: x 5 + 2

Output numbers: 7; 12; 17; 22; 37; 42; 47; 52; 102; 252

5.1

 1 2 3 4 5 6 9 11 12 20 3 5 7 9 11 13 19 23 25 41

5.3

 In 1 2 3 4 5 6 7 10 14 Out 3 7 11 15 19 23 27 39 55

5.3 multiplied by 4 and 1 was subtracted from the answer.

• It can! x 4 – 1
• Own

6.2 1 + 20; 2 + 19; 3 + 18; 4 + 17; 5 + 16; 6 + 15; 7 + 14; 8 + 13; 9 + 12; 10 + 11

10 x 21 = 210

7. 55; 155; 255; 355; 455 etc.

Own

8.1 2

8.2

 Triangles 1 2 3 4 5 6 17 25 Tooth-picks 3 5 7 9 11 13 35 51
• Discussion

8.4 (a) 17 x 2 + 1

(b) 25 x 2 + 1

9.

 In 1 2 3 4 5 6 10 20 50 Out 8 15 22 29 36 43 71 141 351

1.1 Yes

1.2 Yes

1.3 No

2. Only 1 pair of opposite sides are parallel; they are not equal in length.

3. It is a rigid shape.

4. 170 tiles

5. 15 tiles

6. Diagram 4 by 4

7.

 1 2 3 4 5 6 10 12 20 4 7 10 13 16 19 31 37 61

8.

 1 2 3 4 7 8 10 1 4 9 16 49 64 100

10. 5; 13; 21; 29; 37; 45

who was the first nanotechnologist
k
Veysel
technologist's thinker father is Richard Feynman but the literature first user scientist Nario Tagunichi.
Veysel
Norio Taniguchi
puvananathan
Interesting
Andr
I need help
Richard
anyone have book of Abdel Salam Hamdy Makhlouf book in pdf Fundamentals of Nanoparticles: Classifications, Synthesis
what happen with The nano material on The deep space.?
It could change the whole space science.
puvananathan
the characteristics of nano materials can be studied by solving which equation?
sibaram
synthesis of nano materials by chemical reaction taking place in aqueous solvents under high temperature and pressure is call?
sibaram
hydrothermal synthesis
ISHFAQ
how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
STM - Scanning Tunneling Microscope.
puvananathan
how did you get the value of 2000N.What calculations are needed to arrive at it
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Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class