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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

TEST YOUR PROGRESS

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

  • about 8 square cm
  • 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

4.3 multiplied by 5 and 2 was added to the answer.

5.1

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

5.2 multiplied by 2 and 1 was added to the answer

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

Test your progress

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

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
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
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class
Neha Reply

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Source:  OpenStax, Mathematics grade 4. OpenStax CNX. Sep 18, 2009 Download for free at http://cnx.org/content/col11101/1.1
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