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Mathematics

Grade 4

Numbers, feactions, decimals and number patterns

Module 6

Numeric patterns

Activity 1:

To recognise and represent multiples in order to be able to describe, compare and represent them [LO 1.3]
To investigate numeric patterns [LO 2.1]
To describe numeric patterns in your own words [LO 2.2]
To find output numbers [LO 2.3]

1. When we count in 6’s we are saying the multiples of 6.

1.1 Work with a friend. One of you must count in 6’s from 0 to 102. The other one must use a calculator to check you and stop you if you make a mistake. If that happens the one with the calculator must just say, ”Stop!” and show the calculator. The counting goes on from there. Then swap over.

1.2 Now fill in the missing multiples of 6 in the table below:

1 2 3 4 5 6 7 8 9 10 11 12
× 6 6 12 18 24 30 60 66

1.3 Now count backwards in 6’s from 102 to 0. Let a friend check you. Then swap over. Do you notice anything? Yes, multiples of 6 are all even numbers.

1.4 What patterns do you notice? Yes, the last digits seem to be 6;..2; ..8; ..4; ..0. They are repeated and so form a pattern.

Now that you are aware of this, you can count in 6’s for ever (if you concentrate)!

1.5 Count in 6’s and complete the flow diagram:

1.6 How do we programme the calculator to count in 6’s?

Press clear and

1.7 Write down the multiples of 6 from 102 to 0:

1.8 How do we programme the calculator to count backwards in 6’s from 102?

Press clear and

Now you can really count in 6’s easily, so let’s move on to 7’s.

2. Multiples of 7

2.1 Now use your calculator (if necessary) to count in 7’s and complete the flow diagram:

Can you spot any patterns? Two are written below. Try to spot some more and discuss with a friend.

  • They are both odd and even numbers.
  • They seem to be: odd, even, odd, even.

2.2 Now fill in the missing multiples of 7:

1 2 3 4 5 6 7 8 9 10 11 12
× 7 7 14 21 70 77

There seems to be some sort of repetition after the first 9 multiples. Does it continue?

Are there any other patterns? Write down what you have noticed.

  • Count backwards in 7’s from 105 to 0. Use your calculator to do this if necessary.
  • Write the missing multiples of 6 in the table below and then the multiples of 7 in the next row. Do you notice anything?
1 2 3 4 5 6 7 8 9 10 11 12
× 6 6 12 18 24
× 7 7 14 21 28

2.5 Now compare the two rows (across) of answers. A very interesting pattern appears to be emerging.

Look: 1 × 7 = 1× 6 + 1

5 × 7 = 5 × 6 + ……

9 × 7 = 9 × 6 + ……

2 × 7 = 2 × 6 + …….

6 × 7 = 6 × 6 + ……

10 × 7 = 10 × 6 + …..

  1. × 7 = 3 × 6 + ……
  2. 7 × 7 = 7 × 6 + ……
  3. 11 × 7 = 11 × 6 +……

4 × 7 = 4 × 6 + ……

8 × 7 = 8 × 6 + ……

12 × 7 = 12 × 6 +……

3. Multiples of 8

3.1 The numbers jump in 8 wholes. Use the calculator to count in 8’s and write down the missing multiples of 8.

0, 8, 16, 24, 32,……., ……., …………, ………, ………….,…………,………., …………, ……., …….., …………, ……… .

3.2 Another way of saying: 8 + 8 + 8 + 8 is 4 × 8.

Now complete the flow diagram:

3.3 Spot a pattern. Write down the missing multiples of 8 in the table below and look at the last digit of each one.

1 2 3 4 5 6 7 8 9 10 11 12
× 8 8 16 80 88

Look carefully:

8 ; 1 6 ; 2 4 ; 3 2 ; 4 0 ; 48; 56; 64; 72; 80; 88; 96

Questions & Answers

Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Good
Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class
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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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