# 1.5 Halving and doubling

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## Memorandum

If you as educator do not want to do halving just after doubling, leave it for the moment and do it later. However, make very sure that the slower learners in particular understand and have mastered the process of doubling before you do halving. Only do halving of even numbers at first.

It is important for the learners to know that 10 ÷ 2 can have 2 different meanings: division or grouping.

Look at the following two problems:

Divide 10 apples between 2 children so that they receive the same amount.

10 ¸ 2 = 5 Each receives 5 apples.

I have 10 apples and give 2 to each child. How many children were there?

10 ¸ 2 = 5 There were 5 children.

The number sentence is the same, but the presentation differs.

## Activity: halving and doubling [lo 1.10, lo 1.9, lo 1.8, lo 1.7]

• In tens: Yesterday Bonny had 5 sums correct. Today she doubled that number. Now she has __________________________ correct.

Double means: Add just as many.

You must add the same number twice (2x).

Double 5: _________________________ (Think like this: 5 + 5 ) That is 2 x 5.

• Now Tommy wants to double all his numbers. Help him! I want to see the way you think!
• Numbers on either side of the x sign can change places, as with the + sign. The answer stays the same.
• I see 2 children. How many fingers do they have altogether?

There are 2 groups of 10.

Number sentence: 2 x 10 = ________________________

 LO 1.10
• How quickly can you do this?
 2 x 4 = 8 Change them: 4 x 2 = 8 2 x 10 = _____ ____ x ____ = _____ 2 x 3 = _____ ____ x ____ = _____ 2 x 8 = _____ ____ x ____ = _____ 2 x 2 = _____ ____ x ____ = _____ 2 x 5 = _____ ____ x ____ = _____ 2 x 1 = _____ ____ x ____ = _____ 2 x 6 = _____ ____ x ____ = _____ 2 x 9 = _____ ____ x ____ = _____ 2 x 7 = _____ ____ x ____ = _____
 LO 1.9
• Bonny sees 5 bicycles. How many wheels are there?

Think like this: 2 + 2 + 2 + 2 + 2

Number sentence: 5 x 2 = ___________ or 2 x 5 = ___________

There are___________ wheels.

• Tommy sees 8 bicycles. How many wheels are there?

Number sentence: 8 x 2 = ___________ or ___________ x ___________ =

There are___________ wheels.

• Bonny has 20 two-cent pieces. How much money does she have?

Number sentence: 20 x 2 = ________ or ________ x _______. = ________

She has________ c in her purse. Draw the money.

 LO 1.8
• Mom gives Bonny 10 cookies and tells her to give half of them to Tommy.

Half of 10 is 5.

We halved the number 10.

Halving means: divide into two equal parts.

• Halve:

Use the sums above to help you!!

 LO 1.10
• Tommy did 24 sums, but half of them were wrong. How many were correct? He had ________________________________ sums correct.
• Divide 10 apples between Bonny and Tommy equally.

Each gets 5 apples.

This is the same as halving. Number sentence: 10 ÷ 2 = 5

• Think!
• ÷ 2 can also mean that you must divide 10 into groups of 2. Then you must calculate how many groups there are.
• I see 10 wheels. How many bicycles are there?

There are___________________________ bicycles.

Number sentence: 10 ÷ 2 = 5

• Tommy sees 12 ears above the bush. How many rabbits are there? Draw the 12 ears and group them into 2’s.

Now you can count how many rabbits are hiding behind the bush. 12 ÷ 2 =

____________________________ There are _________________________ rabbits.

 LO 1.7

## 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 1.7: We know this when the learner solves and explains solutions to practical problems that involve equal sharing and grouping and that lead to solutions that also include unitary and nonunitary fractions (e.g. 1¼1 , ¾4);

Assessment Standard 1.8: We know this when the learner can perform calculations, using appropriate symbols, to solve problems involving:

1.8.1 addition and subtraction of whole numbers with at least 3 digits;

1.8.2 multiplication of at least whole 2-digit by 1-digit numbers;

1.8.3 division of at least whole 2-digit by 1-digit numbers;

• estimation;

Assessment Standard 1.9: We know this when the learner performs mental calculations involving:

1.9.1 addition and subtraction for numbers to at least 50;

1.9.2 multiplication of whole numbers with solutions to at least 50;

Assessment Standard 1.10: We know this when the learner uses the following techniques:

1.10.1 building up and breaking down numbers;

1.10.2 doubling and halving;

1.10.3 number-lines;

1.10.4 rounding off in tens.

#### Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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
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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
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Mathematics grade 3. OpenStax CNX. Oct 14, 2009 Download for free at http://cnx.org/content/col11128/1.1
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