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Educator section


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.

Leaner section


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


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

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..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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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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