# 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:

 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.

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