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# To count and calculate correctly without using a pencil and paper

Module by: Siyavula Uploaders. E-mail the author

## Memorandum

2.

2.2 less 40

2.3 less 12

3.

3.1 9; 11; 28; 100; 456

3.2 9; 1; 30; 82

3.3 2; 8; 11; 17

4.

4.1 99

4.2 36

## Content

### ACTIVITY: To count and calculate correctly without using a pencil and paper [LO 1.1, LO 1.8]

1. In the previous activity you worked with small numbers. Now let us work with greater numbers. Team up with a friend and count:

1.1 in ones from 985 tot 1 005

1.2 in twos from 640 backwards to 596

1.3 in fives from 2 035 to 2 095

1.4 in tens from 1 890 backwards to 1 760

1.5 in hundreds from 800 to 2 600

1.6 in thousands from 4 300 to 9 300

2. Sometimes one does addition and/or subtraction unwittingly (without being aware that that is what you are doing) to get the right answer. Can you tell your friend what to do to each of these numbers in order to change it into the new number?

 NUMBER NEW NUMBER 2.1 126 ??? 138 2.2 868 ??? 828 2.3 943 ??? 931 2.4 9 987 ??? 9 999 2.5 6 472 ??? 6 500

3. If we know the multiples of 10, 100 and 1 000 well, we can divide by them by doing mental arithmetic (without pencil and paper). Can you give the following answers faster than your friend?

3.1 How many tens are there in: 90 ; 110 ; 280 ; 1 000 ; 4 560 ?

3.2 How many hundreds are there in: 900 ; 1 100 ; 3 000 ; 8 200 ?

3.3 How many thousands are there in: 2 000 ; 8 000 ; 11 000 ; 17 000 ?

Do you see the pattern in the answers? What is the secret of calculating the answers so easily?

÷ 10:

÷ 100:

÷ 1 000:

DO YOU STILL REMEMBER THE FOLLOWING?

An EVEN number is exactly divisible by 2 (can be shared equally amongst 2). An ODD number cannot be divided exactly by 2 without a remainder or without having a fraction in the answer, e.g. 3 can be divided by 2, but the answer is 1 .

4. Now use your knowledge of even and odd numbers to see whether you can solve the following riddles

4.1

4.2

• Now look at the following diagram.

The number that is represented here is 5 243.

five thousand, two hundred and forty-three.

1. We can also write it like this:

5 243 = 5 000 + 200 + 40 + 3

= (5 × 1 000) + (2 × 100) + (4 × 10) + (3 × 1)

This way of writing is called expanded notation.

## 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 1.1: We know this when the learner counts forwards and backwards in whole number intervals and fractions;

Assessment Standard 1.8: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems.

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