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# To determine the equivalence and validity of different representations

Module by: Siyavula Uploaders. E-mail the author

Leaner Section

## Content

### To use strategies to check solutions [LO 1.11]

• During the revious activity you used your own techniques and strategies to solve the problems. In your feedback to the class you probably noticed that there is not only one way in which we can subtract numbers. Divide into groups of three. Read the following problem thoroughly and as a group work through the different methods of solving it.

A rugby match was attended by 32 564 men and 29 436 women.

• How many more men than women watched the match?

32 564 – 29 436

Therefore: 29 436 + 64 = 29 500

29 500 + 500 = 30 000

30 000 + 2 564 = 32 564

64 + 500 + 2 564 = 3 128

Therefore there were 3 128 more men than women.

1.2 I round off the second number to the nearest 100:

32 564 – 29 436

Therefore: 32 564 – 29 400 = 3 164

3 164 – 36 = 3 128

The answer is 3 128 more men.

1.3 I prefer rounding off the subtrahend to the nearest 1 000:

32 564 – 29 436

Therefore: 32 564 – 29 000 = 3 564

3 564 – 436 = 3 128

1.4 I calculate the difference step by step:

32 564 – 29 436

Therefore: 32 000 – 29 000 = 3 000

564 – 436 = 128

3000 + 128 = 3 128

1.5 I first write the numbers in extended notation:

32 564 – 29 436

Thus: 30 000 + 2 000 + 500 + 60 + 4

- 20 000 + 9 000 + 400 + 30 + 6

Now I regroup:

20 000 + 12 000 + 500 + 50 + 14

- 20 000 + 9 000 + 400 + 30 + 6

0 + 3 000 + 100 + 20 + 8

Therefore the answer is 3 128

1.6 I calculate the difference by working with negative numbers:

32 564 – 29 436

Therefore: 30 000 – 20 000 = 10 000

2 000 – 9 000 = – 7 000 (I still have to subtract 7 000)

500 – 400 = 100

60 – 30 = 30

4 – 6 = – 2 (I still have to subtract 2)

The difference therefore is:

10 000 – 7 000 + 100 + 30 – 2 = 3 128

2. 2.1 Which of the above methods is the easiest for YOU? ______________

Why? _______________________________________________________________

_____________________________________________________________________

__________________________________________________________________________________________________________________________________________

2.2 See if your group can think of any another method for calculating the difference.

_____________________________________________________________________

__________________________________________________________________________________________________________________________________________

## 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. 11: We know this when the learner uses a range of strategies to check solutions and judge the reasonableness of solutions;

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.6: We know this when the learner determines, through discussion and comparison, the equivalence of different descriptions of the same relationship or rule.

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