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# To determine the equivalence and validity of different methods

Module by: Siyavula Uploaders. E-mail the author

1.1 378 767

1.2 366 269

1.3 613 751

## LEANER SECTION

### Content

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

1. In the previous activity you saw a variety of methods to do computations. Let's have a look at further ways of finding the difference. Divide into groups of three. Read through the following problem carefully. Your educator will allocate numbers to the groups and indicate which solution each group should look at. First discuss the solution and then explain it to the rest of the class.

What is the subtrahend if the minuend is 631 524 and the difference is 254 637?

1.1 I subtract by counting backwards:

631 524 – 254 637

631 524 – 200 000

• 431 524 – 50 000
• 381 524 – 4 000
• 77 524 – 600
• 376 924 – 30
• 376 894 - 7

= 376 887

The subtrahend is 376 887.

1.2 I use the rule of compensation for subtraction.

631 524 – 254 637

+ 363 + 363

• 631 887 – 255 000

+ 5 000 + 5 000

• 636 887 – 260 000

376 887

• I work with negative numbers and write them as follows:

 631 524 254 637 -3 (4 – 7) -10 (20 – 30) -100 (500 – 600) -3 000 (1 000 – 4 000) -20 000 (30 000 – 50 000) 400 000 (600 000 – 200 000) 376 887 (400 000 – 20 000 – 3 000 – 100 – 10 – 3)

1.4 This is a short method for determining the subtrahend:

5 12 10 14 11 14

6 3 1 5 2 4

- 2 5 4 6 3 7

3 7 6 8 8 7

1.5. Can your group think of another method for calculating the answer?

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2. Which of these methods do YOU prefer?

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Why?

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## 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 numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

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 presented:

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