1.16 To estimate and calculate by selecting and using suitable

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Memorandum

1. Look at the unit’s digit.

If it is 5 or more, the tens digit becomes one more.

If it is 4 or less, the tens digit remains the same.

2. Look at the tens digit.

If it is 5 or more, the hundreds digit becomes one more.

If it is 4 or less, the hundreds digit remains unchanged.

3. Look at the hundreds digit.

If it is 5 or more, the thousands digit becomes one more.

If it is 4 or less, the thousands digit remains the same.

2.

2.1 20 + 10 + 20 = 50

2.2 30 + 10 + 50 = 90

2.3 10 + 20 + 20 = 50

2.4 100 + 200 + 300 = 600

2.5 200 + 100 + 100 = 400

3. “Estimated answer” and “Difference” will be different as a result of the method

applied. Pocket calculator gives correct answer.

4.

a) 279

b) 1 660

c) 6 581

d) 2 843

5. Answers will vary – many combinations possible

6. 35 + 15; 47 + 3; 23 + 27

50 + 150; 25 + 175; 10 + 190; 180 + 20; 170 + 30

250 + 750; 400 + 600; 900 + 100; 200 + 800; 990 + 10

6. 250 + 750; 125 + 825; 950 + 50; 450 + 550; 225 + 775; 415 + 585

7. 5 000 + 400 + 80 + + 9 + 300 + 60 + 2 + 1 000 + 500 + 70

= (5 000 + 1 000) + (400 + 300 + 500) + (80 + 60 + 70 +) + (9 + 2)

= 6 000 + 1 200 + 210 + 11

= 7 421

Activity: to estimate and calculate by selecting and using suitable operations [lo 1.8]

• Now practise your skill at estimating with confidence the answers by rounding off numbers.

1. It is important that we consider once again what rounding off is, and how it is done. Explain to a friend how we round off to the nearest 10, 100 and 1 000.

2. Now work in groups of three and see who is able to calculate the answers without a pocket calculator by rounding off to the closest 10 or 100. (You may not write anything down!)

2.1 16 + 11 + 19

2.2 34 + 9 + 52

2.3 2 + 15 + 23

2.4 141 + 208 + 339

2.5 182 + 149 + 106

3. Look carefully at the following example:

32 + 87 + 96 + 42 becomes

30 + 90 + 100 + 40 (rounded off to the closest 10)

Therefore the answer is approximately 260.

• When we want to add larger numbers, we can round off to the closest 100:

138 + 759 + 304 becomes

100 + 800 + 300

Therefore the answer will be roughly 1 200.

DID YOU KNOW?

• We can also round numbers off to a lower or upper limit!

e.g. 62 + 75 + 94 + 45

Lower limit: 60 + 70 + 90 + 40 = 260

Upper limit: 70 + 80 + 100 + 50 = 300

The correct answer will therefore be between

260 and 300.

4. Now complete the table by rounding off the numbers according to the method that you prefer. Estimate the answer first. Then calculate the correct answer with a pocket calculator. Finally write down the difference between the two answers.

 Calculation Estimated answer Calculator Difference E.g. 308 + 475 300 + 480 = 780 783 3 a) 67 + 98 + 114 b) 896 + 723 + 41 c) 1 892 + 4 689 d) 2 458 + 294 + 91

TIME FOR SELF-ASSESSMENT!

Colour the correct box:

 I am able to add by rounding off to the closest 10, 100 or 1 000 mastered ** have not mastered yet

** Ask your educator to give you some more examples that you can do at home!!

5. There are also other techniques or computations (other than rounding off) that you can use to calculate answers quickly. Look carefully at the examples and try to add more number combinations.

6. Look at the numbers in the diagram below. By finding as many as possible addition strings that give a sum of 1 000, you can calculate the sum of all the numbers in a jiffy! How many do you see? Colour them in the same colour.

 250 585 125 750 825 50
 950 450
550 775 415 225 316 775 415

DO YOU STILL REMEMBER?

We can use grouping to add up. Look carefully at the example!

• = 370 + 245 + 684

= 300 + 70 + 200 + 40 + 5 + 600 + 80 + 4

= (300 + 200 + 600) + (70 + 40 + 80) + (5 + 4)

= 1 100 + 190 + 9

• = 1 299

7. Use this method to calculate:

5 489 + 362 + 1 570

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

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