# 1.17 To calculate by selecting appropriate operations for solving

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## Memorandum

1.1 5

1.2 3

1.3 8

1.4 6

2.1 (39 x 27) + 496 1 549

2.2 (23 x 18) + 852 – 256 1 010

2.3 (67 + 48); 7 705 ÷ answer 67

2.4 3 600 ÷ 30; 82 x 10; answer + answer 940

2.5 2 934 – 816 + 905 – 205 2 818

## 2. different solutions are possible. you are aloud to use a number more than once.

Test 1

• 13 800; 13 750
• 24 360; 24 375

2. 300 000 + 60 000 + 8 000 + 400 + 20 + 9

• <
• =
• 20 500
• 358 490

5. six million eight hundred twenty three thousand four hundred and seventeen

6.1 1296

6.2 6

• 40 000
• 6 million
• 37 000
• 149 000
• 48; 56; 64; 72
• 1; 2; 3; 4; 5; 6; 8; 12; 24
• 11; 13; 17; 19

10.1 true

• false
• false
• 114
• 34
• 70

11.4 6

## Activity:to calculate by selecting appropriate operations for solving problems [lo 1.8.10]

It is very important to really understand and remember the following; otherwise you will not be able to perform easy (or difficult) operations, so that you will get wrong answers!

SEQUENCE OF CALCULATIONS TAKE NOTE AND LEARN THE

FOLLOWING!

The order in which calculations are done is:

1. Brackets

2. Of

3. Division

4. Multiplication

6. Subtraction

The following rules are also applicable:

1. When the operation is + only or x only, e.g. 6 + 3 + 9 + 5:

work from LEFT TO RIGHT.

2. When there is only + and − , e.g. 6 − 3 + 2 − 4 + 9:

work from LEFT TO RIGHT

Thus: 6 − 3 à 3 + 2 à 5 − 4 à 1 + 9 = 10

3. When you only have x and ¸ is, e.g. 2 x 24 ¸ 4 x 10 ¸ 5:

Work from LEFT TO RIGHT

Thus: 2 x 24 à 48 ¸ 4 à 12 x 10 à 120 ¸ 5 = 24

1. Let’s see if you are able to apply the preceding knowledge correctly. Work with a partner and calculate the following:

1.1 f = 9 + 6 ¸ 2 − 7 _____________________________________________

1.2 c = 7 − (18 + 2) ¸ 5___________________________________________

1.3 k = 23 − 16 + 4 − 3___________________________________________

1.4 e = 36 ¸ 12 x 4 ¸ 2_____________________________________________

You may use your pocket calculator now, but it might not help if you do not know the correct sequence of operations. If you are uncertain, read the previous page again. Try to complete the following table correctly:

 Calculate Key to sequence Answer E.g. 15 + 6 × 2 (6 × 2) + 15 27 2.1 496 + 39 × 27 2.2 852 + (23 × 18) − 256 2.3 7 705  (67 + 48) 2.4 3 600  30 + 82 × 10 2.5 2 934 − 816 + 905 − 205

## Time for peer-assessment

How well do you know the last part of the work that we have been doing? Explain the following to a partner. Your partner can then assess you by circling the relevant code:

 Altogether unsure Not very sure Fairly sure Very sure I can explain what multiples are. (LO 1.3) 1 2 3 4 I can explain what factors are. (LO 1.3) 1 2 3 4 I can explain what prime numbers are. (LO 1.3) 1 2 3 4 I can use the constant function on my pocket calculator to determine multiples. (LO 1.8) 1 2 3 4 I can explain what a palindrome is. (LO 1.3) 1 2 3 4 I can explain the properties of 1 and 0 to my friend. (LO 1.3) 1 2 3 4 I know the sequence of calculations and can apply it correctly. (LO 1.8) 1 2 3 4

## Puzzles!

1. Place the numbers 1 to 9 in the diagram in such a way that all the number sentences are true.

2. Place numbers between 1 and 12 in the diagram in such a way that the

sum totals of the different sides are the same.

## Test 1

1. Complete the following number patterns:

1.1 13 850 ; ________________ ; ________________ ; 13 700 ; 13 650

1.2 24 330 ; 24 345 ; ________________ ; ________________

(4)

2. Write in expanded notation:

2.1 368 429 = ____________ + ____________ + ___________ + ___________ +

____________ + ____________

(2)

3. Fill in:<;>or = :

3.1 489 653 * 498 653____________

3.2 10 x 10 x 10 x 10 * 100 000 x 10____________

(2)

4. Which number is:

4.1 350 more than 20 150? ________________________

4.2 10 000 less than 368 490? ______________________

(2)

5. Write in words:

6 832 419

(2)

6. Complete:

6.1 64 = ____________________________________

6.2 one million = 1 x 10¨______________________

(2)

7. What is the value of the digit printed in bold?

7.1 1 4 7 689________________________________________

7.2 6 823 417_______________________________________

(2)

8. Round off to the nearest 1 000:

8.1 36 842________________________________________

8.2 149 099________________________________________

(2)

9. Write down:

9.1 the multiple of 8 between 40 and 80

_____________________________________________________________________

9.2 the factors of 24

_____________________________________________________________________

9.3 the prime numbers between 10 and 20

___________________________________________________________________ (6)

10. True or False?

10.1 42 624 is a palindrome_____________________________

10.2 1 is a prime number________________________________

10.3 36 ¸ 0 = 0________________________________________

(3)

11. Calculate:

11.1 90 + 6 x 12 ¸ 3__________________________________

11.2 36 − (5 x 4) ¸ 10_________________________________

11.3 80 − 6 + 4 − 13 + 5_____________________________

11.4 8 x 5 ¸ 8 x 6 ¸ 5_________________________________

(8)

I got _______________________________ out of 35 right.

Colour in: I feel

 VERY SATISFIED HAPPY CONCERNED I AM ABLE TO DO BETTER

## 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 that involve:

1.8.10: multiple operations on whole numbers with or without brackets.

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