Download - Positive and Negative Numbers. Working with Numbers

Positive and Negative Numbers.Working with Numbers.

LEARNING OUTCOMES:• Identify the value of any digit in a number.• Using directed numbers in everyday life.• Ordering directed numbers.• Adding and subtracting directed numbers.• Multiplying and dividing directed numbers.

• Addition and subtraction.

• Long multiplication.

• Long division.

Place Value.

Positive and negative numbers.

Place value of digits

10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions

Million Hundred thousands

Ten thousands

Thousands Hundreds

Tens Units

1. Write down the value of the numbers below in the number 3 546 281.

6 ________________________________________

4 ________________________________________

Place Value.



10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

1. Write down the value of the numbers below in the number 3 546 281.

6 6 000

4 40 000

Place Value.


2. Write down the value of the 4 in the number 674 893.


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.



4 000


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.




10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.



70 000


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.




10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.



200 000


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


5. Write down the value of the 5 in the number 5 106 782.


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.



5 000 000


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


6. Write the number seventeen thousand, three hundred and fifty two in figures.


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


6. Write the number seventeen thousand, three hundred and fifty two in figures.

17 352


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


7. Write the number thirteen thousand, one hundred and seventy six in figures.


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


7. Write the number thirteen thousand, one hundred and seventy six in figures.

13 176


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


8. Write the number a quarter of a million in figures.


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


8. Write the number a quarter of a million in figures.

250 000


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


9. Write six and a half million in figures.


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Place Value.


9. Write six and a half million in figures.

6 500 000


10 000 000 1 000 000 100 000 10 000 1 000 100 10 1

Tenmillions


Ten thousands

Thousands Hundreds

Tens Units

Directed Numbers.


1. Below you can see the temperature in five towns at midnight.

Town Perth Oldham Oswestry Swansea Wrexham

Temp. °C 6 -6 3 -4 7

a) Which town had the lowest temperature? _________________________

b) What is the difference in temperature between Perth and Swansea? __________

c) By 6am the temperature has risen by 9°C in Swansea. What is the new temperature in Swansea? ________________

d) At 5am the temperature falls by 7°C in Oswestry. What is the newtemperature? ___________________

Directed Numbers.


1. Below you can see the temperature in five towns at midnight.

Town Perth Oldham Oswestry Swansea Wrexham

Temp. °C 6 -6 3 -4 7

a) Which town had the lowest temperature? Oldham

b) What is the difference in temperature between Perth and Swansea? 10°C

c) By 6am the temperature has risen by 9°C in Swansea. What is the new temperature in Swansea? 5°C

d) At 5am the temperature falls by 7°C in Oswestry. What is the newtemperature? -4°C

Directed Numbers.


2. Susan wrote down the temperature at different times on Christmas day.

Time 1am 4am 8am noon 3pm 7pm

Temp. °C -6 -10 -5 7 5 -3

a) What is the lowest temperature? ______________________________

b) Work out the difference in temperature between 4am and 8am. _____________

c) Work out the difference in temperature between 3pm and 7pm. ______________

d) By 11pm the temperature had fallen by 5°C from its value at 7pm. Work out the temperature at 11pm. ______________________________________

Directed Numbers.


2. Susan wrote down the temperature at different times on Christmas day.

Time 1am 4am 8am noon 3pm 7pm

Temp. °C -6 -10 -5 7 5 -3

a) What is the lowest temperature? -10°C

b) Work out the difference in temperature between 4am and 8am. 5°C

c) Work out the difference in temperature between 3pm and 7pm. 8°C

d) By 11pm the temperature had fallen by 5°C from its value at 7pm. Work out the temperature at 11pm. -8°C

Directed Numbers.


3. Place these numbers in order of size, smallest first.

5, -6, -10, 2, -4

Directed Numbers.



5, -6, -10, 2, -4

-10, -6, -4, 2, 5

Directed Numbers.


4. Place these numbers in order of size, biggest first.

4, -3, 1, -5, -7

Directed Numbers.


4. Place these numbers in order of size, biggest first.

4, -3, 1, -5, -7

4, 1, -3, -5, -7

Directed Numbers.



-2, 6, 2, -3, 3

Directed Numbers.



-2, 6, 2, -3, 3

-3, -2, 2, 3, 6

Multiplying and Dividing Directed Numbers.


(+) x (+) = +(-) x (-) = +(+) x (-) = -(-) x (+) = -

(+) / (+) = +(-) / (-) = +(+) / (-) = -(-) / (+) = -

1. Work these out without a calculator.

3 x -4

-5 x -6

-20 / 4

4 x 5

-4 x 6

7 x -2

-3 x -4

-4 x -2

7 x -6

-9 x -2



(+) x (+) = +(-) x (-) = +(+) x (-) = -(-) x (+) = -

(+) / (+) = +(-) / (-) = +(+) / (-) = -(-) / (+) = -


3 x -4 = -12

-5 x -6 = 30

-20 / 4 = -5

4 x 5 = 20

-4 x 6 = -24

7 x -2 = -14

-3 x -4 = 12

-4 x -2 = 8

7 x -6 = -42

-9 x -2 = 18



(+) x (+) = +(-) x (-) = +(+) x (-) = -(-) x (+) = -

(+) / (+) = +(-) / (-) = +(+) / (-) = -(-) / (+) = -


6 / 2

-10 / 2

15 / -3

24 / -6

-12 / 2

-30 / -10

18 / -3

50 / 10

-5 x 6 x -2

-2 x -3 x -4



(+) x (+) = +(-) x (-) = +(+) x (-) = -(-) x (+) = -

(+) / (+) = +(-) / (-) = +(+) / (-) = -(-) / (+) = -


6 / 2 = 3

-10 / 2 = -5

15 / -3 = -5

24 / -6 = -4

-12 / 2 = -6

-30 / -10 = 3

18 / -3 = -6

50 / 10 = 5

-5 x 6 x -2 = -30 x -2 = 60

-2 x -3 x -4 = 6 x -4 = -24

Adding and Subtracting Directed Numbers.Positive and negative numbers.


3 + 4 1 + 3

-3 – 4 -1 – 3

9 – 4 6 – 4

-4 + 9 -4 + 6

2 – 6 3 – 5

-6 + 2 - 5 + 3



3 + 4 = 7

-3 – 4 = -7

9 – 4 = 5

-4 + 9 = 5

2 – 6 = -4

-6 + 2 = -4

1 + 3 = 4

-1 – 3 = -4

6 – 4 = 2

-4 + 6 = 2

3 – 5 = -2

- 5 + 3 = -2



5 + 2

-5 - 2

7 - 3

-3 + 7

4 - 9

-9 + 4

7 + 4

-6 - 5

10 - 4

-5 + 7

3 – 8

-7 + 1



5 + 2 = 7

-5 – 2 = -7

7 – 3 = 4

-3 + 7 = 4

4 – 9 = -5

-9 + 4 = -5

7 + 4 = 11

-6 – 5 = -11

10 – 4 = 6

-5 + 7 = 2

3 – 8 = -5

-7 + 1 = -6

Adding and Subtracting Directed Numbers.



6 + +4

6 + -4

6 – +4

6 – -4

-6 + +4

-6 + -4

-6 – +4

-6 – -4




6 + +4 = 6 + 4 = 10

6 + -4 = 6 – 4 = 2

6 – +4 = 6 – 4 = 2

6 – -4 = 6 + 4 = 10

-6 + +4 = -6 + 4 = -2

-6 + -4 = -6 – 4 = -10

-6 – +4 = -6 – 4 = -10

-6 – -4 = -6 + 4 = -2




4 + +6

4 + -6

4 – +4

4 – -4

-4 + +6

-4 + -6

-4 – +4

-4 – -4



4 + +6 = 4 + 6 = 10

4 + -6 = 4 – 6 = -2

4 – +4 = 4 – 4 = 0

4 – -4 = 4 + 4 = 8

-4 + +6 = -4 + 6 = 2

-4 + -6 = -4 – 6 = -10

-4 – +4 = -4 – 4 = -8

-4 – -4 = -4 + 4 = 0




2 – 7

-4 + 6

-2 – 3

2 – -5

-3 + -4

-2 – -3

6 + -4 - 7




2 – 7 = -5

-4 + 6 = 2

-2 – 3 = -5

2 – -5 = 2 + 5 = 7

-3 + -4 = -3 – 4 = -7

-2 – -3 = -2 + 3 = 1

6 + -4 – 7 = 6 – 4 – 7 = 2 – 7 = -5




5 – 8

-6 – 1

-5 + 9

2 – -3

-6 + -4

5 – 7 – -4

2 + 1 + -5 – 3 – -6




5 – 8 = -3

-6 – 1 = -7

-5 + 9 = 4

2 – -3 = 2 + 3 = 5

-6 + -4 = -6 – 4 = -10

5 – 7 – -4 = -2 + 4 = 2

2 + 1 + -5 – 3 – -6 = 3 – 5 – 3 + 6 = -2 – 3 + 6 = -5 + 6 = 1



4. Layout all cards into a triangular-jigsaw. Put equivalent cards next to each other.

Addition and Subtraction.

Working with numbers.

1. Work out.

328 + 65 463 + 231



1. Work out.

328 + 65 = 393 463 + 231 = 694



2. Work out.

563 – 15

400 – 36



2. Work out.

563 – 15 = 548

400 – 36 =364



2. Work out.

784 – 56

900 – 42



2. Work out.

784 – 56 = 728

900 – 42 = 858



3. Work out.

904 – 256

9004 – 76



3. Work out.

904 – 256 = 648

9004 – 76 = 8928



3. Work out.

603 – 134

6005 – 47



3. Work out.

603 – 134 = 469

6005 – 47 = 5958

Long Multiplication.


1. Work out.

32 x 3

21 x 5



1. Work out.

32 x 3 = 96

21 x 5 = 105



1. Work out.

43 x 2

62 x 4



1. Work out.

43 x 2 = 86

62 x 4 = 248



2. Work out.

43 x 4

72 x 6



2. Work out.

43 x 4 = 172

72 x 6 = 432



2. Work out.

68 x 3

35 x 5



2. Work out.

68 x 3 = 204

35 x 5 = 175



3. Work out.

123 x 3

241 x 5



3. Work out.

123 x 3 = 369

241 x 5 = 1205



3. Work out.

213 x 4

684 x 2



3. Work out.

213 x 4 = 852

684 x 2 = 1368



4. Work out.

45 x 12

31 x 24



4. Work out.

45 x 12 = 540

31 x 24 = 744



4. Work out.

53 x 13

63 x 25



4. Work out.

53 x 13 = 689

63 x 25 = 1575



5. Work out.

124 x 15

204 x 34



5. Work out.

124 x 15 = 1860

204 x 34 = 6936



5. Work out.

253 x 14

302 x 26



5. Work out.

253 x 14 = 3542

302 x 26 = 7852

Long Division.Working with numbers.

1. Work out.

84 ÷ 2

96 ÷ 3


1. Work out.

84 ÷ 2 = 42

96 ÷ 3 = 32


1. Work out.

68 ÷ 2

84 ÷ 4


1. Work out.

68 ÷ 2 = 34

84 ÷ 4 = 21


2. Work out.

78 ÷ 3

84 ÷ 6


2. Work out.

78 ÷ 3 = 26

84 ÷ 6 = 14


2. Work out.

92 ÷ 4

75 ÷ 5


2. Work out.

92 ÷ 4 = 23

75 ÷ 5 = 15


3. Work out.

144 ÷ 4

230 ÷ 5


3. Work out.

144 ÷ 4 = 36

230 ÷ 5 = 46


3. Work out.

258 ÷ 3

300 ÷ 4


3. Work out.

258 ÷ 3 = 86

300 ÷ 4 = 75


4. Work out.

720 ÷ 4

780 ÷ 6


4. Work out.

720 ÷ 4 = 180

780 ÷ 6 = 130


4. Work out.

850 ÷ 5

540 ÷ 3


4. Work out.

850 ÷ 5 = 170

540 ÷ 3 = 180


5. Work out.

253 ÷ 11

384 ÷ 12

288 ÷ 24

325 ÷ 25


5. Work out.

253 ÷ 11 = 23

384 ÷ 12 = 32

288 ÷ 24 = 12

325 ÷ 25 = 13


5. Work out.

276 ÷ 23

294 ÷ 14

672 ÷ 21

525 ÷ 25


5. Work out.

276 ÷ 23 = 12

294 ÷ 14 = 21

672 ÷ 21 = 32

525 ÷ 25 = 21

Review “Positive and Negative Numbers”.




40 000 000


2. Write the number two hundred thousand, nine hundred and fifty one in figures.


2. Write the number two hundred thousand, nine hundred and fifty one in figures.

200 951


3. The temperature at 6am was -5°C. By 10am it had risen 8 degrees. What is the new temperature?


3. The temperature at 6am was -5°C. By 10am it had risen 8 degrees. What is the new temperature?

3°C



9, 16, -10, -3, -1



9, 16, -10, -3, -1

-10, -3, -1, 9, 16



6 x -5 -9 / -3

-12 / 3 x -2 2 x -1 x 3

9 x -2 x -3 -15 / -3 x -4



6 x -5 = -30 -9 / -3 = 3

-12 / 3 x -2 = -4 x -2 = 8 2 x -1 x 3 = -2 x 3 = -6

9 x -2 x -3 = -18 x -3 = 54 -15 / -3 x -4 = 5 x -4 = -20



-2 – 3 5 + (-9)

-2 – (-5) 8 – (-3) - 4 - 9



-2 – 3 = -5 5 + (-9) = 5 – 9 = -4

-2 – (-5) = -2 + 5 = 3 8 – (-3) - 4 – 9 = 8 + 3 – 4 – 9 = = 11 – 4 – 9 = 7 – 9 = -2

Review “Working with Numbers”.

1. Work out.

450 + 375 5003 - 56

34 x 3 436 x 14

156 ÷ 6 276 ÷ 12

Review “Number”.1. Work out.

450 + 375 =825 5003 – 56 = 4947

34 x 3 = 102 436 x 14 = 6104

156 ÷ 6 = 26 276 ÷ 12 = 23

Download - Positive and Negative Numbers. Working with Numbers

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