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.

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 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 (+) = -

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

-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

-3 + 7

-9 + 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.

200 951

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

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

Positive and Negative Numbers. Working with Numbers

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