- NUMBER yyyyyyyyyyyyy ,,,,,, ,,,,,,, ,,,,,, yyyyyy ,,,,,,, yyyyyyy ,,,,,,yyyyyyy yyyyyy ,,,,,,,

RIC-0008 2.8

Foreword This three book series has been written for middle to upper primary students as enrichment and extension activities. The three books cover the major areas of mathematics (number, space and measurement) and provide a variety of activities which aim to motivate and challenge young mathematical minds. The activities in Maths Enrichment - Number are divided into three areas; newspaper maths, number fun and shape number puzzles. 'Newspaper maths' requires students to investigate a variety of mathematical problems using large numbers limited to the daily newspaper. These activities require each student to have a copy of a newspaper and it is suggested that a calculator will be of assistance. 'Number fun' investigates a variety of mathematical concepts with students exploring number patterns in a variety of fun formats including magic squares and a variety of tables. 'Shape number puzzles' require students to utilise their basic facts knowledge to solve a variety of number puzzles.

Contents Section 1 - Newspaper Maths Page Page Page Page Page Page Page Page

1 2 3 4 5 6 7 8

How Many? Large Numbers Percentages Carpets Real Estate Shopping TV Times Buying and Selling Shares

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• Section 2 - Number Fun Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page 16

Multiplying Digits Tables Magic Squares Money and Words Number Trick Number Magic What is the Rule? Prime and Even Numbers

Section 3 - Shape Number Puzzles Page 17 Page 18 Page 19 Page 20 Page 21 Page 22 Page 23 Page 24

Page 25-26

EXTENSION MATHS - NUMBER

R.I.C. Publications www.ricgroup.com.au

i

How Many? 1.

How many of the following items could you buy for \$10 000? Use your newspaper to find the cheapest prices. (a) Colour televisions (b) CD players (c) Computers (d) Cars (e) Mobile phones (f)

2.

Caravans

How many of the following items could you buy for \$100.00? Use your newspaper as a price guide. (a) Blocks of cheese (b) Packets of biscuits

© R. I . C.Publ i cat i ons f oofrmilk r evi ew pur posesonl y• (d)• Litres (c) Kilograms of steak

(e) Loaves of bread (f) 3.

Kilograms of oranges

You have just won a million dollars in a nationwide contest. The contest was organised by your daily paper. One of the conditions of the contest is that you can only buy things which have been advertised in your paper. Make a detailed list of how you spent your \$1 000 000.

EXTENSION MATHS - NUMBER

R.I.C. Publications

1

Large Numbers To answer the questions below you will need to use newspapers, a calculator, a ruler and scales.

1. How many newspapers would it take to make a pile that would be: (a) 1 000 000 mm high? (b) 1 000 000 cm high? (c) 1 000 000 m high? 2. How high would a pile of 1 000 000 newspapers be? 3. Select a page from your newspaper. How many pages would make: (a) 1 000 000 words?

© R. I . C.Publ i cat i ons 4. What would ber the weight of 1p 000 newspapers? • f or ev i ew u000 r p osesonl y• (b) 1 000 000 letters?

5. What area does one newspaper cover? 6. What area would 1 000 000 newspapers cover? 7. If you read five words per second, how long would it take you to read 1 000 000 words?

8. What is the weight of: (a) one newspaper? (b) 1 000 newspapers? (c) 100 000 newspapers?

EXTENSION MATHS - NUMBER

Using large numbers www.ricgroup.com.au

R.I.C. Publications

2

Percentages 1.

A lot of advertisements in the newspaper give a percentage off the marked price. Work out the price of these objects if we reduce them by 10%. (a)

2.

(b) \$495

(c)

\$375

\$1.30

Work out the price of these objects if we reduce them by 25%. (a)

\$123

(b)

\$8 455

(c)

\$205

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

3.

A lot of prices in the newspaper end in 95. For example, \$195 or \$2.95. List 25 prices from your newspaper and work out what percentage of these end their prices in 95.

Percentage of prices that end in 95 is EXTENSION MATHS - NUMBER

Percentages www.ricgroup.com.au

. R.I.C. Publications

3

Carpets Look carefully at the plan of the house below. Use your newspaper to find the cost of carpets. Calculate the cost of carpeting the house with this information.

   ,,   ,    ,,,,, ,,     ,      ,    , 2.

The shaded area in the plan requires tiles. Use your newspaper to find the cost of tiles. Calculate the cost of tiling this area.

1m

Bedroom

Laundry, Toilet and Bathroom

6m

Kitchen and Dining

9m

4m

4m

5m

1.

4m

© R. I . C.Publ i cat i ons Bedroom Lounge •f orr evi ew pur posesonl y• 7m

2m

17 m

You now need to furnish the house. Use your newspaper to find the cost of the following pieces of furniture. • Television set

• Small bed

• Large bed

• Oven

• Large cupboard

• Dishwasher

• CD player

• Telephone

• Lounge suite

• Kitchen table

• Washing machine

• Refrigerator

What is the total cost of carpeting, tiling and furnishing the house?

EXTENSION MATHS - NUMBER

Calculation of area www.ricgroup.com.au

R.I.C. Publications

4

Real Estate 1.

Look through the real estate section of your newspaper and locate the most expensive house which has been advertised for sale. Complete the information below. (a) Price (b) Name of the suburb (c) Number of bedrooms (d) Number of bathrooms (e) Garage (f) Other rooms (g) Special features (e.g. pool)

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 2.

What is the average cost of each room in this house? (AVERAGE = Cost of the house divided by the number of rooms.)

3.

Make a list of twenty houses for sale in one suburb or town. Write down the cost of each house and then work out the average cost of those houses in that suburb or town.

Average cost of the twenty houses is EXTENSION MATHS - NUMBER

Averages www.ricgroup.com.au

. R.I.C. Publications

5

Shopping 1.

Below is a list of common electrical items that can be found in many homes. Find three prices for each of these items in your newspaper. Write them in the boxes from most expensive to least expensive. (a) A video recorder (b) A colour television (c) An air-conditioner (d) A dishwasher (e) A computer

© R. I . C.Publ i cat i ons (g) • Af CD oplayer rr evi ew pur posesonl y• (f)

A refrigerator

(h) A washing machine (i)

An iron

(j)

A power drill

(k) A microwave oven

Total costs 2.

What is the difference between the most expensive list and the least expensive list?

EXTENSION MATHS - NUMBER

Addition and subtraction of money www.ricgroup.com.au

R.I.C. Publications

6

TV Times 1.

How much time do television stations spend on different types of programs? Complete the table below about two television stations from the guide in your newspaper in minutes and find the totals.

Station 1 Type

Mon

Tues

Wed

Thurs

Fri

Sat

Sun

Totals

Sports Children's Soapies Movies News Music

Station 2

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

Type

Mon

Tues

Wed

Thurs

Fri

Sat

Sun

Totals

Sports

Children's Soapies Movies News Music

2.

Which type of program has the 3. most amount of time spent on it between the two stations?

Which television station spends the most amount of time on children's programs?

4.

Which type of program has the 5. least amount of time spent on it between the two stations?

Which television station spends the most amount of time on sports programs?

EXTENSION MATHS - NUMBER

Time www.ricgroup.com.au

R.I.C. Publications

7

Buying and Selling Shares You have been given \$50 000 to spend on the stock market for one week. At the end of that week you must sell your shares. You may keep the profit if you have one. Use the table below to show the shares you bought and sold and their prices. Number Bought

Stock

Total

Selling Price

Total

Profit/ Loss

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 1. What was your profit or loss for the week? 2. Which share made you the largest profit? 3. Which share caused you the largest loss? 4. If you were to complete this activity for a new week, what changes to your initial buying strategy would you make? Buy! Buy!

EXTENSION MATHS - NUMBER

Basic operations - money www.ricgroup.com.au

R.I.C. Publications

8

Multiplying Digits Look carefully at the number pattern below about multiplying digits.

1.

23 (2 x 3) = 6

23 is a one-step number

83 (8 x 3) = 24 (2 x 4) = 8

83 is a two-step number

47 (4 x 7) = 28 (2 x 8) = 16 (1 x 6) = 6

47 is a three-step number

Colour the numbers in the grid below according to the following rules: one step two step three step four step

= = = =

pink blue green yellow

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61 u 62 6i 3c 6a 4 t 6i 5o 6 6s 67 68 69 © R. I . C.P bl n 1 72 73 74 75 76 77 78 79 •f orr evi ew7p ur posesonl y•

2.

70 80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

Use the same rules to colour the grid below. 411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

EXTENSION MATHS - NUMBER

Problem solving - multiplication www.ricgroup.com.au

R.I.C. Publications

9

Tables 1.

Complete the addition tables below. There is enough information to complete the whole table.

(a)

(b)

+

13

6

+ 51

23 23

27 10

21

8

19

42 74 84

29

17

(c)

54 64

(d)

+

+

© R. I . C.Publ i cat i ons 36 29 25 41 •f orr evi ew pur posesonl y•

32

51

61 55 2.

63

23

32

62

62

81

The last table is a multiplication table. Be careful not to add the numbers.

x

83

95

11

9

63

81

42 8

40 33

EXTENSION MATHS - NUMBER

R.I.C. Publications

10

Magic Squares A magic square has all lines going across, down and diagonally adding to the same number. 1.

2.

4

9

The magic number for the magic square to the right is 15. Complete the magic square.

5

7

Below are two more magic squares. Complete them and write the magic total underneath each one.

(a)

6

(b)

12

27

9

6

10

15

21

9

11

13

I . Publ i ca ons 24 © R. 1C 8. 1t 4i

•f orr evi ew pur posesonl y• Magic Number 3.

Magic Number

This large square is not a magic square. One of the numbers is wrong. Find that number and change it so the square becomes a magic square. The incorrect number is The correct number is

18 116 109 39

. .

95

53

60

74

67

81

89

46

102 32

25 123

Magic Number EXTENSION MATHS - NUMBER

Addition of whole numbers/problem solving www.ricgroup.com.au

R.I.C. Publications

11

Money and Words Each letter of the alphabet below has been given a money value. A = \$11

B =

\$12

C =

\$13

D = \$14

E = \$15

F = \$16

G =

\$17

H =

\$18

I

= \$19

J = \$20

K = \$21

L

=

\$22

M =

\$23

N = \$24

O = \$25

P = \$26

Q =

\$27

R =

\$28

S = \$29

T = \$30

U = \$31

V =

\$32

W =

\$33

X = \$34

Y = \$35

Z = \$36 1.

2.

3.

4.

5.

What is the value of this sentence? \$33 + \$18 + \$11 + \$30 W

+

+

+

+

+ +

H

+

+

+

+

+

+

A

+

T

+ +

+

+

+

.

Can you think of a three-letter word that has a value of over \$50?

+ + © R. I . C.Publ i cat i o ns Can you think of any word that has a •off o rr evi ew pur posesonl y• value over \$200? Is there a word that has an exact value of: (a) \$40

(d) \$63

(b) \$37

(e) \$67

(c) \$55

(f)

\$97

Write down the most expensive five letter words you can think of.

EXTENSION MATHS - NUMBER

R.I.C. Publications

12

Number Trick Complete the number tricks below. Think of a number Reverse it Add them together

37 73 37 + 73 = 110

Add the digits of your original number and then multiply by 11. 3 + 7 = 10

10 x 11 = 110

Here is another example. 93 + 39 = 132 1.

9 + 3 = 12

12 x 11 = 132

Complete the trick with these numbers. (a) 77

© R. I . C.Publ i cat i ons orr evi ew pur posesonl y• (c) • 67f (b) 96

(d) 58 (e) 99 (f)

87

(g) 29 (h) 41 2.

Will this trick work for four digit numbers? Try a few.

EXTENSION MATHS - NUMBER

Addition of whole numbers/problem solving www.ricgroup.com.au

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13

Number Magic Magic 37 - you will need a calculator for these problems 1.

Complete these multiplication problems. 37 x 3 =

2.

37 x 6 =

37 x 9 =

Continue this pattern with the help of a calculator. 37 x 15 =

37 x 18 =

37 x 21 =

37 x 24 =

37 x 27 =

37 x 30 =

37 x 33 =

37 x 36 =

37 x 39 =

37 x 42 =

37 x 45 =

37 x 48 =

37 x 51 =

37 x 54 =

37 x 57 =

37. xP 63 u = b x 66 = © R. I . C l i cat i o37ns •f orr evi ew pur posesonl y•

37 x 60 =

Magic 77 - you will need a calculator for these problems 3.

Complete these multiplication problems. 77 x 13 =

4.

77 x 26 =

77 x 39 =

Continue this pattern with the help of a calculator. 77 x 52 =

77 x 65 =

77 x 78 =

77 x 91 =

77 x 104 =

77 x 117 =

77 x 130 =

77 x 142 =

77 x 156 =

77 x 169 =

77 x 182 =

77 x 195 =

77 x 208 =

77 x 221 =

77 x 234 =

EXTENSION MATHS - NUMBER

Multiplication/whole numbers www.ricgroup.com.au

R.I.C. Publications

14

What is the Rule? The four numbers in the middle of the grid have been used to make the numbers around the outside. Find the method that was used. 1.

Use this information to complete the following grids.

(b)

(a)

2.

10

9

7

6

11

7

4

11

5

2

3

5

6

9

7

10

(c)

84 37

43 87

77 39

37 39

59 19

57 99

Use the method to complete these larger grids. (a)

(b) © R. I . C .Publ i cat i o(c)ns • f orr evi ew 3p ur poseson l y• 15 87 27 3 44 55 17 56 16

67 19 33

22 11 66

81 34 78

21 55 17

77 88 99

32 88 51

(d)

(e)

23 72 96 28

77 56 16 32

31 74 69 37

81 34 78 97

19 12 56 77

32 88 51 54

49 84 56 27

17 42 64 73

EXTENSION MATHS - NUMBER

Addition of whole numbers/problem solving www.ricgroup.com.au

R.I.C. Publications

15

Prime and Even Numbers Two prime numbers can be added to make an even number. Look at the example below. 3 + 23 = 26

'3' and '23' are prime numbers that produce the even number 26 when added together. 1.

Find the prime numbers that can be used to make up the even numbers below. (a)

26 =

+

(g)

38 =

+

(b)

28 =

+

(h)

40 =

+

(c)

30 =

+

(i)

42 =

+

(d)

32 =

+

(j)

44 =

+

(e)

34 =

+

(k) 100 =

+

(f)

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 36 =

+

(l)

200 =

+

Now we're even!

Two prime numbers can be subtracted to make an even number. Look at the example below. 19 — 5 = 14

'19' and '5' are prime numbers that when subtracted produce the even number 14. 2.

Find prime numbers that can be used to make up the even numbers below. (a)

6=

(g)

60 =

(b)

18 =

(h)

64 =

(c)

20 =

(i)

88 =

(d)

28 =

(j)

90 =

(e)

48 =

(k) 100 =

(f)

52 =

(l) 200 =

EXTENSION MATHS - NUMBER

Prime numbers www.ricgroup.com.au

R.I.C. Publications

16

2.

Place the numbers 2 to 7 in the circles so each side of the triangle adds up to 12. You can only use each number once.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

Place the numbers 2 to 7 in the circles so each side of the triangle adds up to 13. You can only use each number once.

3. Place the numbers 2 to 7 in the circles so each side of the triangle adds up to 14. You can only use each number once.

EXTENSION MATHS - NUMBER

R.I.C. Publications

17

Place the numbers 11 to 19 in the circles so each side in the triangle adds up to 57. You can only use each number once.

2.

Place the numbers 11 to 19 in the circles so each side in the triangle adds up to 59. You can only use each number once.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

3. Place the numbers 11 to 19 in the circles so each side in the triangle adds up to 63. You can only use each number once.

EXTENSION MATHS - NUMBER

R.I.C. Publications

18

Place the numbers 21 to 29 in the circles so each side in the triangle adds up to 97. You can only use each number once.

2. Place the numbers 21 to 29 in the circles so each side in the triangle adds up to 99. You can only use each number once.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

3.

Place the numbers 21 to 29 in the circles so each side in the triangle adds up to 100. You can only use each number once.

EXTENSION MATHS - NUMBER

R.I.C. Publications

19

Triangle Multiplication 1. Place the numbers 4, 5, 6, 8, 10 and 12 in the circles so each side of the triangle comes to 240 when multiplied. You can only use each number once.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

2. Place the numbers 4, 5, 6, 8, 10 and 12 in the circles so each side of the triangle comes to 480 when multiplied. You can only use each number once.

EXTENSION MATHS - NUMBER

Problem solving/basic facts (multiplication) www.ricgroup.com.au

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20

Place the numbers 1 to 10 in the circles so each magic line leading into the centre adds up to 19. You can only use each number once.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

2. Place the numbers 1 to 10 in the circles so each magic line leading into the centre adds up to 21. EXTENSION MATHS - NUMBER

R.I.C. Publications

21

Place the numbers 1 to 10 in the circles so each magic line leading into the centre adds up to 23. You can only use each number once.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

2.

EXTENSION MATHS - NUMBER

Place the numbers 1 to 10 in the circles so each magic line leading into the centre adds up to 25. You can only use each number once. Problem solving/basic facts (addition) www.ricgroup.com.au

R.I.C. Publications

22

Magic Cross 1.

Place eight of the numbers 1 to 9 in the circles of the two squares to make the lines around each square total 20. Make each diagonal also total 20.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 2. Place the numbers 1 to 9 in the circles so each line of the cross adds up to 25.

EXTENSION MATHS - NUMBER

3. Place the numbers 6, 12, 18, 24, 30, 36, 42, 48 and 54 in the circles so each line of the cross adds up to 150.

R.I.C. Publications

23

Star Addition 1. Place the numbers 1 to 12 in the circles to make each line in the two triangles add up to 26.

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y•

2. Place the numbers 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60 in the circles to make each line in the two triangles add up to 130.

EXTENSION MATHS - NUMBER

R.I.C. Publications

24

ANSWERS Section 1 - Newspaper Maths Answers will vary in this section according to the size of the newspaper used and the individual pages chosen. Only the questions with exact answers are listed below. 7. 200 000 seconds or 55 1/2 hours 1. (a) \$445.50 (b) \$337.50 (c) \$1.17 2. (a) \$92.25 (b) 6341.25 (c) 153.75

Page 2 Page 3

Section 2 - Number Fun Page 9 1. Pink answers Blue answers 11

12

13

14

21

22

23

24

31

32

33

41

42

15

16

17

18

19

20 25

26

27

28

34

35

36

37

38

45

30 40 43

44

53

54

62

63

64

72

73

50 52

51

60

61

70

71

80

81

90

82

83

91

100

92

46

48

56

58

65

29

85 99

47

49

57

59

66 74

93

94

75

95

68

69

78

79

86

87

88

89

96

97

98

412

420

4 21

430

422

471

443

444

462

463

472

473

427

436

437

466

Page 10 1. (a)

415

424

425

432

435

450

441

442

445

460

451

452

470

461

453

454

455

416

418

439 447 456

457

458

459

465 474

475

417 426

414

423

431

413

440

480

433

9

2

12

27

6

10

15

8

3

5

7

9

15

21

9

11

13

8

1

6

24

3

18

14

7

12

Magic no. 45 Magic no. 33 Incorrect number 89 Correct number 88 Magic no. 282 Page 12 1. \$616 2. Answers may vary 3. Answers may vary 4. Examples are: (a) \$40 - AS (d) \$63 - THE (b) \$37 - BAD (e) \$67 - HAND (c) \$55 - TO (f) \$97 - COST 5. Answers may vary 3.

2. No Page 14 1. 111 2. 555 888 1221 1554 1887 2220 3. 1001 4. 4004 7007 10010 13013 16016

77

4

419 428

429

448

449

468

469

478

479

438 446

464

467 476

(b)

477

(c)

+

11

13

6

9

+

16

37

51

7

+

12

43

19

5

28

30

23

26

35

51

72

86

42

24

36

67

43

29

14

25

27

20

23

23

39

60

74

30

32

44

75

51

37

10

21

23

16

19

47

63

84

98

54

18

30

61

37

23

8

19

21

14

17

13

29

50

64

20

43

55

86

62

48

(b)

14 x 11 = 154 15 x 11 = 165 13 x 11 = 143 13 x 11 = 143 18 x 11 = 198 15 x 11 = 165 11 x 11 = 121 11 x 5 = 55

333 777 1110 1443 1776 2109 2442 3003 6006 9009 12012 15015 18018

(c)

123

121

76

74

62

102

106

146

176

134

138

96

121

84

37

121

130

43

87

130

116

77

39

116

76

37

39

76

78

59

19

78

156

57

99

156

74

121

76

123

146

102

106

62

96

134

138

176

2. (a) (d) 10

7 + 7 = 14 9 + 6 = 15 6 + 7 = 13 5 + 8 = 13 9 + 9 = 18 8 + 7 = 15 2 + 9 = 11 4+1=5

222 666 999 1332 1665 1998 2331 2002 5005 8008 11011 14014 17017

Page 15 1. (a)

17

+

(b)

© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 39

55

2. (a)

Page 13 1. (a) 77 + 77 = 154 (b) 96 + 69 = 165 (c) 67 + 76 = 143 (d) 58 + 85 = 143 (e) 99 + 99 = 198 (f) 87 + 78 = 165 (g) 29 + 92 = 121 (h) 41 + 14 = 55

67 76

84

Page 11 1.

(b)

(c)

2. 16

46

30

x

11

7

9

5

25

35

41

71

55

9

99

63

81

45

53

63

69

99

83

6

66

42

54

30

16

26

32

62

46

8

88

56

72

40

65

75

81

111 95

3

33

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Many combinations possible. Examples are: (a) 11 - 5 (g) 71 - 11 (b) 29 - 11 (h) 67 - 3 (c) 23 - 3 (i) 91 - 3 (d) 31 - 3 (j) 97 - 7 (e) 53 - 5 (k) 103 - 3 (f) 59 - 7 (l) 211 - 11

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Possible answers are: 3 + 23, 7 + 19, 13 + 3 5 + 23, 11 + 17 7 + 23, 11 + 19 3 + 29, 13 + 19 3 + 31, 5 + 29, 11 + 23 5 + 31, 7 + 29, 13 + 23, 17 + 19 7 + 31, 19 + 19 3 + 37, 11 + 29, 17 + 23 5 + 37, 11 + 31, 13 + 29, 19 + 23 3 + 41, 7 + 37, 13 + 31 29 + 71, 41 + 59, 47 + 53 37 + 163, 73 + 127, 91 + 109, 97 + 103

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Maths Enrichment: Number

The three books cover the major areas of mathematics (number, space and measurement) and provide a variety of activities which aim to motiva...

Maths Enrichment: Number

The three books cover the major areas of mathematics (number, space and measurement) and provide a variety of activities which aim to motiva...