1.11 Number patterns (patterns)

Mathematics

Number patterns

Educator section

Memorandum

2.

a) 12 321

1 234 321

123 454 321

b) 12 345 654 321

3. a)

i) 9 109

ii) 18 218

iii) 27 327

iv) 36 436

b)

i) 633 763

ii) 81 981

4. a)

i) 111

ii) 222

iii) 333

b) Increases with111

c)

i) 12

ii) 15

d) 888

5. a)

i) 37 037

ii) 37 037

iii) 37 037

b)

i) 444 444 ÷ 12

ii) 555 555 ÷ 15

6. a)

i) 111 111

ii) 222 222

iii) 333 333

b)

i) 555 555

ii) 777 777

7.

i) 1 089

ii) 2 178

iii) 3 267

iv) 4 356

b) First 2 numbers increases with one at a time.

Last 2 numbers decreases with one at a time

c)

i) 99 x 55 = 5 445

ii) 99 x 66 = 6 534

Leaner section

Content

Activity: number patterns (patterns) [lo 1.9.2]

2. Use your pocket calculator and investigate the following patterns:

a) 1 × 1 = 1

11 × 11 = 121

111 × 111 = ________________________

1 111 × 1 111 = _____________________

11 111 × 11 111 = ___________________

b) Now predict: 111 111 × 111 111 = _________________

c) Validate your answer with your pocket calculator.

3 . Complete the following patterns:

a) i) 9 109 × 1 = __________________

ii) 9 109 × 2 = __________________

iii) 9 109 × 3 = __________________

iv) 9 109 × 4 = __________________

b) What will be the answer to:

i) 9 109 × 7? __________________

ii) 9 109 × 9? __________________

c) Now explain the pattern to a friend.

4 . a) Here is another interesting pattern to investigate.

i) 37 × 3 = __________________

ii) 37 × 6 = __________________

iii) 37 × 9 = __________________

b) What have you noticed? _________________________________________

_____________________________________________________________

c) Fill in the missing answers:

i) 37 × ________________ = 444

ii) 37 × ________________ = 555

d) What will the product of 37 and 24 be? ______________________

e) Check your answer with the help of your pocket calculator.

5 . a) Calculate the following:

i) 111 111 ÷ 3 = ________________

ii) 222 222 ÷ 6 = ________________

iii) 333 333 ÷ 9 = . ________________

b) Write down 2 similar sums which will give the same answer.

i) __________________________________________________________

ii) __________________________________________________________

6 . a) Also investigate the following pattern:

i) 1 × 15 873 × 7 = ______________________________

ii) 2 × 15 873 × 7 = ______________________________

iii) 3 × 15 873 × 7 = ______________________________

b) Without using your pocket calculator, predict:

i) 5 × 15 873 × 7 = ______________________________

ii) 7 × 15 873 × 7 = ______________________________

7 . a) With the help of your pocket calculator write down the following answers:

i) 99 × 11 = ______________________________

ii) 99 × 22 = ______________________________

iii) 99 × 33 = ______________________________

iv) 99 × 44 = ______________________________

b) Examine the pattern carefully. Explain it to a friend.

c) Write down the following two sums in the series, with their answers:

i) _______________ × _______________ = _______________

ii) _______________ × _______________ = _______________

Self-assessment

Assessment

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.1: We know this when the learner investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns.