Topic 6: Patterns and Sequence

By the end of this topic, you will be able to:

• recognise and generate number patterns
• explain how to generate a sequence
• describe a general rule when patterns are given
• use number machines to generate a sequence
• determine terms in a sequence

Keywords

• input
• number
• machine
• output
• patterns
• rule
• sequence

Introduction

Suppose the age difference between five consecutive siblings is 3. If the of the youngest is 12 years, how do you obtain the age of the rest. The arrangement of the siblings’ ages is a sequence, knowing the age difference gives the pattern.

In this topic, therefore, you will explore number patterns and sequences.

Recognising and Generating Number Patterns

Activity 6.1 Recognising and generating number patterns (work in groups)

What you need: notebook, pen, calculator.

What to do:

1. Copy and complete 1 to 100 squares below.

2. Shade in all the multiples of 3 on the number sequence.

3. Describe the pattern formed by the shading

4. If Sarah wants to shade same multiples in order to obtain patterns of vertical lines, which set of multiples should she use?

5. Present your work to the whole class

Activity 6.2 Recognising and generating number patterns (work in groups)

What you need: notebook, pen, match sticks.

What to do:

1. Get match sticks and arrange them like the ones below.

2. Arrange match sticks in the 4th figure.

3. Predict a general rule for finding the number of matches (m) in the nth figure.

4. Write a description of the patterns in words.

5. Find how many matches are required to make the

a) 10th figure b) 50th figure

6. Complete the table below

Exercise 6.1

1. Imagine you are a builder and you are using match sticks to investigate housing designs.

a) Draw a match stick design for 4 houses and 5 houses.

b) If y is the number of match sticks required to make h houses, copy and complete the following table.

c) Write a description of the patterns.

d) Write a general rule for the connection between y and h.

e) Predict the number of match sticks needed for the 30th figure. 2. 3, 6, 9 are the 1st, 2nd and 3rd multiples of

3. a) Which position in the multiples of 3 is 93?

b) Which position in the multiples of 3 is 3n?

Generating a Sequence Review

Exercise 6.1

1. How many different ways can you continue the sequence that begins 2, 4, ..? Explain how each sequence is generated.

2. Write down the next 3 terms in each of the sequences and state the rule for each sequence.

Activity 6.3 Generating a sequence (work in pairs)

What you need: 32 counters

What to do:

1. Get 32 counters and divide them into 2 then write down the answer.

2. Continue dividing the resulting counters by 2 until you reach 1.

3. Write the sequence you have made.

Exercise 6.2

1. For each of the following sequences, find the next 3 terms and state the rule for finding the next term.

a) 6, 18, 54, 162,….,…..,….

b) 4, 12, 36, 108,….,….,….

c) 1, 1 1 1 1 , 4 9 16′ 25′

2. Imagine you started a small shop. When you checked in your records, you discovered that the number of customers increases by 3 every week. If the trend continues like that,

a) generate a sequence showing the number of customers in the first 6 weeks, if in the first week only 4 customers visited your shop.

b) state the rule for the sequence in (a) above.

c) how many customers will visit the shop in the 10th week?

d) is there any formula that you can use to get the answer in (c) above? if it is there, state it.

3. For each of the following sequences write the 3 next terms, state the rule used to find the next term.

a) 13, 22, 31, 40, …,…..,….

b) 8, 5, 2,….,……,…..

c) 7, 20, 33, 46,…,….,…

4. Find the next 3 numbers in the sequence 13, 21, 34, 55, —

Generating a Sequence using a Number Machine

The number machine processes numbers according to specified condition.

Activity 6.4 Generating a sequence using a number machine (work in groups)

What you need: papers, pens, ruler.

What to do: Make groups;

1. Draw a number-generating machine as shown below.

2. Put the numbers 1, 2, 3, 4, 5,… into this number machine to generate a sequence.

3. Copy and complete the table below.

4. State the formula for the nth term in the sequence.

5. Present your work to the whole class.

Exercise 6.3

1. Generate a sequence for the input numbers 1, 2, 3, 5, 7, 9, using the following number machine.

2. Put the numbers 1, 2, 3, 4, 5, 6, and 8 into this number machine to generate a sequence. emotiog sdmun menep bro

3. Draw a number machine leading to the sequence: 1, 3, 5, 7, 9.