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Number Sequence Homework Ks1 Bitesize

Term to term rules

The term to term rule of a sequence describes how to get from one term to the next.

Example one

Work out the next two terms in the following sequence and write down the term to term rule:

3, 7, 11, 15, ...

Firstly, work out the difference in the terms.

This sequence is going up by 4 each time, so add 4 on to the last term to find the next term in the sequence.

3, 7, 11, 15, 19, 23, ...

To work out the term to term rule, give the starting number of the sequence and then describe the pattern of the numbers.

The first number is 3. The term to term rule is ‘add 4’.

Once the first term and term to term rule are known, all the terms in the sequence can be found.

Example two

Work out the next two terms in the following sequence and write down the term to term rule:

-1, -0.5, 0, 0.5, ...

The first term is -1. The term to term rule is ‘add 0.5’.

QQuestion

What is the term to term rule and the next two terms of the sequence: 17, 14, 11, 8, ...?

A

To work out the term to term rule, give the first term and then the pattern. The first term is 17, and the pattern is to subtract 3 each time, so the term to term rule is ‘start at 17 and subtract 3’.

The next two terms of the sequence are 5 and 2, giving the sequence as:

QQuestion

What are the next 3 terms of a sequence that has a first term of 1, where the term to term rule is multiply by 2?

A

The first term is given as 1. Each number that follows is double the number before.

Objectives

To be able to count on in intervals of a given number.

National Curriculum

Ma2, 1a, 1d, 1f, 1g, 2b, 2c, 3c.

Resources

You will need Adobe Acrobat reader to access these files. BBC Webwise has a complete guide to downloading and installing Adobe Acrobat reader.

Teaching activities

Introduction

  1. Explain to the children that you are thinking of a number with which to create a sequence.
  2. Write down a series of five numbers, using the number you thought of as the jump.
  3. Ask the children to write the amount jumped on their whiteboards and show after a count of three.
  4. Repeat with different numbers of jumps.

Activity


Medium - Give the children some number cards showing numbers from the 2 and 5 times tables. Ask them to pick one card, decide whether they are counting in 2s or 5s, then find the next card for their sequence. Ask them to repeat this until they have five numbers, all with the same amount of jumps between each number.

Hard - Ask the children to complete the Number sequences worksheet (PDF 90KB), filling in the missing numbers in the sequence.

Really hard - Ask the children to complete the Bitesize Adventure Sequences game (hard level then really hard level).

Plenary

  1. Play the Digger and the Gang Up and Jump game as a class, jumping in 5s.
  2. Repeat the game from the introduction but this time ask the children to write a sequence for their friends to guess.