Sequences

Term 1 starting in week 1 :: Estimated time: 2 weeks

Describe and continue a sequence given diagrammatically
Predict and check the next term(s) of a sequence
Represent sequences in tabular and graphical forms
Recognise the difference between linear and non-linear sequences
Continue numerical linear sequences
Continue numerical non-linear sequences
Explain the term-to-term rule of numerical sequences in words

For higher-attaining pupils:

Find missing numbers within sequences
Finding the nth term of a sequence

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Activities for pupils

Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

Missing Terms Can you work out which numbers are missing from these number sequences?

Matchstick Patterns Create a formula to describe the nth term of a sequence by examining the structure of the diagrams.

Arithmetic Sequences An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.

Arithmetic Sequences Video A reminder of how to find the next term, the nth term and the sum of terms of an arithmetic or linear sequence.

Geometric Sequences An exercise on geometric sequences including finding the nth term and the sum of any number of terms.

Quick Add 'Em Quiz Find the sum of a sequence of consecutive numbers using a quick, efficient, elegant method.

Geometric Sequences Video Revise all you need to know about geometric sequences and series.

Fibonacci Quest A number of self marking quizzes based on the fascinating Fibonacci Sequence.

Venn Diagram of Sequences Find the formula for the nth term of sequences that belong in the given sets.

Sequences Table Challenge Complete the table showing the terms of the sequences and the formulas for the nth terms.

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

Sequences A pattern of numbers following a rule is called a sequence. There are many different types of sequence and this topic introduces pupils to some of them. The most basic sequences of numbers is formed by adding a constant to a term to get the next term of the sequence. This rule can be expressed as a linear equation and the terms of the sequence when plotted as a series of coordinates forms a straight line. More complex sequences are investigated where the rule is not a linear function. Other well-known sequences includes the Fibonacci sequence where the rule for obtaining the next term depends on the previous two terms. Sequences can be derived from shapes and patterns. A growing patterns of squares or triangles formed from toothpicks is often used to show linear sequences in a very practical way. Diagrams representing sequences provides interesting display material for the classroom. Typically pupils are challenged to find the next term of a given sequence but a deeper understanding is needed to find intermediate terms, 100th term or the nth term of a sequence.

Lesson Starters

Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.

1st Lesson

Broken Calculator (3 and 4)

Some keys are missing from this calculator. Just how useful is it?

2nd Lesson

To Be Continued

Work out the next term in the given sequences.

3rd Lesson

Spider Sequences

Find the next term of the given number sequences. Can you also find a general rule for predicting the nth term of the sequence?

4th Lesson

Sign Sequences

Continue the sequences if you can work out the rule.

5th Lesson

Plane Numbers

Arrange numbers on the plane shaped grid to produce the given totals

6th Lesson

Secret Symbol

Place a symbol between the four and the five to get a number greater than four and less than five.

Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.

White Rose Resources

End of block assessments provide a quick progress check at the end of each block of learning to make sure students have understood the content covered.