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- Generate sequences given a rule in words
- Generate sequences given a simple algebraic rule
- Generate sequences given a complex algebraic rule

For higher-attaining pupils:

- Find the rule for the nth term of a linear sequence

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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.

- Number Grids Investigate the properties of number with these interactive number grids.
- Steps Investigate the numbers associated with this growing sequence of steps made from Multilink cubes.
- Missing Terms Can you work out which numbers are missing from these number sequences?
- Leapfrog An investigation of the minimum number of moves required to make the blue and green frogs swap places.
- Matchstick Patterns Create a formula to describe the nth term of a sequence by examining the structure of the diagrams.
- Numbasics A daily workout strengthening your ability to do the basic mathematical operations efficiently.
- Sequence Generator An online app which produces number sequences as words.
- Watsadoo Rotate the cogs to catch the flying numbers in the correct sections.
- Arithmetic Sequences An exercise on linear sequences including finding an expression for the nth term and the sum of n terms.
- Trapezia Which numbers can be represented by groups of circles arranged in the shape of a trapezium?
- 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.
- Prison Cell Problem A number patterns investigation involving prisoners and prison guards.
- 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.
- Aunt Lucy's Legacy Decide which of the four schemes Aunt Lucy proposes will provide the most money. This investigation involves the sum of sequences as well as considering life expectancy.
- Fibonacci Quest A number of self marking quizzes based on the fascinating Fibonacci Sequence.
- Handshakes If everyone in this room shook hands with each other, how many handshakes would there be?
- Venn Diagram of Sequences Find the formula for the nth term of sequences that belong in the given sets.
- Quadratic and Cubic Sequences Deduce expressions to calculate the nth term of quadratic and cubic sequences.
- Sequences Table Challenge Complete the table showing the terms of the sequences and the formulas for the nth terms.
- Parts of Sequences Find the formula that describes the part of the sequence that can be seen
- Sigma Practise using the sigma notation to find the sum of various number series.

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

- Number Spotting patterns is an important skill in many areas of life. The world of numbers contains many fascinating patterns and understanding them enables better problem solving strategies. From seeing patterns in the multiples of numbers shaded in a hundred square to spotting the recurring sequences of digits in decimal numbers there is a great deal for pupils to be introduced to. This topic includes even, odd, prime, triangular, perfect, abundant, square and cube numbers. It uses factors and multiples to find solutions to real life problems and encourages number connections to be investigated for pleasure. There are a lot of puzzles, challenges and games too. See also the Mental Methods topic and our Number Skills Inventory.
- 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.

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

Find the next term of the number sequences.

Find the missing terms from these linear sequences.

Work out what the nth letter will be in a recurring pattern of letters in a person's name

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.