Module 1 Counting and understanding number and associated objectives
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Can I make generalisations about sequences and explain why given numbers do or do not belong to the given sequence?

Example review questions

  • What numbers are missing from these sequences? Explain how you know:
    a) empty box, 7, 10, 13, 16, empty box, empty box
    b) 9.8, 9.1, 8.4, 7.7, empty box, empty box
    c) empty box, 4, 8, 16, 32, empty box, empty box
    d) empty box, empty box, 21, 13, 5
    e) −11, −7, empty box, 1, empty box, 9
  • Sally says that the number 102 will be in this sequence:
    3, 6, 9, 12...
    Is she correct? How do you know?
  • Consider the sequence:
    6, 11, 16, 21, 26 ...
    What statements can you make that will be true for all numbers in the sequence?
    Will 77 be highlighted?
    Explain your thinking.
    A large blue square equally split into forty-nine smaller squares, all of which contain the numbers one to forty-nine. Numbers six, eleven, sixteen, twenty-one and twenty-six are highlighted in yellow.

Teaching guidance

This teaching guidance document suggests some of the key vocabulary, models, images and practical equipment that children should experience and be able to use. It also includes some teaching tips to provide a few starting points for ways of supporting children with this area of mathematics.

PDf file Teaching guidance: Can I make generalisations about sequences and explain why given numbers do or do not belong to the given sequence? | 67KB new window

Consolidation and practice

These resources are to support children in guided or independent work. Roll over the highlighted resources for a description.

PDF file How to use number grid ITP | 360KB new window

SWF file Number grid ITP | 63KB new window

PDF file How to use 20 cards ITP | 220KB new window

SWF file 20 cards ITP | 52KB new window

PDF file Activities to explore sequences using 20 cards | 184KB new window

XLS file Counting stick with further options spreadsheet | 246KB new window

XLS file Increasing number grid generator spreadsheet | 197KB new window

XLS file Decreasing number grid generator spreadsheet | 198KB new window

Visit the nrich website new window for further activities to support practice and application.

Number grid

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This interactive teaching program (ITP) is an ICT-based tool to support the exploration of number, reasoning and problem solving. Number grid ITP allows the child or teacher to generate a number grid with different starting numbers, orientations and numbers of columns. Individual numbers or chosen multiples can be coloured and numbers masked to explore number sequences and patterns and develop children's ability to predict and generalise.

Twenty cards

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This interactive teaching program (ITP) is an ICT-based tool to support the exploration of number, reasoning and problem solving. Twenty cards ITP allows the child or teacher to create a sequence or random set of numbered cards. The stacks created can support work on identifying, describing, extending and generating sequences.

Opportunities to use and apply

Possible contexts include:

  • Investigating patterns and spatial representations of known sequences of numbers, e.g. multiples, square numbers and triangular numbers.
  • Sequences related to properties of shape, e.g. find the total of the internal angles in a triangle, a quadrilateral, a pentagon, etc.
  • Sequences produced from continuing patterns, e.g.
    Three images. The first is of a blue rectangle containing one small yellow square, and two yellow crosses of different sizes, the second is a blue rectangle containing three yellow shapes and the third is a blue grid containing three yellow squares all of which are different sizes.

Confirming learning

Ask probing questions such as:

  • A sequence starts with 1 and has the rule 'add 6'. Work out what the 5th term will be. Amy thinks that the sequence will contain the number 100. Is she correct? Explain how you know.
  • Josh continues this pattern. He counts the squares in each shape and writes this down as a sequence. He says, 'No matter how far you go, there will never be a multiple of 4 in the sequence'. Is he right? How do you know?
    Blue grid containing one one small yellow square, and two yellow crosses of different sizes.
  • Sequence A: 3, 6, 9, 12... Sequence B: 5, 10, 15, 20... Sequence C consists of the terms that appear in both sequence A and sequence B. Give a three-digit number that will be in Sequence C and explain how you know. Can you give another?