# Generating sequences - Secondary Maths ITE

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Stage         Secondary                                     Year             7
Subject       mathematics                                   Term

Generating sequences
Module contents

Module focus
Curriculum focus

Investigating number sequences

Learning objectives

By the end of the lesson pupils will:

    be able to identify and describe simple linear sequences.

Learning outcomes

Most pupils will:

    use a graphic calculator to generate a linear sequence and describe the
term-to-term rule.

Pupils making slower progress will:

    identify a given linear sequence and describe the term-to-term rule.

Pupils making faster progress will:

    identify and generate linear sequences, including positive and negative
numbers, and describe the term-to-term rule.

References

Strategy Framework references

Using and applying mathematics to solve problems

Applying mathematics and solving problems

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    Solve word problems and investigate in a range of contexts: number,
algebra, shape, space and measures, and handling data; compare and
evaluate solutions.
    Suggest extensions to problems by asking ‘What if…?’; begin to
generalise and to understand the significance of a counter-example.

Algebra

Equations, formulae and identities

    Understand that algebraic operations follow the same conventions
and order as arithmetic operations

Sequences, functions and graphs

    Generate and describe simple integer sequences.
    Generate terms of a simple sequence, given a rule (e.g. finding a term
from the previous term, finding a term given its position in the sequence).

The Framework for teaching mathematics can be found at:

www.standards.dfes.gov.uk/keystage3/respub/mathsframework/forewo
rd/

National Curriculum references

Ma2 Number and Algebra

Sequences, functions and graphs

Pupils should be taught to:

a generate common integer sequences (including sequences of odd or
even integers, squared integers, powers of 2, powers of 10, triangular
numbers)

b find the first terms of a sequence given a rule arising naturally from a
context [for example, the number of ways of paying in pence using only
1p and 2p coins, or

from a regularly increasing spatial pattern]; find the rule (and express it
in words) for the nth term of a sequence

c generate terms of a sequence using term-to-term and position-to-
term definitions of the sequence; use linear expressions to describe
the nth term of an arithmetic

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sequence, justifying its form by referring to the activity or context from
which it was generated

The National Curriculum programme of study can be found at:

www.nc.uk.net/nc/contents/Ma-3-2-POS.html.

Use of ICT

Teacher use of ICT

This module will give you the opportunity to:

    use graphical calculators to generate sequences and explore
relationships between terms;
    use a graphical calculator emulator and interactive whiteboard, or an LCD
    evaluate the use of ICT for whole-class teaching.

Requirements

Hardware

    A computer
    Data projector and large screen display or interactive whiteboard (IWB) or
graphical calculator LCD panel and overhead projector

Software

    Word-processing software, such as Microsoft Word
    Spreadsheet software, such as Microsoft Excel
    Graphical calculator emulator software, such as TI-SmartView

Other

    Graphical calculators (at least one between two pupils)
    Individual whiteboards and pens (at least one between two pupils)

You can download the viewers needed for these files on the Software

This document is part of a range of materials designed to help teachers teach using ICT.

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Lesson preparation

A key element of this module is a lesson for you to adopt and adapt to
impact of using ICT for learning and teaching. Display and discuss the
objectives and key vocabulary for this lesson with the pupils.

Some example lesson resources have been created for you to use and
resources before the lesson and adapt if necessary. You will need to
be familiar with generating a term-to-term and a position-to-term
sequence using a graphical calculator. Ensure your computer, large
screen display or IWB and graphical calculator with whole-class
display are set up before the lesson and you have printed sufficient
copies of the worksheet Sequence challenge and, if necessary,
helpsheets for your pupils to use alongside their graphical calculator.

Vocabulary

linear sequence, position, position-to-term rule, predict, relationship,
rule, term, term-to-term rule, sequence

Health & Safety

All standard safety procedures with computers need to be in place.
Information can be found at www.ictadvice.org.uk.

ICT skills guidance

The guidance in this section supports the ICT skills described in the
Module contents.

Pupils' prior knowledge and skills

    recognise and extend number sequences formed by counting from any
number in steps of constant size, extending beyond zero when counting
back;
    know squares to at least 10 × 10;
    know how to generate and describe simple integer sequences.

This document is part of a range of materials designed to help teachers teach using ICT.

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Starter

Display the file What am I on the large screen display or IWB. Ask
pupils if they recognise the object. With your pupils, count the number
of holes in each of the concentric circles that form the nozzle. (
9,12,15,18….). Can pupils see a pattern in the numbers? Ask pupils if
they can predict the number of holes in the seventh circle ( 30). How
do they know this? Can pupils tell you what the term-to-term rule for
this sequence might be. Make sure pupils know that the sequence is
being generated using the term-to-term rule ‘add 3’.

Ask pupils to use the term-to-term rule to predict the number of circles
in the fifteenth circle if the pattern continued in the same way. Ask
pupils if a term-to-term rule is useful if you want to predict the
hundredth term in this sequence and discuss the reasons why.

Main

Using just the graphical calculator with view screen and the whole-
class display, generate a sequence by entering 0.7 and Enter or Exe,
followed by + 0.7.

You might like to ask the pupils:

    Is this sequence similar to any sequences that you know? (multiples of 7)
    Is the number 5.6 in this sequence?
    How do you know? (Because 8 ´ 7 = 56, so 8 ´ 0.7 = 5.6.)

Invite a pupil to input the calculator instructions to generate the
sequence: 0.9, 1.8, 2.7, 3.6…

Give pupils the calculators and ask them to generate multiples of 0.6
(or similar) using the Ans key. When pupils are confident with the
calculators, give out, or display the pupil task sheet Sequence
challenge and ask pupils to complete the first four questions, moving
on to the brainteaser question if they have time.

Invite pairs of pupils to give their responses to each of the questions,
discuss any misconceptions and encourage pupils to use the
vocabulary correctly. Discuss how the same sequences can be
generated using different term-to-term rules. Give pupils some time to
explore the effects of adding and subtracting positive and negative
numbers, e.g. the sequence of multiples of four can be generated by
inputting zero followed by - (-) 4.

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Ask pupils how the fourth sequence differs to the first three and tell
them that sequences whose terms differ by a constant are called linear
sequences. Ask pupils to clear their calculator display and collect the
graphical calculators from the pupils.

Plenary

Give pupils individual whiteboards and pens. With the whole-class
display turned off, generate the following sequence: 0.6 and Enter or
Exe followed by - 0.3.

Press Enter or Exe a sufficient number of times such that the original
calculator key presses are no longer on the screen. Now display this
screen to the class. Ask pupils to discuss in pairs what the instructions
to the calculator could have been and then display them on their
individual whiteboards.

    Can you tell which terms of the sequence have been displayed?
    Can you tell what the constant of addition (-0.3) or subtraction (0.3) was?
    What would the term-to-term rule be for this sequence?

Assessment

In assessing for learning you should consider the following points.

1. Ensure objectives are expressed in language that pupils understand.
2. Give pupils clear success criteria related to these objectives.
3. Give pupils opportunities to discuss their successes and challenges
focusing on the objectives.
4. Provide oral and written feedback to pupils.
5. Encourage pupils to explain their thinking and reasoning in a secure
environment.
6. Provide time for pupils to reflect upon what they have learned and
understood and identify any difficulties.

You can find information on assessment for learning at:

www.standards.dfes.gov.uk/keystage3/respub/afl_ws.

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Pupils requiring additional support will benefit from focusing on
sequences that consolidate known sequences, for example, the
multiples of 3. Build on this understanding by looking at near multiples.

For extension, pose questions that probe pupils' deeper understanding
of the concepts connected with linear relationships. Ask questions
such as:

    If the 4th term in a linear sequence is 19 and the 7th term is 35, how can
you work out an expression for the nth term for this sequence?
    What instructions would you give to produce this sequence using the
graphical calculator?

Evaluation

Lesson reflection

These prompts are designed to help you reflect on how the use of ICT
affected your teaching and pupils’ learning.

Prompts for reflection:

1. How did the use of ICT:
o      help pupils to make better progress towards achieving the learning
objectives?
o      affect the pace of learning?
o      affect pupils’ motivation, interest and time spent on task?
learning?
2. What knowledge or skills have you gained and extended in teaching this
lesson?
3. What adaptations would you make to the lesson and its resources to suit

You may wish to create a record of your evaluation and save it as
template containing these prompts and spaces for your responses.

Materials evaluation

These prompts are designed to help you consider why, how and when
you would incorporate these lesson activities and resources into your
curriculum and teaching plans.

This document is part of a range of materials designed to help teachers teach using ICT.

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Prompts for evaluation:

1. What are the benefits of using these teaching and learning approaches
and resources to achieve the subject objectives?
2. How do the suggested activities fit with your existing curriculum and
teaching plans?
3. What adaptations would be required to the activities or resources to suit
4. Are there any requirements for ICT equipment, other resources, space,
etc. that might limit how and where the lesson is taught?

You may wish to make a note of your thinking for your own records
containing these prompts and spaces for your notes.

resources, supplementary information and extension activities using
the link below. The pack is in a zipped file to minimise file size, but

To extract the files within the module pack you will need either Winzip
or Microsoft Windows Extraction Wizard. This software is freely
page.

This document is part of a range of materials designed to help teachers teach using ICT.