Extension                                  Y7                     AUTUMN TERM
UNIT: Algebra 1 - Sequences and Functions
 PRIOR KNOWLEDGE                      KEY WORDS                           STARTER
Recognise and extend           Sequence, term, nth term,      30 starters (subtangent)
number sequences, such as      consecutive, predict, rule,
the sequence of square         generate, continue, finite,    STARTER OF THE DAY –
numbers, or the sequence       infinite, ascending,           substitution
of triangular numbers.         descending, symbol,
                               expression, algebra,           STARTER OF THE DAY – make
Read and plot coordinates      substitute, trial and          a connection
in all four quadrants.         improvement, plot, quadratic
                                                              SUM OF THE SIGNS
Understand and use the
relationships between the
four operations, and
principles of the arithmetic
laws. Use brackets.
     LEARNING OBJECTIVES                               LEARNING OUTCOMES
Level 5
  To be able to generate and describe a      Know that a sequence can have a finite or
   sequence                                     infinite number of terms
                                              The sequence of counting numbers 1, 2, 3, … is
  To be able to use letter symbols to
                                               infinite and the sequence of 2 digit numbers
   represent unknown numbers and
                                               (where both digits are the same) is finite
                                              To be able to write down first 5 terms and 10th
                                               term, given the nth term of sequences such as:
                                                5n + 4
                                                100 - 10n
                                                3n – 0.1
                                                105 – 5n
                                                n x 0.1

                                              Use a spreadsheet or graphical calculator to
                                               find particular terms such as
                                                   The 24th multiple of 13 in the sequence
                                                   The 100th multiple of 27
                                                   The nth mutliple of 18

  To be able to generate a sequence          Use a spreadsheet to generate tables of values
   when given the position-to-term rule.       and explore term-to-term and position-to-
                                               term linear relationships
     To represent mappings expressed

  Level 6
 To begin to use linear expressions to        Find the first few terms of the sequence and
  describe the nth term of an arithmetic        describe how it continues using a term-to-
  sequence, justifying its form by              term rule
  referring to the activity or practical      Describe the general (nth) term and justify
  context from which it was generated.          the generalisation by referring to the context
                                             Example – Growing triangles

                                             This generates the sequence 3, 6, 9, …
                                             Possible explanations
                                             ‘We add 3 each time because we add one more
                                             dot to each side of the triangle to make the next
                                             ‘It’s the 3 times table because we get’

    To be able to generate sequences from
     practical contexts

                                             The nth term is 3n justification
                                             ‘This follows because the 10th term would be 3
                                             lots of 10.’

                                              Develop an expression for the nth term for
                                               sequences such as
    To begin to use linear expressions to       7, 12, 17, 22, …           5n + 2
     describe the nth term of an                 100, 115, 130, 145, …     15n + 85
     arithmetic sequence                         2.5, 4.5, 6.5, 8.5, …      (4n +1)/2
                                                 -12, -7, -2, 3, …          5n – 17
                                                 4, -2, -8, -14, …          -6n + 10
    LEVEL 7

    To be able to generate a sequence         Find the first few terms in the sequence,
    using position-to-term definition of        describe how it continues using a term-to-term
    the sequence                                rule

   To be able to describe in symbols the
    rule for the next term or nth term in a
    sequence (Quadratic)

                                                    n2   2n2 + 2     n2 – 3

       ACTIVITIES                             ICT                         RESOURCES
 Exploring primes activities:                                      MATHSNET algebra topics
Numbers of factors; factors        Mymaths
                                                                   Square number sequence
of square numbers; Mersenne        Algebra, sequences
                                                                   Squares in Rectangles
primes; LCM sequence;
Goldbach's theorem; n² and                                         Nth term generator
(n + 1)²; n² and n² + n; n² + 1;                                   Match up
n! + 1; n! – 1;                                                    Quadratic Generator
~ Venn diagrams for HCF /                                          (with answers)
LCM                                                                Sequences (slide bars)
                                                                   Taria (Matchup) will need to
                                                                   download software (free)
                                                                   KS3 Y8 Intervention
                                                                   ~ Lesson 8N1.1 Solving
                                                                   number problems 2

Cuisenaire Rods – Interactive Using only 2 rods make all cuisenaire rods

Cross-curricular links with music – sequences generated by beats and rhythm

Rich Learning Task: Swimming Pool

What did you look for in your sequence to help you find the nth term?
How does this link to ... ? (Use the context that generated the sequence.)

Probe further to get pupils to justify specific parts of the generalisation – e.g. explain why
'multiply by 4' is part of your nth term.

The term-to-term rule for a sequence is 'previous term + 2'. What does that tell you about
the position-to-term rule? Do you have enough information to find the rule for the nth term?

What do you look for in a sequence to help you to find the position-to-term (nth term) rule?

How would you go about finding the position-to-term (nth term) rule for this information on a

Position 3 5 10
 Term 11 19 39

Compare a linear to a quadratic sequence. What do you notice about the differences between
succeeding terms?

What clues do you look for when deciding whether a sequence is quadratic?

What can you say about the nth term for a quadratic sequence?

What strategies do you use to find the nth term for a quadratic sequence?

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