# FOUNDATION Y10 AUTUMN TERM by dfhrf555fcg

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```									Extension                                  Y7                     AUTUMN TERM
UNIT: Algebra 1 - Sequences and Functions
TIME ALLOCATION: 6 Hours
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
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
variables
 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
algebraically

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
dot to each side of the triangle to make the next
triangle’
‘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

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
KS3 Y8 Intervention
~ Lesson 8N1.1 Solving
number problems 2
FUNCTIONAL SKILLS and MPA OPPORTUNITIES

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

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

PLENARIES AND KEY QUESTIONS
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?
Why?

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
sequence:

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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