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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
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
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
‘We add 3 each time because we add one more
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
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
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
Rich Learning Task: Swimming Pool
PLENARIES AND KEY QUESTIONS
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?
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?
