Y8
CORE
AUTUMN TERM
UNIT: Number and Algebra 1 – Numbers and Sequences
TIME ALLOCATION:
6 Hours
PRIOR KNOWLEDGE
 How to add and subtract
negative integers
 Recognise negative
numbers in contexts
 Recognise multiples of 2,
3, 4, 5, 6, 7, 8, 9 and 10
 Describe what a prime
number is.
 The square and triangle
number sequences
 How to generate terms
of a simple sequence
KEY WORDS
STARTER
integer, negative, positive,
sign, square, squared, square
root, cube, cube root, power,
factors, prime factors, HCF,
LCM, multiples, BODMAS,
product, sequence, term, nth
term, consecutive, predict,
rule, generate, continue,
ascending, descending,
symbol, index
Sequences in words 1, 2, 3, 4
Find factor and multiples
(choose easy)
Sequences
LEARNING OBJECTIVES
LEVEL 5
 To be able to find squares, square
roots and cubes, and use appropriate
notation.
 Recognise triangular numbers

Be able to find highest common
factors and lowest common multiples in
simple cases



Counting stick adding on
Whiteboards or number fans
ask pupils number facts e.g.
first prime number, third
multiple of 7 etc
Get students to guess the
rule, ask a pupil for a number
you apply the rule keep
repeating until pupils come
up with the rule
LEARNING OUTCOMES
know the square numbers up to 12x12 and can
find their square roots
know that square numbers make square
patterns of dots and triangular numbers makes
triangles
Find the lowest common multiple (LCM) of two
numbers, such as 6 and 8;
6 times table: 6 12 18 24 30…
8 times table: 8 16 24 32…
The lowest common multiple of 6 and 8 is 24.
Find the highest common factor (HCF) of two
numbers, such as 18 and 24;
The factors of 18 are 1 2 3 6 9 18
The factors of 24 are 1 2 3 4 6 8 12 24
1, 2, 3 and 6 are common factors of 18 and 24,
so 6 is the highest common factor of 18 and
24.

To be able to add and subtract
negative numbers.

To be able to generate a sequence
Start at 0 and count on in steps of 0.5. 0.5, 1,
given a rule for finding each term from 1.5, 2, … Each term is a multiple of 0.5.
its position in the sequence:
Start at 41 and count back in steps of 5. 41,
36, 31, 26, … Each term is a multiple of 5 plus
1.
LEVEL 6

To be able to add, subtract, divide and
multiply positive and negative integers

To be able to find the prime factor
decomposition of a number

To be able to describe in words the rule
for the next sequence where the rule is
linear
To be able to find a rule for a linear
sequence

Extend patterns such as:
2+1=3
–3 – 1 = –4
2+0=2
–3 – 0 = –3
2 + –1 = 1
–3 – –1 = –2
2 + –2 = 0
–3 – –2 = –1
2 + –3 = –1
–3 – –3 = 0
ACTIVITIES
Using matchsticks in
pairs, one person starts
a pattern can the other
person continue it
ICT
RESOURCES
www.mymaths.co.uk
 negative numbers 1 and 2
 odds, evens, multiples
 multiples
 factors and primes
 sequences
Multiple and Factors
resources
Generate a sequence from nth
term (Excel)
Negative number ladders
Divisibility tests
Product of prime factors
nth term (Excel)
Negative nth term and term to
term (Excel)
sequences term to term rule
sequences and nth term
nth term match –up game
pupil interactive activity nth term
(Excel)
4 different sequence activities
FUNCTIONAL SKILLS and MPA OPPORTUNITIES
NRich : Factors and Multiples Game,
Factors and Multiples Puzzle
Sequences from a practical context
PLENARIES AND KEY QUESTIONS
Which numbers less than 100 have exactly three factors?
What number up to 100 has the most factors?
Find some prime numbers which, when their digits are reversed, are also prime.
There are 10 two-digit prime numbers that can be written as the sum of two square numbers.
What are they?
The answer to a question was –8. What was the question?
The result of subtracting one integer from another is –2. What could the two integers be?
The temperature is below freezing point. It falls by 10 degrees, then rises by 7 degrees.
What could the temperature be now?
Can you give me an example of a number greater than 500 that is divisible by 3?
How do you know whether a number is divisible by 6? etc
Can you give me an example of a number greater that 100 that is divisible by 5 and also by 3?
Is there a quick way to check whether a number is divisible by 25?
How do you go about finding the prime factors of a given number?
What are the prime factors of 125? 81? 343? What do you notice?
How do you go about finding the rule for a sequence of numbers?
Where do you start? What do you look for? How many terms do you check before you are
convinced you know the rule?
1, 2, 4. What could the next 2 terms be? Why ?