Y8
SUPPORT
AUTUMN TERM
UNIT: Number and Algebra 1 – Numbers and Sequences
TIME ALLOCATION:
6 Hours
PRIOR KNOWLEDGE




integer, negative, positive,
sign, square, squared, square
root, cube, factors, prime
factors, multiples
Recognise negative numbers sequence, term, nth term,
consecutive, predict, rule,
in contexts (e.g. on a
generate, continue,
number line, on a
ascending, descending,
temperature scale)
symbol, algebra, index
recognise and extend a
number sequence by
counting on or back by a
constant number.
Recognise multiples of 2, 3,
4, 5, 6, 7, 8, 9 and 10
Describe what a prime
number is.
LEARNING OBJECTIVES
LEVEL 4
 test to see if a number can be
divided by 2,3,4,5,10 or 100




KEY WORDS
find the pairs of factors of a 2digit number.
know all the prime numbers below
20.
order negative numbers.
find the differences in
temperatures
STARTER




Sequences in words
1, 2, 3, 4
Find factor and
multiples (choose
easy)
Sequences
Square roots – using
the Chinese method
LEARNING OUTCOMES
simple tests of divisibility, such as:
 2 the last digit is 0, 2, 4, 6 or 8;
 3 the sum of the digits is divisible by 3;
 4 the last two digits are divisible by 4;
 5 the last digit is 0 or 5;
 6 it is divisible by both 2 and 3;
 8 half of it is divisible by 4;
 9 the sum of the digits is divisible by 9.
the pairs of factors of 51 are 1 × 51 and 3 × 17;
the pairs of factors of 56 are 1 × 56, 2 × 28, 4
× 14, 7 × 8.
the final position of an object after moves
forwards and backwards along a line;
a total bank balance after money is paid in and
taken out;
the total marks in a test of 10 questions, with
+2 marks for a correct answer and –1 mark for
an incorrect answer;
Know that a sequence can have a finite or an
infinite number of terms, and give simple
examples. For example: the sequence of



describe what is meant by the
position and term of a sequence.
To be able to generate and
describe integer sequences given a
simple term-to-term rule, or
sequence
To be able to generate sequences
from simple practical contexts.
LEVEL 5
 To be able to find squares, square
roots and cubes, and use
appropriate notation.
 recognise triangular numbers



find highest common factors and
lowest common multiples in simple
cases
To be able to add and subtract
negative numbers.
To be able to generate a sequence
given a rule for finding each term
from its position in the sequence:
counting numbers, 1, 2, 3, 4, … is infinite; dots
indicate that counting continues indefinitely.
The sequence of two-digit even numbers, 10,
12, 14, …, 98, is finite; dots indicate that the
sequence continues in the same way until the
final value 98 is reached.
Generate sequences by counting forwards or
backwards in increasing or decreasing steps.
Find the first few terms of the sequence.
Describe how it continues by reference to the
context. Begin to describe the general term,
first using words, then symbols; justify the
generalisation by referring to the context. Eg.
Growing matchstick squares or Squares in a
cross
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.
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
Start at 0 and count on in steps of 0.5. 0.5, 1,
1.5, 2, … Each term is a multiple of 0.5.
Start at 41 and count back in steps of 5. 41,
36, 31, 26, … Each term is a multiple of 5 plus 1.
ACTIVITIES
ICT
Sieve of Eratosthenes to find
primes
On a hundred square, colour in
1, then the multiples of 2 that
are greater than 2 in one
colour, the multiples of 3 that
are greater than 3 in another
colour… so that the remaining
uncoloured numbers are the
primes.
www.mymaths.co.uk
 negative numbers 1 and
2
 odds, evens, multiples
 multiples
 factors and primes
 sequences
Using matchsticks in pairs, one
person starts a pattern can
the other person continue it
Factor generals – pupils
organize themselves into
groups – discuss factors and
primes.
RESOURCES
Multiple and Factors
resources
Divisibility tests
Negative number ladders
Fast factors
Hot numbers
Finding squares, multiples etc
Factor trees
Guess the number
Number sequence game
Functions and sequences
investigation
Counting stick - can hide
numbers in sequences
Term to term sequence
Next term and first term
Negative term to term
FUNCTIONAL SKILLS and MPA OPPORTUNITIES
Handshakes investigation
How many handshakes would there be if 2, 3, 4 etc, people shook hands with other? What
is special about the numbers of handshakes?
Negative Numbers First Connect Three
Factors and Multiples Game, Factors and Multiples Puzzle
Picturing Square Numbers
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 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?