ALGEBRA Equations, formulae, expressions and ... - Suffolk Maths

The National Strategies | Secondary
Mathematics exemplification: Y8, 9
151
ALGEBRA
As outcomes, Year 8 pupils should, for example:
Use a spreadsheet to generate tables of values and
explore term-to-term and position-to-term linear
relationships. For example:
• The nth term is 3n + 7.
1
2
3
4
5
6
7
8
9
10
A
Position
1
=A2+1
=A3+1
=A4+1
=A5+1
=A6+1
=A7+1
=A8+1
=A9+1
B
Term
=A2*3+7
=A3*3+7
=A4*3+7
=A5*3+7
=A6*3+7
=A7*3+7
=A8*3+7
=A9*3+7
=A10*3+7
1
2
3
4
5
6
7
8
9
10
A
Position
1
2
3
4
5
6
7
8
9
Term
10
13
16
19
22
25
28
31
34
B
Sequences, functions and graphs
As outcomes, Year 9 pupils should, for example:
This column has intentionally been left blank.
Arrange a sequence in a table, referring to terms as
T(1) = first term, T(2) = second term, …, T(n) = nth term.
For example, for multiples of 3:
Position n 1 2 3 4 5 … n
T(n) 3 6 9 12 15 … T(n)
Difference 3 3 3 3 …
Explain the effect on a sequence of multiples if a
constant number is added to or subtracted from each
term. For example:
• T(n) = 2n + b:
2n – 1 generates the odd numbers, starting at 1,
because each is one less than an even number.
2n + 1 generates odd numbers, starting at 3.
2n + 2 generates even numbers, starting at 4.
2n – 6 generates even numbers, starting at – 4.
•
T(n) = 3n + b:
If b is a multiple of 3, this generates multiples of 3,
starting at different numbers.
Otherwise, it generates a sequence with a difference
of 3 between consecutive terms.
• T(n) = 10n + b:
If b is between 0 and 9, this generates numbers
whose units digit is b.
Explain how descending sequences can be generated
by subtracting multiples from a constant number:
T(n) = b – an. For example:
• T(n) = 6 – n generates descending integers:
5, 4, 3, 2, 1, 0, – 1, – 2, – 3, – 4, – 5, …
•
T(n) = 110 – 10n generates the 10 times table
backwards.
Explore difference patterns between terms of a
linear sequence of the form an + b. Observe that the
differences are constant and equal to a. Use this result
when searching for a rule or for the nth term.
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