| Each page will give a key question
at the beginning, which should give a context to the following
notes. |
These activities will
concentrate on use of the TI-83 in meeting some of the objectives quoted below
from the National Curriculum for England, and the Framework for Teaching
Mathematics at Key Stage 3. The sections are progressive and build on previous
sections. Section 1 may suit any Key Stage 3 student; Section 8 may be suitable
only for Higher level GCSE students.
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National Curriculum
KS3, Ma2 Number and algebra,
Sequences
6. Pupils should be taught to:
- generate common integer sequences
(including sequences of odd or even integers, squared integers, powers of 2,
powers of 10, triangle numbers)
- find the first terms of a sequence given a
rule arising naturally from a context;
- find the rule and express it in words for
the nth term of a sequence;
- generate terms of a sequence using
term-to-term and position-term definitions of the sequence;
- use linear expressions to describe the nth
term of an arithmetic sequence, justifying its form by reference to the
activity or context from which it was generated;
- express simple functions, at first in words
and then in symbols
- explore the properties of simple polynomial
functions
- use conventions for x- and y- coordinates in
the plane;
- recognise that equations of the form y = mx
+ c (with m and c specified numerically) correspond to straight line graphs in
the coordinate plane;
- plot graphs of specific functions in which
y is given explicitly in terms of x ;
- generate points and plot graphs of simple
quadratic and cubic functions, using a spreadsheet or graphing package in
addition to pencil and paper methods;
KS4 Foundation, Ma2 Number and algebra,
Sequences
6. Pupils should be taught to:
- generate terms of a sequence using
term-to-term and position-term definitions of the sequence;
- use linear expressions to describe the nth
term of an arithmetic sequence, justifying its form by reference to the
activity or context from which it was generated;
- recognise that equations of the form y = mx
+ c (with m and c specified numerically) correspond to straight line graphs in
the coordinate plane;
- plot graphs of specific functions in which
y is given explicitly in terms of x ;
- interpret information presented in a range
of linear and non-linear graphs;
KS4 Higher, Ma2 Number and algebra,
Sequences
6. Pupils should be taught to:
- generate common integer sequences
(including sequences of odd or even integers, squared integers, powers of 2,
powers of 10, triangle numbers)
- generate terms of a sequence using
term-to-term and position-term definitions of the sequence;
- use linear expressions to describe the nth
term of an arithmetic sequence, justifying its form by reference to the
activity or context from which it was generated;
- recognise that equations of the form y = mx
+ c (with m and c specified numerically) correspond to straight line graphs in
the coordinate plane;
- plot graphs of specific functions in which
y is given explicitly in terms of x ;
- generate points and plot graphs of
quadratic, cubic, reciprocal and exponential functions;
National Framework for
Teaching mathematics, Key Stage 3
Numeracy and mathematics
- Use calculators and other ICT resources
appropriately and effectively to solve mathematical problems, and select from
the display the number of figures appropriate to the context of a
calculation;
Introducing and developing algebra:
Sequences, functions and graphs
- Many applications of algebra involve
finding a formula that generates the general term of a sequence: for example,
in predicting the number of matchsticks needed for a certain pattern, or the
number of paving slabs for the border of a rectangular pond. It is important
for pupils to justify their formulae from physical patterns, rather than merely
from number sequences, since this allows them to ‘prove’ their
solutions, not just illustrate or verify them. The apparently different but
equivalent formulae that arise from alternative ways of looking at the problem
can help pupils to understand equivalent algebraic expressions.
- Functions and graphs can be taught and
learned in tandem. At Key Stage 3 the main emphasis is on linear functions and
their graphs. A graphical calculator, or graph plotting software, has an
important role since it helps pupils to learn from exploring
problems.
Introducing and developing algebra:
Features of algebra in Key Stage 3
- using opportunities to represent a problem
and its solution in tabular, graphical or symbolic form, using a graphical
calculator or a spreadsheet where appropriate, and to relate solutions to the
context of the problem;
Sequences: Specific quotes from the
Framework
- P.144 Generate and describe
sequences
- P.144 Explore and predict terms in sequences
generated by counting in regular steps
- P.145 Generate sequences by multiplying or
dividing by a constant factor
- P.145 Generate sequences by counting
forwards or backwards in increasing or decreasing steps
- P.147 Generate and describe integer
sequences,
- P.148 Generate terms of a sequence using
term-to-term and position-to-term definitions of the sequence, on paper and
using ICT
- P.151 Begin to generate a quadratic
sequence
- P.153 Find the next term and the nth term of
a sequence where the rule is quadratic or closely related to T(n) =
n2
- P.154 Find the nth term, justifying its form
by referring to the context in which it was generated
- P.157 Use linear expressions to describe the
nth term of an arithmetic sequence
- P.160 Express functions and represent
mappings
- P.163 Plot the graph of a linear function,
together with its inverse
- P.163 Know some properties of quadratic
functions
- Note that the Framework refers explicitly to
use of graphic calculators and spreadsheets
Year 9 Key Objective:
- Generate terms of a sequence using
term-to-term and position-to-term definitions of the sequence, on paper and
using ICT; write an expression to describe the nth term of an arithmetic
sequence.
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