These resources are roughly sorted by year group. All of the
resources directly available from this site are written and
copyright by me (unless otherwise attributed), and may be
distributed under the terms of the Free Software Foundation's
General Public Licence, Version 2. (Text available here.) Links to external sources are not
covered by this copyright notice. If you have any feedback,
please email me at jdg@polya.uklinux.net!
The Excel spreadsheets here are mostly locked with a password,
preventing people from accidentally tampering with them and
students from spending their time changing fonts and the like
rather than doing the assigned tasks. The password used in all
of these spreadsheets is my initials "jdg" (without the quote
marks). If you wish to change this password, you must also
change it everywhere it appears in the macros, too.
Most of these spreadsheets have unsigned macros, and you will
need to enable macros in order for the spreadsheets to
run. Once you have set an appropriate security level, you must
then enable the macros when opening the spreadsheet, when
prompted to do so. There are different ways to set the security
level in Excel 2003 and for earlier versions of Excel:
Excel 2003: Go to the Tools -> Options ... menu, click on
the "Security" tab in the Options window, click on the "Macro
Security" button near the bottom of the page, then select
"Medium" (if you select High, you will not be able to run the
spreadsheets).
Excel pre-2003: Go to the Tools -> Macros -> Security
... menu and then select "Medium".
Word documents
Yes, I wrote some of them using Microsoft Word. Oh well.
Most I wrote using OpenOffice, an excellent
Free Software Office suite which is on its way to rivalling
Microsoft office, and then saving it in Word format. The
conversion software is not perfect, though hopefully the results
are at least usable. I have provided PDFs in addition to the
source in some cases. C'est la vie.
LaTeX documents
I use Donald Knuth's TeX system with the LaTeX macros quite
regularly. (In fact, I'm even a TeX-hacker, surprisingly
enough.) You can find out more about TeX and friends from the
TeX Users Group website.
These files are provided in source format and PDF format. If
you want the figures included in some of the files, please mail me, as I have not
included them here.
Modular (Clockface)
Arithmetic: A Word document which
leads students through an introduction to modular arithmetic,
where 9+5 might equal 2. This is a significant topic in
advanced mathematics, but the basic ideas are accessible to
good students in Year 5 or 6 (9-11 year olds). This worksheet
gets progressively harder, starting with addition and moving
towards division and powers. Some questions are
straightforward closed questions, others are open
investigations. Full notes and solutions are included in the
document.
Function machines: An Excel spreadsheet with two
sheets; The first ("Term to Term") is for exploring the
function n -> n + a, where a is randomly generated. The
"Negatives?" checkbox determines whether or not negative
numbers might be generated. The first input to the function
box may be changed manually. The second sheet ("Position to
Term") if for the function n -> an + b, where a and b are
randomly generated. The function may be displayed or not
(configurable with a checkbox), and the inputs are randomly
chosen. The inputs may be manually changed, and if a class
wishes to fix the inputs for the next random generation of a
and b, there is a "Lock inputs" checkbox. The original
version of this spreadsheet was by Susanne Watt; all of the
automation was written by me. Maybe we'll even do a quadratic
version one day should the opportunity arise (it wouldn't be
hard). Please see the note above about
my Excel spreadsheets.
Quiz: This Excel spreadsheet is based on one by
Stephen Hewson, and has the ability to check the answers
entered. It would be nice to have the option of having a
large bank of categorised questions and being able to select
the categories wanted, but that seems to be quite hard. In
the meantime, you can just have multiple copies of the
spreadsheet with different question bases for each. The
questions and correct answers are entered on the "Questions"
sheet. Please see the note above about
my Excel spreadsheets.
Multiplying and dividing by powers of
ten: This Excel
spreadsheet is also based on one by Stephen Hewson, and
now has the ability to check the answers entered. There is
an option to use either times or divide. The first
"Decimals?" check-box controls whether decimals are allowed
in the multiplier/dividend or answer. The second
"Decimals?" check-box controls whether decimals are allowed
in the multiplicand/divisor. Please see the note above about my Excel spreadsheets.
Number cards: The numbers
from 1 to 36, with 12 numbers per card, for cutting out, and
all numbers from 1 to 100 with no prime factors besides 2, 3,
5 or 7. The latter are great for playing "Factor Snap": it's
a normal game of Snap, but two cards match (and "Snap" can be
called) only when one is a factor of the other. Available in
OpenOffice format,
converted to Word format
and PDF.
Geometry Guess Who?
Cards: A grid of 24 geometric shapes (squares,
rectangles, etc.) allowing students to play "Guess Who?":
one picks a shape, and the other has to work out which was
picked by asking geometric yes/no questions. Available in
XFig format and
converted to a JPEG
image.
Place value
cards: Cards for splitting numbers into hundreds,
tens and units and back again; also, a variant of the set
for working with HTU and decimals down to the thousandths
column. The integer cards are available in LaTeX and PDF; the decimal
cards are also available in LaTeX and
PDF.
Times Tables Quiz: An
Excel spreadsheet
for checking one's knowledge of the times tables.
Configurable, gives feedback and times your work as well.
Latin squares
investigation: Puzzle to work out: take three cups
and three saucers of each of three colours. Place the cups and
saucers in a 3x3 grid so that each row has one cup of each
colour, each column has one cup of each colour, and the same
for the saucers. Also, each cup/saucer combination must
appear exactly once. Now try the same for the 5x5 and 4x4
cases. Search Google for "Greco-Latin Squares" to find out
more about them. I might write a small little note about the
solution of the 4x4 case, which is the hardest. The 2x2 and
6x6 cases turn out to be impossible to do, but the
n x n case can be done for all
other n. A sheet for cutting out and one with the
questions can be downloaded in LaTeX and PDF format. (I haven't
included the precise images I used; search Google Images for cups
and saucers of your choice if you want to modify the LaTeX.)
Rounding: A number search
for practising rounding, in OpenOffice format
or converted to Word format.
Does need some tweaking - there are too many possible
answers.
Sequences: A series of
exercises using Multilink, again in OpenOffice format or
converted to Word
format.
I started with the 100-square above and used it
to develop Eratosthenes' Sieve.
Some investigations from the Framework (page 54), in OpenOffice and
converted to Word format.
Incidentally, the question about writing primes as sums of
two squares is originally due to Fermat: an odd prime can
be written as a sum of two squares if and only if it
leaves a remainder of 1 on division by 4.
A solution grid for finding sums of squares in OpenOffice format,
converted to Excel format and in
PDF format.
A 100-square with the numbers in outline but primes in
bold in OpenOffice,
converted to Word and
PDF.
A spreadsheet with the numbers from 1 to 100 arranged in
grids with 2, 3, 4, ..., 10 columns, for investigating
prime distribution and moving on to highest common
factors. Available in OpenOffice format,
converted to Excel format and
PDF.
For investigating factors: a table for
calculating d(n) (the number of factors/divisors of
n) for small values of n: the investigation
could be extended to investigate questions such as: (a)
Which numbers have one, two, three, four (harder!)
factors? and: (b) When is d(m)d(n)=d(mn)?
(Answers: (a) 1 has one factor, primes have two factors,
squares of primes have three factors, cubes of primes and
products of two distinct primes have four factors. (b)
This is true when m and n are coprime, that
is, their HCF is 1.) Available in
OpenOffice,
Excel and
PDF formats.
More HCFs and LCMs work: discover that
HCF(m,n)xLCM(m,n)=mn and practice HCFs and LCMs.
Available in
OpenOffice,
Word and
PDF formats.
One final HCFs investigation: exploring phi(n),
the number of numbers in the range 1, 2, ..., n which are
coprime to n. The result is that phi(m)xphi(n)=phi(mn)
whenever m and n are coprime (in fact, if and only if m
and n are coprime). Available in
OpenOffice,
Excel and
PDF formats.
Multiplication
grids: really great tool for "long
multiplication". Can also be used for multiplying
decimals as will be shown in this image (which will be
created soon - please be patient!). Here is a page of 2x2
grids in XFig and
PDF formats, and
also a page of larger grids in XFig and
PDF formats.
Fraction bars:
Photocopy or print these pages onto card, then cut them out,
fold and stick the tabs to make a series of solid fraction
bars. The first page is a whole unit, and then there are
pages for all unit fractions from 1/2 to 1/10. Available as
LaTeX source or as PDF.
FDPRP matching cards:
Cards based on the ones designed by Malcolm Swan, in Issues
in Mathematics Teaching, ed. Peter Gates. Students cut up
the cards, then have to collect them into matching sets,
explaining why they have done what they are doing. Good for
highlighting misconceptions. Available as LaTeX and PDF.
Transformations
Worksheet: A simple little puzzle for
investigating standard geometric transformations (reflection,
rotation, translation). Available as LaTeX and PDF.
Angle work: Three sets of
cards for pairs games (e.g., "pelmonism": the memory game
where you turn over two cards and can keep them if they
match); here, matching cards are ones which add up to 90 (set
1), to 180 (set 2), to 360 (set 3). The cards are labelled
with the required sum. Available in
OpenOffice,
Word and
PDF formats.
Percentages: Three
resources for a high-ability year 9 group:
Here is a three-page handout on percentages, AERs, and
compound interest. It makes reference to an MEP handout,
Activity 11.5 available from here.
The document is available in OpenOffice format and
converted to Word
format.
This is a simple Excel
spreadsheet for investigating credit card interest and
AERs.
A handout on percentage error, available in LaTeX and PDF formats.
Rounding and estimation: A
puzzle to practice rounding to 1, 2, ... d.p. (in OpenOffice
format and converted to Word format) and
a series of workcards on estimation (in OpenOffice format and
converted to Word format,
in a convenient format for guillotining) - note that Q10 in
the latter is context-specific and will need changing before
reuse, and that Q7 might be potentially an issue in some
groups.
Factors and primes: A series
of three investigations (bare bones only) into prime
factorisations, perfect numbers and Goldbach's conjecture.
Available in OpenOffice
format and converted into Word format.
Also an OHP transparency and worksheet on prime factorisation:
OpenOffice and Word format. You'll
need to draw pretty bubbles in yourself.
Transformations of
graphs: A worksheet and revision sheet on this topic:
the worksheet is available as LaTeX and PDF; the revision
sheet is also available as LaTeX and PDF. I also
needed to review basic transformations with this group and
gave them the following task, available as LaTeX and PDF.
Statistics: A Powerpoint
presentation giving an overview of the statistics in maths
A-level for a good group.
Module S1: A Word
document for an investigation into the values of the
binomial coefficients. The students were given the first
page and four counters of different colours and asked to
count the number of ways of picking 2 out of the 12 spaces.
(We had already discussed what the binomial coefficients had
to be conceptually, but had not yet evaluated them.) Then
we progressed to 3 out of 12, and if appropriate, 4 out of
12. The other two pages were useful on a digital projector
to discuss the development of the idea; clearly the second
page is meant to be developed interactively.
Module S1: An Excel
spreadsheet simulating the binomial distribution, and
optionally displaying the expected frequencies. Also displays
the mean, variance and standard deviation of the observed and
expected frequencies. Please see the note
above about my Excel spreadsheets.
Module S1: A worksheet on using the cumulative binomial
tables. Note the there are two pages, and each question on
the first page matches the correspondingly numbered question
on the other page. Available in LaTeX and PDF formats.
Module S1: Introduction to the
normal distribution. An exercise and a spreadsheet. The
exercise is based on one from an old SMP 16-19 textbook, and
invites the students drawing a histogram of a dataset. This
version asks the students to draw a histogram showing
relative frequency density, thus enabling them to
revise (or learn) the ideas of relative frequency and
histogram drawing in addition to moving towards the normal
distribution. The exercise consists of a question sheet (LaTeX or PDF) and a frequency
table to fill in (LaTeX or PDF); the latter
has a solution table included. The Excel spreadsheet
is a simulation of a normal distribution, with the mean, s.d.,
number of samples, number of bars in the histogram and range
of the histogram variable. There is also a checkbox to
indicate whether to display the normal curve or not. This can
be very effective in introducing the concept of a continuous
distribution. Please see the note above
about my Excel spreadsheets.
Number theory talk: A talk
given at Hills Road Sixth Form College on which triangle
numbers are square numbers, moving onto an elementary
discussion of quadratic number fields. There's a presentation
prepared in LaTeX,
and the PDF screen
version resulting from it. There's also a printable PDF version
with notes prepared from the same LaTeX source file (just
change the option "screen" to the pdfscreen package to "print"
to produce it) and an Excel spreadsheet
designed to explore the numerical aspects of this problem.
