introduction
Numbers are labels assigned to
real objects, with particular labels assigned to different
sized groupings of objects. counting
and addition
Tools to learn and to master
manipulation of numbers and counting.
subtraction
& more counting
Separating one or more objects
from a group is the start of subtraction. Continuing
with basic number and sums. Includes sections on
counting in the real world, placeholders, subtraction,
equals, category - logic blocks
.multiplication
Multiplication can be regarded
as repeated addition, or constant addition. But
often, instead of adding just one each time, a collection
or set of items is added again. Continuing basic
number and sums.
division
Division is constant subtraction,
with smaller groups of items are removed from a
larger collection. Continuing basic number and sums.
writing
down sums
When teaching basic arithmetic to pre-literate people, it is less confusing for the learner to grasp the writing of, and the reading of, numbers separately.
Step by step illustrated explanations, in clear language, for additioon, subtraction, multiplication, division, as well as long multiplication and long division sums..
quadratic equations, with model answers
Four worked examples of how to answer questions with quadratic equations from 1970, compared with a question from 2010. With commentary. |
sums, fractions, decimals, percentages and ratios 1
fractions, decimals, percentages and ratios
are all effectively the ‘same’ thing.
This first page concentrates on what are fractions
and how to do simple additions and subtractions
with fractions
fractions, decimals, percentages and ratios 2
This second page on fractions
and decimals focuses on how to do various multiplications
and divisions with fractions.
prime
numbers and factors, the sieve of Eratosthenes
Prime numbers and factors of
numbers are important concepts to understand when
doing sums with fractions.
orders
of magnitude, indices and logarithms
Step by step explanations, in
clear language, of some important tools in maths.
writing down logarithms
Step by step explanations, in
clear language, for using logarithm tools. They
may be regarded as historic, but slide rules and
log tables help learners understand how maths works
more deeply.
complete four-figure log tables
.pdf version of complete four-figure log tables
writing down stats :
using the standard normal distribution table
Step by step explanations, in clear language, for calculations using the normal distribution graph or bell curve,
as well as discussion on aspects of standard distribution and statistics in general.
table of normal curve equivalents,
or standard normal distribution table
simultaneous equations, with model answers
Working with simultaneous equations is working with more than one equation at a time [simultaneously], and with more than one variable. Worked examples with commentary, illustrations. |
‘equality’
or ‘same as’
“There ain’t no
such thing as equality.”
equality
and equations
Keeping sums in balance.
minus
and zero, dealing with no-thing and less than nothing!
If taught sloppily or incorrectly,
zero becomes the foundation for much difficulty
and confusion. abelard clarifies what is zero.
understanding graphs and charts
What are graphs and charts?
Let's show you how they work
abelard’s
maths educational counter
Count up, count down, in binary,
in decimal, in hexadecimal, or whatever you choose.
Even count backwards in negative decimals. An excellent,
fluent and very useful tool for all sums learners
and teachers.
understanding,
calculating, and changing bases
Numbers are counted in groups
called bases, to make it easier to count larger
groups (or sets) of numbers. A simple explanation
of how to count in different bases using abelard’s
educational counter, together with some everyday
examples
understanding
sets and set logic
A set is another name for a
box into which you group similar or dissimilar objects.
How to handle sets.
writing down sets and set logic equations
Including truth tables and how
to work out compound truth values, logic equations. |