four points

some practice with directed number

a ppt is here

you can vary:
the original four numbers (better with an integer mean)
have fewer or more numbers

directed number grid

this task is from Martin Wilson, in Harrogate
as he says, it's good for practice of directed number addition and subtraction because sometimes you are developing the grid forwards and sometimes backward
fibonacci like

a ppt is here

algebra can be used to explain a general rule

directed number addition and subtraction 2 (of 2)

the powerpoint is here

with subtraction, viewed as a 'gap', you can always shift it along to a more convenient location on a number line

add (or subtract) the same amount to both keeps the sum the same

looking at sequences/patterns  to decide what the results should be

directed number addition and subtraction 1 (of 2)

the powerpoint is here

uses directed numbers as vectors
involving the start and end (like stations) and the journey
these journeys can be described in two different (but the same) ways

Simon Razvi, in Birmingham (England) suggested that the positions on a number line are like nouns (e.g. 'negative 4')
and the journeys are like verbs (e.g. 'subtract 4')
usually these get muddled up
and usually I think there's value in muddling them up
[technically I guess you can't add a position on a number line to anything!]
it seems to me that it's (one dimensional) vectors that can be added and subtracted

thanks to Worcester Uni (PGCE) students and Jane Moreton for their comments (in Jan 2018)

temperature changes

temperature seems a helpful context for looking at directed number arithmetic

two equivalent statements are considered

• the end subtract the start is the 'gap'
• the start and then the operation gives the (end) result

directed number arithmogons

the word 'arithmogons' (rather than 'arithmagons') seems to stem from an article by Alistair McIntosh and Douglas Quadling in Maths Teaching number 70 (in 1975)

amongst many other things Leo Moser (1921 to 1970) studied pairs of numbers adding up to totals, including the work in the third resource: pairs of numbers always summing to a square number

the powerpoint goes through various algebraic solution steps - one good reason for studying arithmogons, as well as (in this case) practice with directed numbers

Craig Barton details the reasons he enjoys working with arithmogons and has various tasks based on their structure here

directed number practice makes perfect (1)

a ppt is here

directed number practice makes perfect (2)

a ppt is here