awareness 2 some examples in rod pre-number…

some algebra before arithmetic pre-number awarenesses

examples of free play awarenesses:

rods are good things to play with

we can make pictures

we can build models and buildings

we can play games

we can invent games

we can share our ideas

we can learn from each other

rod colours are in families

rods can be packed away in family colour order if we like

rods can be packed away in other ways

rods have a definite regular order of size

I can recognise rods by how they feel

rods can be named by colour and in other ways

directed informal awarenesses:

rods of same colour are same length

rods of same length are same colour

groups can be made of the same colour

groups can be made of the same lengths

language (word concept) awarenesses:

trains can be made in a variety of ways

rods can be swapped for others

 staircases can be made in a variety of ways

 mats can be made

mats can be made with rows of rods of the same colour

we can answer questions by making patterns of rods

awarenesses relating to adding and its inverse:

I can find one rod to fit two others

I can find two or more rods to fit one

I can find rods to fit long trains

I can find the difference between two rods in different ways

I can find the difference between two trains of any length

awarenesses relating to equivalence, multiplication and factors:

I can find one rod which fits two or more rods of the same colour

I can find rods of the same colour to fit some other longer rods

I can find rods of the same colour to fit some, but not all trains

dave eats a 1 rod and britney spears

davesniffsrods

That’s a bit annoying Dave… we can’t see all the complements to 10 now, we’ll have to imagine that one above the 9, as well as the missing one above the 5…

SONY DSC

what can you see?

complements to 10 and the sum of all the numbers to 10

a nice rectangle 5 x10 + 5 = 55

the old devil al-jebr would see:

 halfnaddn

a half of any number multiplied by the same number plus a half of that particular number is;

the sum of all numbers up to that number.

so, add all the numbers up to 100:  50 x 100  + 50  makes 5050   nice…

the power of al-jebr

by the way, here’s the same infamous Dave eating Britney:

video

( thanks to MMc and J )

going up…million billion godzillion

Here we go…

thousand 10 to the power 3

million10 to the power 6

billion10 to the power 9

trillion10 to the power 12

pattern1?

A 3 rod naturally, as THE COMMON DIFFERENCE in this particular staircase is 3

Just for fun here’s the names of some of the other big guys:

quadrillion 10 to the 15th

quintillion   10 to the 18th

sextillion     10  to the 21st power

septillion    10 the 24th

octillion, nonillion, decillion, undecillion, dudecillion, tredecillion, quatuordecillion, quindeciliion, sexdecillion, septendecillion, octodecillion, novemdecillion, vigintilliion…and so on for ever…

Of Latin origin except for:

godzillion  10 to the power of godzilla