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# Category Archives: fractions

# 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

# 48

The LHS shows 6×8

The RHS shows 2x3X2X2X2 dust ( the 8 is 2x2x2 and the 6 is 2×3 )

As far as the number 48 is concerned the order of rods in the tower is irrelevant, but this needs ‘proving’. Take my word for it at the moment.

So long as the tower is constructed using the rods on the right, the order is irrelevant.

So, as 2x2x2x2x3 is the dust, this means we combine these a pair at a time in any order:

**try it yourself**..that’s best…but

**here’s my mind at work for example:**

start with 2, double it double it double it, that’s 16, times 3 is 48 (2 4 8 16 48)

2 threes are six, double it, double it, double it, that’s 48 (6 12 24 48)

2 twos are 4, two fours are 8, three of them is 24, double it, 48

and so on…..

**IF** YOU HAVE THE **TIME** AND THE **SPACE** IN SCHOOL TO DO THIS **TILL THE COWS COME HOME** AND YOU ARE **LITTLE**, AND YOU **START SLOWLY** WITH THE **NUMBERS UP TO 10** AT FIRST, STUDYING THE NUMBERS **ONE BY ONE** FOR **A DAY OR TWO EACH** FOR EXAMPLE **WITHOUT STRESS**, YOU **WILL** **‘GET A FEEL’** FOR THE NUMBER YOU ARE STUDYING WHICH WILL BE **VERY POWERFUL** IN YOUR FUTURE STUDIES OF THE **NUMBER SYSTEM** AND **OPERATIONS** YOU WILL NO DOUBT BE REQUESTED TO CARRY OUT…

(In general, the present school arrangements almost totally inhibit this…)

**ps 6×8 is one piece of your ‘tables’, using the dust you see and get the ‘feel’ for 6×8, 8×6, 3×16, 16×3, 2×24, 24×2, 4×12, 12×4, never mind ‘half of 48 is 24’, ‘half of 12 is 6’, ‘half of 48 multiplied by 2 is 48’, ‘a quarter or fourth of 48 is 12’, ‘an eighth of 48 is a half of 12’…and so on till the cows come home…**

**yap yap yap…**

TRY IT