Mathematics
Investigation
The mathematics investigation has been based on the question ”What
mathematics do you use in your life” and
“How is the mathematics used in our lives” In looking at this the children have focused
mostly on measurement, money and the symbols in mathematics. Some conceptual
knowledge is present however interest in the number system itself has been a
conspicuous absence in the neighbourhoods. We want to build student
understanding of the base ten system, its connections to everyday life and the
mathematical concepts that they have explored. We need to do this because
children haven’t had the number system explained to them so that they have a
clear connection to why place value is so important. This understanding will
likely move children from a position of knowing how to ‘do’ to a position of
understanding why. We want to communicate to the children what an amazing
invention the number system is and how connected it is to societal needs. It is
with this where the link to the inquiry can be developed. The inquiry question
of looking at the conditions and motivations for change link in to examining
the different number systems and the reasons for the variations based on the
needs of the people using them.
We will be completing our
initial Investigation this week and moving on to a new question. We would like
students to begin thinking about our number system by investigating our base‐10
number system and how we use it. Children will begin an investigation where
they explain through a presentation, how we use the base‐10
number system. They can do this by writing an instruction manual, a
documentary, a presentation or another expression that they can negotiate with
their teachers.
.
During
the week the children have been introduced to the concept behind the base‐10
system.
Teachers have explained
the meaning of the term “number system” We use a number system to describe a
number. Every number system has a base. The base tells you how many symbols you
use in the system. In Australia, we mostly use the base-‐10
system. The base‐10 system uses 10 symbols or digits. The digits we use for
the base‐10 system are 0,1,2,3,4,5,6,7,8,9. We use these to describe
every number.
Using just one of these
digits will describe any number from 0-‐9. If we want to describe a number more
than 9, then we have to position the digit in the right place. We sometimes
call this PLACE‐VALUE because the place the digit is in describes the value
(or the amount).
Before number systems, we
recorded numbers through tallies. A shepherd would count his sheep by cutting a
notch on his stick for each sheep. He would know how many sheep he has got by
the amount of notches he has on his stick. The problem is, he has to count it
to check.
A prisoner would scratch
a line for every day he spends in his cell. This is fine for small numbers like
five or ten. But it is useless when we want to describe big numbers like a
hundred or a million. The great thing about the base‐10
place value system is that you can describe a really big number like one
hundred with just three symbols (or digits).
A one and two 0s. They are placed in columns that describe their value.
100 has 1 in the hundreds column, none in the tens column and none in the units
(or the ones) column. Even a bigger number like nine hundred and ninety-‐nine
still only use three symbols (three 9s). 9 in the hundreds column because there
are nine one hundreds. 9 in the tens column because there are nine tens, and 9
in the ones column because there are nine ones. Imagine what the shepherd’s
stick would look like if he wanted to describe nine hundred and ninety‐nine
with notches! It’s much easier to show nine hundred and ninety‐nine
with three symbols. The order and position is very important. To describe two different
numbers like nineteen and ninety‐one, you would use the same two symbols
1 and 9. Depending on how we position the two symbols, we describe a different
value (or amount). There is a huge difference between 19 and 91. It would be
very annoying if you have to pay $91 for something that should cost $19 and so
the way we position the digits is very important!
Targeted
number learning
As
students begin to further investigate the base-10 number system, some students
will look into how we describe numbers smaller than 1 through the use of
decimal fractions and numbers that are ‘between’ whole numbers. They will begin
by visualising what tenths are through use of materials and then consolidate
this understanding through ordering of decimal fraction numbers.
