Mathematics
Lessons
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Numerals, numbers
When we write, we use different
symbols to mean certain
things. Some of these symbols are called “numerals”
because they
are symbols that represent numbers. The most common numerals used to
represent numerals are: 1 2 3 4 5 6 7 8 9 0
These numerals are arranged in
a specific way to
represent a certain number. We use the numerals 1 and 2 to represent
the number “twelve” if they are arranged as 12 . We
use the
numerals 1 and 2 to represent the number
“twentyone” if they are
arranged as 21 . We use the numerals 1 and 0 to represent the
number “ten” if they are arranged as 10 .
Values of individual
common numerals
We use each of the individual
numerals to represent a
unique number:
We use the numeral 1 by itself
to represent the number
“one.”
We use the numeral 2 by itself
to represent the number
“two.”
We use the numeral 3 by itself
to represent the number
“three.”
We use the numeral 4 by itself
to represent the number
“four.”
We use the numeral 5 by itself
to represent the number
“five.”
We use the numeral 6 by itself
to represent the number
“six.”
We use the numeral 7 by itself
to represent the number
“seven.”
We use the numeral 8 by itself
to represent the number
“eight.”
We use the numeral 9 by itself
to represent the number
“nine.”
We use the numeral 0 by itself
to represent the number
“zero.”
Here is a chart showing each
numeral with the number it
represents and a visual picture of the number's value:
Numeral

Name

Amount

1

one


2

two


3

three


4

four


5

five


6

six


7

seven


8

eight


9

nine


0

zero


Organizing numerals
Rather than use an individual
numeral for each number we
want to represent, we use a combination of numerals to represent most
numbers. We organize numbers using a “baseten”
system, which
means that a numeral represents ten times the value the same numeral
to the right would represent.
Adding two numbers;
addends; sum
Three
people
went into the chapel to
pray. Two more went in to pray with them. How any
people were in the chapel now?
We
can also
write this faster as
3 people
+
2
people
or
3
+2
or
3 + 2 = _____
If
we count the
people we find there
are five of them. We can answer the questions we wrote more quickly
as
3 people
+
2 people
5
people
or
3
+2
5
If
we write our
question in any of
these three ways they will all have the same answer: 5
We
call the
numbers we add together
“addends” (in this case 2 and 3 were the addends)
and we call the
total of the addends the “sum.”
3 people
<addend
+
2 people
<addend
5
people
<sum
or
3
<addend
+2 <addend
5
<sum
Adding with zero
If we have a full pie and an
empty pie pan, how many pie
do we have?
We can also write this as 1 + 0
= ____
Since we know that there is
only one pie, we write 1 on
the line so it looks like this= 1 + 0 = 1
We
can add 0 to any
number and the sum (total) will be the same. So if we have 12 eggs
and get 0 more we will still have 12 eggs. This is called the Identity
Property of Addition.
Adding more than two
numbers/addends
When
we need to add more than two groups
of numbers
at a time, it may be easier to add just two numbers at a time rather
than trying to answer a question all at once.
If
are three clean plates in the cupboard, two clean plates in the dish
drainer, and four clean plates on the table, how many dishes do we
have that we can use for the meal?
We
can also write this as
3 plates
2 plates
+4
plates
or
3
2
+4
or 3+2+4=___
If we want to add two of
the numbers together
before we add the other number or numbers to it, we can use
parentheses to enclose what should be added together first. If we
wanted to add 2 and 4 together first, we can write it as 3+ (2 +
4)=_______ When we add numbers together that are inside the
parentheses, we replace the numbers and signs inside the parentheses
with the total of the numbers. So since 2 + 4 = 6, we replace the
“2
+ 4” with “6” and our question will now
look like this: 3 + (6)
= ___
We can remove the
parentheses from around the 6
because we no longer need them. It will now look like 3 + 6 = ____ We
then add the 3 and 6 and write the answer on the line and it looks
like this:
3 + 6 = 9
If
we write it as
3
2
+4
we can first write it on
the scratch paper like
this
3
2
+4
then if we want to add
the 2 and 4 four
together first we can make a line come from each number and join
together, then write the sum of the two numbers where they join so
that it looks like this:
3
2 \ _{6 }
(show
better picture of this)
+4
/
then
write a new question adding the 3 and 6
3
+6
and
since we know that the sum of 3 and 6 is 9, we write the sum below
the line like this:
3
+6
9
so we know there are nine
clean dishes
we can use for the meal.
Subtraction
If
we had four clean large bowls
and used two for a meal, how many are left? We can write this as
4 bowls

2
bowls
or
4
 2
or
4 – 2 = _____
If
we count the bowls we see there
are two clean large bowls left, so we write 2 under the line for the
first two ways we wrote the question, and on the line for the third
way we wrote the question:
4 bowls

2
bowls
2
bowls
or
4
 2
2
or
4 – 2 = 2
So
we have two large clean
bowls left.
We
call the original number the
minuend and the amount we take away the subtrahend. We call the total
the difference.
4 bowls
<minuend

2 bowls
<subtrahend
2
bowls
<difference
or
4
<minuend
2
<subtrahend
2
<difference
Subtracting
with zero
If we have
a full pie and do
not take any away, how many
pies do we have?
We can also write this as 1  0
= ____
Since we know that we still
have the one pie, we write 1
on the line so it looks like this= 1  0 = 1
We
can subtract 0 from any
number and the difference (total) will be the same. So if we have 12
eggs and take away 0 eggs we will still have 12 eggs. This is called
the Identity Property of Subtraction.
Checking
subtraction with addition; Checking addition with subtraction
If
we add the original difference
and the original subtrahend and it equals the original minuend, we
can see if we subtracted it correctly. So if we have
4 bowls
<original minuend

2 bowls
<original subtrahend
2
bowls <original
difference
we
can setup to add the original
minuend and the original difference
2 bowls
<original subtrahend
+ 2
bowls
<original difference
and
add them
2 bowls
<original subtrahend
+ 2
bowls
<original difference
4
bowls
As
we see, our answer (4 bowls) is
the same as the original minuend (also 4 bowls).
Also,
we can check our addition by
subtracting one of the original addends from the sum, and it will
equal the other original addend. So if we have
3 people
<original addend
+
2 people
<original addend
5
people <original sum
we
can setup to subtract one of
the original addends from the sum
5
people <original
sum

2 people
<original addend
then
subtract
5
people <original
sum

2 people
<original addend
3
people
As
we see, our answer (3 people)
is the same as the other original addend (also three people).
As
with anything else in life,
addition undoes subtraction, and subtraction undoes addition.
