1
00:00:01,160 --> 00:00:04,730
Welcome to the presentation
on basic addition.

2
00:00:04,730 --> 00:00:06,810
I know what you're thinking,
Sal, addition doesn't

3
00:00:06,810 --> 00:00:08,260
seem so basic to me.

4
00:00:08,260 --> 00:00:10,940
Well, I apologize.

5
00:00:10,940 --> 00:00:13,170
Hopefully by the end of this
presentation or in a couple

6
00:00:13,170 --> 00:00:14,840
of weeks it will seem basic.

7
00:00:14,840 --> 00:00:16,990
So let's get started
with, I guess we could

8
00:00:16,990 --> 00:00:18,390
say, some problems.

9
00:00:18,390 --> 00:00:23,100
Well let's say I start
with an old classic.

10
00:00:23,100 --> 00:00:25,950
1 plus 1.

11
00:00:25,950 --> 00:00:29,440
And I think you already know
how to do this, but I'll kind

12
00:00:29,440 --> 00:00:31,960
of show you a way of doing this
in case you don't have this

13
00:00:31,960 --> 00:00:35,050
memorized or you haven't
already mastered this.

14
00:00:35,050 --> 00:00:40,930
You say, well, if I have 1,
let's call that an avocado.

15
00:00:40,930 --> 00:00:45,030
If I have 1 avocado and
then you were to give me

16
00:00:45,030 --> 00:00:48,870
another avocado, how many
avocados do I now have?

17
00:00:48,870 --> 00:00:49,340
Well, let's see.

18
00:00:49,340 --> 00:00:52,300
I have 1, 2 avocados.

19
00:00:52,300 --> 00:00:54,740
So 1 plus 1 is equal to 2.

20
00:00:54,740 --> 00:00:55,910
Now, I know what
you're thinking.

21
00:00:55,910 --> 00:00:58,390
That was too easy, so let
me give you something a

22
00:00:58,390 --> 00:01:00,410
little bit more difficult.

23
00:01:00,410 --> 00:01:01,840
I like the avocados.

24
00:01:01,840 --> 00:01:04,130
I might stick with that theme.

25
00:01:04,130 --> 00:01:09,420
What is 3 plus 4?

26
00:01:09,420 --> 00:01:11,980
This is, I think, a more
difficult problem.

27
00:01:11,980 --> 00:01:14,070
Well, let's stick
with the avocados.

28
00:01:14,070 --> 00:01:17,710
And in case you don't know what
an avocado is, it's actually

29
00:01:17,710 --> 00:01:18,890
a very delicious fruit.

30
00:01:18,890 --> 00:01:21,210
It's actually the fattiest
of all the fruits.

31
00:01:21,210 --> 00:01:22,340
You probably didn't even
think it was a fruit,

32
00:01:22,340 --> 00:01:25,470
even if you ate one.

33
00:01:25,470 --> 00:01:32,270
Let's say I have 3
avocados-- 1, 2, 3.

34
00:01:32,270 --> 00:01:35,120
And let's say you were to
give me 4 more avocados.

35
00:01:35,120 --> 00:01:38,620
So let me put this 4 in yellow
so you know that these are

36
00:01:38,620 --> 00:01:40,610
the ones you're giving me.

37
00:01:40,610 --> 00:01:45,780
1, 2, 3, 4.

38
00:01:45,780 --> 00:01:48,980
So how many total
avocados do I have now?

39
00:01:48,980 --> 00:01:55,790
That's 1, 2, 3, 4,
5, 6, 7 avocados.

40
00:01:55,790 --> 00:01:59,000
So 3 plus 4 is equal to 7.

41
00:01:59,000 --> 00:02:00,290
And now I'm going to introduce
you to another way of

42
00:02:00,290 --> 00:02:01,070
thinking about this.

43
00:02:01,070 --> 00:02:02,180
It's called the number line.

44
00:02:02,180 --> 00:02:05,490
And actually, I think this is
how I do it in my head when I

45
00:02:05,490 --> 00:02:08,920
forget-- if I don't
have it memorized.

46
00:02:08,920 --> 00:02:11,450
So number line, I just write
all the numbers in order.

47
00:02:11,450 --> 00:02:13,850
And I go high enough just
so all the numbers I'm

48
00:02:13,850 --> 00:02:15,470
using are kind of in it.

49
00:02:15,470 --> 00:02:18,000
So you know the first number
is 0, which is nothing.

50
00:02:18,000 --> 00:02:20,020
Maybe you don't know,
but now you know.

51
00:02:20,020 --> 00:02:36,250
And then you go to 1, 2,
3, 4, 5, 6, 7, 8, 9, 10.

52
00:02:36,250 --> 00:02:37,600
Keeps going-- 11.

53
00:02:37,600 --> 00:02:39,360
So we're saying 3 plus 4.

54
00:02:39,360 --> 00:02:41,740
So let's start at 3.

55
00:02:41,740 --> 00:02:45,500
So I have 3 here and we're
going to add 4 to that 3.

56
00:02:45,500 --> 00:02:48,430
So all we do is we go up the
number line, or we go to the

57
00:02:48,430 --> 00:02:50,850
right on the number
line, 4 more.

58
00:02:50,850 --> 00:02:59,130
So we go 1, 2, 3, 4.

59
00:02:59,130 --> 00:03:01,360
Notice all we did is we just
increased it by one, by

60
00:03:01,360 --> 00:03:02,610
two, by three, by four.

61
00:03:02,610 --> 00:03:04,090
And then we ended up at 7.

62
00:03:04,090 --> 00:03:06,030
And that was our answer.

63
00:03:06,030 --> 00:03:07,180
We can do a couple
of different ones.

64
00:03:09,690 --> 00:03:14,030
What if I asked you
what 8 plus 1 is?

65
00:03:14,030 --> 00:03:14,960
Well, you might
already know it.

66
00:03:14,960 --> 00:03:16,390
You know, plus 1 is
just the next number.

67
00:03:16,390 --> 00:03:18,225
But if we look at the
number line you start

68
00:03:18,225 --> 00:03:22,500
at 8 and you add 1.

69
00:03:22,500 --> 00:03:26,340
8 plus 1 is equal to 9.

70
00:03:26,340 --> 00:03:27,445
Let's do some harder problems.

71
00:03:30,370 --> 00:03:32,830
And just so you know, if you're
a little daunted by this

72
00:03:32,830 --> 00:03:34,550
initially, you can always
draw the circles.

73
00:03:34,550 --> 00:03:36,060
You can always do
the number line.

74
00:03:36,060 --> 00:03:39,670
And eventually, over time, the
more practice you do-- you'll

75
00:03:39,670 --> 00:03:41,330
hopefully memorize these and
you'll do these problems

76
00:03:41,330 --> 00:03:42,440
in like half a second.

77
00:03:42,440 --> 00:03:43,240
I promise you.

78
00:03:43,240 --> 00:03:46,250
You just got to
keep practicing.

79
00:03:46,250 --> 00:03:48,380
I want to draw the number line
again, actually, I have a line

80
00:03:48,380 --> 00:03:50,740
tool, so I should give you
all those ugly looking lines

81
00:03:50,740 --> 00:03:52,260
that I've been giving you.

82
00:03:52,260 --> 00:03:52,840
Look at that.

83
00:03:52,840 --> 00:03:54,660
That's amazing.

84
00:03:54,660 --> 00:03:56,810
Let me see.

85
00:03:56,810 --> 00:04:00,230
Look at that.

86
00:04:00,230 --> 00:04:01,490
That's a nice looking line.

87
00:04:01,490 --> 00:04:04,650
I'm going to feel bad
to erase it later on.

88
00:04:04,650 --> 00:04:06,920
So let me draw a number line.

89
00:04:06,920 --> 00:04:28,590
0, 1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13, 14, 15.

90
00:04:28,590 --> 00:04:30,060
So let's do a hard problem.

91
00:04:33,180 --> 00:04:35,290
I'm going to do it in
different colors now.

92
00:04:35,290 --> 00:04:38,550
5 plus 6.

93
00:04:38,550 --> 00:04:40,690
So if you want, you could
pause the video and try this.

94
00:04:40,690 --> 00:04:42,720
You might already
know the answer.

95
00:04:42,720 --> 00:04:45,140
And the reason why I say this
is a hard problem is because

96
00:04:45,140 --> 00:04:48,660
the answer has more numbers
than figures, so you can't

97
00:04:48,660 --> 00:04:50,770
necessarily do it
on your fingers.

98
00:04:50,770 --> 00:04:53,980
So let's get started
with this problem.

99
00:04:53,980 --> 00:04:55,780
Actually, my phone is ringing,
but I'm going to ignore the

100
00:04:55,780 --> 00:04:58,900
phone because you're
more important.

101
00:04:58,900 --> 00:05:00,980
OK, let's start at the 5.

102
00:05:00,980 --> 00:05:05,400
So we start at the 5 and
we're going to add 6 to it.

103
00:05:05,400 --> 00:05:13,980
So we go 1, 2, 3, 4, 5, 6.

104
00:05:13,980 --> 00:05:16,640
And we're at 11.

105
00:05:16,640 --> 00:05:19,670
So 5 plus 6 is equal to 11.

106
00:05:19,670 --> 00:05:22,475
Now I'm going to ask you a
question, what is 6 plus 5?

107
00:05:26,690 --> 00:05:28,540
Well, we're now
going to see that.

108
00:05:28,540 --> 00:05:30,890
Can you switch the two numbers
and get the same answer?

109
00:05:30,890 --> 00:05:32,260
Well, let's try that.

110
00:05:32,260 --> 00:05:33,600
And I'm going to try it in
a different color so we

111
00:05:33,600 --> 00:05:34,520
don't get all confused.

112
00:05:34,520 --> 00:05:36,930
So let's start at 6.

113
00:05:36,930 --> 00:05:39,880
Ignore the yellow for
now and add 5 to it.

114
00:05:39,880 --> 00:05:45,040
1, 2, 3, 4, 5.

115
00:05:45,040 --> 00:05:47,040
We get to the same place.

116
00:05:47,040 --> 00:05:48,840
And I think you might want
to try this on a bunch of

117
00:05:48,840 --> 00:05:50,600
problems and you'll see
it always works out.

118
00:05:50,600 --> 00:05:53,900
That it doesn't matter what
order-- 5 plus 6 is the

119
00:05:53,900 --> 00:05:55,910
same thing as 6 plus 5.

120
00:05:55,910 --> 00:05:56,670
And that makes sense.

121
00:05:56,670 --> 00:05:58,960
If I have 5 avocados
and you give me 6,

122
00:05:58,960 --> 00:05:59,740
I'm going to have 11.

123
00:05:59,740 --> 00:06:01,845
If I have 6 avocados and
you gave me 5, I'm going

124
00:06:01,845 --> 00:06:05,350
to have 11 either way.

125
00:06:05,350 --> 00:06:07,190
Since this number line is so
nice, I want to do a few

126
00:06:07,190 --> 00:06:08,170
more problems using it.

127
00:06:08,170 --> 00:06:10,720
Although as I use it I'm sure
I'll just continue to confuse

128
00:06:10,720 --> 00:06:12,460
you because I'll write
so much on top of it.

129
00:06:12,460 --> 00:06:14,290
But let's see.

130
00:06:14,290 --> 00:06:17,250
I'll use white now.

131
00:06:17,250 --> 00:06:22,320
What is 8 plus 7?

132
00:06:22,320 --> 00:06:26,830
Well, if you can still read
this, 8 is right here.

133
00:06:26,830 --> 00:06:28,820
We're going to add 7 to it.

134
00:06:28,820 --> 00:06:36,910
1, 2, 3, 4, 5, 6, 7.

135
00:06:36,910 --> 00:06:38,110
We go to 15.

136
00:06:38,110 --> 00:06:39,390
8 plus 7 is 15.

137
00:06:42,450 --> 00:06:45,550
So hopefully that gives
you a sense of how to do

138
00:06:45,550 --> 00:06:48,200
these types of problems.

139
00:06:48,200 --> 00:06:50,570
I guess this and you're going
to learn multiplication in a

140
00:06:50,570 --> 00:06:53,880
little bit, but these types of
problems are-- when you're

141
00:06:53,880 --> 00:06:55,830
getting started off in
mathematics, these kind of

142
00:06:55,830 --> 00:06:58,390
require the most practice and
to some degree, you have to

143
00:06:58,390 --> 00:06:59,430
start memorizing them.

144
00:06:59,430 --> 00:07:03,150
But over time, when you look
back, I want you to remember

145
00:07:03,150 --> 00:07:05,650
how you feel while you're
watching this video right now.

146
00:07:05,650 --> 00:07:09,780
And then I want you to watch
this video in like 3 years and

147
00:07:09,780 --> 00:07:11,930
remember how you felt when
you're watching it now.

148
00:07:11,930 --> 00:07:13,340
And you're going
to be, oh my God.

149
00:07:13,340 --> 00:07:16,080
This was so easy because you're
going to learn it so fast.

150
00:07:16,080 --> 00:07:19,940
So anyway, I think
you have an idea.

151
00:07:19,940 --> 00:07:22,500
If you don't know the answer to
any of the additional problems

152
00:07:22,500 --> 00:07:25,735
that we give in the exercises
you can press the hints and

153
00:07:25,735 --> 00:07:28,560
it'll draw circles and you can
just count up the circles.

154
00:07:28,560 --> 00:07:30,020
Or if you want to do it
on your own so you get

155
00:07:30,020 --> 00:07:32,260
the problem right, you
could draw the circles.

156
00:07:32,260 --> 00:07:34,370
Or you could draw a number
line like we did in

157
00:07:34,370 --> 00:07:36,710
this presentation.

158
00:07:36,710 --> 00:07:40,330
I think you might be ready to
tackle the addition problems.

159
00:07:40,330 --> 00:07:41,870
Have fun.