I had to remove all the viewmat images. To see them run the script in
either JHS or JQT
J TECH Grade 1 Summary
J is a mathematical language that responds to the commands you enter and the
statements you make. You get immediate results which allow you to develop
ideas more fully. You form a dialog of entry and response. As you become
familiar with the language, you apply verbs to data and get new results. New
ideas encourage newer ideas.
It is in this conversation that you begin to speak the J language. Many of
the verbs are ones you use in the spoken language. Some have conventional
symbols. However many are simple ideas you already know but have no symbols
for them. Hopefully J will become a tool to make your teaching easier and
allow you to focus on the ideas you are developing. You get to see beyond
the details.
In the first grade there are specific words and symbols you want students to
understand. You must also insure that they develop specific skills. The
suggestions here focus on using a J environment to provide practice and
reinforce your goals. Along the way you will introduce ideas not included in
the curriculum. It is almost impossible not to stumble upon zero when you
begin subtraction. These discoveries are the building blocks for the future.
New ideas foster a sense of excitement in the process. The search to explain
the unexpected is at the heart of learning.
Here are examples of things to use throughout the year. You can judge when
almost all students know a concept. Move to a new idea when they are ready.
Use J when it feels comfortable to you. Don't strive to teach every concept
here. Explore what happens instead. Experience the joy of becoming more
productive. There is a sense of empowerment as students feel they can take
concepts and run with them. Enjoy their excitement and encourage them to
share their successes with each other and with you.
load 'viewmat' A script to make images needs a
GRB=:1 0 2{"1 (#:i.8){0 255 verb viewmat and the noun GRB
'GARFIELD CAT' Letters within Quotes ' ' are
GARFIELD CAT called strings.
<"0 'GARFIELD CAT'
--T-T-T-T-T-T-T-T-T-T-T-┐ Box <"0 puts each item in a box
│G│A│R│F│I│E│L│D│ │C│A│T│
L-+-+-+-+-+-+-+-+-+-+-+--
<"0 'SNOOPY DOG'
--T-T-T-T-T-T-T-T-T-┐
│S│N│O│O│P│Y│ │D│O│G│
L-+-+-+-+-+-+-+-+-+--
$'GARFIELD CAT' Shape of $ string is 12 items
12
$'SNOOPY DOG' You could make boxes and then
10 count them
$'FAT CAT'
7
$' ' Put your first name and last
name in quotes. Put the string
in boxes. Count the boxes. Who
has the longest string? Shortest?
3 + 5 7 + plus 11 is 18
8
7 + 11 Add item to item
18
5 + 1 2 3 4 5 Add item to list
6 7 8 9 10
8 7 6 + 2 Add list to item
10 9 8
8 6 4 2 + 4 3 2 1 Add list to list
12 9 6 3 Number of items must agree
>:i.10 Increment >: or 1 + each
1 2 3 4 5 6 7 8 9 10 Integer i. from 0 to 9
]A=:>:i.10 Same ] result as A Is =:
1 2 3 4 5 6 7 8 9 10 displayed. A now has data
A + A
2 4 6 8 10 12 14 16 18 20
+ ~ A Reflex ~ puts A on the
2 4 6 8 10 12 14 16 18 20 left side of the + sign
(a shortcut for step above)
GRB viewmat A GRB name for colors
viewmat makes image of A
|. A
10 9 8 7 6 5 4 3 2 1 Reverse |. Order of the list A
GRB viewmat |.A Green, red and blue palette image
of the reversed order of A
2 4 6 + table 2 4 6 8 10 + table ma kes a plus table
--T-------------┐ with labels for top and
│+│2 4 6 8 10│ side
+-+-------------+
│2│4 6 8 10 12│ So far, GRB, viewmat and
│4│6 8 10 12 14│ now table are like "phone app's"
│6│8 10 12 14 16│ which produce specific
L-+-------------- results
]B=:2 4 6 + / 2 4 6 8 10 B is + table / of answers
4 6 8 10 12 The verb "table" is always
6 8 10 12 14 available in J
8 10 12 14 16
GRB viewmat B B has three rows and four
columns of color squares
5 4 3 2 1 + / 5 4 3 2 1
10 9 8 7 6
9 8 7 6 5
8 7 6 5 4
7 6 5 4 3
6 5 4 3 2
+/~ 5 4 3 2 1
10 9 8 7 6
9 8 7 6 5
8 7 6 5 4
7 6 5 4 3
6 5 4 3 2
]C=:+ / ~ >:i.10
2 3 4 5 6 7 8 9 10 11
3 4 5 6 7 8 9 10 11 12
4 5 6 7 8 9 10 11 12 13
5 6 7 8 9 10 11 12 13 14
6 7 8 9 10 11 12 13 14 15
7 8 9 10 11 12 13 14 15 16
8 9 10 11 12 13 14 15 16 17
9 10 11 12 13 14 15 16 17 18
10 11 12 13 14 15 16 17 18 19
11 12 13 14 15 16 17 18 19 20
GRB viewmat C Look for smallest numbes
and largest numbers
+ table ~ >:i.10 This is the table
---T-----------------------------┐ of all the plus
│+ │ 1 2 3 4 5 6 7 8 9 10│ facts to learn in
+--+-----------------------------+ first grade
│ 1│ 2 3 4 5 6 7 8 9 10 11│
│ 2│ 3 4 5 6 7 8 9 10 11 12│
│ 3│ 4 5 6 7 8 9 10 11 12 13│
│ 4│ 5 6 7 8 9 10 11 12 13 14│
│ 5│ 6 7 8 9 10 11 12 13 14 15│
│ 6│ 7 8 9 10 11 12 13 14 15 16│
│ 7│ 8 9 10 11 12 13 14 15 16 17│
│ 8│ 9 10 11 12 13 14 15 16 17 18│
│ 9│10 11 12 13 14 15 16 17 18 19│
│10│11 12 13 14 15 16 17 18 19 20│
L--+------------------------------
8 - 3 8 - minus 3
5
7 - 5 4 3 2 1
2 3 4 5 6
10 - 6 4 7 8 3
4 6 3 2 7
5 3 6 5 - 4 2 3 3
1 1 3 2
]D=:14 16 18 -/ 3 6 9 12
11 8 5 2
13 10 7 4
15 12 9 6
14 16 18 - table 3 6 9 12
---T----------┐
│- │ 3 6 9 12│
+--+----------+
│14│11 8 5 2│
│16│13 10 7 4│
│18│15 12 9 6│
L--+-----------
]D=:(10+>:i.10) -/ >:i.10
10 9 8 7 6 5 4 3 2 1
11 10 9 8 7 6 5 4 3 2
12 11 10 9 8 7 6 5 4 3
13 12 11 10 9 8 7 6 5 4
14 13 12 11 10 9 8 7 6 5
15 14 13 12 11 10 9 8 7 6
16 15 14 13 12 11 10 9 8 7
17 16 15 14 13 12 11 10 9 8
18 17 16 15 14 13 12 11 10 9
19 18 17 16 15 14 13 12 11 10
GRB viewmat D The darkest numbers match
the smallest numbers in D
Compare images C and D
E=:(10+>:i.10) - table >:i.10
---T-----------------------------┐ Subtraction facts to
│- │ 1 2 3 4 5 6 7 8 9 10│ learn in grade 1
+--+-----------------------------+
│11│10 9 8 7 6 5 4 3 2 1│
│12│11 10 9 8 7 6 5 4 3 2│
│13│12 11 10 9 8 7 6 5 4 3│
│14│13 12 11 10 9 8 7 6 5 4│
│15│14 13 12 11 10 9 8 7 6 5│
│16│15 14 13 12 11 10 9 8 7 6│
│17│16 15 14 13 12 11 10 9 8 7│
│18│17 16 15 14 13 12 11 10 9 8│
│19│18 17 16 15 14 13 12 11 10 9│
│20│19 18 17 16 15 14 13 12 11 10│
L--+------------------------------
]F=:>:6?6 6 ? deal 6 in random
5 4 1 6 3 2 order
]G=:>:6?6 6 different counting
4 2 6 5 1 3 numbers in new random order
F + table G Sum of deal 1 and
--T--------------┐ deal 2
│+│ 4 2 6 5 1 3│
+-+--------------+
│5│ 9 7 11 10 6 8│
│4│ 8 6 10 9 5 7│
│1│ 5 3 7 6 2 4│
│6│10 8 12 11 7 9│
│3│ 7 5 9 8 4 6│
│2│ 6 4 8 7 3 5│
L-+---------------
]H=:G +/ F Only answers in the table
9 8 5 10 7 6
7 6 3 8 5 4
11 10 7 12 9 8
10 9 6 11 8 7
6 5 2 7 4 3
8 7 4 9 6 5
GRB viewmat H Image of answers.
Find smallest and largest
numbers in H from color image
]I=:F +/ G
9 7 11 10 6 8
8 6 10 9 5 7
5 3 7 6 2 4
10 8 12 11 7 9
7 5 9 8 4 6
6 4 8 7 3 5
GRB viewmat I How do H and I compare?
Interchange of rows and
columns
|: G +/ F
7 12 9 11 8 10 Transpose |. Is another way
5 10 7 9 6 8 to get H
2 7 4 6 3 5
4 9 6 8 5 7 It is a flip of rows and
3 8 5 7 4 6 columns
6 11 8 10 7 9
]J=:(>:10?10) + / >:10?10
7 11 14 16 15 12 8 9 10 13 If you know the answers
5 9 12 14 13 10 6 7 8 11 can you find the two lists
4 8 11 13 12 9 5 6 7 10 of ten numbers that
9 13 16 18 17 14 10 11 12 15 created the table?
2 6 9 11 10 7 3 4 5 8
3 7 10 12 11 8 4 5 6 9
6 10 13 15 14 11 7 8 9 12
8 12 15 17 16 13 9 10 11 14
11 15 18 20 19 16 12 13 14 17
10 14 17 19 18 15 11 12 13 16
GRB viewmat J Possible answers are 2 to 20
4 >. 7 Larger of >. the two
7 numbers
2 3 6 4 >. 1 5 7 3 Selects the bigger
2 5 7 4 number of the pairs
>.table~ >:i.7
---T-------------┐
│>.│1 2 3 4 5 6 7│
+--+-------------+
│1 │1 2 3 4 5 6 7│
│2 │2 2 3 4 5 6 7│
│3 │3 3 3 4 5 6 7│
│4 │4 4 4 4 5 6 7│
│5 │5 5 5 5 5 6 7│
│6 │6 6 6 6 6 6 7│
│7 │7 7 7 7 7 7 7│
L--+-------------
GRB viewmat K
Note the right angles
7 = 8 Is 7 Equal = to 8
0 False, so answer is 0
9 = 9 Is 9 = 9
1 True, so answer is 1
+ / ~ >:i.4 This is a simple table
2 3 4 5
3 4 5 6
4 5 6 7
5 6 7 8
4 = + / ~ >:i.4 Where are all the 4's in
0 0 1 0 the table?
0 1 0 0
1 0 0 0 when you compare two sets of
0 0 0 0 data, all results are 0 or 1
]L=:9=+/~ >:i.8
0 0 0 0 0 0 0 1
0 0 0 0 0 0 1 0
0 0 0 0 0 1 0 0
0 0 0 0 1 0 0 0
0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0
0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0
GRB viewmat L
]M=: 6=+/~ >:i.9
0 0 0 0 1 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
GRB viewmat M
|.M
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 0 0 0
|.|:|.M
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 1 0 0 0 0
]N=:(|:|.M)+(|.|:|.M)+(|.M)+M Add the four tables to
form one
0 0 0 0 2 0 0 0 0 table
0 0 0 1 0 1 0 0 0
0 0 1 0 0 0 1 0 0
0 1 0 0 0 0 0 1 0
2 0 0 0 0 0 0 0 2
0 1 0 0 0 0 0 1 0
0 0 1 0 0 0 1 0 0
0 0 0 1 0 1 0 0 0
0 0 0 0 2 0 0 0 0
GRB viewmat N The data in table N has
only three
Numbers, 1, 2 and 3
The image is black, gray
and white
*6 Signum * provides three
different
1 answers 1, 0 and _1
*0
0 1 is positive, 0 is zero and
_1 means
negative
*_6
*N
0 0 0 0 1 0 0 0 0
0 0 0 1 0 1 0 0 0
0 0 1 0 0 0 1 0 0
0 1 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 1 0
0 0 1 0 0 0 1 0 0
0 0 0 1 0 1 0 0 0
0 0 0 0 1 0 0 0 0
GRB viewmat *N
A square
Maybe you could paste it back together in word.
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