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www.kidsalgebra.com
Welcome to this Lesson on how to do
Multiplication the “Lattice” way.
02
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You need to check with your Teacher if they want
you to learn the “Standard” method of
multiplication or the “Lattice” method.03
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You’re free to check out both methods, but in this
lesson you’ll learn the “Lattice” method of
multiplication.
04
It’s called the “Lattice” method because the layout you’ll use looks like a lattice.
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1 2 3 4 5 6 7 8 9 10 11 122 4 6 8 10 12 14 16 18 20 22 243 6 9 12 15 18 21 24 27 30 33 364 8 12 16 20 24 28 32 36 40 44 485 10 15 20 25 30 35 40 45 50 55 606 12 18 24 30 36 42 48 54 60 66 727 14 21 28 35 42 49 56 63 70 77 848 16 24 32 40 48 56 64 72 80 88 969 18 27 36 45 54 63 72 81 90 99 10810 20 30 40 50 60 70 80 90 100 110 12011 22 33 44 55 66 77 88 99 110 121 13212 24 36 48 60 72 84 96 108 120 132 144
By now you should know all of your Times Tables.
So you’ll know answers like 3 x 8 = 24
without counting.
x
=
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But you also need to know how to multiply numbers bigger than 12.
That’s because you need to be able to solve problems like this one …
Farmer Brown has 23 tomato gardens on his farm.
Each garden has 16 rows of 64 tomato plants.
How many tomato plants does Farmer Brown have?
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To answer this question you need to know how to multiply numbers that
are bigger than 12. Like 16 x 64.
But the biggest single number you’ll ever need to multiply by is 9, so you really only need to remember up to
your 10 times tables.
That’s already made your job of learning multiplication a lot easier!
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So here’s the problem that we’ll solve to show you how to do the
“Lattice” method of multiplication.
Farmer Brown has 23 tomato gardens on his farm.
Each garden has 16 rows of 64 tomato plants.
How many tomato plants does Farmer Brown have?
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To solve problems like this, you have to decide on two things:
(1) What Answer are you looking for.&
(2) What Steps do you need to take to find the Answer.
10
The Answer you want is:“How many tomato plants does
Farmer Brown have?”
Or more simply, the
“Total number of tomato plants.”
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The 1st Step is to calculate how many Tomato plants there are in each
Garden. Each Garden has this many tomato
plants: 16 rows of 64 Tomato plants.
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9 10 11 12 13 14 15 16
1 2 3 4 5 6 7 8
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16 rows
64 per rowThis is what each Tomato garden looks like
12
The 2nd Step is to calculate …How many tomato plants Farmer
Brown has in his 23 tomato gardens.
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12345
678910
1112131415
1617181920
212223
This is what all of his 23 tomato gardens look like from high above.13
You can draw a picture of the two Steps and the Answer like this:
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1st Step 2nd Step Answer
14
So here are the two Steps to get to the Answer.
1st Step: Number of tomato plants in each Garden.
2nd Step: Number of tomato plants in all 23 Gardens.
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1st Step:
16 x 64
2nd Step:Answer from Step 1 x 23
Answer: Total Plants
15
To multiply using the “Lattice” way, you write
16 x 64 = like this.16 x 64
1 66
4
First number across the top.
Second number across
the side.
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You’ll write the number with the most digits across the top. Here both numbers have 2 digits so you can put either number at the
top.16 x 64
1 66
4
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But first let me explain how “Lattice” multiplication works.
You may have seen “Tens” and “Singles” written in columns.
But the “Lattice” way you write them down
like this.www.kidsalgebra.com
T S1 6
SinglesTens
Tens Column.
Singles Column.
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SinglesTens
2 x 8
Here’s the “Lattice” way of doing
multiplication.
You’ll multiply by writing your numbers
like this.2
8
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SinglesTens
2 x 8 = 1 6
You already know this from your 2 Times
Table.
So using the “Lattice” way you fill out the
lattice like this.
61
2
8The 1 in 16 is a “Ten”. Put the 1
in the “Tens” lattice.
The 6 in 16 is six “Singles”. Put the 6 in the “Singles” lattice.
20
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2 x 4 = 08
Let’s look at what you do with a zero in 2 x 4 = 8.
802
4
The “Ten” is 0.
21
Let’s work out the answer to the 1st Step using the “Lattice Method”.
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1st Step:16 x 64
2nd Step:Answer from Step 1 x 23
Answer: Total Plants
22
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First you need to make a lattice that has two columns for the 2 digits in the 1st
number and two rows for 2 digits in the 2nd number.16 x 64 =
1 66
4
First number across the top.
Second number across
the side.23
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Start with the Top-Left Block.
1 66
4
The Top-Left Block.
24
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Multiply the 1 that’s above the top-left block’s column by the 6 that’s in the
right of the top-left block’s row.1 x 6
1 66
4
25
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From your 1 Times Table you know that
1 x 6 = 6.1 x 6 = 6
1 66
4
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Write the 6 from 1 x 6 = 6 into the “Singles” lattice in the block.
1 x 6 = 6
1 66
4
6
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There are 0 “Tens” in the answer 1 x 6 = 6, so you write a 0 into the “Tens”
lattice in the block.1 x 6 = 06
1 66
4
60
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Moving to the block to the right, multiply the 6 that’s above the block’s column by the 6 that’s to the right of
the block’s row.6 x 6
1 66
4
60
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From your 6 Times Table you know that
6 x 6 = 36.6 x 6 = 36
1 66
4
60
30
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Write the 6 from 6 x 6 = 36 into the “Singles” lattice in the block.
6 x 6 = 36
1 66
4660
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Write the 3 from 6 x 6 = 36 into the “Tens” lattice in the block.
6 x 6 = 36
1 66
46
360
32
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Move to the next block down and to the left.
1 66
46
360
33
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Multiply 1 x 4 = 4. There are no “Tens” so put 0from 1 x 4 = 04 in
the “Tens” lattice. Put the 4 into the “Singles”
lattice.
1 66
46
360
0
1 x 4 = 04
434
Move to the next block to the right.
1 66
46
360
04
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Multiply 6 x 4 = 24 and put the 2 in the “Tens” lattice and the 4 into
the “Singles” lattice.
1 66
46
360
0
6 x 4 = 24
42 4
36
Now add “Diagonal Stripes”.
1 66
46
36
0
04
24
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Start at the bottom-right and move left then up.
1 66
4
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63
60
04
24
Start with the 1st diagonal to the right then move to the next diagonal to the
left.38
There is only a 4 in that diagonal.So there’s nothing to add to the 4.
Write the 4 along the diagonal.1 6
6
4
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63
60
04
24
4 The 4 is a “Single”.
39
Move left to the next diagonal and add up all the numbers in
that diagonal.1 6
6
4
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63
60
04
24
4 + 2 + 6 = 12 4The 12 is 12
“Tens”.40
You keep the 2 “Tens” and “Carry” the 1 “Hundred”.
1 66
4
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63
60
04
24
12 41
Carry the 1 “Hundred”.
41
Next add 1 + 0 + 6 + 3 = 10 in the next diagonal.
1 66
4
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63
60
04
24
2 41
Remember to also add the 1 “Hundred”
that you Carried.42
After adding the numbers to make 10, you should cross off the 1 “Hundred” that you Carried so you know not to add it again by
accident.1 66
4
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63
60
04
24
2 41
43
Leave the 0 in the “Hundreds” diagonal and carry the 1
“Thousand”.1 6
6
4
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63
60
04
24
2 4110
Carry the 1 “Thousand”.
1
44
Move up on the left side to the last diagonal. There is a 0 + the 1
“Thousand” that you carried.1 6
6
4
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63
60
04
24
2 410
1
45
Write down the answer to 1 + 0 = 1
and cross off the 1 “Thousand” that you carried.1 6
6
4
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63
60
04
24
2 410
1 11 + 0 = 1
46
Next start from the top left and move down and to the right.
Write down the answer.1 6
6
4
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63
60
04
24
2 4
10
1 1
Start here.
1,02447
The number of tomato plants in each Garden = 1,024. Now you can do the 2nd Step: Number of tomato plants in
all 23 Gardens.
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1st Step:
16 x 64 =
1,024
2nd Step:1,024 x 23
Answer: Total Plants
48
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Put the number with the most digits at the top. Make a lattice that has one
column for each digit in the top number and a row for each digit in the other
number.1024 x 23
1 0 2 4
2
3
Biggest number across
the top.
Two digits across the
side.49
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Start with the Top-Left Block.
The Top-Left Block. 1 0 2 4
2
3
50
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Multiply the 1 that’s above the top-left block’s column by the 2 that’s in the
right of the top-left block’s row.
1 x 2 = 2
1 0 2 4
2
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Put the 2 “Singles” in the “Singles” lattice and because there are no
“Tens”, put a 0 into the “Tens” lattice.
1 x 2 = 2
1 0 2 4
2
00
0 in the “Tens” lattice.
2 in the “Singles”
lattice.
2
3
52
2
3www.kidsalgebra.com
Move right one block. This one’s easy, 0 x 2 = 0. There are also 0 “Tens”
So 0 goes into both the “Singles” the “Tens”.
0 x 2 = 0
1 0 2 4
2
00
0 in the “Tens” lattice.
0 in the “Singles”
lattice.
00
53
2
3www.kidsalgebra.com
Move right one block.2 x 2 = 4. There are 0 “Tens” so the 4 goes into the “Singles” and 0 into the
“Tens”.2 x 2 = 4
1 0 2 4
2
00
00
0 in the “Tens” lattice.
4 in the “Singles”
lattice.
40
54
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Move right one block.4 x 2 = 8. There are 0 “Tens” so the 8 goes into the “Singles” and 0 into the
“Tens”.4 x 2 = 8
1 0 2 4
2
00
00
0 in the “Tens” lattice.
8 in the “Singles”
lattice.
40 80 2
355
2
3www.kidsalgebra.com
Move down one row starting with the block
on the left. 1 x 3 = 3. The 3 goes into the “Singles” and a 0 goes into the “Tens”.
1 x 3 = 3
1 0 2 4
2000
3 in the “Singles”
lattice.
40 80
30
0
0 in the “Tens” lattice.
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2
3www.kidsalgebra.com
0 x 3 = 0
1 0 2 4
2000
0 in the “Singles”
lattice.
40 80
30
0
0 in the “Tens” lattice.
Move right one block. This one’s easy, 0 x 3 = 0. There are also 0 “Tens”
So 0 goes into both the “Singles” the “Tens”.
0057
2
3www.kidsalgebra.com
2 x 3 = 6
1 0 2 4
2000
6 in the “Singles”
lattice.
40 80
30
0
0 in the “Tens” lattice.
00
Move right one block.2 x 3 = 6. There are 0 “Tens” so the 6 goes into the “Singles” and 0 into the
“Tens”.
60
58
2
3www.kidsalgebra.com
4 x 3 = 12
1 0 2 4
2000
2 in the “Singles”
lattice.
40 80
3000 60
21
Move right one block.4 x 3 = 12. The 2 goes into the “Singles”
and the 1 “Ten” goes into the “Tens”.
1 in the “Tens” lattice.
59
Now add “Diagonal Stripes”.
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1 0 2 42
32
00
04
08
0
30
00
60
21
60
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There’s only one number, 2 the 1st
diagonal.
There is only a 2 in the 1st diagonal.
So there’s nothing to add to the 2. 1 0 2 4
2
32
00
04
08
0
30
00
60
21
61
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Write the 2 at the end of the diagonal.
1 0 2 42
32
00
04
08
0
30
00
60
21
2
62
Move to the next diagonal to the left and add 6 + 1 + 8 = 15
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1 0 2 42
32
00
04
08
0
30
00
60
21
2
63
Write the 5 at the end of the diagonal and carry the 1 in 6 + 1 +
8 = 15
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1 0 2 42
32
00
04
08
0
30
00
60
21
51 2
64
Move to the next diagonal to the left.
Add 1 + 0 + 0 + 4 + 0 = 5
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1 0 2 42
32
00
04
08
0
30
00
60
21
51 2
65
Cross out the 1 that you “Carried” and write down the 5 in it’s
diagonal.
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1 0 2 42
32
00
04
08
0
30
00
60
21
51 25
66
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1 0 2 42
32
00
04
08
0
30
00
60
21
51 25
Move to the next diagonal to the left.
Add 3 + 0 + 0 + 0 = 3
67
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1 0 2 42
32
00
04
08
0
30
00
60
21
51 25
Write the 3 in it’s diagonal.
3
68
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1 0 2 42
32
00
04
08
0
30
00
60
21
51 25
Move to the next diagonal.Add 0 + 2 + 0 = 2 and
write the 2 in it’s diagonal.
3
2
69
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1 0 2 42
32
00
04
08
0
30
00
60
21
0
51 25
The last diagonal has just one 0.So just write the 0 in it’s diagonal.
3
2
70
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1 0 2 42
32
00
04
08
0
30
00
60
21
0
51 253
2
Next start from the top left and move down and to the right. Write down the answer. Drop off the 0 at
the front.
23,55271
The number of tomato plants in each Garden = 1,024 and the number of tomato
plants in all 23 Gardens = 23,552. That’s the answer to the problem!
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1st Step:
16 x 64 =
1,024
2nd Step:1,024 x 23= 23,552
Answer: Total Plants
=23,552
72
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You can get a Wall Hanging at
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to follow and practice your
multiplication.
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