The Lattice Form of Multiplication dates back to the 1200s or
before in Europe. It gets its name from the fact that to do the
multiplication you fill in a grid which resembles a lattice one
might find ivy growing on. Let me see if I can explain it with an
example. Let's multiply 469 x 37.

First write the 469 across the top, and the 37 down the right side of
a 3x2 rectangle. (It's 3x2 because the factors have three and two
digits respectively.)

Now fill in the lattice by multiplying the two digits found at
the head of the column and to the right of the row. When the partial
product is two digits, the first (10's) digit goes above the diagonal
and the second (1's) digit goes on the lower right of the diagonal.
If the partial product is only one digit, a zero is placed in the
triangle above the diagonal in the square.

At this point, we have the multiplication done. Now we add along the
diagonals beginning in the lower right to get the final product. Any
"carries" when adding are illustrated outside the rectangle.

Multiplication really takes three steps: multiply, carry, add.
The method we typically use does the multiply and carry steps
together. The lattice method does all three steps separately, so it's
really easier! Centuries ago, the Germans had a method for doing all
three steps at once. That method takes a lot of concentration!

Hope you enjoyed seeing this. I really think it's fun.
Let us know if you have any more questions!

(from the website mathforum.org)
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Solve this Krypto Hand

8,5,5,3,7

And KRYPTO 2

Krypto Rules

The game of Krypto is played with a deck of 52 cards: three each of the numbers 1 to 10, two each

of the numbers 11 to 17, and one each of the numbers 18 to 25.

Sets of Krypto cards — including Primary Krypto (only numbers from 1 to 10) and the Fraction

Supplement — can be purchased from MPH Games, Inc., P.O. Box 1125, Fairfield, CT 06432.

They can also be ordered from Amazon and other online retailers.

Playing the Game

In the center of the table, deal five playing cards, number side up. Then turn over a sixth card which

is the Target Card. Each player will add, subtract, multiply, or divide using each of the numbers on

the five playing cards. Fractions, decimals, negative numbers, roots, and exponents are not

permitted. Each card must be used once and only once to obtain a final solution equal to the number

on the Target Card.

Example 1

Playing Cards: 2, 1, 2, 2, 3 Target Card: 20

2 + 1

3 × 3

9 × 2

18 + 2

Notice that the numbers on all five playing cards were used once and only once to equal the target

number.

Example 2

Playing Cards: 1, 3, 7, 1, 8 Target Card: 1

3 – 1

2 + 7

9 ÷ 1

9 – 8

Example 3

Playing Cards: 24, 22, 23, 20, 21 Target Card: 1

22 + 24

46 ÷ 23

2 + 20

=22 – 21
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ROUNDING WITH NUMBERLINES

Use a number line to show how to round these numbers to the value with the BOLD digit.

Be sure that you show the BENCHMARK NUMBERS as well as the steps between in even intervals. Make sure you show EXACTLY where your given number would rest on the number line and then draw an arrow to show to which benchmark number you would round it.

A) 653 B) 653

C) 1,975 D) 1.975

E) 9.65 F) 31.652

==
==

Mental Math: Using the properties of addition

Commutative Property

13+9+7=13+7+9

Accociative Property

26+9+11=26+(9+11)

Identity

49+21=50+20

For your assignment, change the probelms I have given you using the properties of addition to make them easier to solve. Make sure to SHOW your work, because I cannot see inside your head.

A) 67+4+6
B) 14+83+6
C) 27+5+3+15
D) 77+120+3
E) 99+51
F) 687+293

## Lattice Method of Multiplication

The Lattice Form of Multiplication dates back to the 1200s orbefore in Europe. It gets its name from the fact that to do the

multiplication you fill in a grid which resembles a lattice one

might find ivy growing on. Let me see if I can explain it with an

example. Let's multiply 469 x 37.

First write the 469 across the top, and the 37 down the right side of

a 3x2 rectangle. (It's 3x2 because the factors have three and two

digits respectively.)

Now fill in the lattice by multiplying the two digits found at

the head of the column and to the right of the row. When the partial

product is two digits, the first (10's) digit goes above the diagonal

and the second (1's) digit goes on the lower right of the diagonal.

If the partial product is only one digit, a zero is placed in the

triangle above the diagonal in the square.

At this point, we have the multiplication done. Now we add along the

diagonals beginning in the lower right to get the final product. Any

"carries" when adding are illustrated outside the rectangle.

Multiplication really takes three steps: multiply, carry, add.

The method we typically use does the multiply and carry steps

together. The lattice method does all three steps separately, so it's

really easier! Centuries ago, the Germans had a method for doing all

three steps at once. That method takes a lot of concentration!

Hope you enjoyed seeing this. I really think it's fun.

Let us know if you have any more questions!

(from the website mathforum.org)

=

=

## Solve this Krypto Hand

## 8,5,5,3,7

And KRYPTO 2## Krypto Rules

## The game of Krypto is played with a deck of 52 cards: three each of the numbers 1 to 10, two each

## of the numbers 11 to 17, and one each of the numbers 18 to 25.

## Sets of Krypto cards — including Primary Krypto (only numbers from 1 to 10) and the Fraction

## Supplement — can be purchased from MPH Games, Inc., P.O. Box 1125, Fairfield, CT 06432.

## They can also be ordered from Amazon and other online retailers.

## Playing the Game

## In the center of the table, deal five playing cards, number side up. Then turn over a sixth card which

## is the Target Card. Each player will add, subtract, multiply, or divide using each of the numbers on

## the five playing cards. Fractions, decimals, negative numbers, roots, and exponents are not

## permitted. Each card must be used once and only once to obtain a final solution equal to the number

## on the Target Card.

## Example 1

## Playing Cards: 2, 1, 2, 2, 3 Target Card:

20## 2 + 1

## 3 × 3

## 9 × 2

## 18 + 2

## Notice that the numbers on all five playing cards were used once and only once to equal the target

## number.

## Example 2

## Playing Cards: 1, 3, 7, 1, 8 Target Card:

1## 3 – 1

## 2 + 7

## 9 ÷ 1

## 9 – 8

## Example 3

## Playing Cards: 24, 22, 23, 20, 21 Target Card:

1## 22 + 24

## 46 ÷ 23

## 2 + 20

=22 – 21=

=

## ROUNDING WITH NUMBERLINES

## Use a number line to show how to round these numbers to the value with the

BOLDdigit.## Example: 7

867## 7867 ----------------------------->

7800----------|----------|----------|----------|----------|----------|-------x---|----------|----------|----------79007810 7820 7830 7840 7850 7860 7870 7880 7890## Be sure that you show the

as well as the steps between in even intervals. Make sure you show EXACTLY where your given number would rest on the number line and then draw an arrow to show to which benchmark number you would round it.BENCHMARK NUMBERS## A) 6

53 B)653## C) 1,

975 D) 1.975## E) 9.

==65 F) 31.652==

Mental Math: Using the properties of additionCommutative Property13+9+7=13+7+9Accociative Property26+9+11=26+(9+11)Identity

For your assignment, change the probelms I have given you using the properties of addition to make them easier to solve. Make sure to SHOW your work, because I cannot see inside your head.49+21=50+20A) 67+4+6

B) 14+83+6

C) 27+5+3+15

D) 77+120+3

E) 99+51

F) 687+293

1= =22 =

2 =

46 =

1=9 =

9 =

2 =

20=18 =

9 =

3 =