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Everyday MathematicsLattice Multiplication

Lattice MultiplicationEveryday MathematicsLattice multiplication involves:Using basic facts knowledge;Organizing a multiplication problem using a grid based on place value;Using the distributive property; andFollowing several well-defined steps to find the product.

Lattice MultiplicationSolve: 48 36Since 48 36 is a two-digit numbertimes a two-digit number, we firstdraw a 2 2 lattice box.

We carefully draw diagonals fromthe top right corner to the bottomleft corner, drawing the diagonals one box at a time.

We write one factor (48) across thetop. And we write the other factor(36) down the right side.

4 8

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Lattice MultiplicationSolve: 48 36We multiply each digit across the top byeach digit down the side, in whatever order we choose.Lets start with 8 3.8 3 = 24We find the box where the 8 column and the 3 row intersect.Now we record 24 as shown.

4 82

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Everyday Mathematics

Lattice MultiplicationSolve: 48 364 3 = 12We find the box where the 4column and the 3 row intersect.We record the 12 as shown.

4 81

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Lattice MultiplicationSolve: 48 368 6 = 48We find the box where the 8column and the 6 row intersect.We record the 48 as shown.

481

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Lattice MultiplicationSolve: 48 364 6 = 24We find the box where the 4column and the 6 row intersect.We record the 24 as shown.

4812

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Lattice MultiplicationSolve: 48 36The diagonals separate thedigits by place-value columns.The next step is to add along the diagonals.We start with the ones. There are 8 ones.We record 8 ones. 4812

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648Everyday Mathematicsthousandshundredstensones8

Lattice MultiplicationSolve: 48 36We add the tens.4 tens + 4 tens + 4 tens = 12 tensWe need to regroup.12 tens = 10 tens + 2 tensWe record 2 tens and carry 1 hundred (10 tens) to thehundreds diagonal. 4812

324

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648Everyday Mathematicsthousandshundredstensones821

Lattice MultiplicationSolve: 48 36We add the hundreds.2 hundreds2 hundreds2 hundreds+1 hundred7 hundredsWe record 7 hundreds. 4812

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648Everyday Mathematicsthousandshundredstensones8217

Lattice MultiplicationSolve: 48 36We add the thousands.

There is 1 thousand.We record 1 thousand. 4812

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648Everyday Mathematicsthousandshundredstensones8172

Lattice MultiplicationSolve: 48 36The digits in the answer are 1, 7, 2, and 8.Each digit has a specific place value.1 thousand7 hundreds2 tens8 ones4812

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648Everyday Mathematicsthousandshundredstensones8217

Lattice MultiplicationSolve: 48 36

The final answer is 1,728, because 1 thousand + 7 hundreds + 2tens + 8 ones = 1,728.The product of 48 36 is 1,728.Everyday Mathematics

Lattice MultiplicationChildren often find lattice multiplication easier to use thanother methods. It is actually simple. And the lattice helpschildren organize their work. If children know their multiplication facts and can add single-digit numbers, they can use lattice multiplication successfully.Everyday Mathematics