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Everyday Mathematics Alternative Algorithms. Partial Sums An Addition Algorithm.

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Presentation on theme: "Everyday Mathematics Alternative Algorithms. Partial Sums An Addition Algorithm."— Presentation transcript:

1 Everyday Mathematics Alternative Algorithms

2 Partial Sums An Addition Algorithm

3 268 + 483 600 Add the hundreds ( 200 + 400) 140 Add the tens (60 +80) Add the ones (8 + 3) Add the partial sums (600 + 140 + 11) + 11 751

4 785 + 641 1300 Add the hundreds ( 700 + 600) 120 Add the tens (80 +40) Add the ones (5 + 1) Add the partial sums (1300 + 120 + 6) + 6 1426

5 329+ 989 1200 100 + 18 1318

6 An alternative subtraction algorithm

7 In order to subtract, the top number must be larger than the bottom number 9 3 2 - 3 5 6 To make the top number in the ones column larger than the bottom number, borrow 1 ten. The top number become 12 and the top number in the tens column becomes 2. 12 2 To make the top number in the tens column larger than the bottom number, borrow 1 hundred. The top number in the tens column becomes 12 and the top number in the hundreds column becomes 8. 12 8 Now subtract column by column in any order 5 6 7

8 Lets try another one together 7 2 5 - 4 9 8 15 To make the top number in the ones column larger than the bottom number, borrow 1 ten. The top number become 15 and the top number in the tens column becomes 1. 15 1 To make the top number in the tens column larger than the bottom number, borrow 1 hundred. The top number in the tens column becomes 11 and the top number in the hundreds column becomes 6. 11 6 Now subtract column by column in any order 2 7 2

9 Now, do this one on your own. 9 4 2 - 2 8 7 12 3 13 8 6 5 5

10 Last one! This one is tricky! 7 0 3 - 4 6 9 13 9 6 2 4 3 10

11 Partial Products Algorithm for Multiplication

12 Calculate 50 X 60 67 x 53 Calculate 50 X 7 3,000 350 180 21 Calculate 3 X 60 Calculate 3 X 7 + Add the results 3,551 To find 67 x 53, think of 67 as 60 + 7 and 53 as 50 + 3. Then multiply each part of one sum by each part of the other, and add the results

13 Calculate 10 X 20 14 x 23 Calculate 20 X 4 200 80 30 12 Calculate 3 X 10 Calculate 3 X 4 + Add the results 322 Lets try another one.

14 Calculate 30 X 70 38 x 79 Calculate 70 X 8 2,100 560 270 72 Calculate 9 X 30 Calculate 9 X 8 + Add the results Do this one on your own. 3002 Lets see if youre right.

15 Lattice Method of Multiplication Another Multiplication Algorithm

16 Add the numbers along each diagonal. The lattice method of multiplication has been used for hundreds of years. It is very easy to use if you know basic multiplication facts. It becomes a favorite algorithm of students learning double digit multiplication Draw a box with squares and diagonals, this is called a lattice. Write 45 above the lattice. Write 3 on the right side of the lattice. 45 3 Multiply 3 x 5. Write the number as shown. Multiply 3 x 4. Write the number as shown. 1 35 45 x 3 = 135 45 x 3 1 2 1 5

17 Lets Try Another One! Multiply 7 x 89. 9 3 7 5 6 6 6 8 32 1 7 x 89 = 623

18 2-Digit by 2-Digit Multiplication 34 x 26 34 2 6 0 8 0 6 1 8 2 4 48 1 8 0 34 x 26 = 884

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20 Partial Quotients A Division Algorithm

21 The Partial Quotients Algorithm uses a series of at least, but less than estimates of how many bs in a. You might begin with multiples of 10 – theyre easiest. 12 158 There are at least ten 12s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) 10 – 1st guess - 120 38 Subtract There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess 3 – 2 nd guess - 36 2 13 Sum of guesses Subtract Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 )

22 Lets try another one 36 7,891 100 – 1st guess - 3,600 4,291 Subtract 100 – 2 nd guess - 3,600 7 219 R7 Sum of guesses Subtract 691 10 – 3 rd guess - 360 331 9 – 4th guess - 324

23 Now do this one on your own. 43 8,572 100 – 1st guess - 4,300 4,272 Subtract 90 – 2 nd guess -3,870 15 199 R 15 Sum of guesses Subtract 402 7 – 3 rd guess - 301 101 2 – 4th guess - 86

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