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4.2 Written Algorithms For Whole-Number Operations

4.2 Written Algorithms For Whole-Number Operations. Algorithms for Multiplying Whole-Numbers. An Overview of the Topics . Define what an algorithm is. Discuss the importance of place value and distributivity in whole number operations.

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4.2 Written Algorithms For Whole-Number Operations

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  1. 4.2 Written Algorithms For Whole-Number Operations Algorithms for Multiplying Whole-Numbers

  2. An Overview of the Topics • Define what an algorithm is. • Discuss the importance of place value and distributivity in whole number operations. • Explain the main algorithms for multiplying whole-numbers. • Explain the differences between the various algorithms. • View a problem a student has with using a multiplicative algorithm. • Practice using these algorithms through class activities. • Handout out worksheets and handouts for you to refer back on. • Discuss your questions.

  3. What is an algorithm anyway? • An algorithm is simply the step-by-step procedure you use to find an answer. • Here is an analogy. Suppose you need to brush your teeth. What are the steps you take and what order do you take them in? • Do you open the bathroom door? Do you open a drawer to grab your toothbrush? Do you squeeze just a little of the toothpaste on your brush? • What order do you take those steps in? • It is just like a staircase. You take your first step to reach your second step until you have reached the top. At the top, you will find your answer.

  4. Place Value and Distributivity • When you multiply 10 by 16, when do you use place value? When do you use distributivity? • If we separate the 16 into its separate place values, we have the following: • 10 + 6 = 16 • Now we can bring back the original 10 from our problem. • 10(10) + 10(6) = • Then if we distribute the 10, we have the following: • 100 + 60 = 160

  5. Algorithms For Multiplying Whole Numbers • There are 2 main algorithm for multiplying whole numbers: • The standard algorithm. • The lattice algorithm. • The standard algorithm takes the sets of numbers you are multiplying and places one under the other. Then, you multiply each digit in the bottom set by each digit in the top set.

  6. Examples Using The Standard Algorithm • Multiply 2 by 517. If we use the standard algorithm, we get the following. Keep in mind the importance of place value. 1 517 517 x 2x 2 14 is the same as 1034 20 + 1000 1034

  7. The Lattice Algorithm • The lattice algorithm uses lattice figures to multiply whole-numbers. • The basic idea of using the lattice algorithm is finding the products in the intersecting rows and columns. You separate each digit in the answer by placing the ten’s digit in the top left triangle and the ones digit in the bottom left triangle. If there is a hundreds digit in your answer or any other place value, you carry it over to the next column to the left, as if you were adding. Then, you just add the numbers diagonally.

  8. Examples Using The Lattice Algorithm • Multiply 52 by 673. Use the lattice provided to complete this problem. • 6 7 3 Now, add the diagonals. 3 3 1 5 6 3 0 5 5 9 4 1 1 0 2 9 = 9 =34,996 2 4 6 4 9 3 6

  9. The Differences Between the Standard Algorithm and the Lattice Algorithm Standard Algorithm Lattice Algorithm Uses multiples of ten to obtain answer by use of placing zeros. Is quicker when writing down the problem. Uses lattice to place digits in the appropriate place value. Is more time consuming because lattice is not usually available for each problem.

  10. Place Value Is A Problem • For my research, I interviewed a 5th grade student. After completing some worksheets asking him to use the different algorithms, I found that he missed some problems. • The majority of the problems he missed revolved around place value. • He tried the following problem and solved it the following way: His Way: Correct: 3 31 • 462 462 x105x 105 2307 2310 0000 0000 + 4620+ 46200 6927 48510

  11. Now It’s Your Turn Complete problem #3 from your handout using the standard algorithm. Then, as a class we will complete it together. 3 3 25 x 67 175 + 1500 1675 Is the answer A. 1500 B. 4670 C. 0 D. 1675

  12. More Practice Using Algorithms Please use your handout to complete problem number 4. 485 x 398 3880 43650 + 145500 193030 Is the answer: A. 193030 B. 359490 C. 493990 D. 5895

  13. Are There Any Questions?

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