1. ISD 881 Computation Algorithms Math Trailblazers

2. Computation Algorithms in Math Trailblazers Instead of learning a prescribed (and limited) set of algorithms, Math Trailblazers encourages students to be flexible in their thinking about numbers and arithmetic. Students begin to realize that problems can be solved in more than one way. They also improve their understanding of place value and sharpen their estimation and mental- computation skills. The following slides are offered as an extension to the parent communication from your child’s teacher. We encourage you to value the thinking that is evident when children use such algorithms—there really is more than one way to solve a problem!

3. Before selecting an algorithm, consider how you would solve the following problem. 48 + 799 We are trying to develop flexible thinkers who recognize that this problem can be readily computed in their heads! One way to approach it is to notice that 48 can be renamed as 1 + 47 and then What was your thinking? 48 + 799 = 47 + 1 + 799 = 47 + 800 = 847

4. An algorithm consists of a precisely specified sequence of steps that will lead to a complete solution for a certain class of problems. Important Qualities of Algorithms Accuracy –Does it always lead to a right answer if you do it right? Generality –For what kinds of numbers does this work? (The larger the set of numbers the better.) Efficiency –How quick is it? Do students persist? Ease of correct use –Does it minimize errors? Transparency (versus opacity) –Can you SEE the mathematical ideas behind the algorithm? Hyman Bass. “Computational Fluency, Algorithms, and Mathematical Proficiency: One Mathematician’s Perspective.” Teaching Children Mathematics. February, 2003.

5. Table of Contents All Partials Multiplying Forgiving Division Method Click on the algorithm you’d like to see!

6. 56 × 82 4,000 100 480 12 + 4,592 50 X 80 50 X 2 6 X 80 6 X 2 Add the partial products Click to proceed at your own speed!

7. 52 ×76 3,500 140 300 12 + 70 X 50 70 X 2 6 X 50 6 X 2 3,952 Add the partial products How flexible is your thinking? Did you notice that we chose to multiply in a different order this time?

8. 502 40 6 200080 12 300 52 × 46 2,000 300 80 12 2,392 Click here to go back to the menu. A Geometrical Representation of All Partials Multiplication (Area Model)

9. 2 4 5 0 3 5 3 R 3 3 5 03 5 0 2 1 3 7 43 7 4 7 Click to proceed at your own speed! 3 5 3 Students begin by choosing partial quotients that they recognize and can do quickly in their head! Add the partial quotients, and record the quotient along with the remainder. I know 7 x 50 will work…

10. Click here to go back to the menu. 4 2 9 8 80 0 7 07 0 87 4 R 2 2 8 02 8 0 3 4 9 83 4 9 8 4 1 8 1 6 2 87 4 Compare the partial quotients used here to the ones that you chose! 3 2 0 0 3 2 0 0