Algorithm Workshop

A Quote from a California Legislator All you have to do in mathematics is add, subtract, multiply and divide. Do you agree or disagree with this statement? Please discuss this at your tables. Each table must come to a consensus and tell how the discussion lead them to make a common statement. Pick and choose speakers from selected tables.

Math Message: List 5 ways you use computation in your daily life (adding, subtracting, multiplying and dividing). Do not include ways you do this with children, but rather how computation is part of your daily activities. Each table comes up with a list of five ways computation is used. All tables have a representative stand and if all ideas are shared on their list them they can sit, but must continue to stand until all thing on the list are shared. Move to next slide while the tables are working.

The essence of mathematics is not to make simple things complicated, but to make complicated things simple. S. Grudder

Famous Quote One can flatly state that if students do not feel comfortable with the mathematical reasoning used to justify the standard algorithm for whole numbers, then their chances for success in Algebra are exceedingly small. Hung-Hsi-Wu

Algorithm Development What is an algorithm? Think-Pair-Share An algorithm is a well defined procedure or set of rules used to solve a problem. Algorithms are used in everyday life. A recipe, for example, is an algorithm.

Algorithm Development 45 + 21 = More or Less than 100?

Algorithm Development Discuss how you solved the problem… Did any of you use estimation? How about rounding? Did you use the traditional American Algorithm? Did someone use some other way?

48 + 799 What was your thinking? 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 48 + 799 = 47 + 1 + 799 = 47 + 800 = 847 What was your thinking?

Algorithm Development 43 * 26 More or Less than 1000?

Algorithm Development Discuss how you solved the problem… Did any of you use estimation? How about rounding? Did you use the traditional American Algorithm? Did someone use some other way?

Algorithm Development Find the EXACT answer to these problems using mental math strategies (NOT PENCIL and PAPER algorithms). Then record how you solved the problem. You may use words, numbers, or symbols to describe your solution strategy. Participants will write down their answers and how they solved them.

Algorithm Development 1004 – 97 365 + 399 + 148 68 * 5 196 / 7 Go over solution strategies that teachers used.

Focus Algorithms Why are there focus algorithms? These algorithms were selected for their mathematical “payoff” – they are powerful, relatively efficient, and they are easy to understand and learn.

Click on the algorithm you’d like to see! Table of Contents Partial Sums 2nd Partial Products 3rd Partial Differences 3rd Trade First 2nd Partial Quotients 4th Lattice Multiplication 3rd Click on the algorithm you’d like to see!

Click to proceed at your own speed! Partial Sums 735 + 246 900 Add the hundreds (700 + 200) 70 Add the tens (30 + 40) +11 Add the ones (5 + 6) 981 Add the partial sums (900 + 70 + 11)

+ 247 500 +13 603 90 Try another one! 356 Add the hundreds (300 + 200) Add the tens (50 + 40) +13 Add the ones (6 + 7) 603 Add the partial sums (500 + 90 + 13)

Click here to go back to the menu. Try one on your own! 429 + 989 Nice work! 1300 100 + 18 1418 Click here to go back to the menu.

Click to proceed at your own speed! Partial Products Click to proceed at your own speed! 5 6 × 8 2 4,000 50 X 80 100 50 X 2 480 6 X 80 12 + 6 X 2 Add the partial products 4,592

How flexible is your thinking How flexible is your thinking? Did you notice that we chose to multiply in a different order this time? 5 2 × 7 6 Try another one! 3,500 70 X 50 140 70 X 2 300 6 X 50 12 + 6 X 2 Add the partial products 3,952

A Geometrical Representation of Partial Products (Area Model) 5 2 × 4 6 50 2 2,000 300 40 6 2000 80 80 12 300 12 2,392 Click here to go back to the menu.

A Geometrical Representation of Partial Products (Area Model) 4 5 × 6 40 5 1,600 240 40 6 1600 200 200 30 240 30 2,070 Click here to go back to the menu.

Trade-First Students complete all regrouping before doing the subtraction. This can be done from left to right or right to left. In this case, we need to regroup a 100 into 10 tens. The 7 hundreds is now 6 hundreds and the 2 tens is now 12 tens. 11 13 6 12 7 2 3 4 5 9 Next, we need to regroup a 10 into 10 ones. The 12 tens is now 11 tens and the 3 ones is now 13 ones. 2 6 4 Now, we complete the subtraction. We have 6 hundreds minus 4 hundreds, 11 tens minus 5 tens, and 13 ones minus 9 ones.

Click here to go back to the menu. Try a couple more! 9 12 13 16 7 10 8 14 8 0 2 9 4 6 2 7 4 5 6 8 5 2 8 3 7 8 Click here to go back to the menu.

– 2 4 5 5 0 0 4 9 1 Partial Differences Subtract the hundreds 7 3 6 – 2 4 5 5 0 0 Subtract the hundreds (700 – 200) 1 0 Subtract the tens (30 – 40) 1 Subtract the ones (6 – 5) 4 9 1 Add the partial differences (500 + (-10) + 1)

Click here to go back to the menu. Try another one! 4 1 2 – 3 3 5 1 0 0 Subtract the hundreds (400 – 300) 2 0 Subtract the tens (10 – 30) 3 Subtract the ones (2 – 5) 7 7 Add the partial differences (100 + (-20) + (-3)) Click here to go back to the menu.

Students begin by choosing partial quotients that they recognize! I know 10 x 12 will work… Partial Quotients Click to proceed at your own speed! 2 3 1 1 2 1 2 0 1 0 1 1 1 Add the partial quotients, and record the quotient along with the remainder. 6 0 5 Students begin by choosing partial quotients that they recognize! 5 1 4 8 4 3 1 9

8 5 R6 another one! Try 3 2 2 7 2 6 1 6 0 0 5 0 1 1 2 6 Compare the partial quotients used here to the ones that you chose! 8 0 0 2 5 3 2 6 3 2 0 1 0 6 8 5 Click here to go back to the menu.

Compare to partial products! Click to proceed at your own speed! Lattice Multiplication 5 3 5 3 × 7 2 2 1 3 5 5 × 7 3 × 7 7 2 3500 100 210 6 3816 + 3 Compare to partial products! 1 6 5 × 2 3 × 2 8 Add the numbers on the diagonals. 1 6

Click here to go back to the menu. Try Another One! 1 6 1 6 × 2 3 1 2 2 2 3 200 30 120 18 368 + 3 1 8 3 6 8 Click here to go back to the menu.

Famous Quotes Do not worry about your problems with Mathematics, I assure you mine are greater. It’s not that I am so smart, it’s just that I stay with the problems longer. Albert Einstein

Remember: What we know is not much. What we do not know is immense. Pierre Simon La Place Thanks for coming!