1. Presented By Tracy Flinchbaugh and Lisa Marsteller South Eastern School District Ideas for transitions modified from http://www.swsd.k12.pa.us/baresvle/MathMaterials/alternat_algor.htm

2. Partial Sums An Addition Algorithm

3. 658+ 487 1000 Add the hundreds ( 600 + 400) Add the tens (50 +80) 130 Add the ones (8 + 7) Add the partial sums (1000 + 130 + 15) + 15 1145 Partial Sums

4. 572+ 843 1300 Add the hundreds ( 500 + 800) Add the tens (70 +40) 110 Add the ones (2 + 3) Add the partial sums (1300 + 110 + 5) + 5 1415 You try it!

5. A Subtraction Algorithm

6. 8 1 2 - 5 5 7 Starting with the ones column, ask yourself, can I do 2 minus 7? No, so the 2 goes next door and borrows a ten. We change the 1 to a 0, and our 2 in the ones column becomes 12. 12 0 Next, go to the tens column, and ask yourself, can I subtract 5 from 0? No, so the 0 goes next door and borrows a hundred. The 8 becomes a 7, and the 0 becomes a 10. 10 7 Now subtract right to left. 2 5 5

7. You try it! 9 2 5 - 2 9 9 Starting with the ones column, ask yourself, can I do 5 minus 9? No, so the 5 goes next door and borrows a ten. We change the 2 to a 1, and our 5 in the ones column becomes 15. 15 1 Next, go to the tens column, and ask yourself, can I subtract 9 from 1? No, so the 1 goes next door and borrows a hundred. The 9 becomes an 8, and the 1 becomes an 11. 11 8 Now subtract right to left. 6 6 2

8. Lattice Multiplication A Multiplication Algorithm

9. To solve 56 * 43, write the problem around the grid. 56 4 3 Multiply each of the numbers around the grid writing one number on each side of the diagonal line. Add regrouping (carrying) Add each diagonal column, regrouping (carrying) when necessary. Rewrite the answer with the problem. 5 * 4 = 20 6 * 4 = 24 5 * 3 = 15 6 * 3 = 18 2 0 2 4 8 1 5 1 80 4 2 1 56 * 43 = 2,408 Lattice Multiplication

10. To solve 41 * 38, write the problem around the grid. 41 3 8 Multiply each of the numbers around the grid writing one number on each side of the diagonal line. Add Add each diagonal column, regrouping (carrying) when necessary. Rewrite the answer with the problem. 4 * 3 = 12 1 * 3 = 3 4 * 8 = 32 1 * 8 = 8 1 2 0 3 8 0 2 3 85 5 1 41 * 38 = 1,558 You try it!

11. A Multiplication Algorithm

12. Multiply 80 * 50 86 * 52 Multiply 80 * 2 4,000 160 300 12 Multiply 6 * 50 Multiply 6 * 2 + Add the partial products 4,472 Break down 86 into 80 + 6 and 52 into 50 + 2. Multiply each part of the first number by each part of the second number.

13. Multiply 30 * 20 31 * 27 Multiply 30 * 7 600 210 20 7 Multiply 1 * 20 Multiply 1 * 7 + Add the partial products 837 You try it!

14. Partial Quotients A Division Algorithm

15. The Partial Quotients Algorithm uses basic facts and extended facts that students know. There are multiple ways of getting to the correct answer. 6 158 Ask yourself about how many 6’s are in 158. Are there at least 10? Yes, because 10 [6’s] are 60. Are there 20? Yes, because 20 [6’s] are 120. Record 20 to the right and subtract 120 from 158. 20 - 120 38 Subtract 6 - 36 2 26 R2 Subtract Ask yourself how many 6’s are in 38. Is there at least 1? 2? 3? 4? 5? 6? Yes, because 6 [6’s] are 36. Record 6 to the right and subtract 36 from 38. Can I take anymore 6’s out? No, so I’m finished. Add the numbers on the right, and record the answer with the remainder. +

16. You try it! 12 6,481 300 - 3,600 2,881 200 - 2,400 540 R1 481 40 - 480 1 + Ask yourself about how many 12’s are in 6,481. Are there at least 100? 200? 300? Yes, because 300 [12’s] are 3,600. Record 300 to the right and subtract 3,600 from 6,481. About how many 12’s are in 2,881? Are there at least 100? 200? Yes, because 200 [12’s] are 2,400. Record 200 to the right and subtract 2,400 from 2,881. Can I take anymore 12’s out? No, so I’m finished. Add the numbers on the right, and record the answer with the remainder. About how many 12’s are in 481? Is there at least 10? 20? 30? 40? Yes, because 40 [12’s] are 480. Record 40 to the right and subtract 480 from 481.

17. Math websites www.studyisland.comwww.studyisland.com (PSSA math and reading practice) http://everydaymath.uchicago.eduhttp://everydaymath.uchicago.edu (supports EDM math curriculum) www.mathisfun.comwww.mathisfun.com (timed math facts practice, illustrated math dictionary) http://matti.usu.edu/nlvm/nav/vlibrary.htmlhttp://matti.usu.edu/nlvm/nav/vlibrary.html (great graphics, manipulatives, and enrichment activities) www.aaamath.comwww.aaamath.com (explanation of math skills, interactive practice, challenge games) www.mathfactcafe.com (basic facts practice using www.mathfactcafe.com flashcards, printable worksheets for time and money) http://www.mathleague.com/ (challenging mathematics and math contests for 4th grade and up) http://www.mathleague.com/ http://www.coolmath4kids.com/http://www.coolmath4kids.com/ (an amusement park of math) http://arcytech.org/java/ (tutorial for specific math skills - great graphics) http://arcytech.org/java/

18. Top-It (addition, subtraction, multiplication, and division) Multiplication Baseball Multiplication Wrestling War Games (addition, subtraction, multiplication) Subtraction Target Practice http://everydaymath.uchicago.edu

19. MATH TIPS FOR PARENTS Ideas modified from http://athomewithmath.terc.edu/math_kits.html

20. Number of the day … Find one way to make the “Number of the day”. 38 + 27 – 24 = 41 1 quarter, 1 dime, 1 nickel and 1 penny is $0.41 Find more ways to make the number 100 - (3 x 25) + 16 = 41 82 x 0.5 = 41 Take time to find 11 in your day. The time is 41 minutes after 9:00. How long does it take to drive 41 miles? If someone is born in 1941, how old would they be?

21. Food for thought… How many pizzas do we need for our party? How many guests will we have? How many slices per person? How many batches of cookies will we need to bake for friends and family? How many people? How many cookies per person? How many cookies in a batch? Ingredients and amount needed?

22. How much longer? Talk through the problem. “Are we there yet?” “How long until we eat?” Figure out how much longer. Round to a time that’s easier to work with and then adjust, such as round 5:18 to 5:20. Explain solutions.

23. How much do we save? Talk about grocery coupons and store savings. Cut out coupons with your child. Make grocery list for the week. Predict cost and savings. Use a calculator as you shop or estimate in your head. Have your child pay the cashier and count the change. Find out the savings. Check totals on receipt and compare with predictions.

24. Wish list… How much would you get to spend? $20? $50? $100? $300? $1,000? What would you buy? Browse catalogs, internet, or go window shopping. Have your child make a wish list. Estimate the cost, tax, shipping, and totals. Discuss everyone’s choices. Comparison shopping…did you make the best buys? What would you have done differently?