Welcome to Everyday Mathematics

1. Welcome to Everyday Mathematics University of Chicago School Mathematics Project

2. Why do we need a new math program? • 60% of all future jobs have not even been created yet • 80% of all jobs will require post secondary education / training. • Employers are looking for candidates with higher order and critical thinking skills • Traditional math instruction does not develop number sense or critical thinking.

3. Research Based Curriculum • Mathematics is more meaningful when it is rooted in real life contexts and situations, and when children are given the opportunity to become actively involved in learning. • Children begin school with more mathematical knowledge and intuition than previously believed. • Teachers, and their ability to provide excellent instruction, are the key factors in the success of any program.

4. Curriculum Features • Real-life Problem Solving • Balanced Instruction • Multiple Methods for Basic Skills Practice • Emphasis on Communication • Enhanced Home/School Partnerships • Appropriate Use of Technology

5. Lesson Components • Math Messages • Mental Math and Reflexes • Math Boxes / Math Journal • Home links • Explorations • Games • Alternative Algorithms

6. Learning Goals Secure Skills Developing Skills Beginning Skills

7. Assessment • Grades primarily reflect mastery of secure skills • End of unit assessments • Math boxes • Relevant journal pages • Slate assessments • Checklists of secure/developing skills • Observation

8. What Parents Can Do to Help • Come to the math nights • Log on to the Everyday Mathematics website or the South Western Math Coach’s web site • Read the Family letters – use the answer key to help your child with their homework • Ask your child to teach you the math games and play them. • Ask your child to teach you the new algorithms • Contact your child’s teacher with questions or concerns

9. Thank You for Coming

10. Partial Sums An Addition Algorithm

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

12. 785 Add the hundreds (700 + 600) + 641 + 6 Add the partial sums (1300 + 120 + 6) Let's try another one 1300 Add the tens (80 +40) 120 Add the ones (5 + 1) 1426

13. 329 + 989 + 18 Do this one on your own Let's see if you're right. 1200 100 1318 Well Done!

14. Trade-First Subtraction An alternative subtraction algorithm

15. 12 8 12 In order to subtract, the top number must be larger than the bottom number 13 9 3 2 - 3 5 6 Start by going left to right. Ask yourself, “Do I have enough to take away the bottom number?” In the hundreds column, 9-3 does not need trading. 5 7 6 Move to the tens column. I cannot subtract 5 from 3, so I need to trade. Move to the ones column. I cannot subtract 6 from 2, so I need to trade. Now subtract column by column in any order

16. 11 Let’s try another one together 6 15 12 7 2 5 - 4 9 8 Start by going left to right. Ask yourself, “Do I have enough to take away the bottom number?” In the hundreds column, 7- 4 does not need trading. 2 2 7 Move to the tens column. I cannot subtract 9 from 2, so I need to trade. Move to the ones column. I cannot subtract 8 from 5, so I need to trade. Now subtract column by column in any order

17. 13 8 12 3 9 4 2 - 2 8 7 Now, do this one on your own. 6 5 5 Let's see if you're right. Congratulations!

18. 9 Last one! This one is tricky! 6 13 10 7 0 3 - 4 6 9 2 3 4 Let's see if you're right. Congratulations!

19. Partial Products Algorithm for Multiplication

20. + 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 6 7 X 5 3 3,000 Calculate 50 X 60 350 Calculate 50 X 7 180 Calculate 3 X 60 21 Calculate 3 X 7 3,551 Add the results

21. + Let’s try another one. 1 4 X 2 3 200 Calculate 10 X 20 80 Calculate 20 X 4 30 Calculate 3 X 10 12 Calculate 3 X 4 322 Add the results

22. + Do this one on your own. 3 8 Let’s see if you’re right. X 7 9 2, 100 Calculate 30 X 70 560 Calculate 70 X 8 270 Calculate 9 X 30 72 Calculate 9 X 8 3002 Add the results

23. Partial Quotients A Division Algorithm

24. 12 158 The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. You might begin with multiples of 10 – they’re easiest. 13 R2 There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) - 120 10 – 1st guess Subtract 38 There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess 3 – 2nd guess - 36 Subtract 2 13 Sum of guesses 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 )

25. 36 7,891 Let’s try another one 219 R7 - 3,600 100 – 1st guess Subtract 4,291 - 3,600 100 – 2nd guess Subtract 691 - 360 10 – 3rd guess 331 - 324 9 – 4th guess 7 219 R7 Sum of guesses

26. 43 8,572 Now do this one on your own. 199 R 15 - 4,300 100 – 1st guess Subtract 4272 -3870 90 – 2nd guess Subtract 402 - 301 7 – 3rd guess 101 - 86 2 – 4th guess 199 R 15 Sum of guesses 15

27. Congratulations on a job well done!