Welcome to Everyday Mathematics

1. Welcome to Everyday Mathematics University of Chicago School Mathematics Project Created by Rina Iati, South Western School District, Hanover, PA

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. Created by Rina Iati, South Western School District, Hanover, PA

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. • Starting with kindergarten, Everyday Mathematics was developed one grade level at a time. All seven grade levels were written by the same core of authors, in collaboration with a team of mathematicians, education specialists and classroom teachers. • Over 175,000 classrooms and 2.8 million students are currently using EM Created by Rina Iati, South Western School District, Hanover, PA

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 Created by Rina Iati, South Western School District, Hanover, PA

5. Lesson Components • Math Messages • Mental Math and Reflexes • Math Boxes / Math Journal • Home links • Explorations • Games • Alternative Algorithms Created by Rina Iati, South Western School District, Hanover, PA

6. Learning Goals Secure Skills Developing Skills Beginning Skills Created by Rina Iati, South Western School District, Hanover, PA

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 Created by Rina Iati, South Western School District, Hanover, PA

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 Created by Rina Iati, South Western School District, Hanover, PA

9. Thank You for Coming Created by Rina Iati, South Western School District, Hanover, PA

10. Partial Sums An Addition Algorithm Created by Rina Iati, South Western School District, Hanover, PA

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 Created by Rina Iati, South Western School District, Hanover, PA

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 Created by Rina Iati, South Western School District, Hanover, PA

13. 329 + 989 + 18 Do this one on your own Let's see if you're right. 1200 100 1318 Well Done! Created by Rina Iati, South Western School District, Hanover, PA

14. Trade-First Subtraction An alternative subtraction algorithm Created by Rina Iati, South Western School District, Hanover, PA

15. 12 8 12 In order to subtract, the top number must be larger than the bottom number 2 9 3 2 - 3 5 6 To make the top number in the ones column larger than the bottom number, borrow 1 ten. The top number become 12 and the top number in the tens column becomes 2. 5 7 6 To make the top number in the tens column larger than the bottom number, borrow 1 hundred. The top number in the tens column becomes 12 and the top number in the hundreds column becomes 8. Now subtract column by column in any order Created by Rina Iati, South Western School District, Hanover, PA

16. 11 Let’s try another one together 6 15 1 7 2 5 - 4 9 8 To make the top number in the ones column larger than the bottom number, borrow 1 ten. The top number become 15 and the top number in the tens column becomes 1. 2 2 7 To make the top number in the tens column larger than the bottom number, borrow 1 hundred. The top number in the tens column becomes 11 and the top number in the hundreds column becomes 6. Now subtract column by column in any order Created by Rina Iati, South Western School District, Hanover, PA

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! Created by Rina Iati, South Western School District, Hanover, PA

18. 9 Last one! This one is tricky! 6 13 10 7 0 3 - 4 6 9 2 3 4 Oh, no! What do we do now? Let's trade from the hundreds column Let's see if you're right. Congratulations! Created by Rina Iati, South Western School District, Hanover, PA

19. Partial Products Algorithm for Multiplication Created by Rina Iati, South Western School District, Hanover, PA

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 Created by Rina Iati, South Western School District, Hanover, PA

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 Created by Rina Iati, South Western School District, Hanover, PA

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 Created by Rina Iati, South Western School District, Hanover, PA

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! Created by Rina Iati, South Western School District, Hanover, PA