Everyday Mathematics

1. Everyday Mathematics Riverside Elementary Schools

2. Everyday Mathematics Philosophy The children of the 21st century need a math curriculum that is balanced: *a curriculum that emphasizes conceptual understanding not just teaching procedures *a curriculum that explores the full mathematics spectrum, not just basic arithmetic *a curriculum based on how children learn, what they are interested in, and what they need to be prepared for in the future

3. Research Based Curriculum • Research shows that 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 like presented in this book. • The program allows children to revisit a skill numerous times throughout the curriculum because most children will not master a skill the first time it is presented. • The program establishes high expectations for all students and gives teachers the tools they need to help students meet, and often exceed, these expectations. • The program helps teachers move beyond the basics and teach higher-order and critical-thinking skills in students.

4. Key Features of Everyday Mathematics • Problem solving in real-life situations • Hands-on activities • Sharing ideas through small group and class discussions • Cooperative learning • Practice through games • Ongoing review of skills taught • Home-and-School Connections

5. Lesson Components • Mental Math • Math Messages • Math Boxes • Games • Alternative Algorithms • Home Links • Literature

6. Learning Goals Secure • Skills- The student can consistently complete the task independently and correctly. • Skills-Students show some understanding. Reminders or hints are still needed. • Skills-Students cannot complete the task independently. Students show little understanding of the concept. Developing Beginning

7. Assessment • Grades include mastery of secure skills • Unit Assessments (Checking Progress) • Math Boxes • Journal Pages • Written responses • Slate and oral assessments • Game play

8. Parent Involvement • Read the Family Letters -use the answer key to help your child with their homework • Play Math games with your child • Be involved in Math Nights • Maintain high expectations for your child • Log on to the Everyday Math website or Mr. Morgan’s website at Riverside School District http://www.riversidesd.com/ for extra help • Keep home-school communication open

9. PSSA 2007 MATH SCORES

10. Everyday Math Algorithms

11. Partial Sums (Addition Algorithm)

12. 287 Add the hundreds (200 + 600) + 625 + 12 Add the partial sums (800 + 100 + 12) Partial Sums 800 Add the tens (80 +20) 100 Add the ones (7 + 5) 912

13. Counting Up/Hill Method A Subtraction Algorithm

14. 38-14= Counting Up/Hill Method 24 1. Place the smaller number at the bottom of the hill and the larger at the top. 30 38 +8 2. Start with 14, add to the next friendly number. (14+6=20) +10 20 3. Start with 20, add to the next friendly number. (20+10=30) +6 4. Start with 30, add to get 38. (30+8=38) 14 Record the numbers added at each interval: (6+10+8=24)

15. Trade First (Subtraction algorithm)

16. Trade First 12 1. The first step is to determine whether any trade is required. If a trade is required, the trade is carried out first. 7 11 2 8 3 1 - 4 8 5 2. To make the 1 in the ones column larger than the 5, borrow 1 ten from the 3 in the tens column. The 1 becomes an 11 and the 3 in the tens column becomes 2. 3 4 6 3. To make the 2 in the tens column larger than the 8 in the tens column, borrow 1 hundred from the 8. The 2 in the tens column becomes 12 and the 8 in the hundreds column becomes 7. 4. Now subtract column by column in any order.

17. Partial Product (Multiplication Algorithm)

18. + Partial Product 2 7 (20+7) When multiplying by “Partial Products,” you must first multiply parts of these numbers, then you add all of the results to find the answer. X 6 4 (60+4) 1,200 Multiply 20 X 60 (tens by tens) 420 Multiply 60 X 7 (tens by ones) 80 Multiply 4 X 20 (ones by tens) 28 Multiply 4 X 7 (ones by ones) Add the results 1,728

19. Partial Quotients (Division Algorithm)

20. 9 876 Partial Quotient Start “Partial Quotient” division by estimating your answer. Check by multiplying and subtraction. The better your estimate, the fewer the steps you will have. 97 R3 1. Estimate how many 9’s are in 876. (90) - 810 90 x 9 =810 (1st estimate) Subtract 2. Estimate how many 9’s are in 66. (7) 66 - 63 7 x 9 =63 (2nd estimate) 3. Because 3 is less than 9, you have finished dividing and you now need to add the estimates to get your answer and the 3 left over is your remainder. Subtract 3 97(Add the estimates)

21. “Lattice”(Multiplication Algorithm)

22. Solve: 197 x 23 = 1 9 7 1. Create a 3 by 2 grid. Copy the 3 digit number across the top of the grid, one number per square. 1 Copy the 2 digit number along the right side of the grid, one number per square. 0 1 2 0 2. Draw diagonals across the cells. 3.Multiply each digit in the top factor by each digit in the side factor. Record each answer in its own cell, placing the tens digit in the upper half of the cell and the ones digit in the bottom half of the cell. 2 8 4 2 0 2 4 3 4. Add along each diagonal and record any regroupings in the next diagonal 3 7 1 1 5 1 3 1

23. Answer 1 9 7 1 1 1 0 1 0 2 2 8 4 2 0 2 4 3 3 7 1 5 3 1 197 x 23 4 5 3 1 =

24. Thank you for coming!