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  1. New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others. Click to go to website: www.njctl.org

  2. 4th Grade Multiplication & Division of Multi-Digit Numbers 2012-08-07 www.njctl.org

  3. Setting the PowerPoint View • Use Normal View for the Interactive Elements • To use the interactive elements in this presentation, do not select the Slide Show view. Instead, select Normal view and follow these steps to set the view as large as possible: • On the View menu, select Normal. • Close the Slides tab on the left. • In the upper right corner next to the Help button, click the ^ to minimize the ribbon at the top of the screen.  • On the View menu, confirm that Ruler is deselected. • On the View tab, click Fit to Window. • On the View tab, click Slide Master | Page Setup. Select On-screen Show (4:3) under Slide sized for and click Close Master View. • On the Slide Show menu, confirm that Resolution is set to 1024x768. • Use Slide Show View to Administer Assessment Items • To administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 10 for an example.)

  4. Click on a topic to go to that section. Table of Contents ·Multiplication by Multiples of 10, 100 and 1,000 ·Use Rounding to Estimate Products ·Multiplication Review ·Multiplication of Two Digit Numbers ·Multiplication of a whole number by up to 4 digits by 1 digit ·Division with and without remainders ·Use rounding to estimate quotients ·Find whole numbers quotients and remainders with up to four-digit dividends and one-digit divisors ·Quotients with zeros

  5. Multiplication by Multiples of 10, 100, 1000 Click to return to the table of contents

  6. Multiply 524 X 10 Solution You need to have a thousands' column. Step 1 Multiply each top number by 0. Each answer is 0 Multiplying by 10

  7. Step 2 Add a zero in the ones' columns in the second row. This lines up the columns correctly. Step 3 Multiply the top row by 1. 1 X 4 now goes in the tens' column (4 X 1 ten = 40), and so on. Step 4 Add down ANSWER 524 X 10 = 5,240

  8. Using a Place-Value Chart Do 3724 X 100 with a place-value chart. What column in the chart contains the 3 before multiplying? after multiplying? Solution Before multiplying, the 3 is in the thousands' place, as shown. After multiplying, the 3 is in the hundred-thousands' place. That is because adding 2 zeros "moves" the number over 2 places to the left.

  9. Patterns of Zeros When you multiply by 10, 100, 1000, there is a pattern you can use. Look at 524 X 10 = 5240. What do you notice? If you said that multiplying a whole number by 10 adds one zero to the end, you are right. You can multiply by 10 using this pattern. Try This Use a pattern 1. 230 X 10 2. 4281 X 10 3. 100 X 10 2300 42810 1000 Click Click Click

  10. 1 673 X 10

  11. 2 673 X 100

  12. 3 7103 X 10

  13. 4 5421 X 100

  14. 5 1000 x 59 =

  15. 6 18 x 1000 =

  16. 7 500 X 10

  17. 8 A football field is 100 yards long and 50 yards wide. What is the entire area of the field? (A= L x W)

  18. 9 Each student in 4th grade is planning on reading 50 books this school year. There are 100 students in the 4th grade. How many total books will they read?

  19. 10 The Sea Hawks are practicing their relay passes. If there are 9 people in the relay and 100 feet between them, how far does the ball travel when it reaches the last player? Think about the number of passes it takes to make it to the end of the relay?

  20. There are 10 boys on the basketball team. If each boy sells $219.00 for the candy sale, how much money will the team raise? 11

  21. There are 4 wheels on each of these training wheel bikes. There are 5 boys in each group and there are 10 groups. How many wheels are there in all? 12

  22. Use Rounding to Estimate Products Click to return to the table of contents

  23. Use Rounding to Estimate Products Estimating (rounding) helps to see if the product makes number sense. It is an important skill to develop good judgment about how precise an estimate is possible or reasonable in various circumstances. This skill can be helpful if you don't need an exact answer. Estimate the product of 77 X 28 We still follow the rounding rules: if the digit is between 0 - 4 the number remains the same if the digit is between 5 - 9 the rounding place value goes up by one

  24. Estimating to the nearest tens: Estimation 77 80 X 28 X 30 Since 8 X 3 = 24. Count the number of zeros in the estimation and add the same number to the product. 2,400 is the estimate

  25. Estimate. 14 X 189 189 Round each factor 189 rounds to 200 X 14 to its greatest place. 14 rounds to X 10 2,000 2,000 is the estimate Estimate. 227 X 1,068 1,068 Round each factor 1,068 rounds to 1,000 X 227 to its greatest place 227 rounds to X 200 200,000 200,000 is the estimate

  26. You want to buy an video game system that costs $399.95. If you save $40.00 per month, it will take you ten months to purchase the X-Box? 13 A True B False

  27. Estimate the product of 47 x 430 = 14 A 20,000 B 2,000 C 16,000

  28. A hospital ordered 79 boxes of cotton swabs. There are 52 cotton swabs in each box. About how many cotton swabs were ordered in all? Choose the better estimate. 15 A 40 B 400 C 4000

  29. Estimate the product of 527 x 62 = 16

  30. The basketball team is ordering sweatshirts. They cost $23 each and the team needs to order 17. Estimate what the total cost would be to order them. 17

  31. Estimate the product of 839 x 25 = 18

  32. Multiplication Review Click to return to the table of contents

  33. Multiplying by Repeated Addition Show that 12 X 5 = 60 by repeated addition Solution Add 12 five times 0+12=12 12+12=24 24+12=36 36+12=48 48+12=60 click click click click

  34. Try This Now Use repeated addition to find 5 X 20 0 + 20 = 20 20 + 20 = 40 click 40 + 20 = 60 60 + 20 = 80 click 80 + 20 = 100 click click

  35. Counting Multiples List 8 multiples of 15. Then find 15 X 5 Solution 15, 30, 45, 60, 75, 90, 105, 120 15 X 5 = 75

  36. Multiplying Using a Model Find 3 x 15 Arrange of 3 rows of 15 stars . Using stars to represent ones, you count 45 stars. 45 is a multiple of 3.

  37. The previous examples give strategies to use: 1. Repeated Addition 2. Counting Multiples 3. Drawing an Array We can also use: The Standard Algorithm

  38. Multiplying without Regrouping - Standard Algorithm Find 24 X 2 Steps 1. Write the numbers in columns. TENS ONES 2 4 2. Multiply the ones' digit by 2. x 23. Multiply the tens' digit by 2. 4 8 4. Write the results below the line. ANSWER 24 x 2 = 48 CLICK

  39. Multiplying without Regrouping - Standard Algorithm Find 32 x 3 Steps 1. Write the numbers in columns. TENS ONES 3 2 2. Multiply the ones' digit by 3. x 33. Multiply the tens' digit by 3. 4. Write the results below the line. ANSWER 32 X 3 = 96 CLICK

  40. Multiplying without Regrouping - Standard Algorithm Find 42 x 2 Steps 1. Write the numbers in columns. TENS ONES 4 2 2. Multiply the ones' digit by 2. x 23. Multiply the tens' digit by 2. 4. Write the results below the line. ANSWER 84 CLICK

  41. 19 32 X 2

  42. 20 31 X 3

  43. 21 42 X 3

  44. 22 Jenna is going to paint her bedroom pink. She needs three gallons of paint and each gallon costs $18. How much will the paint cost for Jenna to paint her bedroom?

  45. Multiplying Multidigit Numbers with Regrouping Find the value of 16 X 4 Step-By-Step Step 1: Rewrite the problem to make it easier to solve 16 X 4 Step 2: Multiply the ones 6 X 4 = 24 ones Regroup 24 ones as 2 tens 4 ones. Write the 4 under the ones and the 2 above the tens. 2 16 X 4 4

  46. Step 3: Multiply the tens. 4 X 1 = 4 tens Add the 2 tens you regrouped 4 + 2 = 6 tens 2 16 X4 64

  47. Multiplying Multidigit Numbers with Regrouping Find the value of 87 X 6 Step-By-Step Step 1: Rewrite the problem to make it easier to solve 87 X 6 Step 2: Multiply the ones 6 X 7 = 42 ones Regroup 42 ones as 4 tens 2 ones. Write the 2 under the ones and the 4 above the tens. 4 87 X 6 2

  48. Step 3: Multiply the tens. 6 X 8 = 48 tens Add the 4 tens you regrouped 48 + 4 = 52 tens 4 87 X 6 522

  49. 23 Which shows the correct product for 47 x 4 = ____ ? A 188 B 168 C 158

  50. 24 Which shows the correct product for 99 x 9 = ____ ? A 811 B 881 C 891