Slide 1 / 156 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 Slide 2 / 156 4th Grade Multiplication & Division of Multi-Digit Numbers 2013-03-21 www.njctl.org Slide 3 / 156 Click on a topic Table of Contents to go to that section. · Multiply by multiples of 10, 100 and 1,000 · Use rounding to estimate products · Multiplication Review · Multiply two digit numbers · Multiply 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
Slide 4 / 156 Multiplication by Multiples of 10, 100, 1000 Click to return to the table of contents Slide 5 / 156 Multiplying by 10 Multiply 524 X 10 Solution You need to have a thousands' column. Step 1 Multiply each top number by 0 . Each answer is 0 Ones Hundreds Tens Thousands 5 2 4 X 1 0 0 0 0 Slide 6 / 156 Step 2 Add a zero in the ones' columns in the second row. This lines up the columns correctly. Thousands Hundreds Tens Ones Step 3 Multiply the top row 5 2 4 by 1. 1 X 4 now goes X 1 0 in the tens' column ( 4 X 1 ten = 40 ), and 0 0 0 so on. 2 4 0 + 5 2 4 0 Step 4 Add down 5 ANSWER 524 X 10 = 5,240
Slide 7 / 156 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? Ten- Hundred- Thousand Hundred Thousand Tens Ones Thousands s s s 3 7 2 4 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. Hundred- Ten- Thousand Thousand Thousand Hundreds Tens Ones s s s 3 7 2 4 0 0 Slide 8 / 156 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 CLICK 2300 42810 1000 CLICK CLICK Slide 9 / 156 1 673 X 10
Slide 10 / 156 2 673 X 100 Slide 11 / 156 3 7103 X 10 Slide 12 / 156 4 5421 X 100
Slide 13 / 156 5 1000 x 59 = Slide 14 / 156 6 18 x 1000 = Slide 15 / 156 7 500 X 10
Slide 16 / 156 8 A football field is 100 yards long and 50 yards wide. What is the entire area of the field? (A= L x W) Slide 17 / 156 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? Slide 18 / 156 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?
Slide 19 / 156 11 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? Slide 20 / 156 12 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? Slide 21 / 156 Use Rounding to Estimate Products Click to return to the table of contents
Slide 22 / 156 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 Slide 23 / 156 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 Slide 24 / 156 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
Slide 25 / 156 13 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? True False Slide 26 / 156 14 Estimate the product of 47 x 430 = A 20,000 B 2,000 C 16,000 Slide 27 / 156 15 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. A 40 B 400 C 4000
Slide 28 / 156 16 Estimate the product of 527 x 62 = Slide 29 / 156 17 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. Slide 30 / 156 18 Estimate the product of 839 x 25 =
Slide 31 / 156 Multiplication Review Click to return to the table of contents Slide 32 / 156 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 Slide 33 / 156 Try This Now Use repeated addition to find 5 X 20 0 + 20 = 20 20 + 20 = 40 click 40 + 20 = 60 click 60 + 20 = 80 click 80 + 20 = 100 click
Slide 34 / 156 Counting Multiples List 8 multiples of 15. Then find 15 X 5 Pull Pull Solution 15, 30, 45, 60, 75, 90, 105, 120 15 X 5 = 75 Slide 35 / 156 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. Slide 36 / 156 The previous examples give strategies to use: 1. Repeated Addition 2. Counting Multiples 3. Drawing an Array We can also use: The Standard Algorithm
Slide 37 / 156 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 2 3. Multiply the tens' digit by 2. 4 8 4. Write the results below the line. ANSWER 24 x 2 = 48 CLICK Slide 38 / 156 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 3 3. Multiply the tens' digit by 3. 4. Write the results below the line. ANSWER 32 X 3 = 96 CLICK Slide 39 / 156 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 2 3. Multiply the tens' digit by 2. 4. Write the results below the line. ANSWER 84 CLICK
Slide 40 / 156 19 32 X 2 Slide 41 / 156 20 31 X 3 Slide 42 / 156 42 21 X 3
Slide 43 / 156 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? Slide 44 / 156 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 1 6 X 4 4 Slide 45 / 156 Step 3: Multiply the tens. 4 X 1 = 4 tens Add the 2 tens you regrouped 4 + 2 = 6 tens 2 1 6 X 4 6 4
Slide 46 / 156 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 8 7 X 6 2 Slide 47 / 156 Step 3: Multiply the tens. 6 X 8 = 48 tens Add the 4 tens you regrouped 48 + 4 = 52 tens 4 8 7 X 6 52 2 Slide 48 / 156 23 Which shows the correct product for 47 x 4 = ____ ? A 188 B 168 C 158
Slide 49 / 156 24 Which shows the correct product for 99 x 9 = ____ ? A 811 B 881 C 891 Slide 50 / 156 25 52 X 6 Slide 51 / 156 26 47 x 3
Slide 52 / 156 27 88 X 5 Slide 53 / 156 28 26 X 4 Slide 54 / 156 29 19 X 8
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