Slide 1 / 176 Slide 2 / 176 Fourth Grade Multiplication and Division of Multi-Digit Numbers 2015-11-23 www.njctl.org Slide 3 / 176 Slide 4 / 176 Table of Contents Click on a topic Links to PARCC sample questions to go to that section. • Multiply by Multiples of 10, 100 and 1,000 Performance Based Assessment • Use Rounding to Estimate Products Non-Calculator #3 Non-Calculator #11 • Multiplying Whole Numbers up to 4 Digits by One-Digit Non-Calculator #8 Non-Calculator #17 • Multiplication by Two Digit Numbers End of Year • Basics of Division & Estimating Quotients Non-Calculator #2 Non-Calculator #14 • Division with and without Remainders Non-Calculator #4 Non-Calculator #16 • Find Whole Number Quotients and Remainders with Non-Calculator #6 Non-Calculator #21 up to Four-Digit Dividends and One-Digit Divisors Non-Calculator #7 Non-Calculator #24 • Quotients with Zeros Non-Calculator #11 Slide 5 / 176 Slide 6 / 176 Multiplication Review Multiplication is repeated addition of same-sized groups. For example, 4 x 5 could be shown in the following ways: Use the set model . Use skip counting . Multiplication by (Make 4 groups of 5) (Count by 5, 4 times.) Multiples of 10, 100, 1000 5 + 5 + 5 + 5 = 20 = 20 s Click to return to the table of contents
Slide 7 / 176 Slide 8 / 176 Multiplying by 10 Multiplication Review Let's multiply 7 x 10 using the area model. On the graph below, Use an array . Use the area model . draw a rectangle that is 7 units by 10 units. Shade in your rectangle. (4 groups of 5 s) (a 4 x 5 graph) Teacher Notes Count the number of squares that are shaded. = 20 s = 20 s You're counting 7 groups of 10, so 7 x 10 = ______. When you find the area of any rectangle, you multiply the length ( l ) by the width ( w ). The formula looks like this: A = l x w Slide 9 / 176 Slide 10 / 176 Multiplying by 10 Patterns of Zeros Use the area model to find each product. 10 x 3 = _____ 14 x 10 = _____ When you multiply by 10, 100, 1000, there is a pattern you can use. You just discovered that multiplying a whole number by 10 adds one zero to the end. Based on that, what do you think will happen if you multiply a number by 100 or by 1000? Try These: 230 x 10 42 x 100 100 x 10 2,300 4,200 1,000 click ______ click ______ click ______ 7 x 1000 501 x 100 330 x 1000 What do you notice about each of these problems? Can you 7,000 50,100 330,000 click ______ click ______ click ______ come up with a "rule" or a short-cut to find the product of any number and 10? Slide 11 / 176 Slide 12 / 176 1 Find the product. 2 Find the product. 673 x 10 = 673 x 100 =
Slide 13 / 176 Slide 14 / 176 3 Find the product. 4 Find the product. 7103 5421 x 100 = x 10 Slide 15 / 176 Slide 16 / 176 5 Find the product. 6 Find the product. 1,000 x 59 = 50 x 100,000 = Slide 17 / 176 Slide 18 / 176 7 A football field is 100 yards long and 50 yards wide. What 8 Each student in 4th grade is planning on reading 60 is the area of the field? books this school year. There are 100 students in the 4th grade. How many books will they read?
Slide 19 / 176 Slide 20 / 176 9 There are 10 boys on the basketball team. If each boy 10 There are 4 wheels on each training wheel bike. There sells $219.00 worth of candy for the candy sale, how are 5 kids in each group and there are 10 groups. How much money will the team raise? many wheels are there in all? Slide 21 / 176 Slide 22 / 176 11 The number 234 is multiplied by 10. Select the correct 12 Mr. Soto's bicycle weighs 30 pounds. His car weighs 90 word from each group. times as much as his bicycle. What is the weight, in pounds, of Mr. Soto's car? The numberal 2 in the resulting product is in the _____ place, and the value of this digit is _____. A ones E 2 B tens F 20 C hundreds G 200 D thousands H 2,000 From PARCC sample test From PARCC sample test Slide 23 / 176 Slide 24 / 176 Use Rounding to Estimate Products Why do we estimate? Use Rounding to Estimating (rounding) numbers helps us to see if the product makes number sense. Estimate Products It is an important skill to develop good judgment about how precise an estimate is or whether your answer is possible or reasonable in various circumstances. This skill can be helpful if you don't need to find the exact answer. Click to return to the table of contents
Slide 25 / 176 Slide 26 / 176 Use Rounding to Estimate Products Estimate Products How to Round Numbers: Round each number to the nearest ten. Decide which is the last digit to keep (the place you are rounding to). 1. Round each number to the nearest ten. Leave it the same if the next digit is less than 5 (this is called rounding 2. Multiply the whole numbers. down). 3. Count the number of zeros in the estimation and add the same Increase it by 1 if the next digit is 5 or more (this is called rounding up). number of zeros to the product. 77 80 click x 28 x 30 2400 Slide 27 / 176 Slide 28 / 176 Estimate Products 13 Estimate the product of 47 x 430. Round each factor to its greatest place. A 20,000 14 X 189 (It's helpful to write the problem vertically.) B 2,000 click C 16,000 189 189 rounds to 200 X 14 14 rounds to x 10 2000 click Let's try one more! 227 X 1,068 1,068 rounds to 1,000 227 rounds to x 200 200,000 Slide 29 / 176 Slide 30 / 176 14 You want to buy a video game system that costs 15 A hospital ordered 79 boxes of cotton swabs. There are $399.95. If you save $40.00 per month, it will take you 42 cotton swabs in each box. About how many swabs ten months to purchase the X-Box. were ordered in all? A 40 True False B 400 C 4000
Slide 31 / 176 Slide 32 / 176 16 Estimate the product. 17 Estimate the product 452 x 81 = 527 x 62 = Slide 33 / 176 Slide 34 / 176 Repeated Addition Multiply 12 x 5 by using Repeated Addition Multiplying Whole Numbers up to 4 Digits by One-Digit Starting with zero, add 12 five times . 0+12=12 12+12=24 24+12=36 36+12=48 48+12=60 Slide Slide Slide Slide Click to return to the table of contents Slide 35 / 176 Slide 36 / 176 Counting Multiples Multiplying Using a Model (Array) Find 3 x 15 List the first 8 multiples of 15. Arrange of 3 rows of 15 stars . Using your list, find 15 x 3. Using stars to represent ones, how many stars do you count? Now find 15 x 7. This number is a multiple of 3.
Slide 37 / 176 Slide 38 / 176 Multiply Using the Area Model Multiply Using the Area Model You can use the area model to multiply numbers. To multiply 9 x 3, You can also use the area model to multiply a larger (2, 3, 4+ digit) draw a rectangle with a side length of 9 and a width of 3. number by a one-digit number. Here's an example... 9 78 x 5 When you first look at this problem, it may seem difficult. But, don't worry! You can break it down into smaller parts that are easy to 9 x 3 = __ squares 3 multiply! B r e 70 8 a k d i n o t o w n 7 5 0 7 8 + When you know your multiplication facts, there is no need to count 8 ! squares. You can just multiply the length and the width to find the area (product). Now, multiply each part! To find the total area, find the sum of the two smaller parts. Let's multiply 7 x 6. click to reveal 70 8 350 7 x 6 = ____ 5 x 8 = 6 70 x 5 = 350 5 + 40 40 390 So, 78 x 5 = 390 7 Slide 39 / 176 Slide 40 / 176 Area Model Area Model Let's try a few more problems! Let's try a few more problems! 37 x 9 124 x 6 click to reveal 30 7 270 + 63 = 333 7 x 9 = 9 30 x 9 = 270 100 20 4 63 So, 37 x 9 = 333 click to reveal 20 x 6 = 4 x 6 = 6 100 x 6 = 600 120 24 600 + 120 + 24 = 744 So, 124 x 6 = 744 Slide 41 / 176 Slide 42 / 176 18 Use the area model to find the product of 42 x 3. 19 Using the area model, find the product of 88 x 5.
Slide 43 / 176 Slide 44 / 176 20 Use the area model to multiply 263 x 4. 21 Find the product. 509 x 8 = Slide 45 / 176 Slide 46 / 176 Multiplication Using the Standard Algorithm Multiplication Strategies Find 24 x 2 We just reviewed the following strategies... 1. Write the numbers in columns. 1. Repeated Addition Tens Ones 2. Multiply the ones' digit by 2. 2 4 2. Counting Multiples 3. Multiply the tens' digit by 2. x Answer 2 3. Drawing an Array 4. Using the Area Model. These are all very good ways to help you understand the meaning of multiplication. But now, you will learn to multiply using the Standard Algorithm. Slide 47 / 176 Slide 48 / 176 Standard Algorithm Multiplication Using the Standard Algorithm Now let's multiply 16 x 4. Let's try a few more examples... 1. Multiply the ones. Tens Ones 32 x 3 21 x 4 413 x 2 1 6 2 a. When you multiply 4 x 6, you will not get a one-digit number. x 4 Tens Ones Tens Ones Hundreds Tens Ones b. 4 x 6 = 24 4 Answer c. 24 = 2 tens + 4 ones . x x x d. Write 4 in the ones' column and carry the # # Answer 2 to the tens' column. This is called # # Tens Ones "regrouping". +2 1 6 2. Multiply 4 to the number in the tens column and # # x 4 then add the 2 tens you regrouped. ( 4 x 1 + 2 = 6) 6 4
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