Multiplication REVIEW Using Distributive Property Traveling from Nasty

Easily Memorize the Multiplication Table Watch this video: https: //www. youtube. com/watch? v=v 1 Ih 3 -m. DPUk (3: 58 min) Follow recommended steps to sharpen your skills!

nt e M th a M l a Distributive Property with Multiplication The distributive property lets you multiply a sum by multiplying each addend separately and then adding the products Example: 10(3 + 4) = (10 3) + (10 4) = 30 + 40 = 70 . . The distributive property can be used when multiplying numbers to make them easier for computation by expanding the numbers to their base ten values. Example #1: 4 x 75 = (4 x 70) + (4 x 5) Example #2: 13 = 10 + 3 with single digit = 4 (70 + 20) with multiple digits x 14 = 10 + 4 = 280 = 300 Distribute the tens and units to multiply: (10 x 10) + (10 x 3) + (4 x 10) + (4 x 3) 100 + 30 + 40 + 12 170 + 12 182

PICTURE BUILD 13 x 14 10 + 3 10 + 4 100 (10 x 10) 40 (4 x 10) WHY? Why does the distributive property of multiplication work? 30 (10 x 3) 12 (4 x 3 Units) 100 30 40 12 182

Vocabulary Review Standard Method 12 X 13 36 12 0 FACTOR Factor Partial Product FACTOR PARTIAL Product Distributive Property PARTIAL Product 12 X 13 10 + 2 Expanded FACTOR 10 + 3 Expanded FACTOR Distributive Property: (10 x 10) + (10 x 2) + (3 x 10) + (3 x 2) 100 + 20 + 30 + 6 150 + 6 PRODUCT 156 PARTIAL Products PRODUCT 156

Practice 3 x 1645 = = = Use the 3(1, 000 + 600 + 40 + 5) standard (3 x 1, 000) + (3 x 600) + (3 x 40) + (3 x 5) method to 3, 000 + 1800 + 120 + 15 check each 4800 + 120 + 15 computation. 4920 + 15 16 x 43 = (10 + 6) x (40 + 3) 10 + 6 x 40 + 3 = (40 x 10) + (40 x 6) + (3 x 10) + (3 x 6) = 400 + 240 + 30 + 18 = 670 + 18 = 688 27 x 139 = (100 + 30 + 9) x (20 + 7) 100 + 30 + 9 X 20 + 7 2, 000 + 600 + 29 + 700 + 210 + 63 2, 000 + 1300 + 210 + 20 + 9 + 60 + 3 3300 + 290 + 12 3590 + 12 3602

Step-by-Step Bar Modeling for Multiplication Word Problems 1. Golden Rules of Multiplication Model Drawing When a problem says, “There were ____ times as many…” hone in on what that means. - Add one unit at a time to your beginning unit bar (1 x) = “counting method” - Example: Start with 1 times when comparing variables Jane’s cookies □ (1 x) Jim’s cookies □ (1 x) 2. It is usually helpful to draw a smaller unit bar to begin. Then add units as you count up # of times. 3. Make sure the model mirrors the statement sentence. Step 1: READ Ryan had 4 times as many marbles as Jordan. If they had 60 marbles altogether, how many marbles did Ryan have? Step 2: Write Ryan had _______ marbles. Step 3: List Steps 4 -5: Draw & Adjust Practice this problem in journal. Ryan’s marbles Jordan’s marbles 1 x 2 x 3 x Ryan’s marbles Jordan’s marbles ? 4 x 60 Total Steps 6 & 7: Compute & Answer Ryan had 48 marbles. Monica had 3 times as many pens as Griffin. If they had 220 pens altogether, how many pens did Monica have?

Practice More Complexity: A ribbon that’s 1, 530 inches long is cut into two pieces. The length of one piece is 2 times the length of the other. What is the length of the longer piece? A piece of fabric that’s 1, 640 feet long is cut into two pieces. The length of one piece is 3 times the length of the other. What is the length of the longer piece? The longer piece of ribbon is _____ inches. The longer piece of fabric is _____ feet. 1 x 2 x 1 x Longer piece 2 x Guided Practice Mike had 3 times as much money as Steve. Rick had 2 times as much money as Steve. If Rick had $98, how much money did Mike have? Mike had $ _____ of money. 1 x 1, 530 ? Total 1 x 2 x 1 x ? 1 x 2 x 3 x Mike’s money 3 x Longer piece ? 1 x Steve’s money 1, 640 Total Rick’s money $98 Rick’s Total Shorter piece 2 units + 1 unit = 3 units = 1530 in. 1 unit = ? 32 units + 1 unit = 4 units = 1640 in. 1 unit = ? 2 units = $98 1 unit = ? What is 1 unit? Longer Ribbon ? 3 x ? = 1530 Longer piece = 2 units 1530 3 = ? 510 x 2 (1500 3) + (30 3) (500 x 2) + (10 x 2) 500 + 10 = 510 1, 000 + 20 1 unit = 510 1020 What is 1 unit? Longer Ribbon ? 3 4 x ? = 1640 Longer piece = 3 units 1640 4 = ? 410 x 3 (1600 4) + (40 4) (400 x 3) + (10 x 3) 400 + 10 = 410 1200 + 30 1 unit = 410 1230 What is 1 unit? 2 x ? = 98 98 2 = ? (90 2) + (8 2) 45 + 4 1 unit = 49 The longer piece of ribbon is 1, 020 inches. The longer piece of fabric is 1, 230 feet. Mike had $147 of money. Mike’s money ? Mike $ = 3 units 3 x 49 (3 x 40) + (3 x 9) 120 + 27 $147

EXIT List TODAY WE LEARNED … 1. … to use the distributive property of multiplication as an easy multiplication strategy. 2. … tell HOW to use the distributive method and explain WHY it works. 3. … to practice fluency for multiplication using both the standard algorithm & distributive method. 4. … how to use bar modeling to solve multiplication word problems and justify solutions. Before leaving class read all of these steps and complete them: 1. Math Journal notes should be completed. If you did not have time to write everything, then grab a Lesson 3 Math Journal Slip and finish writing all of the information in your journal. 2. Complete ALL “Guided Practice” problems and “Step-by-Step Bar Modeling” word problems in your journal. 3. Complete the “Independent Practice” student assignment. If it is not finished in class, then it must be completed for homework.

L A N O I PT Today’s handouts given in class and available online. O Back Side