Lesson Two-Digit Number Times Two-Digit Number Common Core State Standards 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. By now students have worked extensively with multiplication, and they have extended their knowledge of place value. With this background, they are ready to multiply two-digit numbers. This involves a more complex application of the distributive property than they have encountered so far. Students apply these skills in later work with the standard algorithm for multiplication. Vocabulary Draw a rectangle on the board, a little wider than tall. Label the height 3 and the width 4. Ask: What is the area of the rectangle? [1 square units] How did you get that? [Multiply height by width.] Say: Any product of two factors can be modeled as a rectangular area. The model is called an area model. Discuss this idea with students. The area model for multiplication is a model in which the side lengths of a rectangle represent the factors and the area of the rectangle represents the product. Arrays and area models can be used to illustrate why multiplication strategies work.
Extending Multiplication and Division Set the Stage Engage WHOLE CLASS Present the problem Mr. Amos bought 5 packages of fruit. Each package contains 4 apples and bananas. How many apples does Mr. Amos have? How many bananas? How many pieces of fruit? Ask: How do you find the number of apples? [5 4] The number of bananas? [5 ] The number of pieces of fruit? [5 (4 + ) or (5 4) + (5 )] Have students consider the expression 5 (4 + ). Ask: If I say the multiplication is distributed over the addition, what does that mean? [The 5-times operates on both 4 and.] Ask: What property of operations is this? [distributive property] Ask: What happens to the expression if Mr. Amos buys another package of fruit and now has (5 + 1) packages? [It becomes (5 + 1) (4 + ).] How does the distributive property apply now? [(5 + 1) is distributed over (4 + )] Warm-Up Use this short thinking exercise to jump-start the instructional session. Foundation Skill Practice Use this VersaTiles activity to help students activate their prior knowledge. Answer Key 3 x 4 = 1 3 x 44 = 13 3 x 444 = 3 x 4,444 = Keep going, and then write three observations. ANSWER: 1,33; 13,33. The products all begin with 1. The products all end with. The number 3 repeats in the middle 1 less time than the number of 4s. COMMENTS & EXTENSIONS: Instead of multiplying by 3, try 4. What do you find? Now try 5 and 6. by 5 =, so 50 0 = Think: 5 = 50 = 0 So, 50 0 = 1,000. 1 3 4 = 1, so 30 40 = 3 7 = 1, so 30 70 = 3 5 6 = 30, so 50 60 = 4 7 4 = 8, so 70 40 = 5 9 = 18, so 0 90 = 6 5 8 = 40, so 50 80 = 7 80 40 = 8 60 40 = 9 90 30 = 40 50 = Use multiplication facts to help you multiply tens. 11 A movie theater has 30 seats in each row. How many seats are there in 0 rows? 1 There are 40 rolls of theater tickets. If there are 0 tickets in each roll, how many tickets are there? ETA handmind 3,000 600,800 1,00 4,000,400 1,800,700,000 3,00 800,0 Extending Multiplication and Division Lesson 4 Hands-On Standards Number & Operations 7 Objective: Find a product of tens multiplied by tens. Online resources available at handmind.com/hosnumbergr4 VersaTiles student book, page 7 3
Introduce the Concept Explore WHOLE CLASS Distribute Base Ten Blocks and Factor Tracks. Present the problem 1 14 = Have students work on a model for 1 14 using the Factor Track. Elicit that the goal is to model the problem as a rectangle with sides 1 and 14. Students build the side lengths in the tracks and they build the product rectangle by filling in the area defined by the sides. Materials Base Ten Blocks Factor Track product rectangle built with 1 flat, 6 rods, 8 units + 4 Lesson Explore & Explain Two-Digit Number Times Two-Digit Number Answer Key 0 40 + 0 8 sketch of area model Try This Use Base Ten Blocks and a Factor Track to model each problem. In problems 1, sketch your model. In problems 3 4, sketch an area model. In each problem, complete the number sentences. 1 1 13 = ( + ) ( + 3) 11 15 = ( + ) 1 ( + ) 5 Have students identify the 4 partial-product rectangles, sketch the area model, and then write the equation suggested by the model. Ask students to explain how these different models represent the same number. 1 14 = ( + ) ( + 4) = ( ) + ( ) + ( 4) + ( 4) = 0 + 0 + 40 + 8 = 168 1 = ( ) + ( ) = ( ) + ( ) + ( 3) + ( 3) + ( ) 5 + ( 1 ) 5 0 0 30 6 156 0 50 5 165 3 0 5 0 4 30 3 13 5 = ( + ) ( + ) 4 4 3 = ( + ) ( + ) 0 5 30 00 50 0 600 40 3 60 15 4 8 = ( ) 0 + ( 3 ) 0 = ( 0 ) 30 + ( 4 ) 30 + ( ) 5 + ( 3 ) 5 + ( 0 ) + ( 4 ) 00 60 50 15 35 600 40 8 768 Fi nd the product. ( + ) ( + 9) = ( ) (30 + 5) (0 + ) = (30 0) + ( ) + ( 9) + ( 9) + (5 0) + (30 ) + (5 ) 5 1 19 = = 0 + 0 + 90 + 18 = 8 6 35 = = 600 + 0 + 60 + = 770 ETA handmind Explore & Explain SMALL GROUPS Prepare ahead Students will need Base Ten Blocks and Factor Tracks. The activity helps students visualize the multiplication of two -digit numbers. It helps them see the role of place value and illustrates the inner workings of the distributive property. Students build and sketch manipulative models, sketch area models, and write equations to find products. Extending Multiplication and Division Lesson 4 Online resources available at handmind.com/hosnumbergr4
Extending Multiplication and Division Reinforce the Concept Explain & Elaborate WHOLE CLASS Have students discuss the activity. Note whether they developed a routine. Ask: Did you notice that you used the distributive property? Refer to problem 5. Present and discuss. 1 19 = ( + ) ( + 9) = ( + ) + ( + ) 9 = ( ) + ( ) + ( 9) + ( 9) Elicit that ( + ) is first distributed over ( + 9), then and 9 are each distributed over ( + ). Have students draw the area model and explain how these different models show the same number. Evaluate WHOLE CLASS Have students find the product 13 18 using drawings and/or equations. Ask students to show you how they used place value to generate the 4 partial products. Re-Engage Use this page to give students additional concrete-to-representational-to-abstract practice. Lesson Two-Digit Number Times Two-Digit Number Use a Factor Track and Base Ten Blocks to build the model. Complete the number sentence. 1 1 11 1 = ( + 1) ( + ) 1 1 = ( + ) (0 + ) = ( ) + (1 ) + ( ) + (1 ) 0 0 13 = ( 0) + ( 0) + ( 1) + ( 1) 00 40 5 Use a Factor Track and Base Ten Blocks to model the problem. Complete the area sketch. Complete the number sentence. 3 13 15 = ( + ) 3 ( + ) 5 4 5 = ( 0 + ) ( 0 + ) 5 5 Answer Key 0 5 0 50 0 400 0 Independent Practice Use this VersaTiles activity to give students more practice with the skills they learned in the lesson. Two by Two 15 3 = Decompose the factors. 15 3 = ( + 5) (0 + 3) Use the distributive property. ( + 5) (0 + 3) = ( + 5) 0 + ( + 5) 3 = ( 0) + (5 0) + ( 3) + (5 3) = 00 + 0 + 30 + 15 = 345 3 30 15 40 3 = ( ) + ( ) = (0 0) + ( ) 0 5 3 5 + ( ) + ( ) + ( 0 ) 5 + ( ) 5 = 0 + 30 50 + + 15 = 195 = 400 + 40 + 0 + = 550 Fi nd the product. Show your work on the back. ( + ) ( + 7) = ( ) ( + 5) (0 + 1) = ( 0) 5 1 17 = + ( ) + ( 7) + ( 7) 6 15 1 = + (5 0) + ( 1) + (5 1) = 0 + 0 + 70 + 14 = 04 = 00 + 0 + + 5 = 315 Extending Multiplication and Division Lesson Online resources available at handmind.com/hosnumbergr4 ETA handmind 1 14 16 = 13 8 = 3 1 5 = 4 3 4 = 5 8 16 = 6 3 = 7 35 1 = 8 18 = 9 15 33 = 44 1 = 11 18 5 = 1 15 34 = 55 936 364 5 768 94 448 495 396 506 40 4 Daily Routine Create an anchor poster with your class to summarize the concept of the area model and distributive property. It might include one-digit and two-digit examples along with area model and symbolic representations. Place this anchor chart in the writing center. Writing assignment: What does the word distribute mean? Explain using pictures, numbers, and words. Objective: Multiply two two-digit numbers. 8 VersaTiles student book, page 8 5
Lesson Two-Digit Number Times Two-Digit Number Try This Use Base Ten Blocks and a Factor Track to model each problem. In problems 1, sketch your model. In problems 3 4, sketch an area model. In each problem, complete the number sentences. 1 1 13 = ( + ) ( + 3) 11 15 = ( + ) ( + ) = ( ) + ( ) + ( 3) + ( 3) 3 13 5 = ( + ) ( + ) = ( ) + ( ) 4 4 3 = ( + ) ( + ) = ( ) + ( ) = ( ) + ( ) ETA handmind 5 1 19 = 6 35 = Extending Multiplication and Division Lesson
Two by Two 15 3 = Decompose the factors. 15 3 = ( + 5) (0 + 3) Use the distributive property. ( + 5) (0 + 3) = ( + 5) 0 + ( + 5) 3 = ( 0) + (5 0) + ( 3) + (5 3) = 00 + 0 + 30 + 15 = 345 1 14 16 = 3 1 5 = 5 8 16 = 7 35 1 = 9 15 33 = 18 5 = 13 8 = 4 3 4 = 6 3 = 8 18 = 44 1 = 15 34 = 55 936 364 5 768 94 448 495 396 506 40 4 Objective: Multiply two two-digit numbers. 8
Lesson Two-Digit Number Times Two-Digit Number Use a Factor Track and Base Ten Blocks to build the model. Complete the number sentence. 1 11 1 = ( + 1) ( + ) 1 1 = ( + ) (0 + ) = ( ) + (1 ) + ( ) + (1 ) = ( 0) + ( 0) + ( 1) + ( 1) Use a Factor Track and Base Ten Blocks to model the problem. Complete the area sketch. Complete the number sentence. 3 13 15 = ( + ) ( + ) 4 5 = ( + ) ( + ) 0 = ( ) + ( ) + ( ) + ( ) = 0 + + + = = (0 0) + ( ) Show your work on the back. 5 1 17 = 6 15 1 = ETA handmind Extending Multiplication and Division Lesson