Lesson Concept: Using Rectangles to Multiply

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Presentation transcript:

Lesson 2.3.1 Concept: Using Rectangles to Multiply Product – The result of multiplying. (For example, the product of 4 and 5 is 20). Today you will explore an area model for multiplication. You will use what you know about place value and area to create the greatest possible product (result of multiplication). As you work with your team, keep these questions in mind: Where should we place the digits? How can we be sure that we have the greatest product? Choose task cards for today…

“Why does that work?” JUSTIFY 51. SPECIAL PRODUCTS Mrs. Rigsbee is going to pick 5 playing cards and record the digits for you to see. Work with your team to use the digits to create a 3-digit number and a 2-digit number that multiply to give the greatest product. Discuss and decide to develop a strategy that you can explain to the class. (be ready…Recorder/Reporter AND a Task Manager) “Why does that work?” JUSTIFY Discuss and Decide Agree on Your Strategy

52. MAXIMIZING AREA Alan and Debra were trying to decide where to place a 2 and an 8 in the boxes shown here: . Their goal was to make the product as large as possible. Think to yourself (no pencils or calculators!) what Debra should do with the other two digits to make the greatest possible product. Write your ideas on paper and discuss them with your team.

b. With your group discuss where in Alan’s picture you can see the 2 (of the 92) and the 8 (of the 18)? What about the 9 of the 92 and the 1 of the 18? 92 * 18 Find the factors multiplied by each digit… 90 x 10 90 x 8 2 x 10 2 x 8 What part of the picture represents the product? Product is 100 + 720 + 20 + 16 = 1,656 90 2 10 100 20 8 720 16

c. If Alan and Debra had done the opposite (put the 8 with the 9 to form 98 and the 2 with the 1 to form 12), would the product (area) have been larger or smaller? Support your thinking by drawing a figure like Alan’s for this new product. 98 x 12 Find the factors multiplied by each digit… Create a generic multiplication rectangle model… Add the four parts of the model to show the product.

53. Alan is working with 1 hundred block, 5 ten blocks, and 6 one blocks. He wants to use all of these blocks to make another rectangle. (Resource Manager) Obtain blocks from the math box. Work with your team to help Alan arrange his blocks into a rectangle. Is there more than one way to do this? Be prepared to share your ideas with the class. Sketch two of your rectangles on your paper and label their dimensions. Are the dimensions of each of your rectangles the same, or are some of them different? Alan labeled the dimensions of his rectangle “10 + 2” and “10 + 3.” Why might these labels make sense? Which of the possible arrangements makes it easiest to see the dimensions and area of the rectangle? Contribute your ideas to the class discussion and then sketch the rectangle that you chose. How are the total value of the blocks and the dimensions of the rectangle related? If the one block has one square unit of area, what is the area of Alan’s rectangle? Explain at least two ways you can determine the area.

Find the product using the traditional computation method. 54. Alan has another idea… This time, he is trying to multiply 12 · 13 and get an exact answer without having to build the product with Base Ten Blocks as he did in problem #53. Alan drew this diagram… Examine Alan’s diagram and discuss with your team how it relates to the shape he built with blocks. Why did he label the sides "10 + "3 and "10 + 2"? The shape that Alan drew is called a generic rectangle, because it represents the blocks he used without drawing each individual block or drawing the rectangle to scale. Copy Alan’s generic rectangle onto your paper and find the areas of the four smaller rectangles. The upper-left section is already done for you. Find the product of 12 x 13 by adding the products in the generic rectangle. Find the product using the traditional computation method.

Tonight’s homework is… 2.3.1 Review & Preview, problems #55-#59. (text page 78) Label your assignment with your name and Lesson number in the upper right hand corner of a piece of notebook paper. (Lesson 2.3.1) Show all work and justify your answers for full credit.