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5.NBT.B.5 *This standard is part of a major cluster Standard Fluently multiply multi-digit whole numbers using the standard algorithm. *Fluently is the end of the year benchmark. In addition to using the standard algorithm, it is appropriate to continue to use strategies and algorithms based on base ten from previous grades. Unpacked In fifth grade, students fluently compute products of whole numbers using the standard algorithm. *Underlying this algorithm are the properties of operations and the base-ten system. In addition to computing using the standard algorithm, students need to recognize and be able to explain WHAT is happening when computing using the standard algorithm. They should be able to draw on strategies and algorithms learned in 3rd and 4th grade to understand how and why the algorithm works. The standard multiplication algorithm is probably the most difficult of the four algorithms if students have not had plenty of opportunities to explore their own strategies first. The multiplication algorithm can be meaningfully developed using repeated addition, model or an area model (connected array), and/or partial products (Van de Walle 2013). This standard refers to fluency which means accuracy (correct answer), efficiency (a reasonable amount of steps), and flexibility (using strategies such as the distributive property or breaking numbers apart also using strategies according to the numbers in the problem, 26 x 4 may lend itself to (25 x 4 ) + 4 where as another problem might lend itself to making an equivalent problem 32 x 4 = 64 x 2)). This standard builds upon students’ work with multiplying numbers in third and fourth grade. In fourth grade, students developed understanding of multi-digit multiplication through using various strategies. These strategies help build understanding for why the standard algorithm works. Refer to 4.NBT.B.5 for examples of other algorithms. Understanding how the standard algorithm works and why it is a good choice (over other strategies) is central to the development of procedural fluency. The main focus in teaching the standard algorithm is not as a memorized series of steps but as making sense of the procedure as a process. Apply the same rule to standard algorithm as to all strategies: If you use it, you must understand why it works and be able to explain it (Van de Walle, 2012). Computation algorithm. A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly. Computation strategy. Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another. In their NCSM article, Fuson and Beckman, describe how standard algorithms are developed in mathematics. There are diverse ways to multiply multi-digit numbers. *While the standard algorithm is the basis of this standard, alternative strategies are also appropriate to help students develop conceptual understanding and make sense of the standard algorithm. The size of the numbers should NOT exceed a three-digit factor by a two-digit factor. Questions to check for understanding and increase the rigor: Write a 3-digit by 1-digit multiplication problem with a product close to 2,000, 3,000, etc.? Model and explain your strategy/s. List two numbers whose product is between 400 and 600. (Extend the thinking with different combinations) Is 4,000 a reasonable estimate for 312 x 9? Explain your reasoning. (Can be extended with other factors, ask students to model thinking, look for patterns, etc.) How does the order of the digits in the factors impact the product? (e.g. 452 x 7 compared to 425 x 7) In a multiplication problem, what happens to the product if each factor is multiplied by 2? What happens to the product if one factor is doubled and the other factor is divided by 2? Is the product of 42 x 63 over or under 2,400? Use what you know about place value in the standard algorithm to explain your answer. You multiply two two-digit numbers and the product is close to 2,600.What two numbers did you multiply? Use 1,2,3,4,5 to make a multiplication problem with the greatest product? How does the placement of the numbers impact the product?