Unit 4, Lesson 6
Standard Algorithm: Multi-digit Numbers, with Composing
Grade 5
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The purpose of this Number Talk is to elicit the strategies and understandings students have for multiplying three factors, one of which is 10. These understandings help students develop fluency and will be helpful when they apply the standard algorithm to find the product of a three-digit and a two-digit number.
Students have an opportunity to look for and make use of structure (MP7) because they can use previous calculations and the distributive property to find a product.
Find the value of each product mentally.
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to see where instructional routines fit in your journey.
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The goal of this activity is to use the standard algorithm to find the products in which composition of a new unit happens once. Students first calculate a three-digit-number-by-two-digit-number example, using a strategy of their choice, and then analyze the same example, with the composition recorded above the product. Students may use different strategies when they try on their own including:
After students discuss how composing new units is recorded in the algorithm, they find the value of two multiplication expressions, using the standard algorithm.
When students interpret a new way of multiplying a three-digit number by a two-digit number, they use their understanding of place value to make sense of the method (MP7).
Find the value of
Lin uses the standard algorithm to find the value of
multiply. two hundred forty one times 23. 5 rows. First row: two hundred forty one. Second row: multiplication symbol, 23. Horizontal line. Third row: seven hundred twenty three. Fourth row: plus four thousand eight hundred twenty. Horizontal line. Fifth row: five thousand five hundred forty three
“Today we practiced using the standard algorithm to multiply multi-digit numbers with new units composed.”
“What do you have to think about when you are multiplying and a lot of new units are composed?” (I have to keep track of how I record the units. I can make an estimate to see if my answer is reasonable.)
Display students’ work for
"Where did we compose new units when we solved this problem?" (When we multiplied to find the two partial products, we had to compose new units above the 2 and the 6 in 264. When we added the partial products, we composed a new 1 thousand above the 2.)
"How is composing new units when we multiply the same as composing new units when we add?" (When we multiply or add numbers, sometimes we get a value that's too much for the place we’re in. The composed units are recorded separately, and then we add them.)
"How is composing new units when we multiply different from composing new units when we add?" (When we multiply, we are multiplying and then adding the new units. When we add, we are adding the whole time, there is no multiplication.)
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