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3.OA.B.6 *This standard is part of a major cluster Standard Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Standard Unpacked This standard refers to various problem structures (table included at the end of this document) and the various problem structures. Since multiplication and division are inverse operations, students are expected to solve problems and explain their processes of solving division problems that can also be represented as unknown factor multiplication problems. Example: A student knows that 2 x 9 = 18. How can they use that fact to determine the answer to the following question: 18 people are divided into pairs in P.E. class? How many pairs are there? Write a division equation and explain your reasoning. Multiplication and division are inverse operations and that understanding can be used to find the unknown. Fact family triangles demonstrate the inverse operations of multiplication and division by showing the two factors and how those factors relate to the product and/or quotient. Example: Sarah did not know the answer to 63 divided by 7. Are each of the following was an appropriate way for Sarah to think about the problem? Explain why or why not with a picture or words for each one. Multiplication and division are inverse operations. They both involve a number of groups, a number in each group and a total number. In multiplication, both the number in each group are usually known, but the total number needs to be found. With division, either the number of groups or the number in each group and the total number are usually known. The unknown number needs to be found. A table of multiplication facts can be used to find division facts. One of the major strategies for division facts is Think Multiplication. The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable. 3rd Grade Mathematics ● Unpacked Content Page 48 Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations. Domain: Speaking Questions/ Activities to check for understanding and increase rigor: Jahyden was sharing his candy with his friends. He shared 32 pieces of candy. How many friends could he have shared the candy with? Explain your thinking. Danielle has 48 lollipops to share with her friends. If she has 6 friends, how many lollipops would each friend get? If she has 8 friends, how many lollipops would each friend get? Why does the number of lollipops change based on the number of her friends? Explain how you can use multiplication to solve a division problem. Use models, drawings and/or examples to support your answer. Rachel says that if you know 4 x 6 = 24, then you know what n equals in 24 ÷ n = 6. Why is she correct? Use the numbers 5, 6, and 30 to write a multiplication story. Write a related division story. Level 1 Entering Explain division as an unknownfactor problem using key words to teacher. Level 2 Emerging Explain division as an unknownfactor problem using key phrases to a partner. Level 3 Developing Explain division as an unknownfactor problem using simple sentences with sentence frames in a cooperative group. Level 4 Expanding Explain division as an unknown factor problem using complex sentences in a cooperative group. Level 5 Bridging Explain division as an unknown factor problem using a variety of simple & complex sentences that justify their thinking independently. ELD Standard #3: English Language Learners communicate information, ideas, and concepts necessary for academic success in the content area of Mathematics.