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Students need to have a lot of experience with tens and ones and Direct Modeling, so they can manipulate them breaking them apart and grouping them together. This will allow them to use invented algorithm an multiply and divide with multi digit numbers.

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Students need to have a lot of experience with tens and ones and Direct Modeling, so they can manipulate them breaking them apart and grouping them together. This will allow them to use invented algorithm an multiply and divide with multi digit numbers.

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Direct modeling with tens. Understanding that tens can be broken apart.

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Direct modeling with tens. Understanding that tens can be broken apart.

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On page 115, sometimes students use Measurement and Partitive Division.

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Direct modeling with tens for multiplication problems requires an understanding of base-ten concepts.

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With adding strategies, children represents each group with a numeral, make use of their invented algorithm, and notate in order to keep track of their computation.

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Manipulating and breaking apart numbers is a higher thinking skill that students need in order to be successful. Students need to develop sense making too and find patterns because math is all about patterns.

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Some strategies lend themselves to specific problems types. For example doubling is a strategy you can use for muesurement division problems, but would be difficult to apply to partitive division problems.

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In Partitive Division problems children organize or break down objects to make tens.This allows students to show higher thinking skills.

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Children will use the necessary strategies to solve the problems

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Children tend to use base-ten materials to solve a multiplication problem only when more than ten objects are in the collections described in the problem.

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Students use invented algorithms but they are also selective in which strategies they will use. They make a choice with the understanding that selecting the right strategy will lead them to the best answer. This awareness is valuable.

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As students begin to learn strategies, many students use tens to help them since it is something that is easy for them to understand.  There are many ways that students can use tens to multiply and divide.

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Understanding the invented algorithms for the different Multiplication and Division problem sets will help to facilitate the conversation with my students to further their thinking in the fall.

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do teachers need to demonstrate prob. solving strategies or should it all be student-guided?

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"Invented Algorithms actually can be more efficient than standard algorithms."
"...Can contribute to the development of children's number sense and and estimation abilities."