# 2. From partial products to standard algorithm (C)

teaches Common Core State Standards 5.3B http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 6.3D http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 6.3E http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html
teaches Common Core State Standards 5.C.1 http://www.doe.in.gov/standards/mathematics
teaches Common Core State Standards 5.AT.1 http://www.doe.in.gov/standards/mathematics
teaches Common Core State Standards CCSS.Math.Content.5.NBT.B.5 http://corestandards.org/Math/Content/5/NBT/B/5
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8
teaches Common Core State Standards MAFS.5.NBT.2.5 http://www.cpalms.org/Public/search/Standard

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Lesson objective: Extend the understanding that the standard algorithm for multiplication is an efficient method for solving multi-digit multiplication problems.

Students bring prior knowledge of multiplying multi-digit numbers using the partial products method from 4.NBT.B.5. This prior knowledge is extended to using the standard algorithm as students compare the partial products method and standard algorithm.  A conceptual challenge students may encounter is understanding the shortened steps of the standard algorithm.

The concept is developed through work with the partial product method, which is examined in a side by side comparison with the standard algorithm.

This work helps students deepen their understanding of operations because they gain an understanding of how place value concepts apply to the steps of the standard algorithm.

Students engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as they compare the steps in the partial products method to the steps in the standard algorithm.

Key vocabulary:

• partial products
• standard algorithm

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