# 3. Multiply decimals (C)

teaches Common Core State Standards CCSS.Math.Content.5.NBT.B.7 http://corestandards.org/Math/Content/5/NBT/B/7
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3

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Lesson objective: Understand that the meaning of multiplication is the same, whether we are working with whole numbers or decimals.

Students bring prior knowledge of multi-digit whole number multiplication from 4.NBT.5 and 5.NBT.5. This prior knowledge is extended to decimals as students multiply a decimal by a whole number. A conceptual challenge students may encounter is understanding that the product of a whole number and a decimal less than one will be smaller than the whole number (e.g., 5 x 0.3 = 1.5).

The concept is developed through work with a rectangular array, which demonstrates why a whole number multiplied by a decimal less than one is smaller than the whole number. Students are also introduced to the compensation strategy for decimal multiplication.

This work helps students deepen their understanding of operations because they can see that the relationship between factors and quotients does not change because a factor is a decimal number.

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they explore multiplying decimals for the first time. They will analyze student errors and the reasoning of others when they explain and discuss why Oliver arrived at the incorrect product.

Key vocabulary:

• compensate
• compose
• decompose
• estimate
• factor
• product

Special materials needed:

• flats, rods, and cubes (base-10 blocks)
• squared paper
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