# 1. Understand that digits in numbers represent 1/10 of what they represent in the place to the left (C)

teaches Common Core State Standards CCSS.Math.Content.5.NBT.A.1 http://corestandards.org/Math/Content/5/NBT/A/1
teaches Common Core State Standards CCSS.Math.Content.5.NBT.A.2 http://corestandards.org/Math/Content/5/NBT/A/2
teaches Common Core State Standards CCSS.Math.Content.5.NBT.A.3 http://corestandards.org/Math/Content/5/NBT/A/3
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7

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Lesson objective: Understand that in numbers, digits represent 1/10 of what they represent in the place to the left.

Students bring prior knowledge of the relationship between the digits within a multidigit number from 4.NBT.A.1 (that each place value is ten times greater than the one to its right). Students also bring prior knowledge of decimal notation for fractions with denominators 10 or 100 from 4.NBT.C.6. This prior knowledge is extended to how place values are further related as students explore how a place value is one-tenth of the place value to it's right. A conceptual challenge students may encounter is believing that memorizing the names of the places in which digits are positioned is the key to understanding place value system, when it is actually the value of each place.

The concept is developed through work with base ten blocks and place value chart, which allows for a concrete model of the new concept.

This work helps students deepen their understanding of equivalence because they will explore the idea of a digit to the right of a given digit being equivalent to one-tenth of the given digit.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they analyze the structure of a decimal number and utilize the consistent nature of the base ten number system.

Key vocabulary:

• decimal

• digit

• hundredths

• tenths

• value of a digit

Special materials needed:

• base ten blocks
• place value chart
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