In this Grade 5 Illustrative Mathematics lesson (Chapter 5), students practice ordering decimals to the thousandths place by comparing place value to arrange numbers from least to greatest. Using number lines and place value reasoning, students work through true-or-false decimal inequalities and identify decimal numbers that fall between two given values. The lesson addresses standard 5.NBT.A.3.b and builds fluency in comparing and ordering multi-digit decimals such as 565.4, 556.040, and 565.004.
Section 1
Finding a Decimal Between Two Decimals
To find a number between two decimals and (where ), rewrite both as equivalent decimals with an additional place value by adding a trailing zero. This allows you to identify a value for such that .
Section 2
Compare by Aligning Place Values
To compare decimals, align them by their decimal points. Compare the digits in each place value, starting from the largest place (leftmost). The first place where the digits differ determines which number is greater.
Section 3
Application: Interpret Comparisons in Context
The interpretation of a "better" rate depends on the context:
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Section 1
Finding a Decimal Between Two Decimals
To find a number between two decimals and (where ), rewrite both as equivalent decimals with an additional place value by adding a trailing zero. This allows you to identify a value for such that .
Section 2
Compare by Aligning Place Values
To compare decimals, align them by their decimal points. Compare the digits in each place value, starting from the largest place (leftmost). The first place where the digits differ determines which number is greater.
Section 3
Application: Interpret Comparisons in Context
The interpretation of a "better" rate depends on the context:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter