Learn on PengiIllustrative Mathematics, Grade 5Chapter 5: Place Value Patterns and Decimal Operations

Lesson 5: Order and Solve Problems with Decimals

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

Property

To find a number xx between two decimals aa and bb (where a<ba < b), rewrite both as equivalent decimals with an additional place value by adding a trailing zero. This allows you to identify a value for xx such that a<x<ba < x < b.

Examples

Section 2

Compare by Aligning Place Values

Property

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.

Examples

Section 3

Application: Interpret Comparisons in Context

Property

The interpretation of a "better" rate depends on the context:

  • Performance (e.g., speed, output): A larger unit rate is greater or faster.
  • Cost (e.g., unit price): A smaller unit rate is cheaper or a better value.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Finding a Decimal Between Two Decimals

Property

To find a number xx between two decimals aa and bb (where a<ba < b), rewrite both as equivalent decimals with an additional place value by adding a trailing zero. This allows you to identify a value for xx such that a<x<ba < x < b.

Examples

Section 2

Compare by Aligning Place Values

Property

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.

Examples

Section 3

Application: Interpret Comparisons in Context

Property

The interpretation of a "better" rate depends on the context:

  • Performance (e.g., speed, output): A larger unit rate is greater or faster.
  • Cost (e.g., unit price): A smaller unit rate is cheaper or a better value.

Examples