Comparing numbers is an important skill in mathematics. It helps us understand the relationship between different quantities and values. When comparing numbers, we use symbols like greater than (>), less than (<), or equal to (=) to show how the numbers relate to each other.

When comparing whole numbers, we look at the value of each digit in the numbers to determine which is greater or less than the other.

Compare the numbers 345 and 278.

First, compare the hundreds place. 3 is greater than 2, so 345 is greater than 278.

Written as an inequality: 345 > 278

Compare the numbers 621 and 621.

Since the numbers are the same, they are equal.

Written as an inequality: 621 = 621

When comparing decimals, we compare the place values of the digits from left to right.

Compare the decimals 3.25 and 3.5.

The whole numbers are the same, so we compare the tenths place. 2 is less than 5, so 3.25 is less than 3.5.

Written as an inequality: 3.25 < 3.5

Compare the decimals 7.89 and 7.89.

Since the decimals are the same, they are equal.

Written as an inequality: 7.89 = 7.89

When comparing fractions, we can use a common denominator to make comparisons easier.

Compare the fractions 1/3 and 2/5.

Find a common denominator. In this case, the common denominator is 15.

1/3 = 5/15 and 2/5 = 6/15. Now we can compare the fractions more easily.

6/15 is greater than 5/15, so 2/5 is greater than 1/3.

Written as an inequality: 1/3 < 2/5

Compare the fractions 4/7 and 4/7.

Since the fractions are the same, they are equal.

Written as an inequality: 4/7 = 4/7

When comparing numbers, remember these key points:

- Compare the digits from left to right.
- Use the greater than (>), less than (<), or equal to (=) symbols to show the relationship between the numbers.
- When comparing fractions, find a common denominator to make comparisons easier.

Practice comparing whole numbers, decimals, and fractions to strengthen your understanding of this important math skill!

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Measurement (NCTM)

Understand measurable attributes of objects and the units, systems, and processes of measurement.

Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute.

Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems.

Understand that measurements are approximations and how differences in units affect precision.

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.

Grade 5 Curriculum Focal Points (NCTM)

Geometry and Measurement and Algebra: Describing three-dimensional shapes and analyzing their properties, including volume and surface area

Students relate two-dimensional shapes to three-dimensional shapes and analyze properties of polyhedral solids, describing them by the number of edges, faces, or vertices as well as the types of faces. Students recognize volume as an attribute of three-dimensional space. They understand that they can quantify volume by finding the total number of same-sized units of volume that they need to fill the space without gaps or overlaps. They understand that a cube that is 1 unit on an edge is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume. They decompose three-dimensional shapes and find surface areas and volumes of prisms. As they work with surface area, they find and justify relationships among the formulas for the areas of different polygons. They measure necessary attributes of shapes to use area formulas to solve problems.