When we compare objects, we are looking at their attributes to determine how they are similar or different. In math, we often compare objects based on their size, weight, length, height, or quantity.

To compare objects by size, we look at their dimensions. We use terms like "bigger than," "smaller than," or "the same size as" to describe the relationship between the objects.

When comparing objects by quantity, we count the number of items in each set and determine which set has more, fewer, or the same number of items.

In math, we use symbols to represent comparisons. The symbols < (less than), > (greater than), and = (equal to) are used to show the relationship between two objects or quantities.

For example, if we have two sets of apples, one with 5 apples and the other with 3 apples, we can say that the first set is greater than the second set (5 > 3).

We can express comparisons using both words and symbols. For instance, we can say "The red ball is smaller than the blue ball" or use the symbol to write "red ball < blue ball."

Comparing objects helps us understand the concepts of size, quantity, and relative relationships, which are important in math and everyday life.

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Measurement (NCTM)

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

Recognize the attributes of length, volume, weight, area, and time.

Compare and order objects according to these attributes.

Understand how to measure using nonstandard and standard units.

Select an appropriate unit and tool for the attribute being measured.

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

Use tools to measure.

Grade 2 Curriculum Focal Points (NCTM)

Measurement: Developing an understanding of linear measurement and facility in measuring lengths

Children develop an understanding of the meaning and processes of measurement, including such underlying concepts as partitioning (the mental activity of slicing the length of an object into equal-sized units) and transitivity (e.g., if object A is longer than object B and object B is longer than object C, then object A is longer than object C). They understand linear measure as an iteration of units and use rulers and other measurement tools with that understanding. They understand the need for equal-length units, the use of standard units of measure (centimeter and inch), and the inverse relationship between the size of a unit and the number of units used in a particular measurement (i.e., children recognize that the smaller the unit, the more iterations they need to cover a given length).

Connections to the Grade 2 Focal Points (NCTM)

Geometry and Measurement: Children estimate, measure, and compute lengths as they solve problems involving data, space, and movement through space. By composing and decomposing two-dimensional shapes (intentionally substituting arrangements of smaller shapes for larger shapes or substituting larger shapes for many smaller shapes), they use geometric knowledge and spatial reasoning to develop foundations for understanding area, fractions, and proportions.