The math your first-grader learns forms an essential basis for his future schooling. Understanding the main mathematical concepts typically incorporated into the first-grade classroom can help you better understand a child's progress and reinforce what he learns outside the classroom.

## Number Knowledge

Learning to count, write and compare whole numbers up to roughly 100 is an important milestone of first-grade math. A component of this number knowledge is an understanding of the base ten number system, which puts an emphasis on groups of tens and ones. For example, your first-grader should understand that ten sets of ten units equals 100 units. In addition, your first-grader should also be able to count upward by multiples of twos, fives and 10s.

## Addition and Subtraction

First-graders should also begin to master the basic principles for solving addition and subtraction problems within a range of 20. This could include using number sentences involving addition and subtraction, such as 5 + 5 + 5 = 15, or it could involve determining relationships between simple addition and subtraction problems, like 2 + 4 = 10 - 4. Other skills that you can reinforce in a first-grader are the ability to indicate addition and subtraction on a number line and the matching of word problems to number sentences.

## Number Patterns

As part of your first-grader's ability to count upward in units of multiples, she should also begin to recognize and anticipate number patterns. For example, if your first-grader understands multiples of fives, she should be able to establish a pattern of numbers by counting five, 10, 15, 20 and so on, predicting the continuation of the series based on her knowledge of multiples. Another example of the acquisition of this skill is being able to discern between even and odd numbers.

## Shapes

Another essential element of first-grade math is developing a preliminary understanding of geometric shapes, such as triangles or circles. This can involve understanding shapes on a two-dimensional and three-dimensional level while also using these shapes to comprehend simple fractions. For example, your first-grader should be able to understand how a circle can be divided into wedges.

## Real-world Applications

A final application inherent in first-grade math is applying basic principles to real-world problems. This can consist of the ability to tell time, count the days and months on a calendar, count dollars and cents and understand temperatures and weights. Comparing lengths is also an important math skill for first-graders. For example, your first-grader should be able to combine a series of equal-sized units or shapes to achieve a requested length.

#### References

- State of Washington: Mathematics K-12 Learning Standards
- National Governors Association Center for Best Practices, Council of Chief State School Officers: Common Core State Standards Initiative: Mathematics Standards, Grade 1
- State of California: Mathematics K-12 Learning Standards
- North Carolina Department of Public Instruction: Instructional Support Tools: 1st Grade Mathematics
- First Grade Common Core State Standards

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