Mathematical learning in fourth grade focuses particularly on multi-digit multiplication and division, equivalent fractions and multiple units of measurement. Because more complex math operations are being taught, the fourth grader is expected to recall basic math facts with ease and fluency. Children who struggle to master this skill may find themselves falling behind, as new ideas in geometry and algebra are also introduced in this year of math.

## Multiplication and Division

Fourth grade brings specific challenges best met by a child well-practiced in math fact fluency. The fourth-grade student needs also to have a logical understanding of place value and a clear awareness of number value. With these skills, the student can estimate an approximate amount when multiplying the multi-digit numbers introduced in this year, and can then verify the reasonableness of the resulting computation. Awareness of the process of division as the inverse of multiplication is also a key component of math understanding, and being able to decide logically what the remainder of a divided amount represents and how to account for it is also a critical part of number sense at this grade level. These more complex ways of thinking can present difficulty for the student who is not at ease with manipulating numbers beyond single and double digits.

## Fractions

A working comfort with fractions and equivalent values (3/9 = 1/3) is another significant concept introduced in the fourth-grade year. Understanding how a single unit can be divided into fractional parts, (a pan of brownies divided to serve a class of students, for example) and knowing how to multiply fractions by whole numbers are ways the fourth-grade child is expected to build on work from third grade that explored simpler fractions. The older student is expected to compare fractions with different denominators (1/3 < 4/5, for instance) and should be able to place them in the proper sequence on a number line. This more abstract expectation of working with numbers is often easier for children who are given tangible objects to manipulate, or drawings to divide and shade.

## Geometry Introduction

Unlike the math standards of the past, the Common Core State Standards Initiative introduces geometry concepts much earlier in the school curriculum. Being able to classify two- and three-dimensional shapes by lines and angles, and talk in specific vocabulary terms (such as face, base, vertex, and edge) are the geometry concepts expected to be understood in the fourth-grade year. Resulting work with transformations and symmetry are explored, as children describe and sketch rotations of some geometric patterns. Drawing lines and angles and measuring them are expected skills the student should prepare to master and can frustrate the child with underdeveloped fine motor skills. Practice drawing lines with a ruler and tracing around simple stencils to prepare the student for work with two-dimensional geometry sketches in fourth grade.

## Algabraic Thinking

Early introduction to algebra is now standard in the curriculum. Its importance in mathematics means that fourth graders need to think flexibly about number operations in order to verify a correct or incorrect expression with a variable (27 - x = 14, for instance). Writing number sentences to represent story problems can be difficult for students without a comfortable working vocabulary for mathematical operations, and can particularly challenge the non-native English language speaker. In addition to mastery of basic math facts, frequent practice with the four math operations (addition, subtraction, multiplication, and division) and real-world experiences with numbers are recommended to help prepare the entering fourth grade student for a new school year.

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