Kindergarten math needs to focus on acquiring and internalizing the concept that numbers are finite and that the value of the numbers will always be the same. Students should learn to recognize and recite digits up to 10, at a minimum. They should understand about the characteristics of things around them, such as size, geometric shape and weight, and be able to separate items by common characteristics. Kindergartners need to be able to demonstrate how to set up a simple math problem and develop a basic understanding of addition and subtraction.
First-graders are expected to build upon the skills they developed in kindergarten. They should now be able to recognize that numbers are symbols representing amounts up to 100. For example, the number 56 is represented by the digits 5 and 6. Addition and subtraction skills are more complex, and students should show a beginning understanding of the concept of dividing things into parts, or fractions. They should be able to read a common mathematical sentence that includes the plus/minus and equal signs.
Concepts learned in first grade are built upon in the second grade. Students should now be able to use the properties of subtraction and addition using larger quantities up to 100 and should have a greater understanding of fractions as being part of a whole. Second-graders should be able to identify shapes as geometrical objects and understand their relation to other shapes. They should understand the concept of measurement, such as inches or centimeters. Problem-solving skills should show an understanding of relationships between numbers and the real world, such as how to tell time and express the time in numeric value. Students should be able to interpret word problems and set up numerical sentences to solve the problems.
Students in the first three grades should understand the concepts of adding and taking away and the relationships to quantities that this represents. These young students should become familiar with the ways simple mathematics is relative to their daily lives, such as through telling time and acting according to schedule. They should understand how money functions. Problem-solving skills should also be emphasized, and teachers or parents should ensure the students know how to recognize mathematical problems or questions when they arise. One such problem would be: "To drive to Disneyland from Evie's house is 420 miles. If she traveled nine hours with no stops in between, how fast was she driving?"