By the end of grade four, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare simple fractions and decimals. They understand the properties of, and the relationships between, plane geometric figures. They collect, represent, and analyze data to answer questions.

• 1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences:

  1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).

  1.2 Interpret and evaluate mathematical expressions that now use parentheses.

  1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.

  1.4 Use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships.

  1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given.

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• 2.0 Students know how to manipulate equations:

  2.1 Know and understand that equals added to equals are equal.

  2.2 Know and understand that equals multiplied by equals are equal.

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