Although grade seven students should be more than comfortable with adding and subtracting whole numbers, some students may have fallen through the cracks and still have difficulty with regrouping and carrying over techniques. The AAA Math website (in the Resources section) has grade seven practice worksheets and explanatory notes for adding and subtracting five-digit and bigger numbers. Seventh-grade students should also feel comfortable adding or subtracting a series of numbers.
Although students may have learned how to add and subtract fractions and decimals in grade six, they should be completely competent in this area before proceeding to more complex areas, such as algebra and order of operations. Students need to understand that in order to add and subtract fractions, the fractions must have common denominators. For adding and subtracting decimals, students must position the decimal numbers so that all of the decimal points line up, including the answer's decimal point.
Although students may have previously learned about adding and subtracting integers and positive and negative numbers, it is important that students review this skill. In particular, students have difficulty grasping the addition and subtraction of integers compared to multiplication and division. It may helpful for struggling students to visually represent the equations, either using a number line or a plus/minus diagram. For example, for the equation (+3) + (-7), you could draw three plus signs and seven minus signs on the board; show how each plus sign cancels out one minus sign to get the answer (-4). Teach students the rules for addition and subtraction of integers, such as if you are adding two numbers with the same sign, the answer will also have that sign; if you are adding two numbers with different signs, temporarily ignore the sign, subtract the smaller number from the larger number and assign the answer the sign of the larger number; and, if you are subtracting a negative number, the minuses cancel out.
Depending on school and skill level, students may start studying algebra in grade seven. They generally start with solving for variables, such as in an equation like x + 4 = 6. Students need to learn to isolate the variable. Often, this involves simple addition or subtraction to both sides of the equation. In the above example, a student would subtract 4 from each side of the equation to yield the answer x = 2. The same skills are required for solving for variables in an inequality statement. Students may also be called to simply algebraic equations which may involve addition and subtraction. For example, in the expression ab + 2x - x +3ab, students can combine like terms to yield 4ab + x.
Order of operations is an important feature in grade seven math classrooms. Students need to become comfortable adopting the mantra BEDMAS, which stands for brackets, exponents, division, multiplication, addition and subtraction. In terms of addition and subtraction, as well as division and multiplication, students need to realize that addition and subtraction are equal in the order of operations hierarchy. They should work through additions and subtractions from left to right, meaning that if an addition comes after a subtraction, the subtraction should be done first.