The easiest way to explain the meaning of an equation is to use a balance scale with clearly marked weights. Explain that an equation is like a balance scale and the two sides of an equation must be equal in the same way that a balance scale must have equal weights in both pans.
Illustrate equation solving by taping over the number indicating the weight on one of the pieces. Encourage the student to find the unknown weight by subtracting equal amounts of weight from both pans of the balance scale until he finds the weight of the unknown piece.
This emphasizes that algebra enables people to find an unknown value by working with values that are known. It also reinforces the idea that, if operations are performed on one side of an equation, they must be performed on the other side also.
Learning abstract concepts is frequently easier when those concepts can be introduced using concrete knowledge the student already has. When solving money problems, for example, place a combination of coins on the table and ask him how much money is there. Suppose he has five quarters, seven dimes and nine nickels. Help him understand that the total amount of money = amount of money in quarters + amount of money in dimes + amount of money in nickels. Furthermore, the amount of money in quarters is equal to (value of each quarter) x (number of quarters). In this example, it is 25 x 5 = 1.25. Similar logic applies for the dimes and nickels. It is easy to set up an equation using q for the number of quarters, d for the number of dimes and n for the number of nickels. As an equation, the total amount of money = 25q + 10d + 5n. In this way, he has made the transition between a concrete amount of money and an algebraic way of representing that amount.
Learning algebra requires making a transition from the printed word to graphs and diagrams. Many students, particularly if their spatial skills are weak, find this difficult. To help a student struggling with plotting points, teach the method, rehearsing it as often as necessary. To plot ordered pairs in which the first number represents an x-coordinate and the second number represents a y-coordinate, tell the student to place her pencil on the origin, the place where the x- and y-axes meet. She should move her pencil horizontally to find the x-coordinate and vertically to find the y-coordinate. If the point is, for example, (- 2, 5), she should move her pencil two units to the left, which is the negative direction on the x-axis, and five units up. After she has moved over and up, she should pencil in a dot. If she wants to plot the point (0, - 2) she should not move her pencil horizontally at all because the x-coordinate is 0, but she should move down two units. Note that when the x-coordinate of an ordered pair is 0, the point will fall on the y-axis. If the y-coordinate is 0, the point will lie on the x-axis.
Check the Internet for sites dedicated to teaching mathematics. Several have good instructional videos and video games that reinforce graphing skills.
If your child knows even a few words in a foreign language, she already understands the idea of translation. Tell her that mathematics is a language and that you have to learn new ways of expressing things using algebraic notation. Ask her how she would learn new vocabulary in a foreign language. She will probably be familiar with the idea of flashcards. You can make flashcards and review them together. Some examples are "the sum of a number and 4" is x + 4 in algebraic notation. "The product of a number and 13" is 12x. Pay particular attention to expressions involving subtraction because, very often, the order of the expressions in algebraic notation is the opposite of the order in English. The expression "5 less than a number" is "x - 5" in algebraic notation and "13 subtracted from a number" is "x - 13."