Define algebra as three things: the study of number properties and equations, the development of mathematical truths, and the application of both.
Tell students they have already been practicing algebra without knowing it. Making this statement will lead them to look for similarities and differences between algebra and what they already know.
Write a number on the board and ask a student to draw a visual for that number. For the number 5, a student might draw five circles.
Ask the students what 5 means. Prompt them to question the concept of number values. Redraw the visual as a quantity of individual units -- five circles spaced out. Explain that in algebra they need to view all numbers this way, as a certain number of individual units. You can use a tower of five blocks to show that 5 is just a certain quantity of single units.
Explain that properties like number value are topics that mathematicians debate but that they agree upon certain mathematical truths, the value of a specific real number being one of them.
Provide a sample problem such as 1 + 4. Ask a student to solve the equation. When he provides an answer, ask him how he arrived at it.
Prompt the students with questions until they reveal that the answer is 5 because addition means putting values together and the value of the numbers together is 5. Allow students to draw visuals to explain their statements.
Explain that complete mathematical equations are like spoken statements: they have specific meanings and explain a truth. For example "1 + 4 = 5" means that when you have one unit and add four more units you get a group with a value of five units.
Write "1 + ? = 5" on the board. Beneath the equation write, "When you have one unit and add an unknown number you get five units." Restate the equation as many times as possible. For example, "I have five units, and I know that you gave me one, how many did Ronnie give me?"
Allow the students time to answer. The question seems like a trick, so it may take a moment for them to arrive at the solution, 4. When the students respond correctly, explain that the "?" doesn't change the other parts of the equation. It just means there is a question about one part of the statement; this is called a variable.
Review the concept that math has truths and variables that are part of a language of equations and numbers. Ask students what happens when different people have different opinions about what is true and what a variable means.
Write "1 + 5 * 10 = ?" on the board. Allow students to solve the equation. Wait until students provide two solutions, 60 and 51. Ask students how they got the two answers. If the students do not offer both of these answers, give the missing value and ask them which is correct.
Tell students that like agreements about sentences and number values, everyone has to agree on how the operations in an equation work, or else they lose their meaning. Explain that 51 is the correct answer because of one of these agreements, the order of operations, which explains which parts of an equation to do first.
Provide additional examples of algebraic concepts. For example, present two problems: 2 + 4 and 4 + 2. Ask for answers. Explain that the reason the two equations have the same solution is an algebraic property called the commutative property of numbers.