Some students find algebra intimidating because they are uncomfortable replacing numbers with letters. However, basic algebra builds directly on things they already know from arithmetic. To teach beginning algebra, set up short exercises within 20-30 minute lessons using equations that are easy to prove.
- Show how algebra works with basic addition
Set up an equation starting with single-digit numbers, such as 3 + 4 = ?. The student provides the answer 7. Increase one of the numbers, as in 3 + 5 = 8, to reinforce the pattern. Ask the student to find the missing number in a similar pattern, as in 3 + ? = 9. The student should answer 6. If the student has trouble, help them count up on their fingers. Let them know that by finding the missing number, they have solved an algebra problem.
- Demonstrate converting addition to subtraction
By the time they begin algebra, most students are familiar with how addition and subtraction relate. Use that familiarity. Check the student's understanding. For example, write 8 + 7 = 15 and 15 - 8 = ?. The student should easily solve the second equation. Next, put the missing number in the middle of an operations, such as 11 + ? = 24. Ask the student to rewrite it as a subtraction problem like the example you showed them. The student should write 24 - 11 = ?.
- Teach the student to solve on both sides
Write a new equation, such as 32 + ? = 51. Tell students they can solve the equation if they can get the question mark by itself, as they did in the other examples. Demonstrate how you can move the 32 to the other side by subtracting it from both sides. 32 + ? - 32 = 51 - 32 0 + ? = 51 - 32 19 = 51 - 32
- Substitute x and repeat
Start using letters instead of question marks or empty boxes. Explain that the letter is just standing in for an unknown number. Repeat the lesson for different kinds of operations.