Practicing with brainteasers can introduce students to algebraic concepts. First, the teacher introduces number sentences such as 8+5=5+8 to familiarize students with the purpose of the equal sign. This gives students the opportunity to discuss mathematical ideas beyond computation. Once they understand the relationship the equal sign illustrates between numbers, the teacher can mix up the number sentences and leave blanks instead of completing the equations, such as 8+5=_+8 or 8+5=_+7. The National Center for Improving Student Learning and Achievement in Mathematics and Science urges teachers to “Provide students problems that encourage them to make generalizations about basic number properties. Have students justify generalizations they or their peers propose.”
Remove the numerical equations and use games that require problem solving. Display pictures of two weighing scales with objects on them. One scale shows one object and gives a weight. The second scale shows that same object along with another object and a weight. You have to guess the weight of the second object. For example, one scale has three presents and two flowers on it and weighs 32 ounces. The second scale has six flowers on it and weighs 24 ounces. By dividing 24 by 6 you can determine that the weight of the flowers is 4 ounces each. Use what you have calculated from the second weight to determine the weight of the presents. The two flowers weigh a total of 8 ounces, so you can subtract 8 from 32 to get 24 ounces. Divide 24 by the number of presents (3) and you get 8 ounces as the weight of each present.
Algebra requires mathematicians to identify patterns. Use pattern sequence exercises to develop this problem-solving skill. A boring way to do this is to list a series of numbers and let the students determine what the next number in the sequence should be. More interesting activities include pattern blocks or number pattern blocks. For pattern blocks, students draw the next shape in the pattern based on what they have seen in the previous block patterns. The same can be accomplished with numbers embedded in block patterns.
Solving puzzles helps to make algebraic reasoning seem less like math and more like fun. To help them get used to seeing letters in place of numbers, set up a coded message that can only be deciphered once the letters have been connected with the proper numbers. For example, your equations can read T + 3 = 5; C - 12 = 0; A - 4 = 10. Underneath the equation there are three blank lines with numbers underneath them. Those numbers are the answers to the equations. When the value of each letter is solved, place the letter above the corresponding number to solve the puzzle. In this example T = 9, C = 12, and A = 6. If you arranged the lines as _12_6_T, the word would spell CAT.