How to Do Flow Proofs

Proving statements in mathematics mystifies many students. While some students might feel proofs are hard in general, others will find that taking another approach to proofs can simplify the process. For more visual learners, the flow proof method can demonstrate how each mathematical statement works together to create the final mathematical fact. Doing a flow proof is like drawing a diagram, only with mathematical statements.

Step 1

Find the conditional statements in a proof problem. Look for statements beginning with “if” or “given.” These are the conditional statements. For example, if your goal is to prove “If y = 3x - 2 and y = -x – 6, then 4x = -4,” you have two conditional statements: “y = 3x – 2” and “y = -x – 6.”

Step 2

Write the conditional statements in boxes, each box in a single column. For the example, problem, you would draw two boxes, one above the other. Inside the top box, write “y = 3x – 2.” Inside the bottom box, write “y = -x – 6.”

Step 3

Use your conditionals to come to a logical conclusion for the next step in the proof. Use your knowledge of math to recognize how the conditionals work together to allow you to make a factual statement. For example, the conditionals “y = 3x – 2” and “y = -x – 6” are together a linear system of equations. You can solve for x by subtracting.

Step 4

Write your conclusion in a box to the right. For the example, write “y – y = 3x – 2 – (-x – 6).”

Step 5

Draw an arrow from the boxes on the left to their conclusion on the right.

Step 6

Continue the process of making conclusions based on your most recent boxes until you reach the end of the proof, the statement that you originally wanted to prove. In this example, your next box would follow from y – y = 3x – 2 – (-x – 6). Do the math and write 0 = 4x + 4. Create a new boxes to the right and subtract 4 on both sides of the equation. The new box would be 4x = -4, which is exactly what you wanted to prove.