One of the best things about this strategy is that it allows the teacher to check for understanding as a class and as individuals, without the pressure of a graded assessment. When teaching multiplication of first-degree polynomials (x+1, -x+3, -2x-4, etc.), the teacher may choose to teach the students by using the “foil” method. This is an acronym that stands for “first,” “outside,” “inside,” “last,” and teaches which terms to multiply in which order, in order to include all terms. The teacher would begin by showing the students how to draw the necessary lines that indicate multiplication.

The first Check for Understanding strategy would be to ask two students (chosen as a sample of the class) to come up and draw the lines as well. This is an easy step, but it is a crucial step to understanding the entire process. The next step may be to begin with the same easy example to show the students what the process translates to in terms of the following table: 

After completing a few of these tables, the teacher could ask multiple students (also chosen as a representation of the class) to come to the board and fill in the table. This is one of the more difficult steps and may trip students up, so it may be necessary to repeat this process to make sure no false positives were received. The next step would be to turn the products in the table into a polynomial: (x²-5x-x+5) = (x²-6x+5). A teacher could use the Check for Understanding strategy again and ask a few different students to use the tables from before and turn them into polynomials. If students struggled with any of these initial checks, it may be necessary to complete more examples or re-teach the process by using a different strategy. By checking for understanding along the way, it leaves fewer opportunities for students to get and stay confused. As the final step, the teacher may choose to have the students complete a few examples on their own paper. The teacher should circulate the room and take mental notes of who understood and who did not. If it seems like the majority of the class got them all right, the job is complete. If it seems like the class did not grasp the material, it may be necessary to try to place the students into groups of varied levels of understanding and give each group more problems to complete, working more closely with those students that need extra help.