We received some comments on one of the questions in the March Math Calendar. We thought we might share some strategies that we use in this blog post.
The question is for March-31st 2016, and is as follows:
This is a very “versatile” question. The answer is specially designed to be a simple round number so that the question can be attempted by students in three different stages.
The first group of students whom we usually give this problem to are the 4th graders. Without specific instructions on how to find the answers, the students usually rely on logic reasoning and Guess-and-Check to find out what B is. Students derive great satisfaction in knowing they are able to solve a problem that looks formidable at first. Here is a video clip of how one of our students solved the question using logic reasoning, with Guess-and-Check.
For more advanced students, we introduce an intermediate method using bar-models. This provides a link between the Guess-and-Check method used by Pre-Algebra students and the formal introduction of solving the System of Linear Equations in middle schools.
Below is another video on how to solve the same problem using logic reasoning and bar models.
It should be noted there are many approaches for this method. For example, we could have equivalently used the pair for variables A and B to solve for B, starting with the last two equations. The key is the use of bar models to visualize the relationships between two variables and deduce the value of B from the given clues.
The last group of students are 8th graders, who are starting to work on Systems of Linear Equations. They would apply the standard method of solving the set of equations and simultaneously derive the values of A, B and C.
What do you think of the use of bar-models as an intermediate step between the Guess-and-Check stage and formal introduction of Systems of Linear Equations? Let us know in the comments below!
For more related resources, please refer to our Bar Models page.