# Practical Problem Solving: Analyzing Relationships in Math

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This post originally appeared on the blog 4MULAFUN: Differentiating Curriculum Through Interactive Notebooks, Work Stations, and more!

Within the Common Core State Standards (CCSS) and Texas Essential Knowledge and Skills (TEKS) new standards have arisen to promote the communication of math skills. Common Core Math Practice Standard 3 states, “Students should construct viable arguments and critique the reasoning of others,” and Standard 8 states, “Students should look for and express regularity in repeated reasoning,” while the Texas Essential Knowledge and Skills Math Practice Standard 1f states, “The student is expected to analyze mathematical relationships to connect and communicate mathematical ideas.”

Last week I talked about the importance of building communication in mathematics while focusing on problem solving and gave some ideas on how to incorporate those in your classroom. If you haven’t had a chance to read that post, make sure to check it out! Communication is the FOUNDATION for building proficient problem solvers and we must make sure that we aren’t the only ones that are communicating but our students are doing their fair share as well!

So what does it mean to analyze relationships in math? “When a student analyzes a mathematical relationship between two or more quantities, he or she looks for a pattern or a structure and uses it to solve a problem. He or she can see how two quantities are alike or different mathematically based on their attributes or properties.” (Strategies for Mathematics Instruction and Intervention, Weber/Crane-2015). Analyzing relationships is one of the highest levels on Bloom’s Taxonomy and therefore a very difficult area of understanding for students due to the complexity of situations and problems at this level.

When we are working with students we need to make sure that we are not only communicating effectively so that they understand what we are wanting from them, but that we also use words that will help spark clear thinking and comprehension. For instance, analyze may be a difficult word for many students as it is so abstract. Teach students other words that are similar so that they can think for themselves when working on an assignment. Here are some useful power words that you may want to use in your classroom.

A common way to use analyzing in the classroom is to choose two related concepts (or even numbers) and compare them. As you can see in this activity from an 8th grade classroom students compared the formulas for surface area and volume of a rectangular prism. While most students wouldn’t think twice about how they were related it is definitely something worth making the connection over.

As I just stated, you can do this with numbers at the lower levels. Think of doing your Number of the Day program (or Number Talks) and how you can incorporate comparing numbers like 937 and 97. Students should see that 97 is approximately 10 times less than 937, the 7 is in the same place in both numbers therefore both numbers show the value of having 7 ones, and so on. There are so many connections that students can make with numbers and this allows analyzing in math to start at the early grades as well.

Building the deductive reasoning skills that are needed when analyzing items is important as that is what allows our problem solvers to think further and become that student that continues to ask WHY?!

What can you do this week to promote analyzing in your classroom?

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Jennifer Smith has been an educator since 2003 with experience in elementary, middle school and college. Math has been her passion since a young age which no doubt resulted in her secondary math teaching career which is where she learned about Teachers Pay Teachers and created her store Smith Curriculum and Consulting (formerly 4mulaFun). Currently Jennifer is a Differentiated Curriculum Designer and Presenter traveling the nation to train teachers on the effectiveness of Interactive Notebooks, Differentiation, and Making Math Purposeful  in the classroom. When she is not traveling and training she lives in Dallas, TX with her four rescue dogs.