Practice Makes Perfect with the Math Practices

My students are becoming better at math than me! While this may seem shocking, I love it because it means The Common Core State Standards are effective and having more of an impact than standards from the past. While memorization, procedures, and “tricks” in math help people get the right answer, there are no mathematical connections that transfer into middle school algebra and higher math courses throughout one’s education. One of the most important but often overlooked parts of the new standards for math are the Standards for Mathematical Practice. While I believe the grade level standards alone are powerful, they cannot be achieved successfully without the implementation of the standards of practice.

The Standards for Mathematical Practice are as follows:

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

So, what do they have to do with the actual grade level standards? Through problem solving, students need to be given opportunities to practice the practices in order to meet the grade level standards. Just like we teach reading strategies and give students opportunities to practice, we have to do the same with math. For example, in reading, students learn to examine the structure and organization of fiction, nonfiction, poetry, etc. In math they need to learn how to make use of structure (Practice 7) in multiplication, division, addition, and subtraction.

I make a daily math goal around the different Standards for Mathematical Practice. For example, when working on multiplication of fractions (4th grade Common Core Standard 4.NF.4c), The goal could be: I can find regularity in repeated reasoning. Through a word problem**, students might solve 4 x ¾ and determine it is 3. They can use this knowledge to solve 12 x ¾ by understanding that there are three sets of 4 x ¾ in 12 x ¾, or 3(4 x ¾) (Associative Property of Multiplication), or even (4 x ¾)+ (4 x ¾) + (4 x ¾) (Distributive Property of Multiplication). Once they have the answer to 4 x ¾, they can repeat that reasoning 3 times to get the answer  for 12 x ¾ (Distributive Property of Multiplication) or simply multiply their answer for (4 x ¾) by 3 (Associative Property of Multiplication). This reasoning is important because it draws on mathematical properties. At first, I identify the properties with my students and model correct representation through number sentences (which could be tied to the Mathematical Practice of “attend to precision”). These are practices students need in order to be truly successful in math.

Implementing the content grade level Common Core State Standards and the Standards for Mathematical Practice has taken my math instruction to a whole new level. It has been a learning journey for me and I am constantly finding ways to improve my math instruction. I would be lying if I said it was easy, but in the end, my students benefit from my hard work...what more could I ask for?

**Word problems are posed with a variety of number choices so students can try easier or more difficult problems based on differentiation.

Example: Ms. K is making ______ peanut butter sandwiches. Each sandwich needs ¾ of a cup of peanut butter. How many cups of peanut butter does she need? (4)    (12)    (16)  (18)