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Eight Mathematical Practices


Explanation of the Eight Mathematical Practices

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
The Eight Practices are:

Figure 1. Common Core Standards for Mathematical Practices


  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 (Common Core Standards Initiative, 2012).

 eight practices

Websites for explanations
Check out this list for a specific description of each.  Click on a standard, then read the "Classroom Observations" section to get a better understanding of each standard.  You can also watch the videos to get further information.
Here's another website with great resources.
And more info from the CCSS website.
But my favorite website for the Eight MPs?  It's this website called ThinkMath.com.  I find their explanations very easy to understand.


Posters to put in your classroom

math practice poster  


But really.  What do the MPs mean?  I'm so confused!

So, what are the MPs?  How can you explain them in really easy terms?  Here goes:

Let’s say I, Amy, ask Shaun to go get me a sandwich for lunch.  Let’s see how he figures out how to do this using the MPs.


1.  Make sense of problems and persevere in solving them:  Shaun has to ask himself, “I wonder what kind of sandwich she wants.”  Then he has to figure out where to go get the sandwich.

2.  Reason abstractly and quantifiably:  Shaun says to himself, “I’m pretty sure Amy will want only a 6 inch sandwich, and only one, not 20 sandwiches.”

3.  Construct a viable argument and critique the reasoning of others:  Shaun tells Kelly that he’s going to get me a veggie sandwich.  Kelly tells him he should really get me some chicken noodle soup and a salad.  Shaun replies, “I disagree with you, Kelly.  Amy’s a vegetarian and doesn’t eat chicken.  I think I’ll stick with the veggie sandwich, but you are right about the salad.  She’s always watching her caloric intake and she likes salad.  I will pick one up.”

4.  Model with mathematics:  Shaun pulls out a piece of paper and creates a table with all the ingredients he knows I want on my sandwich to hand to the clerk at the deli.  And then, just for fun, he draws a diagram of how it should be constructed.

5.  Use appropriate tools strategically:  Realizing that the deli has an app, Shaun pulled out his iPhone, downloaded the app, and uses it to place the order ahead of time.  Then he uses a map to find the deli.

6.  Attend to precision:  Just to make sure the deli gets the order right, Shaun calls and speaks to the clerk.  He states, “Be sure to include 3 tomato slices and 6 avocado slices.  And yellow mustard, not Dijon.”

7.  Look for and make use of structure:  This MP has kids use what they already know to solve problems.  Shaun says to himself, “I already know that the deli has a deal where you can get a sandwich and a side.  I’ll order that for Amy.”

8.  Look for and express regularity in repeated reasoning: Shaun checks himself.  He wants to use a strategy he’s already used and check for reasonableness.  He steps back, realizes he’s ordered sandwiches from this deli before and knows a shortcut how to get there, checks the order to make sure it’s correct, and heads off to get me lunch.

What a good friend!


Checklist to keep records


A Really Clear Video to Explain the Eight MPs 

Mathematical Practices Video part 1 of 2  (if you're watching this at school, you'll have to enter your username and password to get past the block.)
To get information about MP 1, go to 3:16 in the video.
To get information about MP 2, go to 6:06 in the video.
To get information about MP 3, go to 9:02 in the video.
To get information about MP 4, go to 10:28 in the video.
Mathematical Practices Video part 2 of 2  (if you're watching this at school, you'll have to enter your username and password to get past the block.)
To get information about MP 5, go to 0:00 in the video.
To get information about MP 6, go to 6:37 in the video.
To get information about MP 7, go to 7:40 in the video.
To get information about MP 8, go to 8:47 in the video.

MPs in Kid Friendly Language 


Classroom Sneak Peeks:


Standards Bookmarks and Parent Guide:


Explanations and Commentary

Very interesting commentary out of the University of Arizona (go Wildcats!). 
ep1 ep2  
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Thank you to 4th Grade Loma Portal teacher, Amy Kinseth, for creating this page of Teacher Common Core Materials. Please email her with questions or comments at akinseth.lomaportal@gmail.com.