Standards of Mathematical Practices - One Standard at a Time

Mathematical Practices are embedded in every math lesson we teach.  The Standards for Mathematical Practice describe varieties of expertise that math educators at all levels (K-12) should seek to develop in their students.  These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education.

Mathematical Practice #5

Use appropriate tools strategically.

What should students be able to do?

• Use available tools recognizing the strengths and limitations of each.
• Use estimation and other mathematical knowledge to detect possible errors.
• Identify relevant external mathematical resources to pose and solve problems.
• Use technological tools to deepen their understanding of mathematics.

Questions the Teacher Can Ask to Develop Mathematical Thinking:

• What mathematical tools could we use to visualize and represent the situation?
• What information do you have?
• What do you know that is not stated in the problem?
• What approach are you considering trying first?
• What estimate did you make for the solution?
• In this situation would it be helpful to use..a graph..., number line..., ruler...,diagram...,calculator...,manipulatives?
• Why was it helpful to use...?
• What can using a _______ show us that ________ may not?
• In what situations might it be more informative or helpful to use...?

The Power of the Positive Phone Call Home

Here's an idea your parents will LOVE.  

Thanks for sharing this with us, Alysia!

Click on the link below to read the article:  http://www.edutopia.org/blog/power-positive-phone-call-home-elena-aguilar

POWER SCHOOL is Open for Business

is

See the link below for instructions for entering grades into PowerSchool:

http://www.nixapublicschools.net/files/_4ZAmv_/e06dd25d5c278bdd3745a49013852ec4/ELEM_Entering_Grades_for_Standards.pdf

What Are You Reading? Teachers Share Their Professional Reading Favorites

During our first LNW sessions, we <LOVED> that teachers were sharing what they are currently reading professionally.  Another amazing thing to SHARE?  Yes, please!  Love, love, love! :-)

Garrett Lowder, fourth grade, and Lori Elliott and Josh Bennett, fifth grade, shared Notebook Know-How:  Strategies for the Writer's Notebook by Aimee Buckner.  They mentioned Aimee's nonfiction version Nonfiction Notebooks:  Strategies for Informational Writing and her Notebook Connections:  Strategies for the Reader's Notebook as well.

Steinhouse explains that Buckner "provides the tools teachers need to make writers' notebooks an integral part of their writing programs. This compact guide shows how smart and focused use of writer's notebooks enhances and deepens literacy learning for students in grades 3–8, while also addressing many of the questions teachers ask when they start using notebooks, including how to launch a notebook and how to help students who are stuck in writing ruts".

We've all read Harry Wong's The First Days of School.  But Tammy Myers, fourth grade, found a book she likes even better!  WHAT?!?!?  She highly recommended The Cornerstone:  Classroom Management That Makes Teaching More Effective, Efficient, and Enjoyable by Angela Powell.  Angela (now Watson), even has a website with free resources, printables, and a link to her blog.

Tammy is also loving Bringing Common Core to Life in K-8 Classrooms:  Engagement at Every Level of Thinking by Eric Jensen and Leann Nickelsen.  Click on the link to get Solution Tree's printable reproducibles from the book.

The fourth grade teachers at Summit shared these little gems with us while they were at LNW:

 Comprehension Connections Bridges to Strategic Reading by Tanny McGregor

and Genre Connections:  Lessons to Launch Literary and Nonfiction Texts also by Tanny McGregor.

Dr. Kevin Kopp got in on the action by sharing a book he was reading called Best Practice:  Bringing Standards to Life by Steven Zemelman, Harvey Daniels, and Arthur Hyde.  Heinemann describes Best Practice as "the ultimate guide to teaching excellence. Its framework of seven Best Practice Structures and cutting-edge implementation strategies are proven across the grades and subject areas. BP4 creates common ground for teachers, leaders, and principals by recommending practices drawn from the latest scientific research, professional consensus, and the innovative classrooms of exemplary teachers".  

Thanks for the share, friends!

Standards of Mathematical Practices - One Standard at a Time

Mathematical Practices are embedded in every math lesson we teach.  The Standards for Mathematical Practice describe varieties of expertise that math educators at all levels (K-12) should seek to develop in their students.  These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. 

Mathematical Practice #4

Model with mathematics.

What should students be able to do?

• Understand this is a way to reason quantitatively and abstractly (able to decontextualize and contextualize)
• Apply the mathematics they know to solve everyday problems
• Are able to simplify a complex problem and identify important quantities to look at relationships
• Represent mathematics to describe a situation either with an equation or a diagram and interpret the results of a mathematical situation.
• Reflect on whether the results make sense, possibly improving/revising the model
• Ask themselves, "How can I represent this mathematically?"

Questions the Teacher Can Ask to Develop Mathematical Thinking:

• What number model could you construct to represent the problem?
• What are some ways to represent the quantities?
• What is an equation or expression that matches the diagram, number line..., chart..., table...?
• Where did you see one of the quantities in the task in your equation or expression?
• How would it help to create a diagram, graph, table...?
• What are some ways to visually represent...?
• What formula might apply in this situation?

Standards of Mathematical Practices - One Standard at a Time

  

"I used the array model to figure out the problem.  First, I broke apart 32 x 45..."

Mathematical Practices are embedded in every math lesson we teach.  The Standards for Mathematical Practice describe varieties of expertise that math educators at all levels (K-12) should seek to develop in their students.  These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. 

Mathematical Practice #3

Construct viable arguments and critique the 

reasoning of others.

What should students be able to do?

• Analyze problems and use stated mathematical assumptions, definitions, and established results in constructing arguments.
• Justify conclusions with mathematical ideas.
• Listen to the arguments of others and ask useful questions to determine if an argument makes sense.
• Ask clarifying questions or suggest ideas to improve/revise the argument.
• Compare two arguments and determine correct or flawed logic.

Questions the Teacher Can Ask to Develop Mathematical Thinking:

• What mathematical evidence would support your solution?
• How can we be sure that...?
• How could you prove that...?
• Will it still work if...?
• What were you considering when...?
• How did you decide to try that strategy?
• How did you test whether your approach worked?
• How did you decide what the problem was asking you to find? (Was it unknown?)
• Did you try a method that did not work? Why didn't it work? Would it ever work? Why or why not?
• What is the same and what is different about...?
• How could you demonstrate a counter-example?

Missouri Learning Standards Math - Where Do I Focus?

There is a lot of information out there and it can be overwhelming to say the least!  Need a place to start?

First of all, there are computational fluencies for grades K-6 in math.  Fluent in the Standards means "fast and accurate."  It might also help to think of fluency as meaning the same thing as when we say that somebody is fluent in a foreign language:  when you're fluent, you flow.  Fluent isn't halting, stumbling, or reversing oneself.

There are major, minor, and additional clusters within the standards.  The "major clusters" are those standards in which each grade level should be spending the majority of their instructional time.  Please note that no cluster should be left out.

You can search more in depth about clusters at Paul's Self-Proclaimed Awesomeness Document.  It really is an awesome document. :-)  Here is an example of how Paul's document highlights the clusters (with color-coding--LOVE, LOVE, LOVE!).

Classroom Videos Without Fear of Embarrassment

You've heard the horror stories...

The teacher picked out the perfect video to go along with the day's lesson.  It has been previewed and all is well...no glitches, no slow streaming... She may win an award for perfect lesson of the year with this!  She secretly hopes the principal will walk in during this one.  The students file in and she can barely contain her excitement.  The students are enthralled by the video.  Light bulbs are going off in all of the little brains in the classroom!  It is education MAGIC!  The video ends, and immediately an inappropriate ad flashes onto the screen.  The teacher panics...she jumps in front of the Smart Board with the remote, flailing her arms and trying to turn off the screen at the same time.  She prays that the students didn't see what was just posted on what now seems like an IMAX sized screen. 

Has it happened to you?  Don't worry, we won't tell.

BUT...Stephanie Williams has shared a solution which will ensure that in the future, you can watch videos in your classroom without the fear of embarrassment.

ENTER....http://safeshare.tv/

Simply copy and paste your youtube link into the little box and voila!  You will be given a link to your video that is ad and embarrassment free.  Hallelujah!

Go-To Math Resources

When you're looking for a fresh math idea, what are the go-to resources that you use?

This year, we are lucky to have two new resources to add to our tool boxes:  Discovery Education Plus and Smarter Balanced Digital Library.

We thought we'd share some of our other math go-to favorites with you this week!

1.  North Carolina Unpacked Standards - Is it just us, or is it sometimes difficult to unpack some of the standards?  North Carolina has done a magnificent job unpacking the standards for you.  We like to have them handy when we're looking at specific standards just to make sure we're on the same page.  If you haven't checked them out already, it's certainly worth your time.

2.  Fantastic Flipbooks - Like having everything organized in one place?  Yeah, us too!  Check out these flipbooks...available for each grade level!  Wahoo!

Kindergarten flipbook

1st Grade flipbook
2nd Grade flipbook
3rd Grade flipbook
4th Grade flipbook
5th Grade flipbook
6th Grade flipbook

3.  Illuminations - Resources for Teaching Math - The National Council of Teachers of Mathematics (NCTM) has lessons and interactive games and lessons available for teachers in grades K-12.  These are great ways to keep up student interest!

4.  Illustrative Mathematics is a fantastic resource if you're looking for tasks for a specific standard.

5.  You've heard us say her name a million times, but we <HEART> her...seriously.  Check out Dr. Nicki Newton's Guided Math Blog by clicking on the link below.  She also has a Pinterest page for the super pinners out there!

6. Learn Zillion is a wonderful resource that you can share with students and parents, use in small groups, or work with during tutoring.  The lessons are divided by subject, grade level, and standard. You can view videos and complete lesson plans!

Let us know your favorite go-to resources!  

And don't forget to submit a Google form on your grade level page with your BEST resources!  

If you're interested in checking out more resources, see the list we have on the blog HERE.

Standards of Mathematical Practices - One Standard at a Time

Mathematical Practices are embedded in every math lesson we teach.  The Standards for Mathematical Practice describe varieties of expertise that math educators at all levels (K-12) should seek to develop in their students.  These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. 

Mathematical Practice #2

Reason abstractly and quantitatively.

What should students be able to do?

• Make sense of quantities and their relationships.
• Decontextualize (represent a situation symbolically and manipulate the symbols) and contextualize (make meaning of the symbols in a problem) quantitative relationships. 
• Understand the meaning of quantities and are flexible in the use of operations and their properties.
• Create a logical representation of the problem.
• Attends to the meaning of quantities, not just how to compute them.

Questions the Teacher Can Ask to Develop Mathematical Thinking:

• What do the numbers used in the problem represent?
• What is the relationship of the quantities?
• How is ________ related to ________?
• What is the relationship between ________ and ________?
• What does ________ mean to you?  (e.g., symbol, quantity, diagram)
• What properties might we use to find a solution?
• How did you decide in this task that you needed to use...?
• Could we have used another operation of property to solve this task?  Why or why not?

Standards for Mathematical Practices - One Standard at a Time

Mathematical Practices are embedded in every math lesson we teach.  The Standards for Mathematical Practice describe varieties of expertise that math educators at all levels (K-12) should seek to develop in their students.  These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education.  

Mathematical Practice #1

Make sense of problems and persevere in solving them.

What should students be able to do?

• Interpret and make meaning of the problem to find a starting point.  Analyze what is given in order to explain to themselves the meaning of the problem.
• Plan a solution pathway instead of jumping to a solution.
• Monitor their progress and change the approach if necessary.
• See relationships between various representations.
• Relate current situations to concepts or skills previously learned and connect mathematical ideas to one another.
• Continually ask themselves, "Does this make sense?"  Can understand various approaches to solutions.

Questions the Teacher Can Ask to Develop Mathematical Thinking:

• How would you describe the problem in your own words?
• How would you describe what you are trying to find?
• What do you notice about...?
• Describe the relationship between the quantities.
• Describe what you have already tried.  What might you change?
• Talk me through the steps you've used to this point.
• What steps in the process are you most confident about?
• What are some other strategies you might try?
• What are some other problems that are similar to this one?
• How might you use one of your previous problems to help you begin?
• How else might you organize...represent...show...?

Check back next week for Mathematical Practice #2

Take a Minute to Check out All the Wonderful Resources at Discovery Education

Sarah Knight has created a page on each grade level menu page for Discovery Education. 

Learn how to create an account and access Streaming Plus 

if you haven't done so already.

Thanks Sarah!