The Value of Routines

Classrooms with strong routines reap many benefits.  This has become very evident this year as i have seen so many more classrooms begin math instruction each day with a routine.

In this year of continued chaos caused by the pandemic, teachers are finding that through routines, they can reinforce and review skills from previous grades.  They are also able to use routines to preview skills that might not be coming until later in the year.  So many free, well-designed routines are out there for teachers to use that it is easier than ever to find one that meets our students' needs.

Low-floor, high-ceiling routines are wonderful for engaging all students, and they usually involve a visual that helps students to all be able to "step-in" to the learning.  Favorite examples of these types of routines include Which One Doesn't Belong and Same/Different.  Teachers and students alike enjoy these routines because there are so many possibilities within one routine as they allow students to make sense of the problems in ways that make sense to them.

Many of the routines from Steve Wyborney are also loved by teachers and students.  These routines contain visuals, offer great exposure to vocabulary, and build number sense.  Teachers love them because they are professionally made and easy to use, and students love them because they are fun!  

Of course, Number Talks also are a routine that helps to build student discourse and fluency.  Using the book as a guide for these helps students to develop and use strategies when they are ready.  Doing Number Talks regularly has been shown to grow student fluency and flexibility in computation.

As students become more familiar with routines, there are many ways teachers can tweak the format.  For example, they might decide to have students create their own following a favorite routine.  (Creating your own Which One Doesn't Belong isn't as easy it might seem.)  Students can create these routines and share them with other classrooms besides their own giving them a larger audience for their work.  Teachers might also use routines as a daily warmup such as revealing one clue a day to an Estimystery and then discussing the students' thinking at the end of the week.  I've even seen teacher print out images from routines and have students discuss them as they wait outside of a special class like PE or music.  A routine image might be part of a weekly newsletter so that families can discuss it together.   There are many ways that these routines can be used throughout a day's learning in addition to a warmup for math block.

All of these math class routines help to build a strong classroom culture of open, flexible thinking.  They also strengthen students' number sense and confidence while expanding their math vocabulary.  Teachers gain better insight to student development and can use these routines to help determine what next steps to take instructionally. They see quickly how students grow through the use of routines that meet their student needs; the routines may change from year to year.  

Math routines help us to build mathematicians whose confidence help them to take on the math practice standards as part of who they are. 

Individual student toolkits for CRA instruction

If students are in your classroom in August, it will be worth your time to have some sort of math tool kits prepared for your students because it is not recommended that students share resources, and you don't want to be cleaning them every night. What you are able to put in the kits will depend on your resources.  

We know that CRA instruction is vital for conceptual understanding of mathematical concepts.  Just because we will have some limits in place (for everyone's safety), doesn't mean we should abandon best practices.  We just need to adjust and do what we can for our students.

As I have said before, the use of virtual manipulatives will probably increase in your instruction even if you are seeing students in person.  This is especially true for those manipulatives where students usually need a lot of them to do their work--like pattern blocks and base ten blocks. I recommend that you use the virtual versions some in the classroom so that students are comfortable with the websites if they should need to use them from home without your direct support.

You might also consider paper versions of some of these tools to have in students's toolkits.  Not only can you get them easily and cheaply for the classroom, but you can also send them home if you need to without the worry of losing valuable manipulatives.

You may not start the year with all of the items in the toolkits.  You might add some as students are introduced to new concepts. Here are some things you might consider putting into individual toolkits for your students:

K:

five frame

ten frame

hundred grid from nrich.maths.org

number path  1-20 by Berkeley Everett

ten counters (unifix cubes?)

rekenrek

real or paper pattern blocks by Mathwire

+/- Math Flips cards (+/- 1) by Berkeley Everett
Quantity Cards from Erickson Early Math Collaborative

pair of dice

1:

ten frame

double ten-frame

hundred grid from nrich.maths.org

number path  1-20 by Berkeley Everett

twenty counters (unifix cubes ?)

rekenrek

beaded number line

small clock face paper version

real or paper pattern blocks by Mathwire

+/- Math Flips cards (Count on within 10)  (+/- 1 or 10 within 100) (subtraction within 10)

pair of dice

2:

double ten-frame

hundred grid from nrich.maths.org

number line 1-20 by Math Salamanders

twenty counters (cm cubes?)

rekenrek

beaded number line

small clock face   paper version

play coins, dollar bills

ruler

real or paper pattern blocks by Mathwire

real or paper base ten blocks from Tim Van de Vall

+/- Math Flips cards by Berkeley Everett (Doubles/Near Doubles) (make 10 with 2 addends)                        (make 10 with 3 addends) (2 digit + 1 digit) (2 digit + 2 digit) (subtraction within 20) (subtraction within 100)                                                                       

pair of dice

3:

ten frame

hundred grid 

twenty or more counters (cm cubes?)

beaded number line

small clock face   paper version

play coins, dollar bills

ruler

10 x 10 array (laminate)

real or paper pattern blocks by Mathwire

real or paper base ten blocks from Tim Van de Vall

paper Fraction Strip  from Math Salamander (blank version)

paper Fraction Circle Pieces Page 1   Page 2  Page 3

+/- Math Flips cards by Berkeley Everett (if needed from previous grades)

 x Math Flips cards by Berkeley Everett (2s,5s, and 10s) (4s, 6s,& 8s) (3s & 6s) (9s & 4s)

pair of dice

4:

hundred grid 

thirty-six counters (cm cubes?)

beaded number line

ruler

10 x 10 array (laminate)

real or paper pattern blocks by Mathwire

real or paper base ten blocks from Tim Van de Vall

paper Fraction Strip  from Math Salamander

paper Fraction Circle Pieces Page 1   Page 2  Page 3

+/- Math Flips cards by Berkeley Everett (if needed from previous grades)

 x Math Flips cards by Berkeley Everett

pair of dice

5:

hundred grid 

thirty-six counters (cm cubes?)

beaded number line

ruler

real or paper pattern blocks by Mathwire

real or paper base ten blocks from Tim Van de Vall

paper Fraction strip from Math Salamander

paper Fraction Circle Pieces Page 1   Page 2  Page 3

Math Flips cards by Berkeley Everett (if needed from previous grades)

pair of dice

If you laminate many of the paper tools, students could use a dry erase marker to create representations.

What am I forgetting?

Counting Connections

I love choral counting! This is confirmed every time I participate in one in a classroom.  It doesn't matter if it is a Kindergarten or 5th grade.  Choral counting gets everyone thinking--including the teacher!

One piece to choral counting that I have found to be important is the connections that can be made between different choral counts.

For example, this was an eye-opening choral count for some 2nd graders.  We began with the confidence builder of counting by 5s.  We broke it down by looking for patterns.  A lot of good talk and discussion here, but it really kicked up a notch when I challenged them to count by 5s off-decade.  We began slowly, but then the students were able to idenify patterns and get going.  We looked for patterns in this count, too, and then I pulled the two counts up side by side.  The ahas! that the students had were quite exciting!  So important for students to make these connections.

I did another one recently in a 5th grade classroom where we counted by 21s.

Students stepped up to the challenge of counting by 21s and looking for patterns.  But the real excitement came when I asked them to do another count by 2.1.  (I had copied the first count onto a clean page before we had found its patterns.) Students kind of gasped, but then I pulled up the clean screen of our previous count.  They counted by 2.1 as I added decimal points into the numbers.  When we were done, we made connections between the two counts and place value.  We also discussed what would have happened if I had asked them to count by 210.  These place value concepts were things that they "knew," but when we put it on paper, it really clicked for them!

Because I am in and out of classrooms, I did these "double-counts" in one session making the choral count a little longer than usual.  I certainly think that it would work for a teacher to do one one day and the second one the next day.  The importance is the time taken to connect the two counts, and following-up in later days with similar counts in order to help cement the counts into students' minds.

Beginning with choral counting is your first step.  Give one a try!  Once you get past that hurdle, you will feel more comfortable moving into a double-count!

Sorts

Sorts are a great way for students to make sense of things around them.  It could be images or numbers or objects or words....the point is to get them thinking about a subject and have them make sense of it in some way.

Here are some ideas for sorts.  Don't think that these are just for Littles.  Older students enjoy them.  They offer a non-threatening way for students to look at things, and they offer us good insight into our students' thinking.  Sorting is very mathematical even when it is not about numbers.  It is about looking at things carefully, finding patterns, and making sense--that's math!

SORT:
pattern blocks
doors
coins
book characters
drain covers
shapes--2D and 3D
numbers (odd/even) (prime/composite) (square/not square) (multiples)
vehicles
words
patterns
emojis
food
volume/area/perimeter
shoes
states
types of graphs (no numbers or titles are necessary)
expressions
angles

What Does the Data Tell Us?

In a recent conversation with some representatives from a major nationwide business company, we were discussing the needs in elementary math education to help lead students to be productive workers in tomorrow's business world.

The big question they said that students need to learn to answer is, "What does the data tell us?"  We also discussed the importance of probability and statistics,  but in the end, they said that they are looking for workers who can answer this question.

What would this look like in an elementary classroom?   I think it just reframes our questioning.  In many of our activities, we already expose students to real-world information.  We just need to be sure to be more intentional in our questioning in order to get them to look at data.

For example, look at this picture.  I took it thinking that it would be a good one for students to determine what was the best deal. What does it tell us?  What are some possible reasons a person would be willing to pay more for 3 Peep trees when they can get 9 for such a better deal?  

Noticing and wondering is a classroom routine that really benefits our students.  When they notice and wonder, you can ask them what the picture tells them.  Make them infer from the data that they have.  Numberless graphs are a good method of providing data that the students have to make sense of.  Here is a good example of a 2nd grade lesson regarding them.  You can find lots of examples and ideas for using them by reading some of the posts listed here.

What do you notice about this data?  What do you wonder?

We want our students to be able to compute and do basic math, but not at the expense of good math thinking and discussion.  These are the skills that will carry them into the future--not only in their career, but also in their roles as consumers and citizens.

How can you incorporate statistics and probability into your classroom (whether it is a K classroom or a 5th classroom) by framing your questions and your students' thinking around the question, "What does the data tell us?"

THIS is the Message to Begin a New Year

What a great thing for us to do for our students: Help them understand the value of mistakes!  And now, at the beginning of the year, it sends a great message to all stakeholders:  This classroom celebrates mistakes!

"I have not failed.  I've just found 10,000 ways that won't work."  

Thomas A. Edison

Using Puzzles to Create Persevering Problem Solvers

Helping our students to grow through productive struggle is often a challenge for us.  One way to consider as you work to build your students' problem solving skills is through the use of puzzles.  Here are some ideas for you to consider:

Yes--it can be as simple as having a jigsaw puzzle in the back of your classroom.  The visual acuity needed to solve jigsaw puzzles is important for students to build, and who doesn't love to finish a jigsaw puzzle?  Oftentimes, students do not have this opportunity at home, so having one set up in your classroom could help them to develop a new skill or hobby.

Besides jigsaw puzzles, tangram puzzles and pattern block puzzles also help students to build visual and geometric skills.  Allowing students time to explore with tangrams and pattern blocks is important, too, and it allows them to find the creativity in math as well as in themselves.  You can find other resources to help with tangrams in this post as well.

Kenken puzzles are an awesome tool to help build logic, fact fluency and number sense in all students.  The website also has an education portion, and you can sign up to have new sets of these puzzles sent to you weekly.  These puzzles are one of my favorites, but you do need to take a little time being sure your students understand how to do them and reminding them to explain how they know where numbers go in the puzzle.  Too often, students will guess where numbers go.  This method will work for a short time, but as the puzzles become more difficult, guessing will not lead to success.   While Kenkens have some similarities to Sudoku, I think they are better in the classroom because of the decomposition of numbers that is involved.  Many students are familiar with Sudokus, and they are a great type of logic puzzle that can be easily found. More information about Kenkens can be found here.

The website Math Pickle also has a large puzzle bank for you to choose from.  This site offers students the opportunity to play with their work in a way that allows them to better develop math concepts.

These puzzles from the Julia Robinson Mathematics Festival also allow students an opportunity to persevere through problem solving in  a fun way.  Although developed for a building-wide math night, many of the puzzles could be used in the classroom.

Let students decide how they want to do their puzzles.  Sometimes students prefer to solve them alone.  Others need to talk it over and think it through with a classmate.  Neither way is wrong.  Let students build their puzzle-solving skills in the way that feels best to them!

Math is fun.  It is puzzles.  It is visual. It is cooperative.  Sometimes, we get so caught up in teaching a curriculum or a standard, that we forget these important pieces of math.  There are so many good puzzles and problems out there for students; this is not even the tip off of the iceberg.  In what ways can you work to incorporate some of these ideas/resources into your classroom.  How can you help your students to not only become more persevering, but to ENJOY doing math?  

Would You Rather? -- Holiday Edition

If you are looking for some problem solving to get your students thinking and proving themselves while mixing in some holiday cheer, maybe these Would You Rather problems will work for you!

Would You Rathers are something that students are very familiar with, and these just include a mathematical twist.  Students can choose whichever option they want, but they need to have a mathematical explanation of why that is what they chose or didn't choose.  They can be used with students of all ages and offer great opportunities for collaboration.

If you like these, you can find more like them at this site, but I am betting you can come up with some good ones of your own!

Holiday Would You Rather 1

Holiday Would You Rather 2

Holiday Would You Rather 3

Holiday Would You Rather 4

Holiday Would You Rather 5

Continuing to Find Ways to Build Math Talk

I have participated in a number of professional discussions in the last week around the concept of Number Talks.  You may remember that I blogged about Sherry Parish's book before. It is an excellent resource to help you get started with Number Talks.

Many classrooms use Number Talks every day.  It is a great tool for building mathematical discourse, exposure to new strategies, and strengthening students' flexibility and fluency.

However--some people are a little intimidated by Number Talks.  It has some elements of the unknown, and this makes teachers a little leary to try it with their own students.  This is totally understandable.  One way to make this work is for the teacher to work on the anticipation part of the number talk fully.  By anticipating all of the possible ways a student may respond, it will give you the preparation to feel confident as you step into the Number Talk.  It will also allow you time to prepare visual images to represent ways that the students might explain.  It is important that we show the students' ideas using visual representations as this will allow us to reach more students.

I 

Here is a great example of ways that students might see 18 x 5.

I do believe that the term Number Talk is broader than just the use of functions with numbers as is found in the Number Talks book.  Of course, traditional number talks often involve quick-look cards and other visuals to help students visualize the math, but they are still considered to be from the basic concepts presented by Sherry Parrish in her book.

If you click on the tab labeled Routines located at the top of this page, you will find links to resources and videos of a large variety of mathematical routines that will encourage students' math talk.  There are many low-floor/high-ceiling activities which are good to put the students (and sometimes the teacher) at ease when doing a number talk.  In these types of tasks, nearly everyone can find an answer right away, but because these routines lend themselves to multiple answers, we find students recognizing all kinds of things besides the obvious.  Using these type of routines in addition to Number Talks will help your students to grow in ways you won't believe!

Challenge yourself to something new.  Try to add routines to your math class each day--you will be glad you did!

Using Counting Collections in the Classroom

Have you tried counting collections? 



Counting Collections: Kindergarten - a common core classroom friendly exercise from Luna Productions on Vimeo

This activity is a great opportunity for our primary students to gain a better understanding of counting and number, and with some modifications, I think it could be used, at some level, in the upper elementary classroom as well.

You will need to begin by creating some collections.  In the link above, they give some examples of objects you can gather for counting, but I'm sure you can find other items around your home or classroom that will work as well.  You will probably want them to be smaller in size so that storing them doesn't become much of an issue.  Hopefully, you can find other teachers in your classroom to join you, and then you can find a common space to share your different collections. This handout will also be able to help guide you as you plan for your collections and fine-tune the activity.

I think that these would be a great way to kick off your math habits to start the year.  You would be able to learn a lot about your students by interviewing and talking to them as they work on organizing and counting their collections.  

For older grades, I have thought that you could have them count objects in multiples or fractions to get a total.  You could also have them count by sets.  Packs of items...Can they count by 24 or 36? What if you offer them decks of cards? Can they count by 52s?  While they may not be fluent as they move through these unusual multiples, it will certainly aid them in developing mental math strategies.  Introducing fresh concepts through counting offers all students an access point, so students can practice new concepts using the math routine of counting.

Here is an example of a Counting Collection in a 3rd grade classroom:
Counting Collections: Third Grade - a common core classroom friendly exercise from Luna Productions on Vimeo.


Counting collections can adjust as your students develop their number sense. It is a routine that will allow students to think about better ways to organize, more efficient ways to count, and concepts of number. It can be used all year long.

What do you think about this?  How can you make it work in your classroom?  Please share your ideas!

I'd love to join in on the fun as your class does a counting collection!  If you are okay with that, let me know when you think you would like to do one, and I will see if I can join you.

Building Understanding and Developing Culture

I have done this problem with first graders for the past couple years.  The first time I offered it to students, I was surprised by how difficult they found it (due to the majority of my experiences being with older students).  When I did it subsequent times, I offered a lot of "up-front" guidance to help them think about it, and I highly encouraged them to use manipulatives and images to help them make sense. However, they still struggled...

I have decided that if  I work in a first grade classroom next year, we will again do this problem. I have been pondering some different ways to approach it.  

I think it will make a great numberless word problem that we can do with a slow reveal in hopes that students work to make sense of it rather than just trying to solve it. Using the slow reveal will offer a great way to directly instruct the students in the process of notice/wonder and making sense of the problem before trying to solve it.  This use of numberless problems should help them as we continue to build understanding throughout the year.

Doing a general overview as a class, offering the students manipulatives and encouraging them to work with a partner to solve it.  Once they think they have solved it, they must find another pair who has a solution, and each group must convince the other that their solution is correct.  I like this idea, too, as it should help to build mathematical culture int the classroom--collaboration, sharing methods, convincing others of our solution... I think that the deliberate teaching of convincing others with math talk will need to come before this lesson, so that both sets of students don't just say the answer they got and move on.  

I could provide a picture of two spotless ladybugs and then have the students work to put the spots on to match the words in the problem. This one seems very direct, but it does emphasize the importance of using visuals to help us make sense of the problem. Again, I think partner work is a great way for them to approach this.

I think the sharing out of this problem is important and recognizing the different ways that students went about solving it. Determining as a class what we think the correct answer is and acknowledging how we worked with our partners to solve it.  Maybe a gallery walk of our thinking?  

A possible follow-up activity could include students writing their own kind of problems like this and then switching problems with others.

This problem is written with 1st grade in mind.  Certainly, this type of problem could be adapted for different grade levels:
* I have six pieces of candy in my purse.  There are four more pieces of gum than mints. How many pieces of gum do I have, and how many mints do I have?
* We have 27 students in our class.  There are 5 more girls than boys in our class.  How many boys and girls are in our class?
* There are 114 vehicles in the parking lot.  There are 72 more vehicles with 4 wheels than vehicles with 2 wheels.  How many vehicles have two wheels?  How many vehicles have four wheels?
* In my closet, there are 18 shoes on the floor. However, there are 2 more right shoes than left shoes.  How many complete pairs of shoes do I have in my closet?
* I found thirty-five coins in my car.  There were four times as many pennies as all of the other coins combined?  How many pennies did I find in my car?

What do you think?  How might you approach a problem like this with your students? Do any of the ideas I shared seem to be better than the others?  I'd love to hear your thoughts.

4 Triangles Exploration

This exploration comes from Marilyn Burns, and it goes very nicely with her book, The Greedy Triangle.  

In this exploration, small groups work together to see how many polygons they can make with four triangles. The trick is:  the construction of the polygons must follow a specific rule.

To get started, put your students in pairs or groups of three.  The students will need a large paper on which to place their findings. Students must use all four triangles to create their polygons.  The easiest way is to use post it notes and cut them diagonally to form congruent triangles.  You might want to give them two different colors of post it notes so that each polygon they form has two triangles of two different colors.  (The colors just help to make the lines between the triangles more distinguishable.)

As far as the rules, you might want to show them some that don't follow the rules and some that do and see if they can figure out the rules.   

 These two do not follow the rule.

This one follows the rule.

Here is the rule that their 4-triangles must follow:

Sides that touch must be the same length and match up exactly

As students make polygons that match this rule, have them tape onto their paper.  The goal is for them to find as many polygons as they can.  (There are 14).  

Be sure to build in time to have a discussion about what shapes were formed.  Consider taking the time to sort them and have the students decide what rule you used to sort them.  This end of exploration discussion is key to the students making sense of the exploration by talking about it, and it gives you more time to infuse more vocabulary into the lesson!

What do they think would happen if you gave them five triangles?  How would that change the number of polygons?

Possible ways to sort:  number of sides, types of angles, lines of symmetry, convex/concave, perimeter... Do your students know why you can't sort them by area?

Give this exploration a try and let me know what you think--better yet: What your students think!!

Numberless Word Problems

In our ever-increasing efforts to get our students to UNDERSTAND a story problem and what is happening, we want to stress to them the importance of that movie playing in their heads.

Numberless word problems help to encourage just that!  These problems ask students to THINK about the problem as a reader before getting caught up in getting an answer.  

These problems can be made "on the spot" by covering or eliminating the numbers in a problem that your class is contemplating, or you can be even more intentional by building the problem through a "slow reveal" to increase their wondering and thinking about the problem.

A slow reveal might look like this:

1) TERESA IS PREPARING DINNER AND WANTS TO HAVE ENOUGH MEAT FOR ALL OF HER GUESTS.

• What math do you see in this problem?
• Do you see any math relationships?
• What are you wondering?

2) TERESA IS PREPARING DINNER AND WANTS TO HAVE 1/4 LB. OF MEAT FOR EACH OF HER GUESTS.

• How does this change what you know or what you were thinking
• What do we know now?
• What do we still need to know in order to have the full picture?

3) TERESA IS PREPARING DINNER AND WANTS TO HAVE 1/4 LB. OF MEAT FOR EACH OF HER 12 GUESTS.

• What information has been added?
• Do we need any more information?
• What question could we ask about this story?
• How could we use the information that we are given?

Numberless word problems are a good first step for us to take towards better math instruction!  Throughout the lesson, offer many opportunities for students to think/pair/share. Model good math vocabulary as you discuss the math that is presented. Encourage your students to be THINKERS!  Good luck!

A shift in math instruction

I'm sure we have all heard a lot about the "shifts in mathematical instruction," but sometimes I think that we get caught up in the shifts in the content of our instruction at the elementary level.  Who teaches time? Where does money get taught?  Third grade doesn't teach multi-digit multiplication anymore?  

The content that we teach has changed some, but in my experience, it is not the hardest shift in our instruction.  The hardest shift in our instruction is explained in the TED talk included below, The Five Principles of Extraordinary Math Teaching by Dan Finkel.  The video is about 15 minutes long, but in it, he highlights some of the importance in this shift for teachers and parents.

These are the principles he highlights:

1.  Start with a question.

2.  Students need time to struggle.

3.  You are not the answer key.

4.  Say yes to your students' ideas.

5.  Play!

Where do you see yourself in these practices?  Can you choose one that you think you can improve?  What supports can you find to help you move forward?

Same or Different?

Looking for a new routine to use in your daily workshop?  Same or Different could be your answer!

This blog has a great variety of images and videos for teachers to use to get this routine started in their classrooms.  There is also a link to a Teaching Channel kindergarten lesson using this routine.

It's just one more way for us to encourage student talk around math.

More Real World Math Errors

Kids love to find mistakes that others have made.  The attached file is full of errors found in the real world.  Can your students figure out what is wrong?  

Some of these are geared for older students, but there are some in here for the littles, too!

You can use these as a number talk, an opening activity, a collaborative problem solving activity...just be sure to get the best thinking, can they figure out how to correct it?

If your students like these, here are some from an earlier post.

Click for new file

Halloween and Logic

Construct viable arguments and critique the reasoning of others.

This mathematical practice standard is one that needs to be practiced often with our students.  However, some of them get so flustered by the math that they can't explain their reasoning to others let alone listen to other students' ideas.

Consider trying these logic puzzles with your students.  Logic is a great way for students to practice their thinking, and it is often easier for some of our kiddos who struggle with some of our grade level content.

These logic puzzles are October/Halloween themed and vary in difficulty. They are good practice at thinking skills but also in relational words.  I have also created a document for you that has the images for the puzzles.  Often, it helps the students to have something to move around on their desk.  You can just give them a strip of pictures that matches the puzzle you are doing, they can cut the images apart, and then move them as necessary to solve the problem.

If your students like these, consider an activity where groups try to make up their own.  It is more challenging than it looks.

Please share with a colleague.  Comment below if you find other ways to use them in your classroom.

Math Practice Standards--Are you being intentional?

Much like the Engineering Design Practices that are a part of the Next Generation Science Standards, the Standards for Mathematical Practice help us to embed best practices to help our students to grow in their general learning skills.

These standards, unlike the content standards, remain the same for all grade levels, and should be used to help our students to develop better problem solving skills and mathematical practices.

These are the 8 practice standards:

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.

It is very easy to find student-friendly language versions of these standards.  I would recommend that you find one that you like and print it and post it in your classroom.

 But, is posting the practice standards enough?  I think that it would be a good idea to look more deeply at them and find ways to embed them into your workshop.  ( I am sure that you will find that many of these are a part of your instruction already.)  The Scholastic website has a nice little guide to helping teachers understand these standards more completely. They are so much more than just the short statements above. The Inside Mathematics website also has some resources to help you with understanding these standards including videos from a variety of grade levels that match each standard. As you watch these videos, you may notice that many math practice standards can be found in just one snippet from a lesson.  Strong math instruction usually has many of these practices included in it.

While you probably won't teach the standards as independent lessons, I think it is worth our while to include the math practice standard(s) along with the math content standard when we are setting the learning intentions for our lessons. Making it more intentional on our part will help our students better begin to understand the value of these practices and allow us to develop stronger mathematicians.

Building Mathematicians through Number Talks

I have had a number of teachers show interest in adding Number Talks into their classrooms next year.  That is awesome!

Many of you already use Number Talks regularly.  For those of you who don't, I think you will find that you already do forms of this.  The difference between about what you are doing now and a number talk is generally just one thing--intentionality of instruction.

In this video, you will see a 3rd grade Number Talk.  I think you will be able to recognize the intentionality he uses in this lesson.

https://www.teachingchannel.org/video/multiplication-division-in-the-core
There are many things that I like about this video. I like the classroom culture and the way that everyone is engaged in the activity. I think it is wonderful the number of ideas that they share and the way that the teacher acknowledges each one. I love the way the hand signals give the teacher feedback, but don't distract everyone else's thinking.  However, my favorite part, I believe, is when the student says, "I revised my thinking..." How powerful is that?

 There are lots of ways that you can use Number Talks in your classroom. You might use it as a mini-lesson. It might be an opening or closing activity. It might be designated for a certain time of day outside of math time. You might use it once a week, or you might use it every day. All of that is up to you and what works best for you and your students.

Sherry Parrish's book is a great resource. Many teachers and buildings have copies of this great book. This link also will also give you some ideas of different Number Talks you can use in your classroom. 

 As always, I would love to explore this more with you. If your class uses Number Talks regularly, let me know! I would love to visit if you are comfortable with that. If you would like to learn more, or sharpen your skills at these, I'd be happy to chat with you.

What's the problem?

Problem solving is a key component to student growth and understanding in math.  As teachers, we want to find times to allow our students to engage in rich problem-solving activities with their peers.  This helps to develop math vocabulary, reasoning, and perseverance.

Below, I have listed some story problems which might work well in your classroom.  Unlike the 3 Act Tasks that I have spoken to many of you about, these problems tend to be more open ended and focused on persevering through the problem. I find perseverance to be an area for development for many of our students.

I know we often feel that we are under the gun to get through our EM4 curriculum, but I think we could maybe still find some times in our learning to build these in.  Students should work in small heterogeneous groups to solve these problems.  

Maybe... 

• you can choose to have it be a piece of your workshop?  
• it will fit in on a day right before or after a long weekend or break?
• it could be part of a day when you are reviewing for a test or going over the results of one?
• it could be an opening or closing activity?
• it could be done on a Friday as a break from the regular routine?

Please let me know if you would be interested in collaborating to implement more problem-solving like these into your classroom.  I would be happy to help or lead your class for a day while giving one of these a go.

These come from two websites that I depend on quite a bit--youcubed.org and nrich.maths.org.  You can find printable pages and explanations for you and your students at these sites. I have identified them by grade level, but many of them could work in other grades, so feel free to check as many out as you wish!

Kindergarten:  https://www.youcubed.org/task/ice-cream-scoop/

1st Grade:   https://www.youcubed.org/task/leo-the-rabbit/

2nd Grade:  http://nrich.maths.org/7506/note

3rd Grade:  https://www.youcubed.org/task/squares-upon-squares/

4th Grade:  http://nrich.maths.org/1150/note

5th Grade:  http://nrich.maths.org/31

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