First I gave the students “alone” time to write and then let them go compare notes with their partner from the investigation…

Math vocabulary and language

 

What really stood out to me was the very NEBULOUS (vocabulary word!) math language I was hearing.  A phrase that kept coming up was “small fractions” as in “It was harder to fold the small fractions.”

What next?

Reasonable and rigorous expectations

Did you miss Day 1  of this fraction series?  Go take a look!

 

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The post Fraction Misconceptions and Math Language (Day 2 Fraction Concepts) appeared first on The Teacher Studio.

I always invite conversation around how we teach fractions because there are so many ways to help students make sense of them. As I walk through our work, I try to share photos, student examples, and the reasoning behind each step. I do this partly to keep myself honest about my choices, and partly because I love hearing what has worked well in other classrooms, too. If you have ideas or resources that have been successful for you, I’m always eager to learn from them.

Teaching fractions throughout the year

One thing our district math team emphasized when we built our pacing was the importance of giving fractions more than a single stretch of instructional time. We built in two units. We do one one now to develop foundational understanding. Then we built in a later one that connects fractions, decimals, and the more sophisticated ideas students will need. That structure has really shaped how I approach the beginning of this work.

Today I started by asking students to reflect on what they already know about fractions and to rate their overall confidence (using our 4  3  2  1 ) scale (Click here to revisit earlier blog post about this!) and the results were quite amazing!  In a ten minute writing time, I got to witness a number of misconceptions, poorly explained reasoning, and a bunch of “3’s” and “4’s” in confidence!

Good thing I had planned on starting slowly!  Today we started our new math notebooks, and I explained to the students that we are “raising the rigor” one level more. The poor things have heard this all year!  I told them we are going to work hard to use our new notebooks to both record our thinking, our practicing, and our new learning.

I’ll blog more about this later as it unfolds!  For today, we started the section we called “Fraction Concepts” and even talked about what the word “concept” means.  Fascinating!  I told the students that our job through this unit would be to determine some things we could determine to be “true” about fractions and that we would be working our way through a number of these “truths” during the unit.

Today’s fraction “truth”

Today’s “truth” involved ensuring that students understand that fractions represent equal parts of something. (I didn’t really want to use the term “whole” yet–I don’t really like to treat fractions of “objects” and “sets” differently until I have to!) I also told them that we would be spending some time creating equal parts.

Then, I put the students into pairs (I love popsicle stick picking!) and gave them each 3 minutes to find a classroom object that was either a square, rectangle, or circle. The item needed to be bigger than a deck of cards and smaller than a book.  Each team was then assigned a color of paper and we got started.

The Task

With your partner, trace and cut out your shape.  You will need many of these as the investigation unfolds.  Your job is to find ways to divide your shape into equal parts. . . first in two equal parts, then three, and so on.

I made sure that we had plenty of objects accessible in a variety of sizes. You could also have cardboard tracers if that is more appropriate for your learners.

I then showed the students the following charts–each is labeled “halves”, “thirds”, “fourths”, and so on.  I used pieces of bulletin board paper, but you could use construction paper or even just set your shapes on the floor by the headers.  As they discovered a way to fold their shape, they were asked to put it on the correct chart.  I was on the prowl for work that was not accurate and precise.

Voila!  Posters are taped to the ground with deliberate “aisles” so they don’t get trampled on!

Each poster is labeled with the word for the fractional part–I will use the words and different symbols interchangeably throughout the unit.  NOTE:  The chart does NOT say “1/3” because we were not identifying 1 out of 3 parts.

Digging In

Students dug into their work and did need some frequent reminders about using straight edges, working carefully, and so on. (I know–shocking!) That being said, they were very engaged and thoughtful.  I heard some pretty nifty stuff like:

Tracing…

Using a straightedge for precision…

Circles are the toughest as this team found!

The charts started to fill…first halves and thirds, then fourths and eighths…we’ll see how it “unfolds” tomorrow!  Got to love a little math humor, right?

What’s next?

One more thing…

The terms “numerator” and “denominator” did come up in our lesson today.  I made a poster to represent this and hung it on our math board.  You may need to introduce the terms over the next days if your students do not bring them up!

UPDATE!

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you can also sign up for my NEWSLETTER where I start you off with an awesome freebie! You then will get even more teaching tips, freebies, and offers delivered right to your mailbox!

The post Fraction Folding–discovery learning appeared first on The Teacher Studio.

One thing I know to be true about fourth graders and intermediate students is that there is no ONE thing true about fourth graders and intermediate students. It seems like the longer I teach, the more compelled I am to find ways to group and individualize for students, but I have to admit–it is NOT easy for me. It isn’t that I don’t KNOW who the students are or what to do. It’s that whole “structure” or organization piece for a good reader’s workshop.

Reader’s Workshop Routines

One area where I do feel more confident is establishing a culture for independent reading in my classroom.  I really know how to establish routines and procedures to make my reading time run smoothly so students get the most “bang” for their buck. Students need to be taught HOW to be independent.  It simply isn’t intuitive for all of this.  This is especially true for those strugglers who have received a LOT of interventions–often have some learned helplessness. I spend the first few weeks of school working very hard to teach routines and processes and to get my students more independent and successful with their reader’s workshop time.

I went back to my copy of this book to read a little more about one of the key elements of the CCSS–Standard 10. It is one that is inherently vague and I think it’s easy to gloss over it and say, “I do that.” But do we?

So how can we REALLY teach this standard?

When I went back into the text, it talks about the standards 1 and 10 as being the “sides” of the ladder holding up all of the other standard “rungs”. I kind of like that analogy. We must help students read more complex texts in order to accomplish all that the CCSS (and other sets of standards) wants us to–but it won’t happen without careful scaffolding by us. Let’s be honest…we meet with kids in small groups. We do picture walks. We preteach vocabulary.

WAIT! Maybe WE do too much! After all, we can’t sit next to them and “frontload” their standardized tests, can we? Their work in the upper grades?  Their emails when they have jobs?

So . . . I have been on a quest in recent years to really and deliberately TEACH my students how to be independent workers, thinkers, readers, and problem solvers. I really want them to be reflective about their own needs. They need to know how to seek out help when they need it.  Similarly, I want them to pick “just right” books and know when they are not making good book choices. I want them to set goals and reflect on them. They need to study their own behaviors and work to make changes.

• Are we organizing our beginning of the year minilessons to focus on these critical lessons?
• Do we have visual displays and anchor charts that we create with students?  Do we refer BACK to them as we teach and guide?
• Are there systems we can put in place to monitor what and how students are reading?
• Do we set goals for and with our students?
• Do we find ways to show students HOW to preview and select books?
• Is our own enthusiasm for reading evident?
• Are we helping students “see” what independent reading should look like–and why it is so important?

I’ve taken some of these critical concepts and put them together in a little package. You might find this helpful if you feel you want to change up how you “launch” your independent reading for the year. There are TONS of amazing resources out there–but I know what has worked for me and I have finally put it all together. I hope you like it!

I find it so helpful to get students to really understand what good readers do. I hope you think that helping them become independent will help give YOU more time to teach, confer, and more!

Want to learn more about independent reading?

Check out this post about taking “status of the class”!

Or check out this one to learn more about helping students learn those great reading behaviors!

Thanks for stopping by!

The post Launching Reader’s Workshop and Independent Reading appeared first on The Teacher Studio.

It’s funny how some people have misconceptions about the use of picture books in the classroom . . . how we must be pushing our students into more rigorous literature . . . how we don’t have time for those picture book “shared reading” experiences.  Really?  Have you READ some of the wonderful picture books out there?  These are NOT your toddler “going to bed” books!  These are texts rich with language, filled with inferential thinking, and–if presented well–examples of what excellent writing can be!  They have interesting beginnings and endings . . . they are alive with descriptive and figurative language . . . they provide us with the opportunities to get a glimpse into 

They are concise with their words–using just enough to tell the story and help us “see” in our minds what really matters.  They make us think.

Wait a minute–isn’t that what we want our students doing in their own writing?  Their independent reading?  YES!

So–I am on a quest to find the BEST mentor texts out there!  I want to get these rich texts in the eyes, ears, and hearts of students everywhere!  I have started by digging into one of my favorite authors–Eve Bunting–who has written countless picture AND chapter books that accomplish all that I have described above.  

If you haven’t read her books–I beg you to do so and to share them with your students.  The CCSS is asking us to provide our students with rich opportunities to study literature, and Bunting’s books are a perfect vehicle for that.  If you haven’t used picture books in your classroom often, I have created a series of resources that might help you out . . . with more to come if it seems like people like them.  I’ve called my new series “Mentor Text Moments”–because I want you to share these texts with your students and have some of those deep discussions and “moments” with them!  

The resources have some discussion questions that might help you as well as a list of tricky words and phrases that might trip up your English Language Learners and other students with less rich vocabulary.  I have provided the discussion prompts in multiple formats so you can use them in readers notebooks . . . on printable sheets to use to assess students’ thinking . . . or just to use to enrich discussions.  I have also included 2 graphic organizers with each to extend the story and your students’ thinking–as well as a rubric to help you begin to assess the level of thinking against the Common Core.  Interested?  I have put resources for 6 different Eve Bunting texts in my store as well as a bundled set of all 6 if you are interested in that.  I’ll include the link to the bundle below.

What I REALLY want, though, is for you to share out YOUR favorite picture books that you use in your classroom!  Maybe we can all add some new titles to our collection!  Let’s see if we can get a good list going below . . . I’ll start!

“Saturdays and Teacakes” by Lester Laminack is a touching story about a tradition with a young boy and his grandmother.  If you study “memoirs”, this is a must have text! It is filled with descriptive language and drops hints as to what life was like a generation ago!  

OK–your turn!  Let’s hear your best ones!

(and don’t forget about my July special…buy ANY bundle and get an item of $5 or less for free!)

The post Why Mentor Texts? appeared first on The Teacher Studio.

Back into the division trenches today with one of my favorite “kick off” activities!  I love it when a piece of literature can spark a lesson, and this is no exception.  Marilyn Burns turned me on to this idea a few years back, and I have taken the ideas in her lesson and expanded it to really challenge my students.  The lesson unfolds over a few days–I am going to try to paint the picture for you!

Are you familiar with this book?

Flip book version

Here’s what we did THIS year…

Another version…

The post Division Day 2: Cookie Time! appeared first on The Teacher Studio.

I spent the day at a regional music competition watching my son and countless other students show off their hard work and practice. Some achieved their ultimate goal of qualifying for the state contest–others left disappointed. What struck me as I volunteered for the afternoon was the judging. After each student or group performed, the judge walked through their scoring sheet pointing out what they had done well and what they could refine. I heard all sorts of comments like

“What you want to see is your elbow looking like this.” (shows the student a position)
“Listen to the sound my tongue makes–it is the sound you want to make.”
“You need to move your third finger like this. Good–do you see how much clearer that sound is?”

What was the judge doing? Giving feedback to try to get each musician closer to the desired goal. As teachers, we do this all day long. Research clearly states that the better and more immediate our feedback, the more our students will learn, so we MUST get better at it! Watch for more reflections on this in upcoming weeks. For today, I have a favor for you! As you know, I LOVE teaching math–but what I don’t like to do is assign a “score” for the work students do. I know we need to remember that grading is really the least important kind of feedback we can give–unless that feedback can be built into the score. I have been working on a way to try to create a problem-solving rubric that will help me AND my students have a clearer understanding of what “4” level math is! (We grade on a 4 point scale).

I wanted to create something that would address at least some of the Standards for Mathematical Practice, be easy to use, be flexible enough to use in many ways, and both simple and complete. This has not been an easy task! The document I have created asks students to reflect on their work in three areas:

1. Math Strategies
2. Precision “Plus”
3. Clear Explanations

I think it is really important for our students to realize that math is WAY more than getting the correct answer, so the document I have created downplays this. I have worked to define what a “4” would be in each of these areas and am hoping to use it with my students in a variety of ways. . . after team problem solving activities . . . after looking at a problem/problems they solved independently . . . as a self-assessment after paging through their math journals . . . and more!

I would love for YOU to try it out too! Let me know your thoughts–does it work? Could it be more clear? Are there other uses for it? What would make it better? Let’s work together to try to create a document that can really serve to help “coach” our students toward better problem solving.

I have included the link below, and I would love for you to try it out!

The post Problem Solving Rubric–Try out this math freebie! appeared first on The Teacher Studio.

What I often do toward the end of a unit is provide students with a class period or two to work collaboratively or on their own on an assortment of word problems.  Some of the problems are right at the level I would expect them to be able to do and others “push” and help them work on their “problem attack” and perseverance.  While they work, I can circulate and coach as they get started–but then my real goal is to be able to pull small groups and individuals to work on “issues” that have come up in recent lessons.

During this round of problem solving, I wanted to pull students who are still “iffy” on equivalent fractions, on comparing fractions, and on addition/subtraction with like denominators, so I got my collection of problems ready so the students would be focused while I pulled groups.

Here is one way I organize the problems:

This is a little cheap “tent” pocket chart that I think I got a few years ago at “The Bullseye Store”  It has those pockets on both sides.

So . . . on each of my two problem solving days, I did a 15 minute review minilesson to keep cycling back through those concepts covered over the last weeks and then I sent my students off to work in their math notebooks on the variety of problems.  I DO give a little “problem talk” about the problems (8 choices this time) so the students know who the problem is about (often students in the class) and what is happening.  In this collection there was a friendship bracelet problem (I KNEW which 3 girls would make a beeline for that one), a “travel team” soccer problem, a kitten problem, a candy store problem, a “Training for a 5K” problem . . . you get the picture.  Students often gravitate toward problems with topics that interest them no matter what the math content is!  I will also give a warning if I think the problem is particularly challenging or one that I call a good “warm up” which is the sign to those who are hesitant to TRY THAT ONE FIRST!

Drawing pictures to solve the problem . . . notice the use of highlighter to highlight key information.  This is the first class I have ever had that likes that as a strategy.

This student tried problem 6 and then decided to abandon it for now . . . we compare abandoning problems to abandoning books.  You shouldn’t have to do it very often, but sometimes it is the best decision.

This student was stumped!  I spent some time talking with her and then found another student doing the same problem . . .

Together they talked through it and came up with two strategies to try–both worked!  They were so excited! The one thing that got me super excited during this time . . . I had just finished with a small group when one of my “fraction challenged” students came up to me with a question about her problem. The problem states that Mara and her 3 friends ordered pizza and ate 2 1/2 of them.  They all ate the same amount–what fraction of a pizza did each girl eat?  She had drawn a picture and really felt like she had found a way for each girl to get the same amount–but she had no idea WHAT that amount was.  Check out her solution–brilliant, right?  She drew the 2 1/2 pizzas, assigned each girl a number (1-4) and started splitting the pizza up.  She knew each girl could get 2/4 but they would have to all split the remaining half of a pizza–so she split THAT into 4 pieces.  She couldn’t quite figure out how much that added up to be. I sat and listened to her reason through the problem and I noticed several other students starting to hover around (very typical . . . I tell them that smart learners tune in to others’ lessons, so I encourage this!) so I asked if any of them thought they could help. We threw her problem up on the Smartboard. . .  Then asked for volunteers to go up with her and talk through it . . . this student tried to help her see that each of the girls WOULD get 2/4 of a pizza AND 1/8 of a pizza BUT. . .  When it came time to do the math . . .  Something less than perfect happened.  I felt my heart sink until I heard another little voice chime in and say  . . .  “Hey!  Remember . . . when you add fractions you have to have the same denominator!  I think you should turn all the pieces into eighths.” . . . and so she did.  She came up and divided all the fourths into eighths and the THREE of them collectively shouted out “FIVE EIGHTHS!”.  At this point, 8 students had gathered while the others worked. High fives went around the group and they all rushed back to their notebooks to record their thinking.   Victory. Common Core fractions?  CHECK Standards for Mathematical Practice?  CHECK Excitement about math?  PRICELESS Thanks for stopping by . . . the unit is coming to a close!  Let’s hope they are ready for their assessment on  Monday!

The post Fractions Day 16: Word Problems and Critical Thinking appeared first on The Teacher Studio.

Before this unit, I printed a list of the Common Core “learning targets” rewritten in kid-friendly language for my students.  We had looked at this list as our unit started and made little folders to keep them in.

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Today I asked the students to solve some quick equivalency problems (3/4 = ? /16) and so on.  17 of my students aced it, 3 of them missed one (fact mistakes . . . AYE!  So many fact mistakes!!!), and 2 of them seem to still really not understand the concept.  Tomorrow–I will pull the 2 and go back to some paper folding to try to connect to the computation and see where they are missing the boat.

So . . .  today!  What did we do?  I flashed the following direction on the Smartboard:

This group started with a linear number line until one student suggested they made two rows to fit it all on the chart paper.

This group immediately put them in order from smallest to largest–something I thought would be obvious. I was wrong!  Two of the four groups did NOT put them in order from smallest to largest!  One went largest to smallest and the other went . . .  ummmmm . . . “creative”?

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