Small Steps for Differentiation: Same Task – Different Entry Points

When thinking of differentiation in the classroom, it is easy to fall into the trap of putting pressure on ourselves to perfectly level activities for every student. My mind goes to having a rotated set of groups and centers all perfectly ready to go. In this scenario you never run out of time, every student is exactly where they need to be, AND they are accountable, focused and staying on task the entire time.

YEAH RIGHT!

Don’t get me wrong, math workshops are a beautiful thing, but it doesn’t always work as smoothly as we’d like. It is okay to differentiate in small ways, taking small steps to be sure that we are meeting the needs of all children without going crazy ourselves.

This past summer I was lucky enough to read work by Timothy Kanold, and then I was able to work with him in a workshop as well. He proposes that instead of coming up with different activities for every student, we have the same task, but with different entry points. So what does this look like exactly?

Here is an example for a second grade classroom where the learning target would be “I can count money up to a specific amount.”(CCSS 2.MD.C.8):

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Task: How many ways can you build 58 cents? Build it and record it.

All of the students in this group are given the same task, but usually all of the students have different levels of knowledge surrounding this task. So instead of coming up with 25 different activities you have only one.  As the activity begins and students begin to work, two things will happen which we all can predict every time. Some students will struggle, and others will fly.  This is when you strategically give certain students more.

For the students who struggle in this case you would lay down another task next to it, where the number is more accessible, and you may also consider telling them the value of all of the coins.

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Instead of 58 cents, the students who struggle are working with a more accessible number, side by side with the other students.

In this case for the students that are excelling there are many options: ask them to find the solution if you eliminate one of the types of coins, ask them to show their thinking algebraically using a table, give a different amount and have them predict the number of solutions they may find before solving, or ask them to write a story in which you may need to come up with 58 cents worth of change.

The main thing is that you have to truly be walking your room, listening to your students and conferring with them as they solve. The BEST part of this method, is students are working together and hearing one another’s thinking, elevating the learning for all in the room.

What Does Success Look Like?

Pretend with me for a moment, that you have never seen an apple before in your life. Now pretend that someone has asked you to peel it, but you’ve also never peeled anything before in your life.  How do you know what to do to be successful? How will you know when you have been successful?

That in a nutshell is what “success criteria” is.  It’s all about letting students know what success looks like, and how they will know that they have met the learning target.

In my mission to examine learning targets and communicate them, I learned that it wasn’t enough to simply display them for students. It STILL wasn’t enough for students to write them in their math journals.  My students needed to see the learning target, write it, and then have some sort of interaction with it.  This is where I combine this idea of success criteria (Hattie 2012) with Marzano’s Levels of Understanding.

Here is an example of what this can look like.  You begin your content lesson by reading the learning target out loud, allowing students time to write it down in a math journal (or some other place to take notes). Notice the learning target starts with “I can”.  (It would be just like saying, I can peel an apple.)

I can read and write numbers up to 1,000.

Now some students will have prior knowledge about the learning target, so allowing them a moment to interact and think about this learning target is essential.  You can show them (or you can do this orally) what the different levels of understanding look like. Here is what it could be for this particular learning target:

Using success criteria in the classroom can help students understand the learning they are supposed to do.

Using success criteria in the classroom can help students understand the outcome of their learning.

I use Marzano’s Levels of Understanding to anchor my thinking (which I blew up and posted on the wall-this is a free resource by the way!) because the students connect easily to the language.  After I show them what each level looks like, I have the students rate themselves on the current target. Their goal is always the same every day, get to the next level, get higher and get better.

After this mini intro, I teach the lesson. We practice with tiered examples so that everyone is challenged, we talk it through with each other, we help each other come to an understanding.  We break into independent practice work where I can catch the students who still feel like a 1 or 2.  Then we close the lesson with an exit slip or an assignment, rating ourselves once again to see where we fall on the scale.  I take a look at what they wrote for their final rating and catch those students during the review, intervention block or some recess time the next day.

This seems like a lot of work, and I won’t lie that at first it was for me. It was a different way of thinking.  But soon after I started to do this, I noticed that it was easier and easier to think about what a 0-4 looks like.  If I ever skipped the rating part, my students would actually shout at me “What does a 3 look like?!” They wanted to know what it would take to be successful! It was very powerful.  You may not have time to write it out like this for every lesson, but you can do it orally while referring to the levels on the wall.

This tweak to my instruction was a total game changer.  Thank you John Hattie and Robert Marzano for your inspiration!

 

Real Life Examples of Geometry

The number of terms that students are expected to learn in geometry is a little crazy.  We counted 30 different new vocabulary words at the end of four days of instruction.  So I checked out an iPad cart and decided to have the students find real life examples of geometry in the world around them. After introducing the symbols, and describing each term’s features…they solidified their understanding of each new word with photos. (We pulled out some of the trickier ones from our minds as well.)

We recorded the findings on a giant chart!

Real Life Examples of Geometry Terms

Students captured real life examples of: point, line segment, line, ray, intersecting lines, perpendicular lines, and parallel lines with iPads.

It was both motivating and fun to use technology, as well as promote math talk in the classroom.

Open Ended Math Problems Promote Reading, Writing AND Math

Last spring I had the opportunity to take a practice version of our new state assessment (the Smarter Balanced Assessment). In some states in the U.S. the PARCC is the new assessment which is similar in nature.

Talk about a jaw dropping, sweat on my forehead, instant anxiety through my whole body moment.

What the students are being asked to do is way more than a few math problems. They are expected to read, write and use appropriate grade level math in VERY complex ways. I realized that I needed to add some deep problem solving to my math instruction.  So I began to make open ended problem solving problems to introduce regularly into the classroom.

I decided to create Doggy Dilemma, a free problem for anyone to try out.  It is a highly motivating, real world problem in which students must read through information to decide what dog they must adopt. They draw a diagram of the dog pen, calculate the cost of the fencing, and write a letter to their parents explaining why they made the choices they did.

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My third graders have gone crazy over it.  They love it!  There are two full pages of reading involved which mimics the new assessments.  I have enjoyed creating it and want to make it available to anyone who teaches elementary math so that you can give your students the experience they need before the real assessments begin. You can get it by clicking on the picture below:

Open Ended Problem: Rigorous Problem Solving for Elementary Students

I’d love to hear how other teachers are encouraging this type of thinking in their classrooms. Please feel free to share in the comments!

I am happy to link up here:

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Spotlight: 4 Really Cool Math Educators

I’ve really always been a learner, everything I ever do I just try to read and read and soak in every bit of information I can.  It is both a blessing and a curse!

If you are like me (you also have the drive and passion for getting better at teaching math), you have this never ending quest to read about math.  I wanted to introduce you to some great teachers I’ve been virtually meeting along the way.  They are just full of great ideas and also have a lot of interesting things to say on their own blogs as well. Check them out!

Evil Math Wizard: She is the first person I met virtually when I got started blogging.  We definitely think alike and have the same goals for our students in math!

The Elementary Math Maniac:  I also have noticed that we have similar beliefs in math. She also connects technology really well to learning, and reviews websites and apps on her blog.

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The Research Based Classroom:  You won’t find just math here at her site, but other subjects as well.  She is focused on those very young learners, and believes in research based teaching methods. Outstanding!

Mr. Elementary Math: Full of great ideas, you can find Greg blogging about all sorts of classroom activities with lots of bright, vivid photos.

     
Enjoy meeting these fine folks!

Should We Ignore Them? (Tips for When Problem Solving Gets Tough)

Sometimes I feel like a magnet, with a trail of students behind me as I walk around to conference/help during work time.  We are working on Open Ended Word Problem Challenges right now (I have gone through set one in the first quarter, and we are beginning set two.) These problems include a lot of reading, are many steps, and are open ended.  There can be more than one right answer.

So they hit the panic button right away!

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Right now, I am in the middle of training my students to trust themselves, to be okay with feeling a little uncomfortable. I want them to seek the answers to their problem WITHOUT me.  This is very hard for them, especially when we are working on challenging math concepts.

Here is what one of those problems looks like!

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Here are some ways that I try to raise rigor, and to help students persevere:

1. Ignore them! (What? Are you kidding? How horrible!) Of course the kind of ignoring I am talking about, is the kind where they ask for your help without trying the problem first.  There is nothing worse than when you pass out a tough problem, and the hands go up immediately. This leads to my next tip, a very simple tip.

2.  Make sure the students read the problem three times. Read it once to get familiar, read it a second time to zoom in to what you need to do, then read it even closer a third time to circle key details. The answer to their question is almost always in the problem. Most times I’ll read it out loud!

3.  Encourage students to do what they can in the problem while they wait for help. Sitting there with a hand up, or following the teacher around, trains students that they must rely on the teacher to continue on. When I approach students my first question is always: “What parts did you understand?” They realize that they can do much more than they originally thought.

4.  I teach routines when solving problems. For example, my students cannot actually get up and follow me, rather they wait as I circulate so that everyone gets equal time. Sometimes I’ll have a schedule posted where I meet with small groups.  Knowing that they will all get equal time with me makes everyone relax (including me!).

Teach the students that an “I can do it!” attitude is the most powerful problem solving strategy!

Data Doesn’t Have To Be Overwhelming!

The idea of collecting data has really been getting a bad rap lately. Have you heard these comments (or comments like these) in your building?

  • “We are drowning in data!”
  • “All we do is test our kids.”
  • “I feel like our kids are just numbers, like we are ignoring that they are PEOPLE.”
  • “We collect all this data, then we have no time to analyze it and use it.”
  • “I don’t have time to enter in all this data.”

I think we’ve probably all heard some version of this at some time or another. Some of these comments might actually be true in some districts. I’ve heard horror stories about schools that are doing so much test prep, that they really aren’t finding time to intervene and help their students when they struggle. I feel lucky to work in a district that believes firmly that our data should drive instruction, and if it doesn’t, we shouldn’t collect it.

I had an amazing moment about 5 minutes ago. (Yes, I was working on a Saturday night, not totally uncommon around here!) I was looking at some problem solving we did for report card purposes/parent teacher conferences (THAT explains why I’m working on a Saturday night), and I noticed something amazing.

I use multiplication and division word problems in my classroom about 3 days out of the week. I am a firm believer that students need simple problems to try out before diving into difficult and complex ones. I use Practice Problems for Multiplication and Division because according to the Common Core these students must have multiplication and division mastered by the end of grade 3.  There are also 9 word problem types that are broken down in the common core for students to master in grade 3 so why not teach these things together?

Instead of just diving in and giving everyone all the problems in the entire booklet, I first assess each student on each problem type by giving them the first one. Then, I set up a spreadsheet to look at my results.  I noticed that my class was really struggling with the Type 2 problem, only 8 students got this problem correct. (I score this according to a standards based grading scale, it could also be scored pass/fail.)

My chart:

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So we practiced this problem type. We tried this type of problem five times, each time giving students a chance to come up to the chalkboard to explain their thinking.  Awesome strategies were shared, and students asked many questions to see how they solved it.

The student on the left has pretty good knowledge of multiplication, while the student on the right is just beginning. Both strategies are successful.

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Now we fast forward to tonight.  For parent teacher conferences, I decided I wanted a sample problem solving exemplar to show to parents (it also made sense to have the latest info for report cards!). Naturally I choose this same problem type, since we’ve worked so hard on it. I just finished scoring them, and noticed that 21 out of 25 students got it right this time! I started yelling to my husband (who probably thought I was crazy) that I was so proud and excited for my students.

It really DOES work.  Using data to target instruction is a much more focused way of going about planning instruction.  I haven’t wasted any time on problems that students already knew, and now I know exactly who needs a little intervention work with me! The best part is, this entire process was so simple.  (Instructions are included in the Practice Problems for Multiplication and Division resource. You could also set this up with your own problem types!)

I can’t wait to share this awesome news with my class. I am hoping celebrating our success will motivate them to continue to work hard.

When Differentiation Feels Impossible

I know that differentiation is SO important.  I know it is the right thing to do. But sometimes it is SO difficult to make sure I am meeting the needs of all learners.

Right now we’re plugging away with the concept of regrouping when adding 3 digit numbers.

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There is a group of 6 students in my class who’ve gone BEYOND mastering that concept. I know that I can’t spend an extra day with their bored faces staring up at me.  I just can’t take it, and I know in my heart it isn’t right to continue whole group teaching when they need the support of a higher level thinking challenge.

So…meet Open Ended Problems! I’ve used them before when students have mastered content, these problems get them thinking and are REALLY challenging and complex. Great, right?

Well today something went wrong. In a perfect world, I’m instructing the students who are struggling with adding/regrouping as a whole group, while the other students are working on the open ended challenge at their desk. That didn’t happen today. The students who were struggling with adding/regrouping were frustrated…and the students working with the open ended challenges were frustrated. Everyone in the room at some point had red cheeks, tears in their eyes at times, scrunched up faces, and a general lack of unease.

Why the frustration?  What was happening?! I realized that while I was working with my group, we were being interrupted by the students who were working on the open ended challenges.  They weren’t coming up all at once, rather, they were coming up one at a time, every minute or so, interrupting the thought process of the group. They weren’t interrupting to be rude, they simply ran into a problem while they were working, and came to ask me what to do.

That was when it hit me that we are sorely lacking in the Math Practice Standard 1: I can make sense of problems and persevere in solving them.

Instead of making sense of the problem, those 6 student’s first course of action were to come straight to the teacher. Not used to feeling challenged, they were “stuck” because they are used to answers coming quickly.  They weren’t used to having to read the problem more than once, and didn’t even realize that their questions that they asked were answered RIGHT in the problem they hand in their hands.

After about 5 minutes of these interruptions, I explained to the group of students working on the challenges that they would be meeting with me in 15 minutes.  Once they knew this was coming, the tension in the room released. ALL of the students began to breathe and feel more comfortable.  That simple gesture of letting them know that they’d get their time with me was the solution.  The students in front of me relaxed, the students at their desks relaxed and we were able to go on with our work. By the time I got to that group of 6 students, most of them had figured out the answers to the questions they had!

Sometimes, differentiation feels impossible. It is difficult, but it is RIGHT.  Everyone in the room had a challenging task, and that is how it should be.  Now, I’ve just got to reteach and work on my expectations and routines for small group work.

Differentiation looks different in all subject areas, but I find it to be the MOST challenging during math.  How do you differentiate and hold students accountable? Do you do centers, or a math workshop style? I would love to hear suggestions, comments, questions and more!  The more we share the more we learn.

Problem Solvers Aren’t Born, They Are MADE

My first year of teaching, I was the queen of teaching problem solving. I would stand up in front of my students each day, and show them my beautiful strategies for solving the problems. Over and over, they would see my drawings, my number sentences and my solutions. I would ask them to copy them down if they couldn’t figure it out, so that they would have an idea for the next time. As I’d look at my data, I would notice that I had a top group of problem solvers who could always solve it, a big group of solvers that would typically get the problem correct, and a group at the bottom that would NEVER get the problem right.

I was foolish enough to believe that this was okay. I thought that some kids just weren’t very good at problem solving. I was SO wrong, and I am SO embarrassed to admit this now.

My second year of teaching, I heard this quote: “The person doing the talking is the person doing the learning.” I honestly felt sick to my stomach, because I realized that I was doing WAY too much of the solving, working and showing. I needed my students to take ownership, stand up, share their thinking in kid speak and start to GROW. I learned a lot that year, that students aren’t born to problem solve. It is something that requires an immense amount of practice.

I’ve come a long way since then, and would like to describe what I have done to be SURE that all of my students are getting this problem solving thing down before they leave my classroom. First of all, we take TWENTY minutes per day, every day to practice problem solving. This is something that is a priority during my math block. Then, I follow the steps below (UGH, I realize this looks like a TpT commercial, and I don’t mean it to be! You can do all of these things with your own resources.):

1.  I assess what problem types the students can solve. Did you know that there are 9 problem types for multiplication and division in the common core?  I use a series of multiplication and division problems, administering the first in the set to see how they do on each of the 9 problem types.  I compile the results in a data table to see which ones the class struggles with as a whole.  Then, we attack those problems one by one throughout the school year. I assess them again at the end with the last problem in the set to measure growth.

2.  I introduce the Standards for Mathematical Practice. These standards are SO important for students to develop as math habits.  They cannot be stressed enough. It takes us about a week and a half to get through them all, but it is worth the time. I post our work daily on the wall. The vocabulary from these standards becomes a part of our every day language.

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3.  I start small, with practice problems that are simple that they can relate to. Then, we go BIG.  I have three types of problems that I use juggle through and use.

Simple Problems:  There are so many problems out there about trains arriving and leaving on time, or other topics that students cannot connect to.  I finally broke down and created problems over the years that would allow for practice of multiplication and division concepts. The problems are about things that students can understand. These are done on most days, with other problem types sprinkled in from my current math series.  These simple problems are NOT done every day.  That is not enough for students to become strong problem solvers.

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Open Ended Problems: These problems require more reading, more steps and are much more complex. There are times that these problems require two 20 minute class periods to complete. These are the types of problems we will find on the Smarter Balanced Assessment next year.

Here is an example of an open ended problem:

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Project Problems: These are always my student’s favorite type of problem.  They spend several days on these problems and are a bit more out of the box. I always begin with the Book Order Proposal and go from there.

Book Order Proposal (Free to try out!)
Housing Market Analysis
Mini Golf Course Geometry
Party Planning Awesomeness
The Wind Powered Car
Elementary Architects

4.  I make manipulatives available to them from the start, and I encourage their use.  The idea that hands on problem solving is for young students only, or for struggling problem solvers is incorrect.  Manipulatives are wonderful for any level of problem solver, it promotes deep thinking of the math concept you are working on.

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5.  I allow students to model their thinking in front of the class.  More about how I do this you can find in this post. They solve it, explain it to the class and accept questions and compliments from the rest of the students.  This is where the students do the talking, the questioning, the complimenting. They are seeing multiple strategies each day, they can “steal” ideas from each other and are held accountable for their work.  I keep a tally chart right on the chalkboard so that students can see how many times everyone has been up. We try to make it equal, even though problem solving comes more naturally to some than others. This helps everyone know that they are ALL welcome up to the board, even if their solution is wrong.

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6.  I intentionally plan out which problems to do and when.  I carefully monitor my students to be sure we are using our time effectively. I watch to see how we do as a class as we solve the problems.  When the majority of the class is getting the problem type, I’ll switch to a similar problem type that requires a tiny adjustment in their thinking. I always incorporate a problem from the book that has to do with the concept we are studying from time to time as well. A two week plan might look like this (and it is always flexible):

  • Day 1: Equal Groups (Unknown Product)
  • Day 2: Problem from math series covering current concept.
  • Day 3: Equal Groups (Unknown Product)
  • Day 4: Equal Groups (Number of Groups Unknown)
  • Day 5: Problem from math series covering current concept.
  • Day 6: Equal Groups (Number of Groups Unknown)
  • Day 7: Equal Groups (Number of Groups Unknown)
  • Day 8: Equal Groups (Unknown Product)
  • Day 9: Open Ended Problem – Day 1 of 2 (complex, many steps)
  • Day 10: Open Ended Problem – Day 2 of 2 (complex, many steps)

7.  I keep accurate records for myself. I have a class list so that I can see when students are getting the problem correct.  I keep the problem as our daily focus until 90-95% of the class has mastered it.  I have an answer key that allows me to check off when we’ve done the practice problems so that I don’t accidentally repeat the same problem.

8.  I intervene with students when the problem type is a struggle.  I pull small groups during our math work time, in the morning when students come in, during recess, during our intervention block time, whenever I can to get those students up to speed.  Many times they just need more one on one support to be successful.  I don’t wait any more for them to figure it out on their own. I intervene as soon as I notice the struggles.

It sounds like a lot, but once we get in the groove, and routines are in place things get ROCKING!  I didn’t realize how much students love this process until we had a substitute teacher in for a day.  The teacher worked the problem out on the board much to the anger of my students! The next day, they were SO fired up and upset that she didn’t give them time to work it out on their own.  That is when I knew that the students in my classroom were finally owning their own learning.

Just Make it Real World

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I am not sure if you’ve ever had that “moment”.  The moment where you are at a frustration level with why things aren’t working. I used to look for extra worksheets to give more time for tricky math concepts to “stick” with students. I looked online for further practice activities, I asked colleagues for their extra resources for more practice, I looked for games. I felt like I’d tried everything.  That’s when I read some research that making math real world, connecting it to student’s lives was REALLY good practice.  So a few years ago I started to create real world problem solving projects to help this problem.

That was how the Book Order Proposal project started (for my gifted and talented students I’ve used The Housing Market Analysis). I knew that I needed to continually reinforce the concept of rounding/estimation, comparing numbers, and mental math addition strategies. I gave my students the chance to do just that by offering to buy books for our classroom library. I decided to coincide this project with my parent Scholastic Book Club order.  Here is how it worked:

  • I made it my problem of the day for 4 consecutive days, giving 20 minutes each day for the project.  The first three were days for them to work (with a mini lesson or two if needed), and the fourth day was the peer review day.
  • All students were given a budget of $50 (bonus points offset this cost-I was able to get all of our books free this last round) to look through three Scholastic flyers.
  • The students had to put together a proposal, thinking about their classmate’s reading interests, as well as thinking of what we currently have in our classroom library.

What happened was kind of interesting. The majority of the students got within $2 of the $50 budget.  A few of the students tried to hand in proposals that were $1, $30 or $25.  When we talked as a class on the second day, I asked my students if it was okay if someone didn’t get close to $50.  The resounding answer was “NO!”.  When asked why, they explained that it would be a waste of money if they didn’t spend it all, especially since they would become THEIR books for their classroom.  I handed back those few papers and asked them to start again. (Now that is what we call peer accountability!)

At the end of the project we laid the papers out and did a gallery walk. Students voted on their top 3 favorite proposals. The proposal with the most votes actually got ordered!  It was such a fantastic way to end the project.

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My favorite part though, the very best part of the entire project, was the gallery walk and natural reflection. Students could see how others choose to put the proposals together. Some were neat and organized, others were missing information, some of them had a hard time with their handwriting, and other student’s numbers didn’t quite add up.  It led to great discussion, and the students wrote goals on their proposals for the next time we have to present information to our peers.

It has been clear to me that making math real world, and connecting it to their own lives is a powerful thing!