# Test Prep without Pain

Math test prep for spring standardized testing is always a bit daunting. Teachers face the same dilemma every year:

1. Trust that we’ve taught everything we need to teach and go in with the confidence that students can apply it….
2. Panic about things such as spiral review, cram in one last topic/unit, review vocabulary words and teach best test taking tips…

Both of those options are perfectly okay, but both make teachers and students feel a bit uncomfortable.  Without teaching any test prep, we worry that students won’t be able to “figure out” questions. Students feel nervous not knowing what to expect and want to feel confident going in. But too much test prep stresses out the teacher and the students, putting tons of pressure on them as they go into a testing situation.

I propose some test prep (for math anyway) without the pain of these feelings.  I came up with Reasoning Puzzles when we first began teaching with the Common Core State Standards.  As I looked at our state test, last year I realized the rigor has most definitely increased, especially the ability for our students to take apart questions and look for multiple solutions and answers.

Instead of flashing up multiple choice questions, students participate in small group discussion about “puzzles”and statements about those puzzles. Allowing them to talk over these puzzles, and make their mathematical thinking visible to each other, they become much more confident.  Testing truly is just trying to make sense of a problem, and looking for small nuances in how the question is asked, combined with calculations of some sort. This sort of test prep is fun, builds confidence in your students, and if done all year can create very powerful mathematicians.

I used them with my own third graders for years, and now with my intervention students.  I received a tweet from a woman named Lisa who took it even a step further and had her students write their own statements. What a great way to extend the learning!

Reasoning Puzzles give students a chance to think critically and to use the standards for mathematical practice effectively.  Feel free to check out the free sample to try them yourself if you’d like.

# Level Your Games: More Small Steps for Differentiation

Recently, I had two first grade teachers approach me about fact fluency. They were feeling both frustrated and scattered. They weren’t sure how to organize the time, how to organize the many games, or how to reach students at all the different skill levels they were at.

It is the same story we all have where every child that we teach is functioning at a different level. Some students didn’t even know their combinations to 5, many were learning combinations to 10, and even a few of the students could work within 20.  The games that we were using were just not reaching every student with what they needed…they were flat and one dimensional. WAY too difficult for the students who weren’t on level, and WAY too easy for the students that had already reached mastery.

Enter the post-it note.

In “Steal the Cubes” each post it assigns each group to a level that is right for them.

Those sticky things are my savior when it comes to flexible grouping.

After talking it through, we thought that we would choose just FOUR fact fluency games that the students could rotate through daily. Once they get bored with the same four, we might introduce a new one.  Time in the day is precious, so we knew that they had to be “go-to” games that could be setup, played and cleaned up quickly. We also knew that students grow fast as they learn, and that our groups had to be easy to change in and out.

So here is what we did:

1. We taught ONE game to the students each week.  They played them for a week until they understood the ins and outs of them. Then, once the routines of the games and the game playing behaviors/expectations were taught, we were ready to rotate through them.
2. Each day the teacher chose the game by putting the color of the game out first, leveling the game like in the photo. Each game can be easily modified with different numbers, different cubes, etc. by just changing the post it note.
3. We attached a third level of post it notes for the partners/groups that stayed in the same place for each of the games, the teacher can simply change up the post its when students move levels.

So once again, differentiation can truly be a little small step.  While this one takes a little bit to set up, the students aren’t bored which makes that classroom game time so much more productive!

# 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):

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.

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.

# Small Steps for Differentiation: Tier It!

I’m still searching for ways to differentiate in small ways that take just a second or two. An activity that is tiered is something that is leveled differently. A true tiered activity means that there are two (or sometimes more) options that account for a different level of thinking.  Not everything can be tiered, but some basic math skills can be tiered quite easily. Here is an example.

I saw this post on Pinterest the other day for a primary classroom. So easy and so creative!

This is an awesome activity for students that are just starting out with numbers and subtilizing.  But what about that small group of kids that the K-1 teacher doesn’t have time to differentiate for? Well, I think that the answer is all about having the right materials, in this case more advanced dominoes. I pulled this together for my kindergartener at home and we had a blast doing it.  (Hello 20 minutes of math play!)

I think if we systematically think about what the next “level” of some of those basic math skills are, we can slowly incorporate the correct materials into our centers, our assignments and our games. In this way we ensure all students are making growth!

# Release of Materials: More Small Steps for Differentiation

I struggled to understand a very basic thing when I taught third grade, and I see it’s importance all the time now that I am in many classrooms K-4.  Math is incredibly abstract for elementary minds, and the need to provide them with hands on tools and manipulatives is essential for conceptual understanding. So often we skip this step (or at least I did) because we as teachers are developmentally past needing this to understand numbers.  So often we skip this step (or at least I did) because tools are messy, noisy and the students play with them. So often we skip this step (or at least I did) because we run out of time to grab them, or it takes too much time to get them out and put them away. Despite all of this, we really need to allow students to have them so that we can see where they are developmentally.

Which leads me to another small step for differentiating in your classroom.

When introducing a concept, provide tools always to the students. Then, as you notice that some students need more of a challenge, ask them to try it without the materials to see if they can make the connection with just the numbers and symbols. For example, Make 8 Go Fish:

This is a great, easy game for K-1 students. They play Go Fish but ask for pairs that make a given number. In this case I chose 8 for a student that I am working one on one with right now. She struggled to find combinations that sum to 8, so we built them using ten frames before we started the game. Some students may need this support, while others may be ready to do it without ten frames or any tools at all.

Sometimes we force tools on all students, or we just don’t provide them at all to any of them.  Put it in your student’s hands by teaching them how to recognize that feeling of when they do or don’t need them.  Challenge them by releasing those materials when they no longer need them!

# Fly on the Math Teachers Wall – Squashing Fraction Misconceptions

When I was an elementary student, fractions were by FAR my most difficult subject.  I could not ever wrap my brain around them and embarrassingly enough, I still struggle to understand them. The other day I had trouble trying to figure what half of a 3/4 cup of butter would be! My cookies tasted a little more buttery than I would have liked. So today I am talking about misconceptions about fractions, because I’m really a pro!

This question was on a fourth grade test on fractions this week at one of my schools.

Amazingly, many students answered the question by saying they agreed with Molly. Their explanations said things like:

• “4/8 and 1/2 are the same number because they are equivalent.”
• “The diagram below each shows a half, so they are always the same.”

So somehow, somewhere we have a misconception here. Students are missing the idea that fractions can be different amounts if the whole is a different size. After all, one 8 inch pizza is not the same as one 16 inch pizza, right? I’d MUCH rather eat 1/2 of the 16 inch pizza!

My favorite way to clear up misconceptions is to relate it to real life…especially food. Food lends itself beautifully to math in so many ways. Once I brought in the skittles, suddenly light bulbs turned on.  Equivalent fractions may be the same number, but they are not always the same amount.

I think we miss this step very often when we work with students. I think that real life connection is what helps them figure out what the symbols stand for. When we leave that out, students are unable to make sense of a problem.

If you want to see more examples of misconceptions that us math nerds have uncovered, check out The Math Spot:

# Differentiate in Small Steps: Give Them Two Problems

Differentiation is difficult. There is no doubt about it. I’ve been on a mission to find small ways to differentiate without stressing myself out, and without stressing out the teachers I work with.

I often found myself realizing that I was giving one math problem to the whole class when I’d look at my gifted kids faces. You know that look on their face? That boredom in their eyes look…where they’d rather be someplace else than sit and do another problem that they already know how to do. That is what inspired my idea of just putting two problems up, a meets the target (happy) problem and an exceeds the target (stressful) problem. I always explain to the students that if you are able to complete the happy problem correctly, you are meeting the target. It is even more impressive if you can do the stressful problem, but it’s not necessary.

Here is an example. Today in a second grade classroom the learning target was adding 2 digit numbers mentally (without regrouping).  I put up two problems, the happy one was a check for me to see who had it.  (They worked in their notebooks but it’s also great to use dry erase boards.)  The stressful problem is the one that students who need to stretch their thinking just a bit might try after doing the happy problem.

Using two faces makes it both visual and fun for students. Cut them out and reuse them over and over!

I keep those little face headings handy, they go up on dry erase boards, chalkboards, and easels…wherever we are doing math.  If I forget to put two problems, the students definitely remind me. They love to see the stressful problem face, especially the first time when I draw it in front of them.  You can use this method during quick checks, problem solving, mini lessons, practice, mental math…the possibilities are limitless.  This is something that can be done quickly, and doesn’t require hours and hours of work.

# Student Talk Leads to Deeper Thinking

I witnessed this cool thing the other day, the thing that I keep on blogging about because I keep on seeing it over and over. I was in a second grade classroom where students were adding two digit numbers.  The lesson was to add the ones first, then the tens by decomposing numbers. The well meaning adult in the room (me) kept on teaching it according to the lesson.  Students were making mistakes and errors like crazy.  Then, I gave them the freedom to try whatever way they pleased.

I was astounded by their thinking, they came up to share one by one with different strategies that made WAY more sense to each other than what I was preaching. It was pretty amazing to see what they were coming up with. Not only did their ways make sense, but they were also accurate. Another reminder that I need to SHUT UP!

This student made tens, and then added the ones and tens in the order that made sense to him.

So let them talk! The deep thinking and learning that will come from it will be amazing.

# Help! What’s My Error?

Every so often I have one of those moments where I want to stop the entire class to show everyone something a student did. Today was one of those moments when I watched how a student tackled a word problem. He had asked me for help and I was guiding him through it.  He was doing some mental math, realized that something didn’t seem right and checked his thinking. When he realized that he was 10 away from the target number, he very quickly realized that he could adjust his thinking and his answer. (You can see he changed 44 to 34.)

This is perseverance and precision!  This is what we are constantly hoping that kids will do without us having to remind them. The problem is we are running around asking students to do this on an 1-on-1 individual conference. Imagine how powerful it would be if students shared examples like these and learned from them, how much more time would be free up in our classrooms to really dig deep with kids!

Here are some simple ways to share:

1.  Stop the entire class and have the student show their error and how they fixed it.

2.  Build in share time at the end of your lesson for students to tell a story of how they found and fixed an error in their thinking.

3.  Here is my favorite idea…make a “What’s my Error?” chart!  This is a simple chart where students (while they are working on an assignment) could put up problems that they are stuck on.  We’ve all been there before where we keep on getting the same answer, but we know that something isn’t right.  Other students during a share time could help figure out the error and write their thinking on the chart.  So often adults turn to others for help when we need it (for technology, for many things), but often in math class we leave students to figure out these things alone.  A “What’s My Error?” chart could help students explain their thinking AND help them to be more interested in finding the error in their ways in the future.  Like all things, you have to manage it by making it a routine and having general expectations (imagine the students fighting over the markers, crowding around the chart), but isn’t that a good problem to have?

Let me know if you try it I’d love to hear how it goes!

# What Exactly IS Subitizing?

For a few years, I saw the word “subitizing” and I had no idea what it meant. It is one of those things where you don’t know the word very well, but once it enters your consciousness, you start to see it more and more.

Last summer I learned what subitizing is (I pronounce it soob-i-tizing, some people say sub-i-tizing), and how important it is for K-2 students to be able to do. Quite simply, subitizing is the ability to count a collection of items without having to count each item individually. For example, when you roll a dice you automatically know the number without having to count each dot individually.

Subitizing is important because it means that children can hold an image in their minds. They are able to group collections effectively so that they no longer need to count by ones. We want them to do this with regular patterns and irregular patterns. You know that children are subitizing if they can tell you the number in the collection when it is flashed at them quickly.

Here is an example of an irregular pattern, and what we want the student to think in their minds:

We want students to group items together to count efficiently.

There are several videos (if you google it) that people have created to help children practice this skill.  Here is just one (warning: it flashes fast!):

How do you have students practice this skill in the classroom?