Tag / elementary education

by Beyond Traditional Math

Start Geometry Vocabulary Early!

I love to be sneaky with using vocabulary in the classroom. One of the ways that I like to embed it is through game playing. For example, instead of using two color counters, we pull out the pattern blocks. Instead of saying “I want blue!”, I tell the students that I would like them to sound more like a fancy mathematician. Instead you must say, “I would like to play with the trapezoid, please.” It causes a laugh with the kids, but even better it starts to get them to use those words more regularly and with purpose. Plus they love to say the word trapezoid! There is a nice benefit to getting these words in their mind early, they’ll start to connect that vocabulary to real world examples of lines, points, segments and other geometry terms.

There is a natural reason to determine the difference between the two tools in the photo below, and to examine how the rhombus and trapezoid are different so that they know which one to pick. This can start as early as the primary levels! Most pattern block sets come with hexagons, triangles, rhombuses, parallelograms, and trapezoids.

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by Beyond Traditional Math

I’m Taking a Big Risk!

I used to hate teaching math when I began my education career. It was scary! I didn’t know what I was doing and had ZERO confidence. 18 years later, you’ll find me traveling across the country teaching other teachers the best ways to teach math. My number one goal in starting this blog is to help YOU love to teach math. However, blogging isn’t the main form of learning these days. I find myself going to social media to learn so many things. So…I am (very nervously) trying a new idea where I do things way beyond my skill and comfort level:

  1. I have started an instagram account (a professional one), you’ll find it by clicking here: @beyondtmath
  2. My goal is to release as many teaching tips as I can using reels or video posts.
  3. I want every video to be under 60 seconds, and something you can try immediately.
  4. I plan to try to do these weekly.

It feels worrisome to put myself out there, but I’m going to be posting all those tips that I tell teachers and I hear back: “I wish someone had told me this!” or “I love that idea!” or “I am SO trying that!” or “That finally makes sense to me!”

My first post is about how to develop number sense with cubes. I hope you’ll venture over and find me! (Please, please, please!)

How to teach number sense.
by Beyond Traditional Math

Assume Nothing! Why Some Strategies Might Not Work (At First)

Remember when analog clocks were the only kinds of clocks around? I grew up with them, digital clocks didn’t really creep into my life until I was in middle school. I learned to tell time at a very early age because of the lack of cell phones and computers with their digital displays. So, I always assume (which I NEVER should) that my third graders know how to tell the time.

I was reminded once again last week that assumptions are a foolish thing!  We were in the middle of learning about multiplication.  My goal is to expose my students to as many strategies as I can think of to learn multiplication, especially when the strategy relates to real life. I was so excited to share this strategy:

Multiplication Strategy

I shared it with my students, eager to see their familiar “oh, I get it” or “I can connect with that” faces.  I got absolutely NONE of that. They just kind of gazed at me with blank eyes.

So I said, “You know, if the minute hand is on the 7, then you know 5 x 7 is 35…?”

Again, nothing.

I couldn’t believe it. I asked (very gently), “Do you all know how to tell the time?” (We haven’t done a time unit yet this year, so I haven’t checked their understanding regarding analog clocks.) Instead of a resounding “yes”, I got many downcast eyes.  I took an anonymous poll by asking them to close their eyes and raise their hands if they know how to tell the time on the clock on the wall.  I was surprised to see only 2 hands go up out of 26. Ouch.

We really cannot assume anything of our students.  Now that I’ve unearthed this little gem, we’ve got two things to work on at once! We came up with the solution of labeling our classroom clock with the numbers to help us get more familiar with each tick mark.  When we get back from break, I am going to brainstorm with my students how we can use the clock in our classroom more often.  The more we use it, the more useful this particular multiplication strategy will become!

by Beyond Traditional Math

Let THEM Make Those Math Connections!

One of my favorite parts about teaching math (and multiplication specifically) is all of the amazing patterns and connections from one thing to the next.  When I first started teaching I would to preach these patterns to my students.  They thought they were cool, but that was about all.  One day a student in my class saw a pattern I hadn’t seen before, and I realized that it has WAY more meaning if they discover the connections themselves.  Now, when THEY discover the patterns/connections it feels even more amazing, not to mention the fact that it sticks in their minds.

My students finally connected with a multiplication concept today.  We are at the beginning stages of teaching multiplication, so the whole thing is a little mind blowing to them.  They learned to multiply with repeated addition, equal groups, arrays, and with using a number line.  I noticed that they didn’t seem to understand how they were all related.

So I sat them down with a blank piece of paper with the words: “Multiplication: It’s all related!” I asked them to see if they could find how each thing I put on the chart was related.  I didn’t speak as I put up each one, one at a time.

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The moment came when I got to the third one…arrays…and placed each square up (in rows of 5).  I heard a few “oh’s!” and hands flew up in the air.  Then they started to predict what my number line was going to do (I drew it out first before the hops-again not even saying a word!).  Seeing them predict meant that many of them were catching on to how they are all connected.  At the end I asked them what they thought the multiplication fact was, and the answer was shouted to me by 26 children.

“5 times 3!”

 

by Beyond Traditional Math

There is ALWAYS More Than One Way

When I was young, we were told that there was a specific way that we had to show our answers/thinking in math class. We could only show the way that was taught, and we were often times deducted points if we didn’t show the correct algorithm or method. I think that did a great disservice to our generation of mathematicians. I think it limited us in our thinking, and taught us that we were either good or bad at math. There are times that I think math is more about finding creative solutions, than knowing the “right” way.

Take this classic example that happened in my class last week!

We are working on multiplication and division right now, but there is a group of 5 students who pre-tested right out of this topic.  Their knowledge at the beginning stages of multiplication and division was so far beyond the rest of the class, that I have them working independently on my On Stage! Holiday Concert Performance Task.  In this project they are charged with planning a whole entire holiday concert for their classroom.  It is really fun to watch them work through each of the tasks in the problem. I schedule in a time to meet with them daily, and loved this moment I had last week.

Pictured below is one step of the project (there are 6 total). It is my sample invite that I pull out if they are struggling to understand that particular part of the task.  In this part of the project they are asked to find half of an 8.5″ by 11″ piece of paper, draw the rectangle on the given paper and design an invitation for the concert.

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I asked the students to describe the way they figured out the “half size” rectangle. I was, and always am, amazed at the many different ways they found it:

  • Method 1:  “I just folded a piece of paper, measured each side, and then drew those measurements on the paper.”
  • Method 2:  “I figured out that half of 8.5 is 4.25, and that half of 11 is 5.5, so I drew those lines on my paper.”
  • Method 3:  “I had no idea how to figure this out, so I folded a piece of paper in half and traced it right on my paper. It seemed like the easiest way.” (LOVE the HONESTY here!!!)

We talked about how each way was just fine for each type of learner.  For someone who understand fractions/decimals, method 2 is great.  Perhaps you don’t have a clue how to use a ruler, then method 3 can work. We discussed that there was always more than one way, even if your way isn’t “perfectly mathematical”, we can then think about how we can do it mathematically the next time. The student who used method 3 became a sponge as she listened to how the other two students described the way they figured it out.

Allowing students to share their ideas allows them to see that there is ALWAYS more than one way!

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by Beyond Traditional Math

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!

by Beyond Traditional Math

Struggling to Learn Their Math Facts? One Way to Help

I know you have the student (or maybe you have many of them) that I am about to describe.

  1. They count on their fingers as their only strategy to recall their math facts.
  2. No matter how many ways they try to learn math facts, they come very slowly.
  3. They are at least a grade level behind in math fact fluency.
  4. They feel helpless, like they will never learn their facts.

There is this strange attitude with these types of students, as if they think they will never learn their facts. Their parents or siblings will say “I never really was very good at memorization, or learning my facts.” Those comments validate the student’s struggles and they feel like they, too, will never learn their facts.

Nonsense!

They CAN and they WILL learn their facts. They just need some good tools.

First and foremost we must teach strategies. There are many ways that students can interact with their facts. They can use ten frames, number lines, fact families, pattern work etc.  Time tests alone do not teach students their math facts, and we cannot rely solely on flashcards/memorization.  We must first saturate their minds with a variety of ways to work with and look at their math facts. That is when memorization works, after they’ve seen the fact so many different ways they are sick of looking at it. This works for the majority of students as they learn their math facts.

But for some students with learning difficulties, it STILL won’t work. THEN, we must boost children up by giving them intentional memorization strategies.  The strategy I am referring to is called incremental rehearsal.

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It is adapted from a strategy that I learned over at Intervention Central.  Their strategy is amazing as well, but I found it was overwhelming for my struggling students to have so many facts involved (Instead of 10 but I’ve narrowed it down to 5 at a time).

There are a variety of ways I’ve used this strategy:

  1. Parent volunteers come in to work 1 to 1 with my most needy students.
  2. I’ve had peer tutors from upper grade levels come in to work with students in a math fact recess club. (Bring candy or treats, they’ll feel amazing to be a part of the “club”!)
  3. I’ve worked with small groups in intervention block with specific facts.
  4. If all else fails, I’ve sent home the facts to work on in baggies with the instruction page (see below).

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Some students truly are going to take longer to learn the facts…but they WILL learn them.  Especially if we never give up on them.

Thanks to Charity Preston for the link up!
Classroom Freebies Manic Monday

by Beyond Traditional Math

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.

by Beyond Traditional Math

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.

by Beyond Traditional Math

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!