Thursday, January 19, 2017

5 Tips for Helping Students Make Sense of Word Problems

teaching word problems
How many of you have ever given your students a challenging problem and within SECONDS heard something like...

"I don't get it." 

or

"What are we supposed to do?

This is the point where every teacher sighs and wonders where they went wrong as teachers--or where the students have been during the last months of teaching!  I think part of the problem comes from the fact that we too often make assumptions about what our students know about "tackling" problems.  Whether they struggle with reading--or maybe with motivation--looking at a problem can often lead to shut down from some students.  I have a few tips that I have found to be successful.  See what you think!

1.  Sometimes it's ok to read the problem to the class (or to a small group or individual).  Yes, part of math is being able to make sense of a problem independently, but we also need to remember that separating the reading from the math provides equal access for all students.  Let's not make all our struggling readers math deficient as well! Reading problems aloud can get students' brains working, focused and ready.  Think about your goal--if your goal is "Students will independently be able to read and make sense of a problem", then this tip is not useful.  If your goal is more math oriented--like "Students will work to solve multi-step problems." or "Students will use estimation strategies to check their work.", reading certainly can be taken out of the equation (pun totally intended).
problem solving
2.  Encourage students to take "Think Time" before putting pencil to paper or before working in groups.  Ask them to reread the problem.  Ask them to imagine or "visualize" what is happening.  This could be a great time to ask students to find the question or think about what they need to do or what operations they might need to use.  After some think time, ask them to work a bit independently--even if you DO plan on having them work together.  By each getting started on their own, they bring something to the table for their group to discuss.  This really helps minimize having one partner or team member completely take over--because everyone has SOME sort of start to talk about.
cooperative problem solving
3.  Remind students that sketches, drawings, and charts can help them get key ideas or details down on their paper so they can start making sense of them.  Simply rewriting key information or labels can help too--it can help students get started processing the information.  ALL students can do this--they can all start looking for key information to record.
problem solving
 4.  Two heads are better than one!  Cooperative problem solving can be SUCH a game changer for students who tend to sit back passively.  That being said, it does take some work up front with students to learn the art of partnering.  I have a blog post from this fall about it if you are interested.  Just CLICK HERE to read it!  Some students navigate this seamlessly with minimal coaching and others need help.  Put your observation "lens" on and watch to see how students work together--and giving reminders about what is expected in partnerships is a great idea.  Creating an anchor chart together about how partnerships work gives you a visual to refer to all year long.
problem solving
5.  Finally, sharing ideas and talking about problems AFTER students finish can give new insight as to ways to organize work, alternative strategies, and more.  If students are already in pair, match two pairs together to share out their strategies and solutions.  Hear something interesting as you circulate?  Bring it back to the entire class so everyone can benefit.

So...we really need to put our students in positions where they can take some ownership and dig in without us "'spoonfeeding" them and coaching too much!  Coming soon--a blog post about how to do just that!  Want to see another blog post about helping students makes sense of problems?  Just click the image below to take you there!
The problem pictured in this post is from the following resource if you are interested in checking it out!
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math strategies for word problems

Sunday, January 8, 2017

Angle Studies Part 2

Geometry ideas
So, yesterday I showed you how I got my angle studies kicked off with  my students--how I solidified understanding of "right angle".  We had lots left to accomplish--so I'll try to share some of the different lessons and activities we did over the next days!

Tip 1:  If you can get your hands on thin drinking straws....like the kind you might get in a school cafeteria...taking 2 of them and threading a twist tie between them.  (I forgot to snap a picture at school so I did a mock up at home--but these are big straws.  The skinny ones are WAY better.)  These "magic angle makers" are great for showing students different angles, how they can "get smaller" and bigger.  Students often don't realize that a "big" angle means it is open more--not that they rays are longer.  These little buggers are great for helping show that.
teaching geometry
So we worked on building acute, right, and obtuse angles...went hunting around the room for them...sketched them...made our bodies into them...you get the picture.  We also worked to develop our mathematical rules for them--that acute angles are less than 90 degrees, and so on.

Because we had done our folded circles earlier (Missed it? CLICK HERE for that post), my students were ready to do a little more estimation practice.  We had done the right angle concept sort yesterday, but today I wanted them to use their "reasoning" to estimate the relative size of different angles.  
Angle lesson ideas
 I loved walking around and hearing the math talk!  I did quite a bit of prompting and cuing to help them use their prior knowledge to explain their thinking--but overall it was GREAT to see that they were able to handle this task!
Angle lesson ideas
 I wanted to give my students something concrete to continue their work with acute, right, obtuse, and straight angles, so it was time for some angle art!  (Both of these activities are a part of my Amazing Angle Activities resource available HERE.)

I wanted students to show their understanding by folding paper strips into the different angle types.  They spent some time arranging them on their page, had to "prove" to a classmate that they had all four angle times, then glued them down and made a key.
Fourth grade geometry lessons
Fourth grade angle lessons
We think they look pretty cool!
Geometry projects
The next step in our journey was to actually break out the protractors and learn how to use them.  If you have ever taught this skill, you know it can be really tricky for some students.  Here are a few of my tips in case this is on your agenda for this year!

1.  Work with students in small groups.  I worked with 4 at a time and it makes such a difference.  In 15 minutes, a group of 4 can master it pretty quickly...and if they can't, you sure can tell who is struggling to work with more later!

2.  Stress the importance of estimating.  With most protractors, the two sets of numbers can be very confusing.  If students always ask themselves, "Is it smaller or larger than 90?", it can be really helpful.

3.  I try to keep my directions very simple--a phrase you here in my classroom a lot is "Dot on the dot, line on the line" which means, "Line up the vertex on the center dot and make sure the ray is on the protractor line pointing to 0.".  

4.  Make sure you explicitly teach students how to measure angles facing in different directions, angles that are part of shapes like triangles and quadrilaterals (MUCH harder than just two rays), and that you have students DRAW and correctly label angles as well.  Some students struggle with the drawing part--so spending some time on that is certainly valuable.

5.  Working in partners is SUCH a meaningful way to work with angles.  Having students draw angles for each other, measure them, and try to get within 2 degrees is a great way to tackle precision and get tons of practice in!  If they don't get within 2 degrees, have them work together to figure out why.  I love to hear the coaching they do with each other!
Angle lesson ideas

Teaching protractor skills
 6.  Provide lots of different opportunities for practice.  I love these big cards printed on bright cardstock.  They are easy for students to use and can also be used as an assessment tool.  I use the sheet that is included to help practice estimation as well (This is also a part of my angle resource mentioned above).
Using a protractor
 Along the way, I did some formative assessment to check on student progress. (I made this into a freebie in my store if you want to grab it--just click the picture below!)
Angle lesson ideas
 The next steps of our angle studies involved composing and decomposing angles.  We started to tackle this that first day when we divided our circle...students started to see from the beginning that angles can be divided into other angles.  Each day, we "played" with this idea a little bit more.

"If I divide a right angle into two angles and one angle is 34 degrees, how much is the other one?"

"If I divide a 180 degree angle into three equal angles, how big will each be?"

"What are three different ways to divide a 360 degree circle into 4 different angles?"

My students were loving these problems so I decided to come up with something more for our Angle Art wall...I simply told the students one fact.  I told them that the small angle on a tan pattern block is exactly 30 degrees.  From that point, I asked them to spend some time playing with pattern blocks and making discoveries.  Students quickly began to make connections....the green pattern block had 3 equal angles of 60 degrees.  The blue pattern block had two 60 degree angles and two 120 degree angles.  Light bulbs were going off like crazy!

So I decided to push them a little bit.  We have an Ellison machine with the die cuts for pattern blocks so I went and cut a bunch.  I told the students to take 10-15 shapes and build a design of their choosing.  When they finished, we went on a "hunt" for angles--by combining angles and looking for ways to "compose" 360 degree circles!  They had so much fun--and now our hallway has even more math art for our friends to check out!
Angle lesson ideas

Geometry problem solving
After our in depth work, I think they are ready for our summative assesssment next week!  We will revisit these concepts again later this year when we work more with 2D shapes, but I think for now we are in great shape!  Want to see more angle ideas?  Just click below.

Saturday, January 7, 2017

Teaching Angles: Part 1

geometry angles
This week was "Angle Week" in my classroom...a week of intense work with angles to help us prepare for later work with geometry!  I love this unit for a bunch of reasons--one, many students who struggle with computation-based concepts shine with more "spatial" concepts.  I love it!

Another reason I find angle studies to be so much fun is that I LOVE watching students start to make connections between all the other work we have done and a brand new topic.  Composing and decomposing?  CHECK!  Estimating?  CHECK!  Connecting to fractions?  CHECK!

So the first thing I did to kick of this unit is to make sure that students understood the third grade concept of "right angles".  You see, in the past, I have found a number of misconceptions related to this and this year was no exception.  Many textbooks and worksheets present right angles looking the same way...something like this:
angle misconceptions
Which is fine--it certainly is a right angle.  But what I have found is that students don't always generalize....so when they see THESE images, I get some of the following comments!
angle lesson plans
So you can see--there is a huge danger in creating misconceptions if we don't dig in.  Here was our first activity.  I gave each student a circle of paper and, under the document camera, modeled the following.  I'm giving you the abbreviated version...hopefully you can visualize how this unfolded (literally AND figuratively!)

We first wrote "360 degrees" on the back to remind us of our "whole" circle.

Then we folded in half, traced that fold line, colored one half, and labeled it with "180 degrees".  We talked about the concept of "straight angles" and noted that a full circle is comprised of two 180 semicircles.  I had them fold again, trace the fold line on half of it, color a new color, and asked how many degrees it must be (they easily knew 90). Again, we tied it back to the full circle...being 1/4...1/2 of a 1/2...and so on.  We then folded the circle into it's fourths so only the right angle was exposed and we went on a "hunt" around the room to find examples of right angles.  We found them everywhere--the corner of the whiteboard, the lights, the door, their name tags...students were turning their "right angle finder" at all sorts of angles to find them!  We then came back and folded our circle in half AGAIN to find a 45 degree angle and went back on a hunt!
teaching angles
 Students found angles in letters, in the angle our easel was set at, and in dozens of other places!  I loved watching them really start to "see" how big these different angles are--a huge help in our ability to estimate relative sizes and to check for reasonableness.
angle lesson plans
 So after I was pretty sure we were in good shape with right angles, I knew I wanted to test it with a concept sort.  If you aren't familiar with concept sorts, I have a bunch of blog posts about them so I won't bore you here with the details.  Just search in the right side bar for "concept sorts" if you want to find more posts.

This one was simply geared toward getting students talking about right angles and defending their thinking based on the foundation we had gotten with our folding activity.
geometry lessons fourth grade
 One of my rules for concept sorts is that nobody can place a card in a category without the team agreeing...it is super easy for students to grab cards and start sorting quickly--meaning that the assertive, confident students get the work!
No thank you!

Groups are required to go one card at a time and take turns leading the discussion.  I circulate and ask probing questions, ask them to "prove" it to me, and so on.
teaching angles
 For this sort, some students asked if they could use "tools".  I shrugged and told them that I didn't care how they did it--as long as they all agreed!
angle lesson plans
 After about 10 minutes of sorting, I passed out a different colored crayon to each group.  I gave them about 5 minutes to do a gallery walk to see what others did--and then mark an "x" on any cards that they disagreed with.  Those were the ones that we then projected under the document camera and discussed.
angle lesson ideas
 As we talked about the tricky ones, students had to work on using their specific math language (a big part of "precision") until we could all come to an agreement about whether or not the angle was truly a 90 degree angle.
angle lesson ideas
Next steps?  Acute, obtuse, and reflex angles....protractor use...and composing/decomposing angles.  Stay tuned for that post coming soon!

Looking for angle help in your classroom?  Check out this teaching tandem and see what you think!
Want to pin it later?  Here's a pin for you!

Saturday, December 31, 2016

Chilling With a Good Book

snowman bulletin board
Teaching minutes are precious, so being able to teach real content while still engaging our students' creativity is key!  Check out this book review project that reinforces opinion writing, reading, revising and editing--and creates a beautiful bulletin board as well!  I asked my students to think hard about one of the BEST books they have ever read (or heard)--because I wanted them to be ready to write about it. I gave them a few days to think and talk about it so they all had an idea ready.

As a class, we talked about what we remembered about OPINION writing--and how good opinion has a clearly stated thesis statement, so students worked to craft quality first sentences that would state their opinion about their book.  We did our drafting in our writer's notebooks and then did some peer revising and teacher editing.  I had asked students to only write 3-5 sentences which kept them on topic AND made it easy for me to get to everyone for editing!
winter bulletin board
 After they finished writing, self-revising, and peer revision, they put their names on the "teacher time" list on the white board and got ready to "build" their snowman!  I had a variety of circle tracers set out as well as colored paper.  I explained that they could create their snowman while they waited for their edits--and then they could do their final copy to add to their project.  It was fun to see so many students design their snowman to "match" the book they chose!
winter bulletin board
 When their snowman was built and their final copy done, it was time to finish the project!
book report project
 How stinkin' cute is this one?  She worked SO hard and was so proud of it!
snowman project
After they were all finished, I tore a paper snowhill out of bulletin board paper and hung our new friends above our lockers.  The students had a blast...got some great writing practice...and I have a beautiful new display that can be up for a VERY long time!  
snowman book report
Interested in the letters and the template?  Here you go!

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Friday, December 30, 2016

Pioneer Research! Learning Collaboratively

fourth grade social studies
One thing that I love to do is immerse my students in resources on a topic we have in our curriculum--with a specific task to accomplish.  If your school is like mine, social studies and science time are getting reduced more and more, so we need to be constantly searching for meaningful ways for students to incorporate this real world learning into our language arts curriculum.  Informational research "mini projects" are a great way to combine the two!

This book by Christopher Lehman is a really great way to think about research in a little different way...it's FULL of strategies that are super helpful in getting students to master key elements of research.  For this little project, I focused on a strategy he calls, "Slow and Steady Wins the Race" where he stresses the importance of helping students pause before writing notes to make sure they read, stop, cover the information, and then jot notes.  This really helps reduce the direct copying.  I add one more layer to the process by having students read, cover, then explain to a partner where the two together decide if the information is important enough to write down.  If you are interested in more of his strategies, I put an affiliate link to his book at the bottom of this post.  It's short and easy to read--and I have it FULL of sticky notes with ideas!

So here is what we are doing...I went to our library and got all the books possible on pioneer life and westward expansion--the next step in our social studies curriculum.  The textbook is another option, and I will be using it as well--but I really want my students to understand that true research uses multiple sources.  True research also involves students generating their research questions--and this project is too small for that.  What I really want is for students to practice their paraphrasing skills and to refine their ability to find facts that are most important. To keep the project small in nature, I gave the students categories to "collect" facts about...and to record in this research guide.  We used the textbook, the library books, and even some ebooks that our library has (if you haven't looked at TrueFlix, check it out!).  I gave the students two work times to work together to gather facts, practice paraphrasing orally and then in writing, and then we prepared to select the most important information to display.
pioneers
I then show my students a sample of how the lap book can be arranged--and tell them that it is their job (with the input of their partners) as to what is the most important information to include on each flap.  Students take their notes, explain in their own words, and then get creative!
fourth grade history

interactive notebook lapbook
It's fun to watch students take on this project and get creative...and the best part is I know that they are learning the content, working together, and learning more about informational reading and writing.  I love watching them share their "lap books" in small groups and compliment each other on how they did things!
interactive notebook lap book
Interested in the lap book (or you can use as a part of an interactive notebook) resource?  Here it is!
Here is the Christopher Lehman book that I love!
Thanks for stopping by!

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