January 2017 - The Teacher Studio: Learning, Thinking, Creating
teaching math
This week we are starting our "big multiplying" unit.  Not facts--but "big" multiplying.  Our standards state that our students must be able to multiply up to 1 x 4 and 2 x 2 digit multiplication, and for some of my students--I know this is going to be a biggie.

Because of that, in my planning this week I am planning ahead to be ready to free myself up to pull small groups as much as possible.  I know that some students already know the standard algorithm--and others are still not really even confident with arrays.  This is going to take some navigating and planning!  If you are interested in any of the resources pictured in this post, simply click the image to learn more about it.

Here are a few of my "rules to live by" when faced with this type of situation.  After all, if I'm going to be working with a small group--I want to do way more than just keep the other students "busy".  Right?

1.  Know where your students are and where they need to be.  Make sure you are clear on your content--and have a plan for assessing students formally and informally throughout your teaching so you can really target your instruction to exactly what they need.  I'm not a huge fan of pretesting (I think it's tough to make decisions about concepts based on one or two problems) but I am a HUGE fan of formative assessment along the way.  If a student can demonstrate mastery, they may need SOME work to build fluency--but their time is better spent doing other things.  I use my formative assessment resources all the time to take quick snapshots of progress.

2.  So what if they need that "something else"?  I love to immerse my students in challenging, open-ended tasks.  For this unit, I am presenting my Thinker Task Valentine Challenge to the class as one of these options.  Notice that I said TO THE CLASS.  I make sure ALL students have access to these quality problems.  Some students may not get as far into the challenge as others--but we so often "dumb down" our instruction for our struggling students and don't give them access to rigorous and meaningful tasks.  I might encourage them to use a calculator...to work in teams...or to use the easier version (I love that these have 2 levels for just this reason!).  Again--if I am pulling small groups, there will be time for students to do other work--and this is a great way for students to ALL have a common task.
Valentine problem solving
3.  Building fluency is another great thing to do when not in teacher-led groups.  Playing games can be a great thing--as long as the students are working on games that are "just right" for them.  If students are already fluent with facts, their games should involve some strategy.  If they AREN'T fluent, make sure they actually are ready for the skill on the test.  There is nothing worse than asking a child to play a game to build fluency and for them to not have the strategies to do it--instead, they spend time practicing wrong!  I certainly don't want students who don't know their multiplication facts to practice them incorrectly because I need them to be independent.  I'll have to find another skill for them to do independently.  For the next two weeks, I am making these multiplication fact fluency games available--each at two levels of challenge.  They aren't right for ALL of my students, but they are for MOST.
multiplication game
4.  Another great thing for students to work on when they aren't with you is word problems.  Whether you have them try them alone or work in partners--problem solving is NEVER a bad use of time!  Try to find problems that will be engaging (these all have a February or Valentine's Day theme) and are at a variety of levels.  I keep mine cut apart and in a pocket chart on my wall and try to put the easier ones toward the top.  Many of these also have an "extra" component so students can tackle that piece if it is a good fit for them.   As I transition between groups, I'll do some laps around the classroom checking student choices and doing some coaching along the way--but they really do a nice job of coaching each other!
Valentine problem solving
5.   One more option is to provide the class with a meaningful "warm up" problem or set of problems.  By starting off a class like this, you can make sure students understand the task and that they can be productive while you work to pull other groups.
Valentine printables
So...as you are planning for instruction you know might be difficult where you might need to do some focused attention, think about what kind of MEANINGFUL activities you can provide for your students.  I can almost guarantee--if you give them engaging things to do, the management concerns all but disappear and you are free to work your magic!

Want to pin this for later?  Here you go!

fraction number lines
If you missed my post the other day about using number lines to improve fractional reasoning, you might want to take a peek at it before digging into this post!  Just CLICK HERE if you missed it...because I want you to know that the lesson featured today was not the FIRST time my students had worked with this number lines....and the lesson is one that should come after they have had some other experiences using number lines and having conversations about them.

So let's dig in!  

Step one--present students with a number line task.  As I mentioned the other day, even a number line task can be simplistic and obvious.  I am partial to a more "open" number line--where partitions are not already drawn.  When you include those partitions, you've done so much of the thinking FOR the students!  Remember, I always ask students to THINK before they pick up their pencil so they have a starting point.
teaching fractions
As students worked, I walked around and checked out their work and hunted for misconceptions.  I would make note of how they were organizing their work or strategies they used that I thought might be worth talking about.  In my last post, the next step involved pairing up and having discussions together and coming to consensus.  Today?  Not so much!
standards for mathematical practice
My next step was to ask students to come up and place a blue dot on this "class number line" to show where they had marked in in their math journal.  I reminded them to NOT change their answer based on what they see--because they need to trust their gut!
fraction number lines
By the time all the dots were up, it was time to have a discussion where we "critiqued the reasoning" and defended our thinking.  We had to use math language and vocabulary with our sharing--so I heard things like...

"The dots on the far left can't be accurate because they would really be past 0 and into negative numbers."

and

"I think [pointing to a dot] this isn't possible because there is no way that you can keep equal parts."

and

"It was more clear to me when I put in all the whole numbers so I could find where they 1/3 really should go."
fraction lesson
Some students needed some convincing--and we had frequent "turn and talks" throughout to get EVERYONE involved in discussion the ideas people shared.   It was great to see some light bulbs REALLY go off!  After our discussion, I sent the students back to their own notebooks to study what they had done and to "revise" their thinking if necessary.  SUPER powerful stuff!

This was a very nice and quick warm up for our lesson--and the process can be used not just with number lines but with ANY problem type!  Stay tuned for another post coming soon with more fraction fun!

Want to see the resource that these number line problems are from?  Lots of different problems and options...
Also available bundled with whole numbers to 1,000 and whole numbers to 1,000,000.
Want to pin this for later?  Here you go!
fraction number lines

fraction number lines
It seems like I have picked a few topics lately that just don't fit into one blog post!  I wanted to share two different "warm ups" I did with fraction number lines--and two different types of "math talk" that resulted from them.  Give these two lessons a try and see what you think!  I went kind of "photo journalism" style because I thought the pictures helped tell the story!  Watch not just for the important fraction understanding--but the immersion in the Standards for Mathematical Process as well!

First of all...if you have followed me for long, you know I love number lines--especially number lines that think "outside the box"--even number lines can be rote and low level--so we want to watch for that!

The other day I gave my students this one...it had the 0 and the 2 marked--and asked student to identify what number they felt that "dot" was showing.  My first step is always to ask them to THINK before they even pick up their pencil.  While they think, I remind them to consider what they know and can tell from just looking at it.  I really think slowing them down before they start writing can lead to deeper understanding and reduce careless errors.  Plus--for those students who ARE slower processors...not having to watch 20 other students get to work feverishly while they sit is SO refreshing and validating for them.  After some think time, they were off!
teaching fractions
 Some asked if they could use rulers...I simply said, "If you think it will help..."
Standards for Mathematical Practice
 I noticed that some students seemed to be putting fractions on their number lines WITHOUT adding the whole numbers first.  I asked, "Are you sure 1/4 goes there?  How do you know?"  Their answers told me a ton about their level of understanding.  Some had already visualized where the "1" went--others were simply putting it "where it looked right".
number lines and number sense
 As with all my number line work, I want them to be able to explain their reasoning both in writing and orally.  As students were working to finish, I had students begin to write their ideas down so they were ready to buddy up.
critiquing reasoning
 When we were all in a good place (in other words, essentially finished), I put students in pairs and trios and gave them the following direction:

You must all come to consensus about what fraction you will assign your dot.  When you are all in agreement (and this took SOME debate in some groups!), you will mark it on the white copy and start explaining your thinking.  When you present, I will call on whoever I want so make sure everyone is accountable for the information and explanation.

(or something to that effect)
teaching fractions
 I circulated and listened and coached and looked for misconceptions and mistakes.  I also looked to see the variety of strategies shown so I could have a variety of ideas to share under the projector.
math talk
For this particular problem, we had some debate.  About half the groups believed the dot to be at 3/4 while the other groups had a variety of answers.  One by one, they presented their solution and defended their logic.  Along the way, there were a few "a-ha's"...and a few stubborn souls who stood their ground despite very good arguments from others!
math discourse
 At one point, we put two different solutions up and had students try to determine which one they felt was "more right"...and which explanations seemed most plausible.
fraction number line
 We also showcased different strategies that seemed to help some groups.  This group used different colors for each step along the way--and other groups agreed that this seemed to make their explanation easier to follow.
standards for mathematical practice
 Finally, we ended up grabbing a spare number line and doing some folding to find those midway points and really "prove" what the 3/4 teams were proposing.  We had a great discussion...and SO much learning happened--and the students did it ALL!  Consider trying the strategy:

1.  Think time
2.  Independent time
3.  Partner/consensus time
4.  Whole group sharing and debating time

Watch how engaged your students will be...and let me know how it goes!
fraction lesson ideas
Looking for the fraction number line resource pictured?
I also have two other number line resources and a bundle of all three...see what you think!  I use them ALL year long.
Want to pin this post for later?  Here you go! And watch for several more fraction posts coming soon!

Looking for an entire fraction UNIT to get students thinking and talking?  Check this one out! 
(the number lines are not a part of this resource)
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!

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.

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!

Back to Top