Measurement Mash Up... Why Twitter Is Awesome

Saturday, October 17, 2015 / 4 comments
My students have never learned measurement so well as they have this year!  A few years ago I taught measurement the way it was taught to me.  Something pretty much separate from other standards, maybe if I'm lucky a tiny bit of estimation thrown in.  It actually seemed to get in the way of all the important math we were doing, but at least it was a short unit... It only took about 4 days out of my life.  Don't judge.  I told you I lived in literacy land. 

Math was something to get through...  Now, it's what I look forward to most and I have a hard time not doing math all day.  Seriously, take a look at our morning message... It's a problem.

Last year I entered the math world.  I just dove in and gave it my all.  It was a tremendous year of growth in teaching and learning of mathematics.  To this day I still want to apologize to the students I had before last year.  

(Data from the 2013-2014 and 2014-2015 school years.
3 = meets standard, 2 = approaches standard, 1 = far below standard)

While reflecting on my performance in teaching measurement last year I don't think I gave it its deserved attention.  My kids did better than the previous year, but I knew I could do better.  This year I dug deep into the standards using the California math framework as my guide.  
I also consulted Student Centered Mathematics by Van de Walle who noted that the use of too many non-standard units is confusing for young mathematicians.
So I made a plan based on what I researched.  This was the progression that I developed.  If you have notes on this, please let me know!  
(P.S. I'm not suggesting that measurement only takes 4 days, this is just the order of the progression I used.)

1.  Compare and order 2 objects to 3rd object
Possibly describe relationships between lengths using symbols < > = etc
Activity:  I gave students a glue bottle (you can use any classroom object) and asked them to use that to compare lengths of objects in the classroom.  
Students recorded findings in math journal.  When they finished, we shared findings with class and charted them.  Ask students if they agree? Why?  (Put up an incorrect one to get kids to disprove it.) Use comparison symbol between objects to promote reasoning. 

When I did this activity we made a discovery.  A student noticed that we have different sized glue bottles in our classroom (something I missed, but was a happy accident) so it was possible to have an object that could be considered both longer and shorter than a glue bottle depending on the length of the glue bottle size (unit length).  I wasn't planning on this coming out until later, but it was actually pretty awesome.

2.  Connect number to length using manipulative units that have a standard unit of length (unifix cubes work) -the  framework even mentions using rulers
Lesson focusing on end to end, no overlapping, no spaces - address these misconceptions about procedures of linear measurement - We experimented with all of these.

3.  Compare results of measuring (number) to direct comparisons (which is longer, shorter?) - Is there a relationship there?  This relationship validates the need for measurement.

Next: We used Graham Fletcher's (@gfletchy) "lil sister" 3 act task.  My kids loved it!  You can find it here:

Act 1: We looked at the first picture and I asked them what questions they had and I wrote them all down.  

(This is the pic from Graham's 3 act.)

(Questions students came up with.)
One student asked how much taller the older sister was than the younger sister so we investigated that.  (Graham has how much shorter is the younger sister.)
I asked each of the students to make an estimation of how many cubes taller the sister was.

We put these estimations on a string number line - it really is a string taped to the whiteboard ( Note to self: I need to buy some of those Command hooks.)... not super fancy, but helps greatly with number sense and reasonableness of estimations.  This idea is stolen from Andrew Stadel @mr_stadel or #Estimation180.  We have been using it almost daily in our estimation routines.  
Next, the students identified that they don't have enough information and they told me what they needed to know, the height of the girls.

Act 2:  Reveal the height of the sisters. 

Then, have students use their tools to solve.  These were bigger numbers to work with so it was a little tougher.  As I walked around and saw some kids struggling with using their faithful part part whole mat or counters I saw others more effectively using their 120 chart or the number line that is up in the classroom.  I would say, "Oh, I can see that the 120 chart is really helping you with these big numbers, Ryan.  Great idea!"  Other students who had stalled a little heard this and reevaluated their tool choice.  (They really needed a tool to help them solve the problem, and not just represent their thinking.)

Act 3: I displayed different strategies and tools kids used and made connections, then revealed the answer from Fletcher's page.  

This lead us to another discovery about how much taller/shorter the sisters were.  The difference was the same either way the problem was worded.  We charted both.  

Act 4:  Fletcher has a fourth act where you ask kids what would happen if you changed the length unit.  We ran out of time...  so we came back to it a couple days later. 

What I appreciate about Graham's task (aside from how engaging 3 act tasks can be and that shouldn't be understated) is that he is combining a standard like measurement with other major clusters. He only lists two standards for each task, but there are many that could be applied.

The next day I partnered kids up and had them estimate the difference in height between themselves and their partner. (They were much closer in these estimations than they were in the previous task.)  Again, the kids used the string number line to record their estimations and results.  The kids loved this task!

4.  Nonstandard units of measure - intention is to show a need for standard units - same object, but different size (This was discovered in my room on the first lesson with the glue bottle so we will circled back to it.)
The next day I held up a cube and a full length straw and asked how many straws tall they thought they were.  Again we estimated on our string number line and talked about the reasonableness of the estimations and this time we added a too low and a too high estimation (We always try to make brave estimations - if estimations aren't brave they can't go on our brave number line).  At the end of the lesson, we answered questions like, "Why wouldn't people want to measure in straws, glue bottles or even cubes all the time?  

It was a great conversation.  The need for standard units came out.  We compared about 5 different rulers or yardsticks from the class and found that they were exactly the same regardless of what color they were or whether they were made of wood or plastic.  Then the kids all went and compared their own rulers with their classmates to make sure that it would always work.

The final lesson was awesome.
I pretended to be distraught.  "Boys and girls, our principal wants me to measure the length of our class whiteboard in straws and I only have one straw left!  I just don't know what to do!  It's impossible!"

Then of course, the kids chimed in.  "Don't worry Mrs. Duncan!  We can help you.  It's not impossible.  You just need to use one straw and put your finger at the end and move it and count."

Me: "I'm not sure I get it.  Can you show me?" 

Students came up and used one straw marking it with a marker each time they moved it.  Then, as a class we counted and came up with 15 and "half of a half" straws. It was great, but it gets better.
I pretended to send an email to my principal to tell him that we had solved yet another problem about the length of the whiteboard, but I told the kids that I had another email.  He wanted me to measure the length of the whiteboard using only one ruler.  
Again, I acted like the village idiot.  The kids came to my rescue and again used a whiteboard marker to mark the end of the ruler each time they moved it down.  We noticed that there are 12 inches on one ruler so we wrote 12 where the ruler had been each time. When we were done we were left with 9 rulers (feet) and 10 inches left over.  I asked the kids, "How can we find the total number of inches?"  One student said he knew 12+12=22 so he came up to prove it and ended up disproving it while explaining it.  
Then, another student suggested that we use the making tens strategy he remembered from number talks.  Thanks #mNTmTch and @themathdancer, @mathminds , @DrRuthParker!  (Number talks are something I am pretty comfortable with after implementing them last year and this year, but I am still trying to learn more.  If you're interest search #mNTmTch - making number talks matter on Twitter.)

The student broke up each 12 into a 10 and 2.  (We noticed that what we wrote looked like a number bond.)
Me: Now what
Student: Add up all the tens first.
Me: Why?
Student: It's easier to count by tens.
Me: Do it.
It came to an even 100, but then we had nine 2's left to count.  The students as a class counted on from 100 by 2's until they got to 118.

This was a whoa moment for me.  
I asked the students if they knew what they just did. They didn't entirely.  So then I wrote this on the board:
12 + 12+ 12 + 12 + 12 + 12 + 12 + 12 + 12 + 10 = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 100 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 100 + 18 = 118
Me: How is this like what you just did?  Talk to your partner.  Then we shared.  
They were amazed with themselves.

Our class measurement wall.

On Friday my kids took their measurement assessment.  Class average on the assessment was 98%.  

I know some are thinking, How do you really know your kids got it?  Well, aside from the assessment, I would say by the representations of student work, discourse and through their math journals.  

I give much thanks to my math boss, Ryan for helping when I had questions.  This unit wouldn't have gone so well without his input, the framework, Van de Walle, Stadel, Fletcher and number talks.  It is so exciting to see the work of so many people come together in such a powerful way in one little classroom.  



  1. Wow Jamie!
    What a great write-up. Thanks for sharing. My favorite part was, "Math was something to get through... Now, it's what I look forward to most and I have a hard time not doing math all day."

    Keep up the wonderful work!

    By the way, I'm sharing this on Global Math Department in November.


    1. Thank you so much! I had so much fun teaching and learning with the kids. I still haven't taken the measurement wall down... Thinking I will bind it into a class book that the kids can read. Need more wall space. My heart is attached to that unit. LOL

  2. I love this! Thanks for sharing.


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