Math Problem Solving: Measurement--Length

Inchworm, inchworm, 
Measuring the marigold.
You and your arithmetic...

You'll probably go far!

So here is the beginning of my Kindergarten Measurement Unit. This is a fun unit, and that's a great thing, because we spend a lot of time on it! The unit is divided into 4 sections: length, surface area, weight and capacity. (We're also supposed to do temperature, but we cover that so much in science that we skip it in math). As with everything, we start out with lots and lots of hands-on, concrete learning activities. But once I feel like they have had enough practice, I give them a more abstract problem so that they can apply what they've learned. 

So let's start with LENGTH!

In Texas, kindergartners only need to be able to compare 2 or 3 objects and tell whether they are longer, shorter or the same (and the Common Core Standards look similar). But my children usually master that concept very quickly, so we move on to measuring with non-standard units. 

K(10)  Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions. The student is expected to:

(A)  compare and order two or three concrete objects according to length (longer/shorter than, or the same).

K.MD.1. 

• Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

K.MD.2. 

• Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

Day 1

A space stick (if you're wondering) is a tongue depressor. We have them in our supply buckets and use them to help us leave spaces when we're writing. 

I really use this activity as a formative assessment--to see what the children already know. I do not give the kids a lot of direction, I just give them a space stick and let them go forth into the room to find their objects. As they are working, I circulate and talk to the children. I ask them to show me objects that are longer/shorter than the sticks. I ask them How do you know? and What does that mean--shorter? (or longer?) I get a general idea of where the class stands as a whole in their understanding. I also look for children that are struggling so I can make sure to keep an eye on them as we move forward.

During share time, I have the kids show examples of longer/shorter objects. I have children demonstrate how they compared the objects. I have some children show how they lined the objects up at one end. We discuss why that's important and what happens if we don't. We also talk about the words longer, shorter, taller, bigger, and smaller. How are they the same? How are they different? When would you use them? (For example: A giraffe is _____ than I am. This pencil is _____ than the scissors). We talk about what length is. What are we measuring when we measure length? 

Day 2

This is a quick activity to see if children can place objects in order according to their length.

During share time, I might ask a student: I noticed you lined the crayons up on one end as you put them in order. Why did you do that? What would happen if you didn't do that?

Day 3

My favorite measuring activity!

I have the kids sit in a big circle and give them each 1 or 2 objects that I have gathered from around the classroom. (I choose objects that can easily be ordered by length). I tell them that we are going to put all of these objects in order from shortest to longest. I start by putting one object down. We review why it's important to line objects up on one end and come up with a strategy to do that for all of the objects. (Here we used the strip between the carpet and tile). 

I call on a student to place his/her object down. I do not show them where to place it. They have to estimate where it will go in the whole scheme of things. For example, it wouldn't be the best idea to put the paperclip right next to the yard stick. Mostly, I let kids put things where they think they will go without interfering. Moving objects around to make room for new objects is part of the whole problem-solving process, and if I step in, I'm defeating the purpose. I do, however, guide them through questioning: I noticed you left a lot of room between your marker and the apple pointer. Can you tell me why you did that?

The more objects that are on the floor, the harder it gets. Some objects are very close in size, and the kids really have to focus to see which is longer. It is an excellent opportunity to revisit good strategies for comparing lengths (i.e. lining objects up on one end).

After a student places an object, I ask the class: Do you agree or disagree? If someone disagrees, I have them explain why.If the object needs to be moved, I have that person work with the student who placed it to move it to the correct spot.

Eventually, we get all the objects placed. 

The next day, I have the students complete a smaller-scaled version for their math notebooks.

Day 4

Some students will still struggle with lining the objects up at one end. In this case, I would ask the student: Which is longest? How can you tell? Is the ___ longer or shorter than the ___? Why does the marker look like it's longer than the pencil? How could we fix that?

When they are done, I have the students record their answers in their math notebooks.

Day 5

Here is another activity where students place objects (wiggly worms) in order according to length. I pre-cut strips of green construction paper in various lengths and have the children pick a piece. They cut out and decorate their worms any way they want. 

As with the classroom objects, we work together to put the worms in order from shortest to longest. Worms get moved around as needed. There are usually a few heated debates about worms that are close in length. Finally, when we're all in agreement, we glue them down!

Day 6

Here's the classic comparing names by length activity. I use this activity as a bridge between comparing objects and actually measuring them with non-standard units. 

I start by writing 2 names on the board. I will choose a really long name, like Alexandria, and write it in skinny letters all smushed together. Then I will choose a much shorter name, like Drew, and stretch those letters out so that his name is actually longer than Alexandria's. Then I ask: Which name is longer? There is a very heated debate--some kids think it should be done by the number of letters in a name. Someone will almost always tell me "You have to make all the letters the same size!" So then we discuss why and how we could do that. Then I show them the grid paper (see below) and ask (not tell) them what we should do. 

The kids write their names, one letter to a square. (Longer names will need strips taped together). And just like the worms, we put the names in order from shortest to longest (or longest to shortest!) We talk about how the squares on the paper helped us keep our letters the same size and why that's important. We will revisit this idea again!

Download Measuring names

Download Grid Paper

Day 7

This activity introduces measuring with non-standard, or informal, units. 

The children partner up and take turns tracing and cutting out each other's feet.

I do not directly model how to measure the feet. I give the kids a tub full of cubes and let them work it out on their own. We take a break about halfway through and have a discussion. I will call on several kids who are doing the things I want to see and ask them to explain. I prompt them with questions: I noticed you snapped your cubes together. Can you tell us why you did that? What would happen if you didn't? I noticed you went right down the middle and not from side to side. Why?

Then we have more discussion. I ask several students: How long was your foot. How long was your partner's foot? Whose foot was longer? What did you notice about how many cubes it took to measure your foot versus how many it took to cover your partner's? (It took more cubes to measure the longer foot). Why?

Follow-Up Activity

I show the students a cut-out of my foot and a smaller one. I ask: Which is longer? 

Then I proceed to measure both feet with paperclips. As you can see, I have a variety of sizes, but the kids usually don't seem to notice or care at this point. Until, that is, we count the paperclips! So we talk about it. It took 4 paperclips to measure my foot and 6 to measure the smaller foot. Does that make sense? Why or why not? What did I do wrong? How can I fix it?

Use paper clips that are all the same size, of course! This is a very concrete example of why it's important to use units that are the same size when comparing objects based on their size! (Just like when we wrote our names in the squares for the comparing names activity).

A quick note about non-standard measurement: It is essential that kids get lots of practice using non-standard units of measurement before they move on to standard units, like inches, and centimeters. Although it is easy to teach kindergartners how to correctly use a ruler, do they really understand what an "inch" is? And if you move to these abstract, standard units too soon, students can develop serious misconceptions. After reading the teachings of people like John Van de Walle and Marilyn Burns, I am perfectly content to sticking with non-standard measurement in kindergarten!

Day 8

I like to give the kids lots of practice measuring, so first we do an avtivity where they have to measure common classroom objects. 

Often times, the actual measurements will include a 1/2. I generally tell my class to use their judgement and measure to the nearest cube. Some kids already understand the concept of 1/2 and write it down (although I get a lot of this: 12 in a haf). 

Download Meauring with cubes

 And then I let them choose what they want to measure. 

Download More Measuring with Cubes

Day 9

With this activity, we explore measuring the same things (in this case, pieces of tape) with different units and then comparing the answers. I put 3 pieces of tape around the room and label them A, B and C. The kids measure each piece of tape with cubes and popsicle sticks.

As you can see, the numbers are very different...

Download Mj_measuring sticks v cubes

So then we ask the question: Why are the numbers different? It's a good discussion, and the kids usually get it pretty quickly. Here is one little girl's writing:

The numbers are different because: It is not because of the tape. It is because of the object that you measure with. The popsicle stick is longer so the number is "shorter." The cubes are shorter, so it is a bigger number.

Another little girl wrote:

The numbers are different because the popsicle sticks were bigger than the cubes and took up more space.

Even though this is a simple activity, we are helping to build our students' schema. In the future, when they start learning about inches and feet and conversions, they will have had this experience--something to build on!

Day 10

So here's a chance for the kids to apply what they've learned. I'm gonna warn you, at at least half of the kids, even the really bright ones, will say the puppy without a second thought. Afterall, 13 is bigger than 2!

They will also ask to see the teddy bear and puppy, which is difficult, because they don't actually exist. I tell them: I don't have them, but we do have plenty of space (popsicle) sticks and cubes. So--what can we do?

They figure out that they're going to have to lay down 2 popsicle sticks and 13 cubes to see which is longer. As a few kids figure it out and the buzz starts making its way around the room, the ones who initally said the puppy is longer get out cubes and popsicle sticks to see if they are right or wrong. It's fun to see their reaction when they figure it out!

It's hard to read, but this student wrote: The teddy bear is longer because the popsicle sticks were longer than the cubes.

And One More!

Again...the first thing they ask is "Where's the rocket?" I tell them: It crashed, so what are you gonna do?

Most lay out 5 space (popsicle) sticks and then measure them with cubes. 

But I have had several students figure out that one space stick is 8 cubes long, so they just added 8+8+8+8+8. Way faster (and easier) than lining up 40 cubes!

Wow...this was a very LONG post (I'm so punny!)

Have fun measuring!

Comments

[Tara West]

I just LOVE your website. I really want to implement the math journal this year! I attempted a version of a 'cookie cutter' journal last year. However, it just didn't offer very much out of the box thinking and it ended up being more busy work. Your journal is just awesome! Also, I noticed in one of the pictures the kiddo was measuring a Journey's leveled reader! I'm always excited to find another Journey's user! Tara West
Little Minds at Work

[Cathy]

This was soooo helpful!!! Thank you for being so detailed and taking us from start to finish.

[susan warder]

Your site and your lessons are innovative and hugely appropriate for little kids. I began using Math Notebooks last year and am excited about implementing more of the elements this year.
Have you listed anywhere on the site the order in which you present the different units? Looking at the examples illustrated here, (and knowing how kindies develop) the measurement unit seems to be late in the school year. What is is the sequence of your math studies? Thanks

[Jackie]

I just love your blog, and your explanations of how you teach things. Thanks for sharing them, and giving confidence to others to do the same.

[melissa clancy]

Thanks for sharing these great ideas! The math journals are great and I love how detailed your students work it!

[Constance Harrington]

I also love your lessons and the level of detail you present. I'm also very interested in your time line for your lessons. Measurement is late in the year in our system's pacing guide, but there are so many opportunities for measuring throughout the year--their height at the beginning of the year, apples and pumpkins in Fall, their height in the middle of the year, etc. I'm pondering doing some of this at those times and revisiting during the designated time in March/April. Any suggestions?

[Erin]

I hope you post soon about the next part of your measurement unit! I would love a timeline of your math units as well! Such great information and ideas!

[Cortney MacDonald]

I am very excited to try some more investigations and use a math journal next year! Thank you so much for your blog. You are an amazing teacher.

[Gail P]

You did a fantastic job here. We use Investigations Math at our school and many of these activities are in that but your pacing seems smoother with more whole class work rather than "Math Workshop" which gets boring over time and often seems to drag or skip.

[Lindsay]

Hello! I love love love your blog. Your units of study are top-notch. I'm curious- do you have your math journal prompts available for purchase? I know many of us would buy! Thanks for all you do. :0)

[Laura]

Do you have math warm-ups, problem-solving activities, or math units available for sale? They look awesome!! Thanks for sharing ideas from your classroom :)

[Christina Killeen]

I have spent countless hours pouring over your site!! You are such an inspiring teacher. You inspired me to try math journals for the first time this year and I am loving the whole process. Thank you for taking the time to share your ideas and for being so generous with your resources!! You rock!!

[Marilyn Benbow]

Thanks for the detailed lessons. It is just what I was looking for. I really enjoy your website because I am always able to find great ideas.

[Bev White]

Thank you for the details. I particularly needed help with appropriate questions to get the kids really thinking.

[Chelsea Decker]

This is Awesome! I was looking for some great measurement comparing activities, and this is it! Thank you for sharing! I'm sure my kinders will love it!

[Beverly Garriga]

This is great!!!! Can't wait to use them in my classroom!

[julia]

This is the first time I have taught measurement, and your step by step guide was sooo helpful, as were the resources. Thanks so much!

[Jo]

Thanks for sharing some great ideas. Looking forward to trying them with my class.

[Aubrey McGee]

I will be starting measurement with my Kinders when we get back from spring break. I wasn't crazy about the way the curriculum set it up. This is perfect!! THANK YOU for sharing :)

[Patti K-5]

AwEsOmE post:) My favorite is the Wiggly Worms activity! Thank you for sharing!!

[Tarah]

Oh my goodness! I am in love with this! I start my measurement unit next week and I am so excited to use some of your ideas. Love the wiggly worms, my kiddos will have so much fun with that activity! Thank you, thank you!

[Darlene]

I agree with Tarah, I too am starting a Growing and Changing theme next week. Thanks for the excellent lessons I will be using with my 3s and 4s!

[Elena Gruwell]

Thanks for your ideas. I am teaching measurement this week and these activities are great to try on at this time.

[Mari Poloni]

I loved your lessons! Thank you for being my teacher. Thank you for sharing. I am interested to buy whatever you have for sale.

[Samantha]

Such a wonderful post!!! Thank you so much!!!