Math Problem Solving: Exploring Capacity

Kids have a lot of misconceptions about capacity, and they can really only be cleared up through hands-on exploration.

Sadly, I don't think they get opportunities for this like we did when we were kids. Instead of playing in a sand box or with cups and bowls in the bathtub, kids are playing with iPads and Wii's. And so many districts (mine included) are taking away sand and water tables from kindergarten, in favor of more "rigor." Because of this, kids are not building the schema necessary to understand more abstract concepts about capacity.

So please, please give your kids lots of time to explore by filling up cups with water, sand, rice, beans, cubes...whatever you have! If you are lucky enough to still have a sand or water table, it is the perfect excuse to use it. Don't let anyone tell you it's not "rigorous"!

Day 1

I start my unit by showing a quick little powerpoint, to get a discussion started.

You can download the PPT by clicking the link below:

Download Will an Elephant fit in a Bathtub

The kids are able to quickly give the correct answers. But I push them--I want to know why! (Because the blue bucket holds a lot more than the red cup, so you won't need as many bucketfuls. It will be quicker...)

Then I show the kids several bottles, cups and other containers and have them put them in order from what would hold the least to most amount of water (smallest to largest capacity). I make sure it is very obvious which containers hold more/less water. I'll make it trickier soon enough!

Finally, I have the kids draw and label something in their math journals that would hold more water than their water bottles...a milk jug, a pitcher, a vase, a lake, the swimming pool, the ocean... They usually come up with some good ones!

Day 2

NOTE: We do not record anything in our journals for this "problem". We are going to play with water, and water + math journals = very, very stressed teacher. So the math journals stay safely tucked away, warm and dry. Don't be afraid of the water, though. Clearly lay out your expectations (Please keep as much of the water in the containers as possible, no splashing, etc). Bring a couple of big towels to school. Clear off your tables and let them explore!

So on Day 1, I made it very obvious which containers had larger and smaller capacities. On Day 2, it gets a little trickier! I tell the kids that I am really thirsty and show them 2 cups.

The obvious answer would be the blue cup. It is much smaller than the green cup and will, therefore, hold much less water. But then (insert evil laugh here), I show them the red cup...

Now the answer is not so obvious! The kids usually guess that the green cup holds more, because it is "bigger" (taller). But I tell them I want to know for sure--how are they going to prove it? I do not show them how to figure it out. I give each table a green cup, a red cup, and a tub of water. I also leave out a variety of other containers, including some small dixie cups, and tell them they can use whatever they want to try and figure the problem out. I let them work together and discuss their various ideas. And I push them in the right direction with questions only when I think they need it.

There are several strategies the kids can use. The most obvious is to fill up one cup, and then pour it in the other to see if there's room left or if it overflows. Another would be to use the smaller dixie cups to see how many it takes to fill each cup and compare the answers. Another yet would be to fill up both cups and then pour them into a common container to compare.

Your job as a teacher is to guide them. Tell me what you're doing? Why did you decide to do that? What does that tell you? What are you going to do next? (And only when they're completely stuck) What would happen if...?

So which cup do you think has the larger capacity? It turns out that they're pretty darn close, but the red cup holds just a few ounces more.

The most important part of this investigation is the discussion afterwards. Have the kids demonstrate what they did and talk about what worked and what didn't. Which cup had the larger capacity? WHY??? The green cup is taller, shouldn't it hold more? (Ahh...but the red cup is wider.) Remember--kids learn from each other so much better than they learn from us!

Day 3

Here's a chance for kids to learn about capacity and practice their estimating skills at the same time. You can use cubes, or cups of beans, or any other unit of measurement you like.

Day 4

For this activity, I give the kids a variety of containers. The dollar store is a great place to get them. (Like you need another excuse to go to the Dollar Store!) Do not make the answer obvious (i.e. make sure the containers do not fit one inside the other like measuring cups.) Make sure some are tall and some are wide, so the kids will actually have to fill them with beans to place them in order.
 

We use little plastic "Dixie" type cups to measure. Don't make the containers so large that it becomes frustrating for the kids. See the square sandwich container below? It actually holds the same amount as...

...this cylinder take-out container. It's true. Even I had to fill them up with beans before I would believe it!

If you can get your hands on some graduated cylinders from your science lab, the kids LOVE them. Just make sure you have a variety of shapes and sizes.

Day 5

More practice comparing capacities. I do not tell the kids what to do. I let them decide the best way to figure out which one holds more.

Challenge Problem

This is a very abstract and challenging problem!

But every year, I have several kids who can handle it. So I'm giving it to you in case you can use it. By the time we do our measurement unit, we've already covered quite a bit of basic joining and separating--so we have a solid foundation, already. This is a classic Join, Change Unknown problem. Once again, I do not tell or show the kids how to figure the problem out--I just guide them with my questions.

This is a really fun unit, for both the kids and the teacher. So take a deep breath, and...

Let them play!

Comments

[J]

Hi!
Would love to download your powerpoint but it doesn't seem to be working! Is is just me?
Thanks for all the fantastic resources that you share and congrats on your TPT store. I'm sure you will do very well!
J. :)

[Pennie]

This is a great lesson. I was able to download the ppt without any issues. I sure hope you are going to share more of your lessons.

[Cheryl]

Wow! I wish I had all this info when I taught Kinder! Great ideas!

I have nominated you for an award...you can pick it up at Spotted Around the School.blogspot.com

Cheryl

[Jeneva]

I love this. My kids play with cups and measuring tools all the time but after this I'll add more to it next time.

[Angela]

LOVE this!! You are so amazing! I am so grateful for your detailed lesson units! THANK YOU SO MUCH!!

[Amber]

Seriously, you are a genius. I want to be in your class! Thank you so much for sharing the PPt and journal prompts. I cannot wait to try these activities with my little peeps this year!

[Knitty Gritty Homestead]

Beautiful site! Found you through pinterest. In Ontario, we're reverting to a play-based curriculum...while the curriculum is perhaps more rigorous in that the government "wants" all children going into grade one to know how to read (beginning stages), all centres are play/exploration based. I was shocked to read that sand and water tables are being taken out of classrooms! What a crying shame.
Thanks for this wonderful unit!!

[Stefanie]

Our sand/water/rice/pasta tables are the highlight of our play-based learning - and excellent for looking at capacity! Thanks for sharing your ideas - I'm so glad I've seen them because they've given me so many ideas to use when capacity comes around again this year. Very inspiring!

[Carol]

What great ideas! Thanks!
-Carol
Mrs. Cobb's Kinder Sprouts

[Isabelle]

I love this blog! Learning while having fun! In this generation where technology and gadgets are just around the corner, kids are getting too much attached to them. Good thing that they can still use these great tips in learning.

[Valerie]

I am not able to download this file & it is adorable!!!!!!!! Help.

[Susan]

Any updates on when the problem solving math journal prompts will be available on TPT? I can't wait to get them!

[Donna Newdiger]

I can't get the powerpoint to open either. I just get a bunch of randomness. :(

[I love kidz]

Please help.....I was unable to download the PPT. Love your site!!!!!! Thanks for sharing all your wonderful ideas :-)

[Laura]

This is such a great idea!! I am a school librarian and always looking to find new ways to connect the library lessons to the curriculum!

[Karen]

This is awesome! I can't wait to try it with my kinders! :)

[Kirsten]

I can't get the PPT to open either, I just get a page of random writing. please help. Would love to be able toPuse it with my prep class.

[D. L.0]

I love the lesson. I liked the comment you made" don't let them tell you this is not rigourous". You made my day! Thaks for sharing these awsome lessons!

[Carla]

Fantastic powerpoint and ideas thankyou.

[alison mahoney]

I love this unit! Though, I am also having a hard time downloading the PPT. Help!

[Shaz]

Hi there,

I just wanted to say I LOVE your site! I'm a pre-service teacher on my first practical experience placement and teaching kindrgarten for four weeks. Your site has been absolutely invaluable in helping me write my lesson plans. Thank you so much :)

[Megan]

Please assist with downloading your ppt... I'm starting a capacity unit with my 5 year olds next week and have been inspired by your blog!
with thanks!

[haima]

wonderful i wish i were a teacher in a kid school which uses such methods
haimamani indiaComment below or sign in with Typepad Facebook TwitterGoogle+and more...

[Caitlin]

I cannot open the powerpoint. Could you help with the download?

[Ann-Marie Parisi]

This is fantastic! I find 'capacity' a tricky concept for 3-5 year olds. We have a sand table and sensory bin and do a lot of hands on activities. Thank you for sharing your great ideas.
Ann-Marie Parisi
mrsparisisclass.blogspot.com