Recently, I was invited into a 2nd grade classroom to work on money (2.MD.8Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately). The teacher wanted to try out something new to go along with this standard. My suggestion was to try out the clothesline. Let’s see if students could put different variations of coins from least to greatest. It totally make cents (1st bad money pun)
And it went splendidly.
Each student was given a card to work on. They calculated the total amount and put their answers on a post it note. When they were ready, the hung their cards on the clothesline.
When they were finished, we went over each card and made sure that we added each coin correctly.
At the end of the session, they students asked why they were doing the activity now (they were well passed their money unit). I answered by telling them how many skills were involved with this activity.
recognizing each coin and its value.
practicing their addition skills with one and two digit numbers
comparing and ordering the numbers
showing equality with some of the coins (for example- 1 dime is the same as 2 nickels which is the same as 10 pennies)
realizing what happens when you have more than 100 cents.
After my answers, I realized how much “bang we got with our buck.” (2nd badmoney pun). This activity had a lot going on it. And all we did was put up a string and gave them cards. But the thinking that went on was nothing less than incredible.
Back in February, I came across a blog post from Telanna about shapes. She saw a Twitter post from Sarah Caban asking a simplistic question.
How would you define the word “shape”?
Not wanting to miss out on the bandwagon, I decided to jump in. Considering that I have access to such a grade span, I patiently waited for the right time in each grade level’s curriculum to pop in on a few classrooms and have a conversation. Each teacher that I chatted with was also intrigued with my master plan and wanted to see/hear the results.
And so my journey of defining shapes began with Mrs. Z’s kindergarten in March. She was right in the middle of her shapes unit (perfect timing) and so she asked the kiddos the question “What is a shape?”
shapes have points and angles. (T asked –do all shapes have points)
Not all shapes have points.
shapes you can trace or cut out.
Everything we color or write or draw is a shape.
Shapes are everywhere because they are.
The kiddos keep having side conversations asking questions like “are they lines?” and “what about letters?”. One child proclaimed “the sky is not a shape.” Upon hearing this, another child replied, “but what’s in the sky? Sun, Stars and Clouds”.
After the in-depth conversation, Mrs. Z asked them to get up and make shapes with their bodies. First, they made a circle (or the attempt at a circle) and then a rectangle. Some students ran up to me to show me the shapes with their fingers/hands.
Fast Forward three weeks—->>>
My next door neighbor, Ms. N, teaches third grade and upon hearing about my shape quest, invited me in to lead the discussion on shapes. They were also in the middle of their geometry unit, so the kiddos wanted to impress me with their growing geometry vocabulary. They also corrected me in that they are discussing POLYGONS, not shapes.
something that has sides
has a vertex (corner of a shape)
has angles—> can be 90 degrees
has different sides
could be a quadrilateral
has to have more than 3 lines
has to be closed —-> all lines connecting
can be a polygon
shapes are all around us
convex —> shape doesn’t have a cave in it
can have a concave in it
rectangle can have opposite sides
can have parallel sides
OK OK OK. I have a guilty conscience about this one. I cheated. Full admission of guilt.
I didn’t have time to go to a fifth grade classroom. Time became of the essence for the fifth grade teachers with reviewing for CAASPP testing.
HOWEVER—- I have an a 11 year old son (5th grader) who was happy (** sarcasm**) to have a conversation with me about shapes. Yes…this is what we do during our commute into work/school.
shapes are in everything
there’s no one thing that doesn’t have a shape
shapes are the building blocks of life. (how philosophical of my son)
they can have an infinite number of sides, but then that might turn into a circle
the sides are not always the same.
there are squares, rectangles, hexagons, circles, triangles,
rectangle has uneven sides
square has all even sides
I asked what he meant by “uneven” and my son said that it was when one side was larger than the other.
Students in the primary grades start by being introduced to their shapes. It becomes just identification which is the first level of learning. By third grade, they are being exposed to more specific language and vocabulary. This third grade wanted to impress me with their knowledge of geometry. They had been testing out different shapes to see which would pass their definitions. As for 5th grade, they have a broader view of what shapes are. They have also explored 3 dimensional shapes as they discover volume.
If I had a chance to follow up with each class, I could ask the question, “what does NOT make a shape?” It would be a great contrast to their base knowledge. It would challenge their thinking and we could probably have an in-depth conversation about their comprehension of shapes.
Like I was saying in another blog-post, I’ve been exploring the different ways and types of writing that could go on in a math classroom. Last year, I was asked to present on the subject.
This is a topic I dabbled in when I was in my own classroom, so I was pretty excited to share with my elementary teachers.
It’s been a question that’s been in everyone’s heads for such a long time. How do we incorporate writing in math? I know that it should be done, but I wanted it to have be meaningful. I wanted it to be authentic. A student’s writing is one way for us to see inside their heads. What’s going on in that brain? How is he/she approaching problems?
As a parent, I’ve seen my own son come home with those “write to explain” questions at the bottom of his worksheets. Usually his answers are short and blunt. Or some of us have seen writing like this…
Yup…this kid is going places. I do appreciate the humor in this, however this is not what we are going for.
Some elementary teachers have admitted to me that they usually skip the “explain” questions at the end of the homework. And let’s admit it…what student completely takes ownership of those questions at the end? How much thinking/reasoning are teachers seeing out of those questions? It’s not happening.
We need to get our students’ buy-in. We need them to take ownership. We need them to be engaged in the problems. We as teachers have to be creative. As William Zessner said, “Writing is a way to work yourself into a subject and make it your own.”
So here’s a few ways I’ve engaged students into writing.
Performance tasks/PBL – Performance tasks are a perfect way to engage a student into a problem. It’s a spring board to have them create their own writing. This is a 4th grade task that one of my teachers tried out. Stone%20Soup A teacher can cover at least 3 subjects in one task.
Exit cards. I have used exit cards to ask questions. I think of it as an extension of a number talk. For instance, explain to me that 17 x 28 is greater than 16 x 29.
Error Analysis. One question I ask students as closure is “how will you know when you’ve learned this?” Usually I get answers like “when I get an A on the test.” I’m never convinced. I’m looking for the student to give me the answer of “when I can show/teach you the concept.” I’ve created a template that can change with the concept. For instance, here’s one on division. Div Err Analysis
Start with the answer...I haven’t used this one yet, but I’ve seen a few versions of it. Let’s say that you start with the answer of 6. The student has to write a math story to go with it. I see this especially for 1st and 2nd graders who need practice with their addition and subtraction (and also writing).
I know I don’t have all the answers. I’m just starting the exploration. I would welcome others to leave comments as to how they tackled this topic.
Ahhh. April Fools Day. It’s one of my favorite days of the year. Yes, it’s a day that I have grown older by 365 days. Yes, it’s a day that I notice more grey strands in my curly brunette hair. And yes, it’s a day that I see a few more wrinkles on my ever aging face.
However, it’s also a day of fun, jokes and shenanigans. If you know my personality, you would say that April Fools Day is the perfect day for me to be born. I’m full of energy, always willing to have a laugh, give a smile, and just have fun. We only have one life to live, so why not make it a positive experience! But in the spirit of the day I started to recall all the zaniness that I’ve encountered on this majestical day. And so I have a question….have you ever wondered what’s it’s like to have a birthday of April Fools Day? Oh…let me begin to tell you.
One would assume that I would be the one to play tricks and pull shenanigans(can you tell I love that word?) all the time, but in actuality I’m fairly tame. Sure, the threat of pranking my friends and family is always looming but I know when and where to cross that fine line. What can I say–some people have better senses of humor than others. And there’s always the balance of how far to push those boundaries. In pulling a good prank, you want the victim to have a smile or a laugh. However some people cross that line of propriety and the results are not favorable. There’s a lot of pressure on the prankster to get it just right.
The big question I usually get is…am I usually the one playing the tricks or do people play tricks on me? And the answer is Yes and Yes.
Usually on April Fools Day, I love to tell my students all my zany stories of all these tricks. However, since I don’t have my own classroom of students, I’ll regale you with some of these stories.
Tricks I’ve played on people…
In college, snuck in and dumped a full bucket of cold water on a roommate while she was taking a hot shower.
In college, I’ve “baby powered” my neighbor’s room (put a folded up newspaper filled with powder under the door, and use a hair dryer to spread the powder)
Short-sheeted several beds(if you don’t know what it is—look here for directions)
One of my colleagues had a jar of marbles on her desk. For days/weeks, I would take 1-2 marbles out (when she wasn’t around) until one day someone heard her exclaiming “I think I’ve lost my marbles.”
One of my masterpieces happened last year. This was my friend’s car. Gotta admit that I was a little nervous dealing with an Audi, but I persevered. Got in a lot steps that day. And it only took one roll.
Price of GladWrap – $3.49 Joy of playing a terrific joke – priceless
Tricks played on me….
When I was a kid, I was told once that my birthday wasn’t really on April 1, but on April 2.
When I was a kid, I was told I was adopted.
For my 16th birthday, just before I was leaving the house for a dinner with my friends, someone called pretending to be the restaurant to tell me that the restaurant was flooded with water and rats (?).
My family and I have tons and tons of other stories to tell (my brothers have pulled doozies). Let’s just say that I come from a family that knows how to have fun and keep the smiles & laughter going. Never a dull moment.
Now you know a little bit more about me. And this is why I call my blog “The Mind of an April Fool.”
It’s incredible to have teachers take something you introduced them to (in this instance–the clothesline) and see what they do with it. And I can’t emphasize enough to my teachers that they should use whatever I give them and make it their own. I usually tell them to “make it work for you.” And then, they invite me in for me to see how they made it work.
In this instance, it’s Mrs. Z, my kinder all-star. Mrs. Z decided to type her class list of students’ names onto cards and see what the kiddos would do with it. How would they want to put their names on the clothesline? Quite a innovative way to make use of the number line. I was curious too
I assumed they when asked, the students would want to put them into alphabetic order. Seemed like an obvious choice. Nope…alphabetic order didn’t even come up as an idea. Instead, the students decided to count their letters in their names and put them in order from smallest name to longest names. “Medium is in the middle,” I had one student tell me. Got it! Thanks for explaining.
And little by little, they started placing their cards. And they did really well. Yes these pictures look like that are incorrect because they are not in alphabetical order. Remember though that they were putting them in order by number of letters in their name.
And one night for a parent evening for kindergarten, I saw this.
So much fun to see. What a thrill to see one of my routines expanded and used. This only proves that there are so many possibilities to the clothesline activity.
My kindergarten collaborator, Stacy and I recently attended a 2 day workshop with Graham Fletcher and it re-ignited our passion for 3 act tasks/lessons. She’s made it her goal to collaborate with me and create one task per topic. I happily accept her challenge and told her, “GAME ON!”
The most recent topic in her curriculum was sorting. This is a skill that we all take for granted. We sort our trash into various recycling bins. We sort through mail. We sort our clothes while folding laundry. How do we get little ones to understand how things are alike and yet different?
She already uses the “Which One Doesn’t Belong” routine and asks students “how would you sort these?” However, how can we bring this standard (K.MD.3 Classify objects into given categories; count the number of objects in each category and sort the categories by count.) to life in the form of a 3 act task?
Our answer was this….let’s give them a scenario they should be accustomed to.
As always we started with a notice and wonder routine.
I saw crayons
Math Wizard said “clean up”
He’s drawing a rainbow and boxes
Crayons are everywhere
I see markers
I heard the Math Wizard
She has a son ?!?!
He needs to pick up his stuff before school
It must be night time because it’s dark
Was he cleaning up to go to bed?
Was he cleaning up before dinner?
Was he cleaning up because he was done?
Does he have a brother or a sister?
I was really curious how Mrs Z was going to push their thinking beyond their notice and wonder. She inquired further. She showed the Act 2 picture.
“What would you do with that stuff? What if Mrs Z said ‘clean up’? What would you do with it? Where would you put the stuff?”
The students thought about her questions for a moment and slowly put their hands up. One student piped up with “I’d put the pencils away”. And Mrs Z next asked, “How?”
“The markers go together. The pencils go together and the crayons go together.”
“I WOULD ORGANIZE IT!”—>And there it was. Just the answer we were looking for. And that is a big word for this student.
And so we discussed how they would sort them. Some students said by size. Some students said by color. One student said he’s organize them between caps and no caps (Markers have caps on them versus no caps.)
Usually at this part of the lesson, the students do some kind of calculations or reason out their answer. How could they be expected to sort from a picture? That’s where Mrs. Z comes in with her bag of tricks. Prior to the lesson, she made bags of pencils, colored pencils, and crayons. Each group would be showing all the different ways to sort their bags. Oh–let the games begin!
Mrs Z and I wandered around the room eager to see what the groups would do. She informed me that they don’t work in groups too often, so she was curious of how this would go down.
Here’s one group’s explanation.
Here’s another groups explanation.
At one point, we noticed that a group put all their pencils together. We asked them how they could further sort this group.
Just when I thought we were pretty much done, Mrs Z runs around a throws unifix cubes on to their tables. The kiddos didn’t bat an eyelash and just incorporated them into their categories. Here’s one groups way of organizing. What do you notice about the picture?
Having the students work in cooperative groups for this lesson gave us opportunity to see which roles the students would fall into. You can see who lead the pack and who followed along.
Student usually come up with more answers than you can anticipate, but we are never disappointed.
I love the hands-on exploration part. We got to see how they were organizing their items.
In my research, I hadn’t come upon a 3 act lesson in which the students had to divide. My 4th grade teachers wanted to see what a division 3 act lesson would look like, so I created one. This lesson also helped me in learning how to use more features on the iMovie application.
I ran around to about 5 classrooms in the last three weeks to try it out. The first time, I had major tech issues. The 2nd time, I questioned my own judgement in regards to the Act 1 movie. By the 4th time, I was convinced it was a decent lesson. Why? It promoted really great discussion (Notice & Wonder), got the students showing multiple strategies in solving the problem, and as any 3 act lesson is….it was engaging!
I present to you “Divided Hearts.” (yes, those are the same heart candies from my other 3 acts. The way I see it–I like getting more lessons out of one purchase.)
Act 1 –
Notice – (compiled between 4 classes)
instead of putting in–> hearts are coming out
video in reverse?
glass filled with hearts –>boxes pulling them out
used 2 boxes at a time
glass empty at the end
candy all different colors
the hearts were divided into different boxes
shows one box at the end
didn’t use hands
are the candies divided equally among the boxes?
how did they get candy inside the box?
how many candies were in the glass?
are there an even amount of candies in the cup?
how many candies were in each box?
how did they fly up inside the box?
What surprised me after each class was how fascinated the students were with showing the video in reverse. Some of them couldn’t get past that. However, I later told them that if I showed the video forwards, it would show how I’m adding hearts to the cup. That might give them the idea of addiction or multiplication. That wasn’t my intent.
Before I continue with the lesson…take a moment to look at how many hearts are laid out. Take it all in. Stare at those hearts. Those hearts and that layout became the bane of my existence for a few days. I must have laid out those hearts and recreated the Act 3 video a good 4-5 times. Sheesh. But anything for the betterment of the students. Ok..rant over.
There were a range of strategies seen in every classroom.
Let’s start with these two… there were a few students who didn’t know what else to do but start by counting out 168 candies. The student on the right decided to use small lines. It must have been exhausting to keep so many counted.
A few more strategies popped up that I have no explanation for (see below). I had the students try to tell me about their work, and I was still stymied. It’s not very often that I walk away still scratching my head. I know they were onto something. If I had more time, I would have spent more time with them.
And then there were some who saw patterns and were making sense of what they had to do. They were avidly checking their work frontwards and backwards. The 3rd student worked on her multiples until she got to 168. She kept on persevering and that’s what mattered most.
Without saying a word to any of the students, I showed the last clip of the lesson. At first, I heard groans because they thought they’d have to sit through 5 minutes of watching this random arm separate 168 hearts into 8 boxes. However, once the video sped up, the fascination with movie making came back. And when they counted the last hearts that fit into one box, the classes excitedly yelled “Yes” with a round of high fives. That’s the moment that you eagerly anticipate as a teacher.
Technology is evil. Always have a back up plan. Because I save my videos to Vimeo, I was able to save myself and the lesson.
My teachers have been learning just as much as I learn from the teachers and the students. Some of them never knew of lessons that create so much discussion and intrigue.
Don’t want to ever count hearts again. I’m good for awhile (until next February).
It’s that time of the year when our students are running to ___________(insert convenience store here—I prefer Target) to buy gobs of chocolates, candies, cards and all of the Valentine’s paraphernalia that is attributed to this holiday. And in the spirit of such heartsy, lovey, dovey emotions, Mrs Z. and I put together another 3 act lesson. What better way to embody Valentine’s Day then to share with the ones you love. In our case, it was sharing with your classmates.
Act One –the fight.
Along with every Three Act lesson, we encourage the students to inquire about what they are seeing with the questions, “What do you notice?” and “What do you wonder?”
Notice – (Compiled between 2 classes)
hands are fighting
I heard the math wizard’s voice
I see a box
They were ready to share.
Inside the box was candy
Candies are hearts
tried grabbing with hands
Candies are different colors
Wonder – (what are you curious about? What questions are running through your head?)
Why didn’t they get their own box of candies?
Did they have enough to share?
Are there other people there?
How many candies are in the box?
Why were they fighting?
Why weren’t there 2 boxes?
A bonus concept for the kinder teachers was that there were a few talking points to review. Some students talked about what it means to share. One class focussed on sharing so that the results are fair. In one class, I had a
Act 2 – How many hearts are in the box?
Act 2 consisted of us giving the students the information that there were 12 hearts in the box. Using this candy-hearts template, we had the students figure out how many candy hearts Jared and his mom should get. You can see the multiple ways that the students went about solving it.
Mrs. Z called me over to listen in on one conversation. Take a look below at what we observed.
Terrific piece of evidence. This student observed that she knew that they were the same because they had the same number of cubes and had the same shape.
Act 3 – The big reveal
Act 3 is usually my favorite because it reveals the answer. It’s really the best part of the lesson because you can hear the “YES!” or see the high fives spreading throughout the entire class. Here’s how we revealed the answer.
Overall the lesson went better than planned. There was another teacher that observed Mrs. Z doing this lesson and whispered, “this is dividing.” I nodded and told her that was true, however I knew that Mrs. Z had begun working on some addition. I also told her that you never know what our students are capable of until you give them that opportunity.
Some of my 6th graders went back to kindergarten. They didn’t know it and we didn’t tell them till the end of the activity. The teachers and I just wanted to do it out of sheer curiosity. And it turned out to be a curiosity that was worth exploring.
Let me back up a bit. Just last week, I led a workshop on the clothesline activity. I like starting off with the teachers trying one out on their own. I pulled out my weight cards that were used for kindergarten. These cards are filled with colorful pictures of a bike, building, tree, a leaf, and other objects. Students are asked to order the objects by weight (the lightest being on the left and the heaviest objects toward the right).
When I tried this out in kindergarten, we had the students put their cards in 3 basic categories—-light weight, medium weight, and heaviest weight. We were not looking for precision. However, 6th grade brought in the precision aspect. Because they have more background knowledge, they were not only integrating math, but science, social studies, and language arts. The 6th grade teacher also told me that this was great because the students were persuading their peers as to which order the cards should go. They had been working on argumentative statements in the weeks prior to this activity. (Gotta love when you can bring more than one curriculum into an activity—I call it “more bang for your buck!”)
Let me give you a visual…
Kindergarten – put these in the “light category”. No arguments from them.
6th grade – argued whether the leaf or the feathers should be switched. One student brought up the fact that the leaf was made of water and the stem makes it heavier. Another student claimed that there were 2 feathers compared to just one leaf.
Kindergarten – put the train in the heavy category although some questioned whether it was a toy train or a real train.
6th grade – put it in the heavy category althought argued whether it was a toy or real. One student said it was a toy because of the multi-colors. Another student argued back that it was real because of the smoke coming out of the smoke stack. Another student questioned whether it was made of wood or metal.
Kindergarten– put this card in the heavy side. No questions/arguments.
6th grade– put this card on the heavy side, however others had issues with it. One student wondered if it was a toy plane. Another students said there was blue sky behind it and so it was real. Another student said the weight might vary because we don’t know if it’s full of people.
Kindergarten – put this on the heavy side. They said they have seen these trucks on the roads and highways.
6th grade – put it on the heavy side. Questions of whether or not it was a toy were brought up. Another student asked it if was filled with anything because that would make a difference. For instance, the weight would vary if it were filled with feathers versus bricks.
Kindergarten – put this in the middle category. They did wonder if it was filled with anything.
6th grade– Wondered if it were filled with anything. One student said that when she bought a new backpack it was filled with paper to make it look full. Another student said it could be filled with books.
One last thing. We did not say a word about this being a kindergarten activity to the 6th graders. We just told them to put the cards in order from least to greatest. At one point, an exasperated student exclaimed “THIS IS SO COMPLICATED!”
Below is the final clothesline that the 6th graders “settled” on. (There were some that were still not happy with the outcome.)
If you’d like to download your own set of weight cards..gohere.
Using clotheslines as an interactive number line has been a hot routine this year. Last year, I slowly and carefully rolled it out into a few classrooms for use of fractions. This school year, I’ve expanded into more classrooms, but am proud of how my teachers have especially made it work in K-2 classrooms. It’s been extraordinary to see using a routine where you get so much “bang for your buck.” There are a good 2-3 content standards that students have been using, let alone multiple Standards of Math Practice.
The clothesline makes sense of numbers and number placement. I especially love the fact that it’s interactive, provokes discussion, and gives insight as to a child’s thinking. Students are actively learning and using multiple strategies to complete the task. And more importantly, it is a tool and a model for students to see the “big picture”.
Let’s breakdown each grade level and how they’ve used the clothesline.
Kinder – I’m a true believer that if you can make a routine work for kindergarten, you can make it work for any grade level. Ever since I introduced this to my kindergarten team, they’ve come up with MANY different ways to bring clotheslines to life! It was rough to begin with, but my kinders have now been through the routine 4-5 times and they’ve got it! Parents are now asking my teachers what kind of math they’re doing because the kids are telling their parents about what they did. (Score!) In September, Mrs. Z and I started with number 0-5 first. Within weeks, we did 0-8. And by November we did, 0-10. It’s imperative to point out that kinders are not working on proportionality of the numbers. They are just working on counting and cardinality (and measurement and data). We also tried out using the clothesline with weight. Instead of literally putting each object in order from least to greatest weight, we kept it simplistic with the light items being placed on the left while the heavier items went on the right. If they were sure of an item, they placed it in the middle.
First grade – tried it out with numbers 0-25. Lots of conversation. Teachers got insight into how their students were thinking about numbers.
Second grade – tried it out with numbers 0-50. Lots of conversation. What was unique is that students were using their strategies of counting doubles for a few particular cards.
Third grade – have used this with benchmark fractions. One 3rd grade team just designed a card set with multiple representations of multiplication. This will be tried out in the new year
Fourth grade – will be using it for fractions.
Fifth grade – one teacher used it for decimals. The students had been doing all the operations with decimals and wanted to see their number sense when it came to placing decimals on a number line. What happened was a complete shock to her. Students grouped the decimals according to number of digits (for instance, .4 and .5 would group together because they have one digit.) That completely blew my mind. Surely, we can’t always assume that our students have a true understanding of a concept when we ask them to apply their knowledge elsewhere.
Sixth grade – teachers will be using clotheslines for integers and integers integrated with decimals, fractions, and percents.
If anyone is interested in downloading the sets of cards for their own use, look here for my sets of cards.