On one evening, he was having trouble with conversions of measurements. This was his homework.
I asked him about his notes from class. “How did your teacher teach this? Where are your notes?“
And this is what he showed me.
I was not thrilled to see “memorize” on my son’s notes. It dawned on my husband and I that our son’s teacher has only been teaching a few years. He’s probably used to just memorizing steps and procedures. I don’t like to teach that way. I like to teach for understanding. I like to teach more conceptually. I like to have my students make sense of a problem rather than “memorize” steps.
Just for kicks and giggles, I went to page 290 to see what is said. This is what I found.
I sat and stared at his paper and at the “steps.” If my son didn’t understand and remember the steps, how could I get him to comprehend what they were asking?
I looked at the 1st question again. “If 16 C = 1 gallon, then 8 gallons = ________?” Rather than doing a fancy algorithm or proportion (which he hadn’t done in the curriculum–my husband had an issue with that.), I went back to the basics. Let’s draw a picture.
16 cups are in one gallon (rectangles). 8 gallons with 16 cups in each. Once I sat and explained the situation to my son, the lightbulb went off in his head. “Oh mom, all you have to do is multiply 16 times 8 to get the number of cups.” BINGO!
And the rest of the hour, we drew pictures, diagrams, and whatever else helped him make sense of the conversions. And each time we drew a new picture, the lightbulb kept going off in his head. (Proud Math teacher and Mom!)
The next day after school, I asked my son if his teacher said anything about the homework we did. My son told me that his teacher said, “you should have done it the way I told you too.” ARE YOU KIDDING ME?!?!?
MATH RANT – – After close to twenty years of teaching math, this just blew me out of the water. It is no secret that there are many ways to get answers to math problems. I usually give the anecdote that there are many ways to get from here to New York. Some ways are faster, some ways are slower, some ways are more expensive and that’s ok. Pick which way works best for you…..as long as you get to NY. Same goes for math. It is our job and soul purpose to teach our students. It is well known that one size doesn’t fit all. One approach to solving conversions doesn’t work for everyone. Why are we still having students memorize procedures if they don’t understand the problem? What happened to making sense of things? It only happens to be the first standard of math practice!!! It baffles me that this is from a newer teacher who hasn’t done any conceptual lessons and/or applications. The whole thing blows my mind! Maybe it’s also the realization that not every math teacher thinks or teaches like me.
So what do we do? Do we challenge teachers like this? Is it worth the fight when they may not understand the importance themselves?
My son’s situation just proves that there’s more work to be done out there. Teachers still need training. And just because we, in our youth, learned to memorize procedures, doesn’t mean we actually made sense of things.
Math rant over. Disengaging.
Until next time,
Kristen
This lesson started when I realized how many coins my family had collected in a jar. We usually run off to our local grocery store to exchange them for Amazon money. It was all I could do to hold off my husband from exchanging them. I saw much potential in this pile of coins.
While planning over the summer, I came across the standard 6.NS.B.3- Fluently add, subtract, multiply, and divide multi-digit decimals using the standards algorithm for each operation. With the suggestions from my son, this new 3 Act lesson, Sassy Cents, was born.
Act 1 –
While the video played, I wrote down the classes comments to each other. Some sat in silence. As the video progressed to show the emoji, I heard “OOOOHHHH.” “She’s rich” “That’s a lot of change.” “It’s huge!” “How long did that take?”
(Awesome—I have them hooked!)
My students love doing notice and wonder. They know the routine so well and expect with any new “thing” I show them.
Notice –
Wonder –
The next step was an estimation bit. I wanted them to estimate how much money the emoji was worth. A great observation came from one of the students. Do we estimate in dollars or cents? They settled on dollars and cents. Their best estimates ranged from $20 to $80.
Act 2 consisted of making sure they knew what a bit of info. I gave them info on what one stack of coins looked like. I also gave them the amount of stacks for each part of the emoji. For differentiation reasons, I figured it would be helpful to give them a choice of how they wanted to solve for the emoji.
The students worked vigorously on their calculations. This was a perfect way for them to practice their multiplication and addition of decimals. Lots of practice with decimal points.
At one point, one of my students sat there finished. I checked his work and asked him to explain his method. This is what he told me….
It was a relief to see one of my students articulate his thinking so well. Many of the other students seemed to figure out each part separately before adding their totals up. This child did his own thinking and that’s ok with me.
I love telling my students that’s there’s many way to get to New York. Some ways are faster, some ways are slower, some ways are longer….but the important thing is that we get there. Math is the same way—many different ways to get to an answer, but the important idea is that you find a method that works for you and you go for it.
Until next time,
Kristen
Recently, Mark Chubb (@MarkChubb3) hosted a #elemmathchat and posted this.
My students know that I love throwing them a “challenge” question every now and again. I use lots of things that I find on Twitter or just online. I’m just curious as to what their perspective will be and what their conversations will be. And they are getting used to me bugging them for a picture of their work so that I can blog about it later.
Here’s a slide show of some of their answers
Click to view slideshow.These two students had a pattern similar to what I would think would be the next shapes.
What do you think it should be? Or do we need more info?
After this experience, I’m thinking of re-trying this type of exploration with Visual Patterns.
Until next time,
Kristen
But then I found this……
This was a picture I found a long while ago and kept it in my files, never knowing what to do with it. I saw the math in it, but didn’t have a solid idea. However, over the summer, inspiration struck and I got to work.
Have you ever asked your students about millions, billions, or trillions? Do they truly understand the magnitude of these ginormous numbers? It was worth a conversations.
Part one of our investigation was showing the above picture and simply asking “what do you notice and what you wonder?”
My students recognized notice/wonder which thrilled me. Some perked right up when they saw those questions (which made me smile). I noticed that my students focussed on the picture itself. Some of my higher thinkers started pondering the saying. Finally, we got to the question I was looking for….which was how many pictures are in a video.
Here’s the information we were looking for…
We decided we needed to figure out how many pictures were in a second, then a minute, and so on. They determined that one second of video would be worth 2400 words. And the video would have to be less than 1 minute. One minute of video would be 1,440,000 words. Not bad for my 6th graders. They were getting the hang out this.
Then I asked them how long it would take them to draw a billion circles. Saw this at a workshop given by Graham Fletcher back in January and I finally found a use for it. The students were thrilled to investigate this for sure.
With much enthusiasm, the students were jumping with energy on this one. One girl raised her hand and asked, “are were really doing a billion?” I looked at the clock and responded, “we got a few hours left so I don’t see why not.” Their eyes got bigger.
First we took guesses. I felt like I was on the Price is Right. “I’ll say 7 hours…I’ll say 7 hours and 15 minutes.” One group kept whispering about the question and concluded that it should take about 1 second per circle. I loved this observation because I could tell they were not only thinking, but trying to make sense of the problem. The class concluded that we should just try it for a minute. Before we got started though, there was more discussion on how big of a circle they should draw. Wouldn’t that be a factor in how many they could draw in a minute?
I started the timer and the students worked vigorously on their circles. The looks on their faces was priceless. They focussed, they concentrated, they were super-serious about getting this done.
When the timer went off, they counted up their circles. We took a poll to see how many circles were drawn and the range was between 80 to 120. For our purposes, we kept using 100. Next, we figured out how many circles in an hour, a day, and then a year. Finding out how many circles in a year was a bit of a doozy for them, but they persevered. I was also happy to report that they knew how to read their place value very well. Whew!
We even discussed what would 2 years looked like, and they told me it would only be one hundred million circles. “That’s not enough.”
I revealed the answer and they were floored. I’m not going to reveal the answer in this post because I want to leave a little mystery to the question. Go ahead…do the math yourselves. (Answer is in the lesson PDF below).
We weren’t done yet. For the last piece to this investigation, I remembered this Twitter pic from Mark Chubb. And I also saw a ripe opportunity to break out the clothesline. I asked my students “Where would 1 million go? Where would 1 billion go?”
After much debate and moving cards back and forth, this is what they agreed upon. I was puzzled because they didn’t really know the relationship between billion and trillion. I let them watch a video I found on Youtube and some referenced that when they were validating their answers.
However, I wanted to push them further. I inquired why each of the cards was equally spaced. Were there an equal amount of numbers between each number? Some answered yes. Some were completely puzzled. Rather than beat the horse to death, I wrote a few new numbers on cards to see if they could show me the relationship. I wrote 0, 10, 100, 1000. The conversation got a little more exciting because my students were dealing with numbers they could relate to a bit more. Unfortunately I forgot to take a picture of the final clothesline and specifically where they moved the cards.
Final thoughts…
Here’s the lesson if you’d like to try it out for yourself.
Until next time,
Kristen
Here is it…the night before my first day at a new school, new routines, new students, new colleagues—actually, they aren’t that new to me. I’m supposed to be trying to rest up and review my plans for tomorrow and all I can think about is “I have to blog about this!”
To catch you all up….I used to be a middle school math teacher for 16 years. The last 2 years, I was a elementary math coach. Now I’m going to conquer teaching 6th grade, but at an elementary school. I get to be with little kiddos again. Ok…my kiddos won’t be so little, but I get to experience the joy, the smiles, the high-five moments, and the celebrations that come with learning.
This transition was tough at first. In the months following my decision, I had weeks where I was raring to go and then weeks when I was doubting myself. I kept asking myself if I made the right decision by heading to an elementary school. My 6th grade buddies at the other elementary schools were cheering me on every step of the way. And with positive mindset, much support from the other 6th grade teachers, and lots of studying over the summer, I’m ready for my challenge. This is going to be an awesome year.
In diving into this new experience, my inner elementary teacher started coming out. I spent a good 2 months planning for decorating my classroom. One of the kindergarten teachers at my site asked me back in March, “what’s your theme going to be?” My reaction was “Theme?!?!? Middle schools teachers never did a theme!?!?!?” I go home and tell my husband about the conversation and he starts looking up things on Pinterest (he is totally a teacher’s husband!). Low and behold, he holds up this picture….
My classroom is completely decked out with college stuff for my theme. I created something from nothing. All of what I’m about to show you is because of this single picture. As a matter of fact, I’m calling it Acosta Academy. I’ve had colleagues come in to see my progress and were completely floored with what I had done.
Click to view slideshow.I also had a revelation. I put more energy into putting together this elementary classroom than I had in all my 18 years of teaching. I embraced the belief “Go big or go home!” More is more in elementary.
And in the little time that I’ve been in the elementary community, I’ve learned so much. For instance, who knew that you could buy Walmart flat bed sheets for $5.00 and they were big enough for your bulletin boards/walls? And I’ve discovered the joys of lamination. It’s such a magical treat. I can’t get enough.
And I’ve created some goals for myself for this year….
On a side note, I’m proud to announce that my kindergarten collaborator and I have been asked to speak at 2 conferences. One of them will be at Calif. Math Council’s northern conference in Asilomar. The other is at the Southern California Kindergarten Conference in February in Pasadena.
I’ve also been asked the speak at my alma mater, Frostburg State University. Sloop Institute on Leadership & Excellence has asked me to present on “Empowering Others.” I love the topic choice and have already outlined what I’d present. Even though the conference isn’t until March, it’s never to early to brainstorm.
There’s more exciting plans coming in the 2018-2019 year, but I’ll wait to report on that when things are more finalized.
Until next time,
Kristen
Sumboxes is a new subscription company that comes to your door step. It’s essentially math-in-a-box. In all my years of teaching, I haven’t seen “teacher” boxes, let alone subscription boxes that include math. The sample box I received was geared for teachers or parents of kindergarteners. Upon further research of their website, they also have boxes for first grade and second grade.
Let’s get to the nitty gritty before anything else. Watch below….
Let’s lay it all out…. You have 2 math activities that include directions/notes, 2 PVC zipper bags, dice, cards, dinos, a magnet, and a sticker —-all included in a neatly blue and yellow schemed wrapping.
Upon my inspection, there’s a lot going on in this box. First, I liked that there was not one, but two quality activities. I can totally see kinders at my school excited by the fact that they were playing games with dinos (who doesn’t get excited by that?!?!). Secondly, the instruction cards, notes, and activity boards were on good quality card stock. They weren’t flimsy at all. It seems as though they will survive some wear/tear from little ones. I also was thrilled to see that I can store the activities in the zipper bags (if you haven’t come across these before….get them!!!!) Lastly and most importantly, it’s all there. As teachers, we scour the internet (Pinterest, Teacher Pay Teacher, or blogs) or our activity books (blow that dust off of them) to find quality activities. If/when we do find activities, we then have to rummage around for the right materials, supplies, etc. All of this takes time, effort (copying, laminating, cutting), and money. And sometimes—in the case of TeacherPayTeacher—-you don’t truly know what you’re getting until you download the file (just because it has a cute font doesn’t make it good).
Long story, short — it is refreshing to see an idea like this come along where more math content is being offered. No fuss, no muss.
Heading back to the Sumboxes website, I read about the company more and came across this.
It’s usually perceived by parents and students to be hard, difficult, and boring. To read this mission statement is refreshing. This mission statement also aligns with my views that math can be intriguing, invigorating, and enjoyable. Why can’t students play games and do activities that practice math skills? I can imagine the look on students’ faces when we take out one of these boxes. Pure excitement!
Here are a few questions that rattled around in my brain…..
(As I ponder more, I will be adding more questions in the future.)
My advice for teachers and coaches would be to check out Sumboxes. I can see schools/principals subscribe to this for individual teachers and/or grade levels. Teachers could try a box out for a month and rotate them among their colleagues. The potential to for support in math is there. It’s a great tool/resource to have around which will engage our students in math.
****This review was completely unsolicited. I’m not getting paid and compensated in any way, shape or form. I just like math stuff. ****
My year in review….
6. More of everything… In my reflection last year, I made it a goal to just have more of everything. And I got that. I was in so many classrooms. During my busiest day, I was in 6 classrooms, plus was scheduled to meet with my boss. I ran marathons on certain days. But once again, to empower teachers, see smiling kids enjoying math and understanding it—was all worth it.
I’m having difficulty writing this part. The reason is that I’ve been told my position has been dissolved. I’m going back into the classroom. For months I’ve had to carry on with my work knowing that my hardworking, dedicated teachers would no longer be receiving my support. I was crushed. It is only recently that I’ve come to terms with the district’s decision.
With that said, I have accepted a position in my district teaching 6th grade at an elementary school. There was a lot of strategic thinking involved in my decision. It happens to be my son’s former school. This school is also where the staff really made an effort in trying out my math strategies techniques. It’s also where my collaborator, Stacy, works (she’s already asked me to be kindergarten buddies with her–and we are going to be doing some awesome math projects). And when it was announced to the staff that I’d be joining the team, the staff was excited and so happy. The math wizard has a new home.
It would have been too easy to head back to middle school and fall right back into my routine. Going back to my elementary roots after 16 years at the middle school level will be a challenge. But I’ve never met a goal that I couldn’t reach. I love taking on a new challenge.
And there is plenty of other opportunities to look forward to. First of all, Stacy and I submitted two proposals to speak at conferences. The first proposal was submitted to the CMC North conference in Asilomar. The second proposal was submitted to a kindergarten conference in Pasadena. We are not able to make it to the CMC South conference this year, but we have several ideas for the next round of proposals. Secondly, I’ve been recently asked to join a team of people to present at the National Council of Teachers of Mathematics. Andrew Stadel has contacted me and I’ll be representing the elementary side of clotheslines.
Recently, a teacher asked me if I regretted taking the position. I don’t live a life of regret. I’m really proud of the work that I’ve done. My work has never been about me. It’s been about the teachers and the students. To see teachers smiling and invigorated by new strategies has been a thrill. To see students engaged and excited to do different activities and lessons was amazing. And to see my work being talked about via Twitter or this blog has been fulfilling. Finally, if I didn’t take this position 2 years ago, I wouldn’t have had the stories and experiences I can talk about now. None of this would exist.
I’m just going to see where life takes me. I am open to all possibilities and opportunities. That’s all I can do.
Until next time,
Kristen
Fast forward a few weeks, when I met with my 4th grade teacher, Mrs. P. We planned a lesson which would introduce the kiddos to a numberless word problem. During our planning session, we came up with the idea of putting a bunch of problems together so that the students could review all the previous material. Little did I know, this one planning session turned into me running between 3 different schools showing all 3rd and 4th grade students numberless word problems.
Now let’s begin with my favorite —the marble problem. I did separate marble problems for both 3rd and 4th grades. And both problems created the most conversation.
I got the students into a routine by starting off with “notice & wonder” before drawing any concepts or figuring any of the problem out. I created this template to help the students navigate through the problem. It also helped that they kept track of their thoughts throughout the process.
3rd grade (each number was a separate slide of a powerpoint)
Was a little apprehensive about doing a problem on fractions with 3rd grade, but they stepped up to the plate and were superb with their problem solving.
Here are a few pics to see…
Click to view slideshow.
4th grade – each slide was a separate slide of a powerpoint.
2. Ty has more marbles than his sister, Pam. Pam has many marbles.
3. Ty has more marbles than his sister, Pam. Pam has many marbles. Louis has marbles.
4. Ty has 6 times as many marbles than his sister, Pam. Pam has many marbles. Louis has marbles.
5. Ty has 6 times as many marbles than his sister, Pam. Pam has 34 marbles. Louis has 202 marbles. Who has more marbles, Ty or Louis?
By the time we got to number 3 (…..Louis has marbles.) the students were freaking out. “Who’s Louis?” “Why does he need marbles?”
By the time they got to the last layer of information, they were excited to find the answer. More importantly, they knew what they needed to do.
Final thoughts….
Such a worthwhile routine especially before testing where there are MANY word problems. Here’s hoping that all of it transferred to the test.
Crossing my fingers…
Kristen
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.
Click to view slideshow.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.
After my answers, I realized how much “bang we got with our buck.” (2nd bad money 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.
Until next time,
Kristen
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.
Kindergarten
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?”
Here’s a snap-shot of what was discussed….
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.
Third Grade
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.
Fifth Grade
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.
I asked what he meant by “uneven” and my son said that it was when one side was larger than the other.
Final Thoughts
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.
A magnificent exploration. Much thanks to Sarah Caban & Telannannalet.wordpress.com for the inspiration.
Until next time….
Kristen