Author Archives: Ms. Espo

Visual Proof, Algebra, WWII, and more Geoboards!

The fourth graders finally finished their visual proofs for multiplication. As I hung the first one out in the hallway, a student said, “Ahhh, the feeling of success!” I know this activity was a little frustrating for some, but that really is OK. If you’re coming for Back to School Night, please stop by to check out their work. The best part is that some of the criticism that stung a little yesterday seemed to be a little easier to deal with and to make changes. Everyone grew a little as they worked on this activity.

Second grade math learned a little more about algebra today as they had to solve equations that only had numbers on one side. Their equations had sea animals on one side and a number on the other side. For instance, a sea horse + crab =9, a sea horse + a sea horse = 8. Students had to determine what the sea horse and the crab were worth. They also have to explain their answer, which has proved to be the trickiest part of the assignment. An important lesson we’re working on involves knowing when to ask for help. There is a happy medium between asking too soon and waiting too long. As second graders, they will become better at this skill as the year progresses. I introduce the assignment, then sit at the “fire pit” (the kidney-shaped table) and wait for them to come to me. It’s all part of the dungeon theme about which they like to complain.

We’ve been reading an Eyewitness WWII book to go along with The War That Saved My Life. We had our first great discussion today. Students had great questions about the war itself, as well as the connections to the novel. We did get off on a few tangents that maybe weren’t in the book but were relevant to the discussion. Book discussions with fourth graders are by far my favorite thing to do. They’ve really started to think about the world around them and their place in it and I never know quite where a discussion will go once we’ve started.

Third grade math continued to try to determine the area of a polygon using a geoboard. One group graduated to a piece of paper, but the other groups are close behind. They were allowed to start with rectangles but can no longer do so, which means they now need to decide how to measure using fractions of squares. There is a lot of math tied up in what they’re being asked to do. This will give them a solid understanding of area, as well as the difference between area and perimeter. Last, but not least, it will also help them understand the concept of area as multiplication, further cementing their understanding.

I hope to see you at Back to School Night this evening!

Gallery walk, coin equations, what if, and who am I?

The fourth graders took a gallery walk of the multiplication visual proofs done by their classmates. We talked about the concept of constructive criticism – what was helpful and what was not. We also discussed the concept of “listening with resilience,” which was a little trickier to master. After reading some of the feedback students seemed quick to brush it off because it was offered by classmates rather than reflect on the feedback itself.  This was a great learning experience, though I’m not sure the bulk of the learning involved math.  We do a lot of these activities in fourth grade because as students get older they need to learn to give and receive constructive criticism from a variety of sources.

Second grade math had to write new equations for new money amounts today. They were shocked when I revealed they had dipped their toes in to the algebra pool. We’ll explore that idea a bit more tomorrow when they move past dipping their toes and move into putting a whole foot into algebra. I am encouraging them to continue working, even when they think they’re finished. Some students were content to come up with only an equation or two while the assignment was to come up with as many different equations as you could manage.

Third graders continued to work on their “What If” not-quite-autobiographies. On Thursday, we’ll talk about adding details and organizing a story to make the most sense.

In second grade reading, we explored the question, “Who Am I?” again. Last week they created posters, for the next week or so they’ll be writing about who they are. We started with a discussion of what they could be – and the list was quite long – but my favorite answer belonged to the student who said she was a writer! I love that she can already see herself that way. I’m really looking forward to seeing who they think they are at the beginning of second grade. We’ll take that piece of writing and then apply it to the stories they’ve read and the stories they’ll write.

Picking good books, writing, Tiny Polka Dots, and geoboards

Fourth grade math had their last creating day on their visual proofs. On Monday, they’ll do a gallery walk and offer constructive criticism on the other teams’ work and then revise their own work based on the critiques they received.

We jumped into how to pick a good book with my second grade reading group. Second grade, in my opinion, is the most challenging for picking good books. My students are often ready to read books that are longer than their stamina can handle. Many of the books that are at their reading level can also contain content that just isn’t yet appropriate for second graders. We talked a bit about how to pick a good book – I taught them the five finger rule (read a page from the middle and if there are five words you don’t know, it might be too hard; if there are no words you don’t know, it might be too easy). More importantly, we also talked about the content of a book and that there were sometimes a story within a story. Mostly I had a lot of confused looks from that, but they’ll eventually learn what I mean. Perhaps the most important part of the day was when I a) told them I hated books that had talking animals (cue the shocked gasps) and b) told them that by the end of the year, they wouldn’t be allowed to read my Junie B. Jones books any more. Second graders love Junie B, but they cling to them (and books like them) for too long because reading bigger books can be scary, so halfway through the year I emphatically tell them it’s time to move on. Mostly they laugh at me, but they know I’ll give them a hard time if I see them reading one.

I had a chance to spend some time in Mrs. Wayland’s class listening to their writing. I love conferencing with students on their writing and hearing how much detail they can add when it’s time to revise. I can’t wait to read their finished pieces!

I played a few rounds of Dot Ten using my Tiny Polka Dot deck of cards.  Students had to find matches using 2-3 different types of cards. This was a new purchase, so I loved giving it a try with some happy to help me learn kindergarten students!

Third graders broke out some geoboards in order to work out how you measure the inside of a polygon. It was pretty frustrating once I told them they couldn’t use rectangles, but this required a lot of thinking. We’ll continue with this activity on Tuesday.

Visual proofs, what if, coin equations, and planning

Fourth grade continued with some very productive struggle while trying to prove efficient multiplication strategies. I had some great conversations with students as they worked. Each group was at a different place, so each conversation was different. Though I’d planned to wrap this activity up tomorrow, it’s clear we need a little more time to work through some misunderstandings about the conceptual underpinnings of multiplication which are really important to their long-term success in math.

Third grade reading assessments continue. I love these assessments, but then are time-intensive. Today students who weren’t being assessed began work on a new assigned designed to loosely tie-in to the writing they’re doing in class. Students were given a choice of assignment: a speech to convince people to follow a rule designed by the student, a memoir for a person to be added to the student’s family, a last will and testament leaving a million dollars to others, with instructions on how to spend it.

I had a great plan for second grade math, but they assured me they’d done something similar in their classroom – which is good because we want to enrich and extend what’s going on in the classroom – but it meant a change was needed. Rather than using pattern blocks to create equations, students were asked to make equations using coins. They were allowed to choose (from 4 provided) their target equation. The trick to this was that they weren’t adding numbers, but were being asked to use algebraic symbols to create those equations. For instance, one equation might be written as 3Q+6P= $0.81. These will come home next week after I get a chance to review them. They’ll do a similar activity on Monday, but with a different number and with some additional instructions.

The fourth grade reading group was forced to renew their productive struggle with me. I’m pretty sure they were happy to see the last of me this morning. They are reading The War That Saved My Life in their classroom and will be reading War War II – an informational text. As I explained to them, I was putting them in charge of their learning. They were asked to come up with a calendar of dates for their reading assignments. This was a struggle, but it was a good struggle. It was frustrating for some but that was also good. We spent some time also talking about time management and planning, which will be an ongoing conversation throughout the year.

Visual proofs, more assessments, more flexible thinking, and inverse relationships

Fourth grade continued to work on their visual proofs. We did take the opportunity to talk about the purpose of the assignment – which is to find different ways to multiply efficiently. Creating an array for a 2-digit by 2-digit multiplication problem is not an efficient mathematical strategy, though it is a strategy with which they are very familiar.

Second grade math continued to show their flexible thinking by creating equations for large numbers. They’ll do a quick gallery walk on Thursday and then we’ll move on to new and exciting activities.

I continued to assess third and fourth grade reading students using the QRI. I completed fourth grade today and handed them the book they’ll read with me while they are reading The War That Saved My Life with Mrs. Rickabaugh. Students started asking me about World War II based on some of what they’re reading in the novel. As anyone who knows me knows I am always more than happy to talk about history, I went into the Closet of Doom and came up with an informational text book on World War II. Students need to read pages 6-11 by Thursday. They have post-it notes to write down anything they thought was interesting or any questions they’d like answered. On Thursday, we’ll have more time to plan. I will give students a deadline for the book to be finished and then a good chunk of our time will be spent making a plan for finishing the book before that date. Much of what we do in fourth grade will be designed to teach students independence and give them support on planning when and how to get their work done.

Third grade math wrapped up their exploration of equal groups by discussing the inverse relationship between multiplication and division. While I assured students that if they could multiply, they could also divide, I’m not sure they all believed me. The activity we’ll do on Thursday and Friday, as well as next week should convince them I’m right.

 

Visual proofs, posters, flexible thinking, and assessing

I’m not yet pulling kindergarten or first grade groups. I’m spending the time I have set aside for those groups helping teachers do assessments. In math, kindergarten and first grade students are assessed using a program that helps to determine their number and number sense. These assessments are tied directly to activities students can do in the classroom to improve their grasp of number and number sense. First graders were given these assessments at the end of the year. I’m assessing students who maxed out on the end of the year assessment to help their teacher ensure that they are getting the right activities.

In reading, some first grade students – and a very select number of kindergarten students – are being given the Qualitative Reading Inventory (QRI), which help their teacher pinpoint their reading instruction. The QRI requires students to answer questions that are more difficult than other assessments. for students reading above grade level, this is a great way to determine if their reading comprehension matches their ability to decode the words. Very often there is a mismatch: Students can often decode words far above their ability to comprehend what they’re reading. In those cases, teachers need to spend more time on the comprehension piece of reading instruction rather than the ability to decode more sophisticated words. As their comprehension catches up to their decoding, the teacher will again move into helping students decode more complex words.

Today in fourth grade math, students were shown a visual proof for the multiplication problem 24×5. They spent some time explaining the different ways the problem had been solved and how the pictures included helped them to understand those different ways. Pairs of students were then given their own multiplication problem and asked to create visual proofs for their problem. This will take us quite a few class periods, as students will collaborate, share their work, critique and revise, then create a final visual proof.

In second grade math, students continued to work on their number problem. Last week they were all given a three or four digit number and asked to come up with as many equations to equal that number as possible. Today students walked around to look at the types of equations their classmates had come up with and were then asked to go back and see what they could use for their number. Though very often people view math as a solitary endeavor, there is a lot of research that suggests that collaborating and sharing ideas in math is a very effective way to learn. Students in all of my math groups will spend at least as much time collaborating as they do working independently.

I am continuing to assess the third graders using the QRI to pinpoint their instructional needs as well. At the same time, both second and third grade reading students are continuing to finish their “Who Am I?” posters. We’ll share posters and then move into a discussion of characters and how we know who they are.

Four 4s, Sharing Crackers, and Who Are You?

This morning fourth graders concluded their exploration of the Four 4s. I threw some new information on them, which made it a little easier to make equations for a few numbers they hadn’t previously managed. We talked about square roots (and showed how they worked using arrays) and factorials. Once they had these two pieces of the puzzle, there was much excitement as they raced to find new answers. Towards the end of class we talked about what they learned, the strategies they used, and I pointed out a few strategies they might have missed (using both square roots and factorials as parts of a fraction, for instance). They were agog at the idea you could do such a thing, which is often my goal.  We’re going to leave their poster up in the classroom so that they’ll be able to add to it as the year goes on.

Second grade reading met for the first time today. Last year my small group spent some quality time learning about volcanoes, specifically Krakatoa. Just before school started, Anak Krakatoa (child of Krakatoa) erupted, shooting out lava bombs. Today we spent about 90 seconds looking at the video. They seemed to be suitably impressed with watching a volcano erupt. There was some debate as to how we could tell if it was ash or steam, but that generated good conversation.  Students were then asked to create posters for themselves: Who are they? and Who do they want to be?

This again generated a lot of good conversation as they repeatedly asked for more specific directions. They were marginally frustrated by my refusal to give them, but that forced them to think a little harder about what they wanted to show. It also allowed them a chance to chat with each other about what they wanted to show. We made some good progress on them and we will finish them on Monday.

I spent some time with Mrs. Rickabaugh’s class in writing today. They were discussing how to write a story about a “small moment.” Very often students want to write every detail about everything they think might go into a story. This lesson asked them to really focus on the big picture about an event that took no more than 20 minutes. It was so much fun to listen to them ask questions as they tried to push the boundaries on what was allowed in the story. I can’t wait to see their writing.

Third grade math continued to explore the sharing crackers activity. It was made a wee bit harder as they were given more tiles. Each group had 52 tiles, which has considerably fewer factors than 36. This was a little frustrating for them but was also illuminating. The conversation we had after, as they described the strategies they used was a good one. We’ll wrap this activity up next week with a discussion of factors. Though they were quick to tell me they already knew about factors, when I asked them to relate factors to our activity they weren’t able to, which was great news for me though they did not agree with my assessment of the situation.

So much thinking!

This morning I read That is NOT a Good Idea to the last two kindergarten classes. I had so much fun watching little faces react with horror as the goose seemed to willingly head to her doom and the relief at the end when the goose managed to win in the end.

Fourth grade math took a break from their Four 4s activity to brainstorm, based on yesterday’s work, what good group work looks like and what it doesn’t look like. They’ll continue with the Four 4s activity tomorrow while trying to implement their new group norms, which included things such as: encourage and support your group, ask good questions, and participate.

Third and fourth grade reading continued to work on their “Who Am I Posters” while I do some additional reading assessments. Students are being given the Qualitative Reading Inventory, which is a more in-depth inventory of reading and comprehension than some of the other assessments done in the classroom. Students are asked both explicit and implicit questions, as well as being expected to answer questions without looking back at the passage. If necessary, students are asked questions a second time with the passage in front of them. This gives me (and their classroom teachers) a much better idea of what they need to work on during the course of the year.

Third grade math continued their Sharing Crackers activity. Today focused on listing all of the possible combinations and looking for patterns within those combinations. Tomorrow we’ll explore those patterns and compare them to the fact families they already know. This is a great introduction to the inverse relationship between multiplication and division.

Starting off our new year

I saw my first groups today and had a chance to read That is NOT a Good Idea by Mo Willems to two kindergarten classes today. I will read the same book to the other two kindergarten classes on Thursday.

In fourth grade math, students started with an activity called Four 4s. Students must find every number between 1 and 20 using only four 4s. For instance, 4+4+4+4=16 or 4/4 +4/4=2. It’s a pretty challenging task, but really requires students to think about numbers flexibly. We’ve only just started this activity, though it will be blended with additional back to school activities over the next week or so.

Third grade reading started out by checking out the new books in my library. Most students left with 1-2 books to read. Some left with books that are likely not “just right” fits for them, but I think the will likely figure that out sooner rather than later. In every one of those cases, students left with books that I think may be a little too long for them at this point in the year. We talked a little about the books they like to read and some of what they did this summer.

Fourth grade reading also started by checking out new books in my library. There was also some cheering as students were reminded they could now read books in the “Fourth Grade Only” bin. I do my best to ensure that students are reading books that are appropriate for them, but as they get older that gets a little harder to manage as students mature at different paces. If your child comes home with a book that you feel is inappropriate, please let me know and I will have a conversation with your child about picking good fit books.

In third grade math, students will be working with the concept of equal groups. While they have started working on the concept of multiplication in their math classes, this pushes their understanding of multiplication by tying it to the concept of division. Students will have to determine all of the different ways they can share 36 crackers. Once they are sure they’ve managed that, they must then look for patterns in their answers and we will discuss how this relates to multiplication and division. This is an activity that will take quite a few days, but will really help students to build a solid conceptual understanding of what is going on as they multiply and divide.

 

Back to School Shenanigans

While students are settling into their new classrooms, I have the opportunity to sneak into those classrooms to do some growth mindset read-alouds and lessons. In addition, all third and fourth grade students will come into my classroom to try their hands at breaking out (or into a locked box).

Breakouts are a lot of fun, but can also be frustrating. Students are given a puzzle to solve. In order to “breakout” students must find keys to the locks and solve puzzles to help them open the combination locks. We use 3 and 4-digit locks, word locks, and a directional lock. The puzzles are tricky and really require students to work together with their group in order to solve them. Other skills we try to teach during these activities: knowing when to ask for help, listening to all the members in your group, working together as a team rather than one person being the boss, etc. It’s a great team-building activity and it’s a really awesome way to watch how students approach a problem.

As I’ve stated before, these can be pretty frustrating for some students. I’m OK with that and we do our best to make sure students become OK with that. Not every group breaks out, and in some cases, no groups break out. This is also OK. We do a debrief at the end of every session asking students to talk about things they did really well and things on which they need to work. In each session, we tie those ideas back to school and academics.

Second grade classes will hear The Girl Who Never Made Mistakes, which is an excellent introduction to the idea of learning from your mistakes and why it’s so important to take risks. We spend time discussing mistakes we’ve made and how we learned from them. As always, I encourage students to connect those ideas to school – specifically academics. It’s important for students who think that learning will always be hard to hear this message, but it’s equally as important for students who think that learning will always be easy to embrace this message. Many bright students have the idea that they’re smart because school is easy. While there’s nothing inherently wrong with that idea, it causes many issues as soon as that student runs up against an idea or concept that is hard. Suddenly the very foundation of their identity as a smart kid is undermined.

The Most Magnificent Thing is the third grade read-aloud. This book follows the story of a girl who tries to make a magnificent thing, but no matter how awesome people tell her it is, it just isn’t what she imagined and she ends up very frustrated. This book teaches a few different lessons: to keep trying, take a break when you get frustrated, and to look for the good in your mistakes to help you move forward. Conversations center around different ways of dealing with frustration, that quitting is rarely your best option, and that there are often great things in your mistakes, if you’re willing to take the time to look for them.

Last but not least is my favorite of the bunch: Your Fantastic, Elastic Brain: Stretch It, Shape It. This book looks at the mechanics of how your brain works. It explains, in age-appropriate detail, the different parts of the brain and their function. It discusses the importance of practice and making mistakes. As we finish the book, students are asked to create a classroom neural network using pipe cleaners. We start with a single word: community. We start by finding a word that makes us think of community. As we brainstorm these words, students connect new words to the words on the neural network. By the time we’re done, students’ words may have connected with the idea of community or neighborhood or population or jobs or a million other things. This serves as an example of how their brain works – connecting new ideas to old ones.