Author Archives: Ms. Espo

Base 5, Reading, Fractions, and A Wrinkle in Time

Fourth grade math had a breakthrough today! Most groups figured out I was asking them to add in base 5. Despite the frustration that led to the breakthrough, I think most students were not unhappy with their determination. They had to do a lot of mathematical reasoning to get there, but in the end, it was all worth it. Tomorrow they’ll give subtraction in base 5 a try, which will really get at the heart of what we do we when “borrow” or regroup as we subtract.

Third grade reading had another day of simply reading books on ancient civilizations. The favorite book seems to be Poop Happened: The History of the World from the Bottom Up, which is not surprising. It’s a fan favorite every year. Students have given me their ranked choices for which ancient civilization they’d like to study. They will receive their assignments next week. I’m looking forward to this project!

Second grade found out that it’s harder than you’d think to make more than 1 using fractions. Their assignment today was to make 2 in as many different ways. Some found patterns that made it easier to come up with a lot of different equations while some struggled a bit with making that leap over one. Since all of this goes well beyond grade level expectations, I’m not worried by or for the students who struggled. Struggle is good and reminds everyone that we really can’t know everything and there’s always more to learn.

We had several more amazing conversations while discussing A Wrinkle in Time. Conversations ranged from “How do you square a square?” to “How can you balance between who you think you are and who other people expect you to be?” As the fourth graders start inching towards 5th grade and another school – no matter where that might be, these are important conversations to be having. Students will soon be meeting so many new people and and it’s important for them to be able to think about who they are as well as who their friends expect them to be.

Not Base 10, More Civilizations, More Fractions, A Wrinkle in Time and Prime Climb

Fourth grade was reminded why I’m not always their favorite person. They were given the following addition problem and asked to explain how it could be correct: 421 + 43 = 1014. There was a lot of complaining and a lot of asking for the answer. Rather than giving them the answer, they were given a few clues but were asked to keep working. There were some great conversations that show their understanding of our number system and many of them are pretty close to having a breakthrough. Alas, I won’t see them again until Thursday so they have another whole day to contemplate just how mean I can be. I was delighted by the fact that they continued to ask about the math problem when I saw them again for reading and then again at lunch.

Third grade readers were asked to choose which civilization they’d most like to study for the remainder of the year. While I will do my best to ensure everyone gets their first choice, some students may not. We will spend a good chunk of the rest of the year doing research on ancient civilizations. Students will learn how to organize information, how to plan ahead, how to ask good questions, and how to share the information they’ve learned with an audience. This is a pretty big undertaking, but I know they’re up to it!

If you heard any strange noises this morning around 10:30ish, it was the sound of second grade brains exploding. We’re wrapping up our study of fractions, but I couldn’t let that study go without pushing their understanding beyond what would be expected of second graders. Rather than using Cuisenaire Rods, we reviewed yesterday’s work. One group made the best mistake yesterday and I made a big deal about how much I loved that mistake. When asked to come up with many different ways of making a whole, they used their Cuisenaire Rods and then wrote equations. One group’s equations showed an imperfect understanding – one that is very common – about fractions. An example: 2/4 + 1/2 = 3/6. We spent some time drawing pictures and trying to work out what they’d done. Along the way, we learned how to add fractions with unlike denominators, that drawing pictures is often a good way to help understand what we’re trying to do, and that 1/2 is equal to a LOT of different fractions and even though they have different numerators and denominators, they all represent the same fraction of a whole number.

Fourth grade reading jumped right back into their discussion of A Wrinkle in Time. It can be frustrating for some as our conversations often veer away from the book’s specifics and into the bigger picture the book is trying to convey. Today we talked about how Meg is trying to figure out who she is and who she’s trying to be. Along with that we discussed how you can never really know someone’s story and for that reason, it pays to be kind even in the face of friends who make poor choices and to never assume that everything is great for someone, even when it might look that way on the surface. It was a great conversation and I look forward to another one on Thursday as we try to catch up on our reading discussions.

I didn’t see everyone in third grade math today. Market Day is coming up, so some students were busy making their goods and another class was in iSTEM. I took the opportunity to teach my smaller group of students how to play Prime Climb. It is a fabulous math game that really requires students to think about where and how they’re moving. We didn’t finish, but they started to see how tricky it can be to make progress considering the rules of the game. This game is a great way for students to practice their math facts – from addition to division.

Games, Civilization, Adding Fractions, and Socratic Seminar

Welcome back from break!

I eased fourth grade math back into the school year by playing a game called Don’t Break the Bank. This game starts with 9 empty squares organized in 3 rows of 3. Students roll a 10-sided die and must put that number in one of the 9 squares. Once the die has been rolled 9 times, students must add the three 3-digit numbers. Their goal is to come as close to 1000 without going over. This game requires students to think strategically, but also to estimate across three different place values in order not to go over 1000. While students can (and do) easily estimate what should go in the hundreds place they often don’t take into account the ones and tens place, which can have them going over 1000. Estimating is an important skill and is one in which most fourth graders need a lot of practice. They had fun and one group even asked me to send the game to their classroom teacher so they could play with other students once they were back in class.

Third grade reading jumped back into their discussion of civilizations. We looked at what some of the hallmarks of a civilization are, which has required some vocabulary work as talk about hierarchical social structures as well as what we mean when we say culture. We did dip back into our study of Britain as we looked at the succession of the British crown. The girls were, naturally, very unhappy to learn that as recently as five years ago, girls would not become king if they had a younger brother. They were happy to learn that’s been changed, but it’s always interesting to see how recently these things have changed.

Second grade math was given a challenge today: to use their Cuinsenaire rods to determine all of the many ways of adding to one whole. I modeled the activity by using all of the easy ones (8 1/8th cubes, 4 1/4 cubes, and 2 1/2 cubes and then told them they couldn’t use those combinations but they could mix and match them. It took a few tries, but the sound of “Ohhh!!!” in the classroom was repeated again and again as students began to understand how to add fractions of different sizes to make a whole. Tomorrow we’ll go a step further and I expect a few brain explosions before the day is over.

Second grade reading dipped their toes into a new activity today. They will be learning how to conduct a Socratic Seminar. We’ll be taking this slowly as this is a very new way of learning and talking about what they’re reading. Today’s challenge was learning how to take turns talking when you’re not allowed to raise your hand. We’ll go back to this on Friday, but I’m definitely looking forward to hearing what they have to say. This is a very opinionated and lively group of students!

Place value, writing, Geography Bee, and base 4

Fourth grade math learned the definition of place value today. We assume it’s something they know, but I like to make sure they really, truly understand that the value of a numeral depends on its place within the numeral. We also talked about the pattern involved in naming each place. So much of math is about patterns but we don’t always do a good job making that connection explicit. Next week we’ll learn about other numeral systems, which will confuse them initially but then really cement their understanding of base 10.

Second graders continued to write their stories while I conferenced with students about that writing.

Mrs. Rickabaugh’s class did the Geography Bee today. They did not give up even when the questions were really hard. I was very impressed with how seriously they took it. The Geo Bee is really one of my favorite activities of the year. I get to do it with the entire grade and some kids are always shocked by their performance, though their teachers and I never are.

Some third grade math students are still working on adding in base 4 while some groups have moved on to subtracting in base 4. Both groups are grappling pretty hard with the concepts in regrouping in another base. They’ve had some very productive conversations, so I’m letting them continue to grapple.

Place value, Hades, fractions, Declaration of Independence and 24.

Students cheered when I told them we were going to do place value today.  Some thought it was going to be easy, but they soon learned otherwise. Fourth graders reviewed the differences between a number, a numeral, and a digit. Students created a place value chart and had to show me, using popsicle sticks, the number 126. What I thought would be an easy part of the assignment turned out to be more challenging. We didn’t get a chance to discuss what they were thinking, but we will tomorrow. Don’t be alarmed – everyone could show 126, but how they did it raised some questions about how deeply they understand the concept.

Third grade reading read a myth about Hades. It was a little trickier as we couldn’t write a summary using our usual method. This turned out to be good for some and not so good for others. While our usual summary method makes it a little easier to sort out the details from the main idea, this was a free-form summary, which meant that there were more details than needed in most summaries. They’ve made a lot of progress on this skill.

Fractions continue to bedevil the second grade in the most delightful way. I don’t know that I’ve ever had a student say they hoped we didn’t get snow because it meant they’d miss a day in my class, but there it was. Today we briefly explored the idea behind equivalent fractions. We put fractions on a number line and played with cuisenaire rods to show that 12/4=9/3=6/2=3. These are pretty complicated concepts and not everyone is there yet – nor do I expect them to be. I love watching how amazed they are when they do figure something out or see something that excites them.

The fourth grade reading group heard the Declaration of Independence. We talked about how complicated history is, how complicated a man Thomas Jefferson was, and how important it was to be able to see that nothing is easy when it comes to understanding big ideas. As always, they asked amazing questions, which had us talking about slavery and its impact in the North as well as the South, we discussed the cotton gin and its impact on slavery, and what happened once the international slave trade was abolished in the US. Next week we’ll dig a little deeper in the Declaration and talk about how the United States continues to strive to live up to its ideals. This will allow them to create a baseline for their independent projects.

Geometry, Comparing Myths, and Fractions

Fourth grade completed their geometry project today. Most students were able to figure out how to determine the area of a non-quadrilateral shape. Some needed a few questions to help them on their way but they did a spectacular job. Thursday it’s on to place value. I’m excited, which has made them a little nervous. I have no idea why.

In third grade, I read a myth about Minerva and Arachne. We compared that to the myth we’d read earlier about Athena and Arachne. We discussed how Greek and Roman myths were similar and often had the same gods and goddesses with different names. They immediately noticed that Roman gods had been named after planets. After explaining that the planets were named after the gods, we had a quick word lesson – which seems to be a fan favorite – on the root word tele when discussing the word telescope. We also looked at telephone, television, and telegraph. It’s a lot of fun to watch them work out word meanings as they’re told what individual word parts mean.

Second grade math continued to grapple with fractions. Today they use cuisenaire rods to put fractions on a number line. For the most part, students did really well putting 1/3, 1/4, 1/2, etc on a number line. They ran into a little trouble when asked to put 2/4 or 5/6 on a number line, but this lent itself it to a great conversation about number lines and how they work, along with the idea that while each piece might be 1/6, when you have 4 of them together, you have to write it as 4/6.

Geometry, Summaries, Fractions, and Writing

Fourth grade math continued their geometry exploration. Tomorrow will be our last day. Today they had to figure out how to determine the area of a shape that was not a quadrilateral. The idea was to see if students could use what they know to figure out what they didn’t know. Most students found this easier than I expected. A few students can now determine the area of a triangle based on what they know of quadrilaterals.

Third grade reading had a breakthrough! One student wrote a fabulous summary. We were able to discuss how hers was just a little bit different from some of the others that had been turned in. Students are starting to figure out the small pieces that make a strong summary. I’m excited by their progress as a whole, though I know some of them are less excited – they’re doing a great job!

Grappling seems to be the word of the day. Second grade math grappled with some difficult fraction concepts (if this rod is 3/4, which rod is the whole?). We reviewed that as a class today and I know some left still a little perplexed. Again, this is completely expected and will come as they deepen their understanding of fractions. We moved on to putting fractions on a number line and I feel like I might actually have seen some brains explode. This is something they’ll work on tomorrow, but it is something that is a difficult concept. Understanding a visual representation of a fraction is a little easier than understanding how it relates to a number line. I started by putting the number zero at one end and the number one on the other end. Most of the class told me that couldn’t really be a number line with only two numbers. Once we started adding fractions, there was more brains exploding. It was a great day in math.

My second grade writers continued to write their stories. I’m excited to see where they end up. Each student is taking a different path, but I’m having great conversations with students as they write.

Geometry, Writing, Geography Bee, and Adding in Torran

Fourth grade wrapped up symmetry a little earlier than expected, though I had a few students who asked for more clarification. In order to make that happen, I assigned a geometry project for those who didn’t need or want the clarification and then sat down with the group who did. The geometry project involves creating an alien outpost or some other place with houses and buildings. Students must have at least three buildings, they must determine the area and perimeter of at least three buildings and at least one of those buildings cannot be a quadrilateral. One student immediately pointed out that he had no idea how to find the area of something that wasn’t a quadrilateral, which was actually the point. Once they get to that point, I’ll ask a lot of questions that will point them in the right direction. They will grumble about the questions, but will shine when they figure out those answers. The second group moved from clarifying questions about symmetry, to asking additional questions about area and perimeter. Somehow we stumbled on to a question about finding the area of a triangle – we’ll get back to that on Monday.

Second grade continues to write. One of my favorite things about writing is that I get to sit down with kids and talk about their individual needs and address their specific issues. I had a conversation about adding details to a story. Another conversation about how a simple change to a plot diagram made their entire story make more sense. Another conversation about how dragging one’s feet means that you miss out on fun opportunities – like sharing your story with the class. Kids are excited to write and even more excited to share their progress with students and adults alike.

I started the Geography Bee with Mrs. Crawley’s class. It’s one of my favorite activities. Very often students shine in ways they expect. It’s a tough set of questions, but everyone learns something interesting and it usually generates more questions than I can reasonably answer. Every student in Mrs. Crawley’s class tried their hardest and no one gave up – even when the questions got crazy hard. Mrs. Rickabaugh’s class will do their preliminary round next week, with Mrs. Wayland’s class getting it done on the 14th. Once each class is done, I’ll likely have to run a tie-breaker to determine the top 10 scores in the grade. Our school-wide Geography Bee will be held on Monday, January 14th in the auditorium. Parents will be notified if their child earns a spot in the final.

Third grade continued their exploration of Torran numbers by trying to add in base 4. One group managed to get it done this afternoon, a couple of other groups are close, and a few other groups are grappling pretty seriously with it. As they finish, they’ll be given a subtraction problem to conquer as well. Understanding the concept of regrouping in other bases is a great strategy to help students solidify their understanding of what goes on as they regroup in base 10. A lot of things suddenly click as they see it done with a different base.

Symmetry, Poseidon, Fractions, Project, and Torran Numerals

Fourth graders continued to work on geometry. Today we talked about symmetry. I snuck in a lesson on vocabulary, reviewing the root sym and metr and how they work together. We reviewed other words with similar roots. Symmetry didn’t seem to present much of a challenge, so we’ll move on to place value a little earlier than planned. Place value is my favorite and will definitely make their heads’ hurt.

Third grade reading went back to reading today. They were a little unhappy because they knew there was summarizing in their future. I know they’re still frustrated, but they have made so much progress! Where only one part of the summary was correct before, most students were getting two or three pieces of their summaries correct.

Fractions are still giving second graders a headache, but in the best possible way. The best part of the entire exercise is that students are also way more comfortable asking for help. They’re better at asking for help – they can tell me what they get and what they don’t get and can ask specific questions about their work. We’ve been using cuisenaire rods, which are a great way to learn about fractions. Students were given a specific rod and told, “If this rod is 3/4, what is the whole?” or “If this piece is 1/5, which piece is 2/5?”

Fourth grade reading’s time will be split between two projects. We’ll be reading A Wrinkle in Time and having those discussions on Tuesdays. Students will be allowed to choose an independent study project, but first we’re going to ask some questions, do some primary source research and talk about some really big ideas. Today I posed a few big questions to get some initial thoughts:

  • What is freedom?
  • What is the role of government?
  • What rights should all people have?
  • Is violence ever OK?
  • What other questions should we consider?

Third grade finally had the big reveal on Torran Numerals. They were working in Base 4. We drew pictures of the Base 10 chart and drew a Base 4 chart. This blew a lot of minds and will take a few days to settle in and to really understand. We’ll continue to work on this for the next few days. As we ended class, I asked them to do an addition problem in Base 4. We didn’t finish, but we’ll start again tomorrow. They will be encouraged to use math manipulatives as a way of building understanding. Learning and understanding bases other than Base 10 will really cement students’ understanding of Base 10 – specifically regrouping which can be tricky as students begin to apply mathematical computation.

Geometry, Research, Fractions, Wrinkle in Time, and Torran Numerals

Fourth grade continued its exploration of geometry today. Yesterday they were given the definitions of various geometric transformations and today they were asked to give them a try and to try to recognize the different types of transformations. Students started by working independently, but as they finished, they had to collaborate to determine whether they were right or wrong. In most cases, this was not a problem, but in a few instances students had to discuss why they believed their answer was correct and another student’s was incorrect. Being able to explain your mathematical thinking is a big part of what we do.

Third grade continued our discussion regarding effective research. We touched on Wikipedia – it has its uses, we talked (again) about bias and perspective, and touched on primary and secondary sources. It is unlikely that students will use primary sources during their research into ancient civilizations, but it will come in handy sooner rather than later.

Yesterday second grade was very, very sure they knew all there was to know about fractions. Today they are less sure about knowing all the things. They once again used cuisenaire rods to work with fractions. The first couple of problems they were asked to solve were pretty easy – Find the orange rod, figure out which rod is half of the orange rod (it’s the yellow one). There was some good-natured grumbling about how “easy” this assignment was right up until they turned their paper over. When told that the white rod was 1/5, they had to determine which rod was 2/5. This required more thinking than they realized. Mrs. Johnson stopped by to see what we were up to this morning and she remarked about how excited they all were as they tried to answer the questions they’d been given.

A Wrinkle in Time is up next for the fourth graders in reading. They were given the book and asked to determine how many chapters they would read a week, keeping mind that they are already reading books for their classroom teacher and in some instances another book with Mrs. Flowers. They decided on two chapters a week, with four chapters read during winter break. They are allowed to read ahead if they like, knowing that they cannot spoil anything that was not in that week’s reading and that they always have to know what’s in that week’s assigned chapters. Once they made that determination, they filled out calendars that would help them stay organized. Somehow, those calendars ended up laminated so they wouldn’t get messed up.

Third grade math continued to grapple with Torran numerals. The week before Thanksgiving students were asked to learn the difference between a number and a numeral. They were then asked to compare our numerals with those of a planet called Tor. This has caused some frustration, but also a lot of good conversation. Students are looking for patterns and trying to explain how the number systems are related. Today students were encouraged to use unit cubes to help show the number and to see if they saw a pattern. This was helpful for most groups. Students sometimes feel that math manipulatives are for kids who aren’t good at math. I have explained that manipulatives are good for everyone. I hope this activity reminds them of that lesson. On Wednesday, they will grapple with that idea a bit more (two groups are pretty close to being able to explain what is going on). Then I’m going to make them add and subtract using that number system which will definitely make some heads explode.