Geometry, Media Literacy, Fractions, and Writing

Sorry for the silence. A plethora of short weeks and I fell out of blogging practice, but I can assure you we’ve been hard at work.

Fourth grade math has been learning about geometry. With that has been a lot of work on vocabulary and word parts. Some students have expressed an interest in learning more about how words work. We’ve reviewed characteristics of quadrilaterals and how to classify them, we’ve talked about angles, sides and what congruent means and what it looks like. Today, we moved from static geometric images to how they move within a coordinate plane. I introduced them to the concept of a coordinate plane and how it relates to latitude and longitude. Then we moved on to the heart of the lesson – which was geometric transformations – reflections, translations, rotations, and glide reflections. We’ll continue this exploration for the rest of the week.

Third grade reading will be doing a fairly in-depth research project during the course of the year. One important aspect of research is the ability to think critically about one’s sources. To that end, be sure to ask your child about how they can save the Pacific Northwest Tree Octopus. We touched a bit on biases and being sure to find out who is doing the writing.

Second grade math dipped their toe into fractions this morning. Students will be using cuisenaire rods to aid their conceptual understanding of fractions. They were pretty sure they knew all the things they needed to know about fractions until I asked them if a half was always the same size. There was some spirited debate, but it also became clear that they still have much to learn.

Second grade reading spent their time writing their stories. A few students are still working on their plot diagram, but the time spent on that will pay off when they do start to write. Reminding students to use what they’ve learned in their classrooms on this writing has proven to be more challenging than expected, but it’s good practice.

Division, place value and graphing

Third grade had their math term test during our reading time today so I did not see them this morning. I will see them on Thursday.

Fourth grade math continued their division practice today. Some students needed a refresher on the steps needed to use partial quotient division. Some students decided that writing down the steps would help them to remember the steps – which is not only a great strategy, it’s also a great example of students thinking about what they needed and getting it done.

Second grade math went a little deeper into place value this morning. They built numbers using base 10 blocks and recorded the results on a worksheet where they were asked to decompose the number, draw a picture of it, and show it in expanded notation. This is a task that used to be very difficult for second graders. This year it seemed pretty easy for this crowd, which is in direct relation to the changes made in kindergarten and first grade that have students focusing more on the conceptual understanding of numbers and equations rather than simply memorizing facts.

Third grade wrapped up their chart and graph making. On Thursday they will critique the charts and graphs of their classmates. They will also try to determine where the faulty data might be.

 

Associative property, Athena, place value, and writing

Fourth grade math learned about the associative property. As we’ve been working with larger numbers and asking students to multiply by those large numbers, I’ve repeatedly heard different versions of, “I multiplied 8 times 3 and then added a zero” to when they’re asked to solve 8 x 30. It’s really important that they understand that they’re multiplying by 10 (or 100) and they’re not just “adding a zero”. They will learn to apply this to division and once we move into decimals understanding the math behind it will be vital. Students learned that (8×3) x10= 8 x (3×10). In my class they are no longer allowed to say, “I multiplied 8×3, then just added a zero.” They need to explain what they’ve actually done. It was another hard day in the dungeon.

Third graders read about Athena today. The story was a bit longer, which will make the summarizing much harder. We’re working hard on putting only the most important pieces into the summary. There are still too many details going into summaries. This is normal, but will take time to sort through. If you are reading with your child at home, or as they finish their nightly reading, I’d encourage you to ask them to summarize it using the “somebody wanted but so then” strategy.

Second grade math dipped their toes into understanding place value. We talked about the pattern in our number system and talked about the place value chart using whole numbers. We expanded our place value chart past the thousand column all the way to millions, which enabled students to see the pattern in what we name each place. We reviewed number prefixes, which allowed them to name billions and trillions and to understand what they represent. Surprisingly, one student correctly guessed the mill- prefix, which means a thousand. Most students guess that it means a million, but in fact a million is a thousand thousands, so if you were asked if you knew what 1000×1000 was last night, they were showing off what they learned in class this morning.

Second grade writing took advantage of the great weather yesterday to sit outside and to work on their writing. I’ve seen such a vast improvement I’m excited to start turning their paragraphs into stories. Students are working at very different paces, so while some students will be ready to start on their story soon, other students are still moving slowly, but surely, through the process.

Division practice, Hera, Broken Calculators, and Graphing

Fourth graders continued to practice as appropriate on division. Different students were doing different types of practice. There were a lot of individual conversations about very specific things each student could be working on. We’re working not just on knowing how to execute the strategy, but also in doing so in the most efficient manner, which is a slightly more sophisticated skill. It is a skill on which we will work for most of the year.

Third grade reviewed their Hera chapter from yesterday. We talked about reading strategies for hard words – reread, read on, ask a question, substitute a different word that might fit, etc. We then moved on to summarizing the chapter. They were definitely better than the first chapters. It’s nice to see progress, but we still have plenty of room in which to grow. They started reading the Athena chapter, which is much longer than the first two and will require a little more work on their part, but I’m excited to watch them try.

Second grade math continued their broken calculators activity. Most students were trying to find 22, 52, or 25 without a 2 or a 5. I chose 2 students who had to find those same numbers using only +7 and -3, which caused them great consternation but was fun to watch. A few students continued to stick to a single strategy rather than trying new strategies, which is the point of the activity. Students are working together which should give them plenty of new ideas from which to choose. The ability to think flexibly is an important skill that will benefit them down the road, so they’ll hear that from me a lot.

Third grade continued to work on their flawed graphs. We will finish them next week.

I will only see a few groups on Thursday and no groups on Friday as I will be out of town. Look for more updates next week!

Division, Hera, Broken Calculators and Who Am I?

Fourth graders continued their exploration of division.  I have three different groups working on a variety of activities. One group is working on solving word problems using variables, while another group is practicing partial quotient division, and the last group learned how to do partial quotient division today. One of the great things about having a small group is that it’s easy to hit kids where they are and give them exactly what they need. Each group will work with word problems before we’re done, though the complexity of the word problems will vary according to readiness.

Third grade reading went back to Greek myths where they read about Hera today. They’re mostly pretty grossed out by Zeus marrying his sister, but once they were able to move past that, I can say that their summaries are getting better, though I haven’t told them that. Writing a summary is difficult and requires that students can sort through the main idea and its details. There are still too many details being added to summaries, but there’s a definitely improvement.

Second grade went back to broken calculators. Students are really good at coming up with a single strategy that works, that they then apply over and over. I’m trying to get them to apply a variety of strategies, which is why we’ll spend some additional time on this. Today their goal was to make the numbers 13, 31, and 33 while with the numbers 1 and 3 broken.

This year, Charlottesville City Schools has implemented a new writing curriculum and I love it. From what I’ve seen the students and teachers love it (almost) as much as I do. If you haven’t had your conference yet, ask your child’s teacher about it! I have seen so much growth in their writing! We went back to writing Who Am I, but I made them start over and the difference is amazing. Rather than lists, I have paragraphs from most of them, with detail. I am really super excited by what they’ve written. If a student finished the who am I part, they were asked to write a paragraph describing their favorite place. Next up will be describing a problem they had and its solution. Students will take that and turn it into a story that has all of the major story elements in it.

So much division, so many words, and so much 24

Fourth grade continued to learn about division. As I mentioned on Tuesday, this is something that students learn at different paces. One group was practicing word problems – including some that contained variables which I thought would stump them but didn’t – while another group worked together on a division problem, and yet another group worked with me to learn the partial quotient method of division. The first group learned the partial quotient method on Tuesday and used the word problems to practice what they’d learned. The second group was introduced to this method, but it included one of my favorite moments of the day. Two students in this group had worked out very elaborate methods for dividing that worked some of the time, but not all of the time. I loved that they were willing to try new things. We talked about why their methods worked when they did and why they wouldn’t work all the time. One student said, “The bubble method just doesn’t work for me.” I felt my heart grow at least three sizes. THAT is exactly what we want. We want them to know when something works and when it doesn’t. I taught this group the partial quotient method and it was almost like watching a light bulb go off over their heads as they saw a more efficient way of dividing that also made more sense for them.

Second grade reading should have done some writing today, but I decided I wanted to make their heads hurt a bit so I changed my plans as we walked into class. Most of the group also sees me for math, which meant that some of it was a review, but we talked about word parts and their meanings. It was delightful to watch their heads explode as they saw how these word parts came together to give a word its meaning. I sincerely hope they don’t go home and call any of their grandparents or great-grandparents octogenarians this weekend, but if they do, please apologize on my behalf.

Almost half of our third grade math group was absent today. I changed those plans on the fly as well. Every graphing group was missing at least one person, so we’ll come back to graphs on Monday. Today we went back to my favorite game – 24. Students have a card with 4 numbers on it. They have to combine those numbers by adding, subtracting, multiplying or dividing them to arrive at 24. They work together on these, though the game is supposed to be competitive they’ve never played it that way, and their conversations are a great lesson in collaboration. While they (mostly) find the game to be fun, I have listened to their conversations develop and become more sophisticated as they locate patterns which make it easier to get to answer.

Summarizing, broken calculators, and graphing

Fourth grade went to the symphony today, so I didn’t see them.

Third grade reading is quite sure their brains are going to explode and they are not happy about this fact. We continued to work on summarizing while reading their myths. I haven’t had this much fun since teaching thesis statements to sixth graders. A lot of the day was spent telling students where they were right, but mostly where they were wrong. It was really hard for them to hear, but it was also really good for them. At the end, we created a summary together and talked about why it worked. This is a really difficult skill and one we will continue to work on.

Second grade math class was a wee bit shorter than usual due to our earthquake drill and the short debrief afterwards. Once we wrapped that up, we moved on to our activity, which is a recurring favorite of mine because it has a million different uses. It is called Broken Calculator. Students had to hit a target number of 87 on their calculator without using the broken keys :1, 8, 7, and +. This really requires flexible thinking and was harder than some expected. A few students tried to tell me they were done after completing a single equation. Their goal was to come up with as many ways as possible. I had them work independently for a bit and then they were allowed to collaborate with others. I’m going to take a look at their work and based on what I see we may work on this again on Monday. The ability to decompose numbers and to think about their parts is an essential piece of understanding multiplication, division, and fractions.

Third grade math had a grand time today coming up with faulty data sets. Their data had to contain factual information with a few bits of faulty data so that they could construct charts and graphs for students to critique. Some groups struggled to determine what would constitute a good data set. The idea is for students to become critical consumers of what they see – to look for mistakes and flaws that might cause misunderstandings.

 

Division, Mythology, Geometry, WWII, and Graphing

Today fourth grade students were given a division problem (2,472 ÷ 6) and asked to solve it. Most students used what we call the bubble method, which is a good, though fairly inefficient strategy. Some students immediately used bigger numbers such as 100 or 200 to start with while other students used smaller numbers. Both strategies are fine, though using bigger numbers is more efficient. As students mastered that problem, they were then asked to solve a second problem that included a remainder just to see if they knew what to do with that remainder. While most students were still working on the first problem, a few finished with both problems. Those students came back to what we like to call the “Firepit,” (we also have the cave – for when you want to work by yourself, and the water-cooler – for when you’re working with a group) which is the table where I pull small groups to learn a more efficient way of dividing. This method is called the partial quotient method and while it is more efficient than the bubble method, it is not quite as efficient as the algorithm itself. This is the perfect stepping stone for students.

While most students will leave fourth grade having mastered the partial quotient strategy, a few will move on to the actual algorithm. I know that it may seem like a weird way of teaching division, especially when you were taught a completely different way. This strategy helps to cement their conceptual understanding of division rather than having them simply following steps they don’t understand.

Third grade reading started their study of Greek mythology. We talked a bit about word parts having meanings by breaking up the world pantheon to help us understand it and why it’s important in our study of Greek mythology. We will likely continue to have discussions like these during this unit and Greek and Latin roots make up a sizable chunk of the English language. We also discussed the importance of understanding what you read and paying attention to whether or not you understand it. They have a bookmark of sorts that they will use during this unit to help them with the “Fix-it up” strategy. It gives them a series of suggestions on what to do when they realize they’re having trouble with what they’re reading. For bright kids who have had few issues with learning to read, they often don’t realize when they’re missing important information so that will be one of the most important aspects of this unit. In addition, they are being asked to write a summary about each story using the “Somebody wanted but so then” strategy. Using Cinderella as an example, students might write: Cinderella wanted to attend the ball but her step-sisters wouldn’t let her so a fairy godmother helped her then she married the prince. It is a quick and easy first step towards learning how to summarize.

Second grade math completed their study of geometry. We talked about the differences between 2D and 3D shapes, how many faces each had, vertices, etc. Geometry is very much about vocabulary so we reviewed the root words for numbers.

Fourth grade reading had another great conversation about World War II. Today we discussed propaganda and the Holocaust. Students asked some hard questions and we took a few detours as I tried to answer those questions in the most age-appropriate way while also honoring their thoughtful questions. I’m interested to see what they want to do next. They’ve asked for a chapter book and I think I might have one in mind that will push them to think a little harder than they’re used to – even if they’ve already seen the movie.

Third grade math worked on graphing. Today I gave them a chart and a graph that had discrepancies. They were asked to share their observations about the data they were given. All of the groups spotted the discrepancy between the chart and the graph, but all of the groups also missed the data that was not reasonable. We talked about how important it was that, when looking at data, to evaluate its reasonableness as well as checking for any errors that might be present. On Thursday they will be asked to create their own set of faulty data that they will have to share with other students who will then be asked to determine where the mistakes are.

Division, Cindy Ellen, Geometry, and Plot Diagrams

Fourth grade (mostly) finished up their  What’s the Missing Side assignment. I’ll meet with one group tomorrow to touch base on their understanding but we are ready to move on to some more concrete understandings about division. This is one of those topics that requires a lot of differentiation. Not all students will get to the same place, but all students will advance their understanding and application of the concept of division.

Third grade reading finished reading Cindy Ellen, which was a cowgirl retelling of Cinderella. We once again talked about how stories can tell you what is important to a culture or to a group of people. We’ll begin with Greek myths and some reading comprehension strategies tomorrow.

Second grade math is just about ready to wrap up its study of geometry.

Second grade reading read I Want My Hat Back and That’s Not My Hat and created plot diagrams for them both. We talked about story elements, but focused on the problem/solution part of the story.  Students can easily tell all of the other story elements but sometimes struggle on the solution part of the problem.  We took a quick break from the “Who Am I?” writing activity to focus on story elements because they will soon be writing a story with a character based on that writing. The story will have to include all of the story elements and that can be tricky!

What’s the Missing Side and Graphing

Second grade went on a FABULOUS field trip today and had a gorgeous day for it, which means I didn’t get to see them at all.

We are almost done with our What’s the Missing Side assignment. Students completed a gallery walk today. During their gallery walk they look at the work produced by the other groups and offer constructive criticism designed to make their visual proofs stronger. This is the second time they’ve done this type of activity and they were even better this time than last. Students then took the suggestions, read them, applied or discarded them as appropriate and are in the process of creating a final copy that will hang in the hall next to their visual proofs for multiplication. While this activity took many days to complete, it really does help students to understand what is going on when they divide.

Third grade math continued to work on their graphing activity. We’ve had quite a few bumps, but despite this students claim this is the MOST FUN EVER. I may need to switch up my game or risk losing my title as dungeon keeper. We’ll continue to work on graphing next week, as this tends to be a weirdly difficult concept to master when you take into account all of the little rules students must be able to apply when it comes time to show off their understanding on the SOL test.