We have a strong connection with our 5th/6th neighbors. Some manifestations of that connection are informal and some are intentional. Students blend for choice time activities, eating lunch, our Wednesday morning sing, some trips, special projects such as making our dulcimers, and also for math instruction. We began the year working with only our own students, but after we got to know their math skills and learning styles better, we concluded that we could provide our two classes with more learning peers and more instructional flexibility if we combined to create 5 groups that meet every afternoon for 45 minutes when they are not with their specialist.

We did that until Conference Week in November. In the weeks between then and winter break, we returned to working with just our own students. Our group explored geometry in a variety of ways, as has been described here in previous blog posts.

When we returned from Winter Break, we went back to our blended instructional groups. Because one of our major resources is the Math In Focus series (an adapted version of “Singapore Math”), we decided that it was best to create our groups based on grade level in order to work within the textbook sequence. So I am teaching two sixth grade groups, while Diane is working with another group of sixth graders, Jeri has a group of fifths, and Diane and Jeri together have the rest of the fifth graders. (We will almost certainly change around the teaching responsibilities at least once.)

What have our groups been doing?

Diane: “My sixth grade group returned to its work in The Number Devil which it does each Wednesday (and which includes one fifth grader).”

My note: That book is a fantasy in which a boy who dislikes mathematics meets with “The Number Devil” in his dreams for 12 nights. He is guided through a series of essential topics: infinite numbers, prime numbers, Fibonacci numbers, and more.

“This week we looked at permutations (combinations in which the order matters). This incorporated previous work with triangle numbers and Pascal’s triangle in this chapter as well, which the kids readily recognized. Our permutation work was largely pulled from Harold Jacob’s book, Mathematics: A Human Endeavor. Other days, we are working with Hands-On Equations. We are finished with Level I (lessons 1 – 7). Today we turned to the related word problems. I read quite a few problems aloud today, and they named the variable, set up the equations, and solved them. They are doing this in writing for homework. We’ll continue at least through Level II as they are very excited to work with negative numbers.”

Jeri: “Since my group of 5th graders returned from winter break, we have been working on bar modeling, starting with addition & subtraction, then multiplication and division, and now we have moved into mixed operation & other multi-step modeling. I have been using the Step-by-Step Bar Modeling book to present problems and follow up questions for both class and homework, and they are doing the work in their LGB (little graph books, as they named them). We have reinforced the modeling concepts through the Thinking Blocks section of the Math Playground website.

Next, we will be working on division, starting with short division, since they all have said that they do not know this operation well, if at all. We will go back into our Math in Focus texts to explore this operation, then (what I believe will be a review of) order of operations. Following that is a section of word problems that will combine all of these skills, including the modeling.

Diane: “The fifth grade group [that I teach with Jeri] at first returned to its work with bar modeling. We had turned to that for a more practical change of pace from the multiplication work they had been doing. Their computer work shows development in their understanding. They will need more in terms of drawing their own down the line. They also will need specific work around division. For the time being, though we have turned our attention to fractions, particularly to building the conceptual understanding necessary for working with adding and subtracting fractions. They are working through Key To Fractions (Book One) for homework, but in class we’ve made the fraction strip kits and are playing the games from the Marilyn Burns Fraction Set. It seems to be a good match for them. We are also pulling in some other activities (i.e. today’s fraction hunt) to work on ordering and comparing fractions. We will jump into the MIF fractions chapter as soon as they are ready for it.”

My note: That is our largest instructional group. Sometimes they split into two smaller groups and work with just one of the two teachers in order to better individualize the lesson.

Lynn: Both of my sixth grade groups have been working further in the Math in Focus chapter that deals with multiplying  and dividing fractions and decimal numbers. We’re going to start division by and of decimals next week, when many of our instructional strategies described below will also apply to that topic.

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Next week’s blog post will contain information about our “That’s My Kind of Book!” project, which is coming to a close.

We’ve used our part of our 11 – 12:15 whole-group time just about every day to give students time to design and build. The interest in and enthusiasm for the many available activities has been gratifying.

A group of girls decided to work on the “chaos machine” kit and got it assembled and running in just a couple of days. A combination of written directions and YouTube videos led them through the complicated steps. There was a lot of debate as they ran into problems — does it go together this way? Why is the marble falling out of the track? How much should we angle the trampoline so the marble bounces into the basket? They went back to the paper and internet many time, discussed options, and found solutions.

Other students worked in pairs or alone on a lot of other different things. One student is carefully following the directions to create a little book of circuits that use adhesive-backed copper tape and LED stickers. Several are assembling a walking robot from a kit. Two are using our MakeyMakey circuit board with a notebook computer and a lot of aluminum foil to create electronic drums, pianos, video game controllers, and more. Two have experimented with the powered propeller that makes a well-constructed paper airplane fly farther and faster.  A couple of students are working with a “Snap Circuits” board and components to do small projects. The scroll saw is getting used mainly to cut cardboard-backed pictures to make jigsaw puzzles, but I think its use will expand into other cardboard and wood projects. When the weather improved a bit, several went out to use wood and tools at the workbench and have figured out how to take clementine boxes apart to use its thin wood parts for new purposes.

Will it fly?

Working on the robot.

Cutting cardboard (while wearing a cut-resistant glove)

building at the workbench

Exploring the “Snap Circuits” kit.

Will the LED light up?

MakeyMakey becomes a game controller!

calendar page + cardboard + saw = jigsaw puzzle

Do kits get in the way of our students’ opportunity to create on their own? I don’t think so. There is a lot of good learning that goes on when the directions are followed carefully and they see how components can go together to build something that moves, makes noise, or lights up. There are always problems, no matter how carefully the directions are followed. Students then need to figure out why something is not working as expected and use that knowledge to fix it. My hope is that the various kits will inspire students to go beyond them and do new things with what they have learned.

Next week: What’s happening in math classes, our book project, and our chapter book (Lassie Come-Home).

We began with a whole-building welcome-back breakfast on Wednesday morning. Our two groups arrived hungry and left with full tummies and lots of appreciative comments. Diane ran the waffle station (fresh strawberries and whipped cream!).  Jeri kept the serving tables organized and stocked with orange juice, milk, fruit and hot items , and I did the sausages and scrambled eggs. Several children expressed hope that this would become a weekly event (no chance). One walked in, saw the waffle irons, and exclaimed, “Oh, it’s like a hotel!”  (Apparently, he does not live in a waffle-making family.) Unfortunately, we were all too busy to take any photos. The kids ate all together in one room, and the conversations were endless and delightful. Anne, Kate, and Julia joined us for a while, and then our groups went off to enjoy a whole-class art or science time. What a delightful way to return from break!

In math this week, we continued our work with various aspects of geometry.  On Wednesday, we used compasses to make a lot of circles and turn them into snowflakes. The tricky part was learning the folding steps that would give us hexagonal flakes: first, fold the circle in half, then fold it in thirds. Halves were easy, but thirds were not.

We watched a video about the life of Wilson “Snowflake” Bentley, a Vermont farmer with limited education who made researching and photographing snowflakes his life’s work. His creativity and perseverance were impressive. He started trying to photograph snowflakes at age 17 and didn’t get a satisfactory picture for three years. Although the scientific community was slow to acknowledge the originality and importance of his work, he gradually achieved the respect he deserved. His snowflake photos remain a subject of great interest and amazing beauty. We have a book of them, a poster that relates the temperature to the type of precipitation that falls (including how it affects the structure of snowflakes), and also several books of more recent snowflake photos using a camera with an electron microscope. Snow will never look quite the same to our students again, we hope.

On Tuesday and Wednesday afternoons, we picked up the compasses again to learn about some fundamental geometric constructions: copying a segment, copying an angle, creating a perpendicular bisector of a segment, and bisecting an angle. All of these things can be done in little time with Geometer’s Sketchpad, but we believe that it is important for students to understand the processes, to appreciate the work of ancient mathematicians who had only the simplest tools, and to learn to analyze the step-by-step diagrams that teach the processes. We were delighted when one student, after figuring out how to bisect an angle, observed, “This is really just like bisecting a segment!”  Although the steps were not the same, there was a similarity, and he was correct.

On Wednesday, after learning to bisect angles, we started working on making designs. We have several books with complex constructions and only minimal information about how to create them. Our constant litany is that every step of any construction starts from a definite point and goes to a definite point. For some students, this was the hardest concept to internalize. For others, handling the compass was difficult. Everyone gained skills in working with the visual information and handling the tools. Although we are going to return to our blended math groups on Monday, we will find other times in the week to keep this topic going for a while. There’s a lot of interest. One student took a compass home for the weekend so she could continue exploring on her own.

We started reading a new chapter book: Lassie Come-Home by Eric Knight. Published first as a short story in 1938 and then expanded into a novel in 1940, this remains one of the great dog stories in the English language. Although the writing style is somewhat old-fashioned, the plot is engaging and the characters are well drawn. There is a lot of good modern fiction out there, but I enjoy introducing students to some classics that they may have missed. This is one.

We spent a little time with the current issue of Junior Scholastic. The article that we will continue reading next week is about vocabulary that students will need to understand many news events: undocumented immigrants, ISIS, executive order, Obamacare, and more. In the course of discussing the vocabulary, students are learning more about the events to which they are connected.

We will be doing “tinkering” and “making” and just playing around with tools and materials for the next couple of weeks. Along with woodworking supplies, cardboard, glue guns, and a lot of tools, we have some kits that we think will be interesting to many of the group. The highlight will probably be the “chaos machine” that has been sitting in a box since September, waiting to be built. We looked at a couple of YouTube videos that gave information about putting it together and what it looks like in operation. Most students sound very eager to open its box and get it assembled. Although there are instructions, there is also lots of room for modification and experimentation. Good videos about it that we haven’t yet seen in class include:

It all looks like a lot of fun as well as an opportunity to learn a bit about the whole mathematical concept of chaos.

In February, we will begin our unit on the ancient Celts and Romans. But all of this construction and invention seems like a worthwhile side trip to take first. Let’s hope that our snowflakes don’t magically cause too many snow days!