My fourth grade students have been exploring measurement and geometry during the past week.  They started out by learning about perimeter, area, and are now in the midst of discussing volume.  Students are working on a project where they’re building rectangular prism models and constructing cities.  They document the dimensions, cut out the rectangular prism that matches the measurements and places it on a map.

The groups have been working diligently over the past days.  What I found interesting on Friday were the student conversations.  As I peered over each group I eavesdropped on what was being said.  Students are in groups of 2-3 and there’s plenty of conversation happening.  Students are recognizing that the length, width and height all impact the volume of a rectangular prism.  Mistakes are also happening.  That’s a good thing.  Students have had to use multiple grid sheets because they either cut out the faces too large or too small.  They just grab another grid sheet and start over again.  Their perseverance and being able to “lean into the struggle” is evident and I made sure to remind them of that.  Students were even getting creative in adding sunroofs and open decks with their prisms.

Projects like this take time, but they’re often worthwhile in helping students build conceptual understanding.  I’m looking forward to adding a question component for the groups on Monday.  The questions will relate to cubic units and how the volume is found when combining multiple rectangular prisms.

I believe that this activity helps students apply volume formulas.  I want students to come away with a better understanding of why the formula V = b*h is used and have them feel more confident in being able to see geometry/measurement relationships.

After this activity students will take a brief formative checkpoint where they’ll be answering questions similar to the below image.  This is also how students will be assessed in a couple weeks.

The projects should be finished by the end of the next week.  I’m looking forward to seeing how the cities finish up and the student reflections that follow.

## Representing Volume

My fourth graders are starting a new unit on fraction computation this week.  Last week, students finished up month long unit on volume and area.  After grading the tests, I started to reflect on a few different activities that seemed to help students understand volume a bit better.  One particular task will be highlighted in this post. I’m not going to lie, this task was quite challenging for kids, but I feel like the students were able to make some amazing math connections in the process.

So last week, I brought the students to the front of the room and we discussed area and volume.  Students provided examples of area and volume and referenced the city that they created earlier in the year.  Students then randomly came up to the room and drew out a slip of a paper.  The slips indicated a particular volume task. The tasks were all related to making a 3D shape that matched a certain dimension range.

Students drew the small little sheets out of a cup.  It was exciting as students weren’t quite sure which sheet they were going to get.  Students were then given the direction sheet, where they were asked to create the net, tape/glue it together, place it on the sheet, and then take a picture and send it to their digital portfolio.

Students were then given the centimeter grid and were off to the races.  Some students had to take multiple grid sheets as they missed the required dimensions on many different attempts.  Eventually, most students calculate the volume that they needed and used a formula.  Students then used the formula to calculate the volume before creating the net.

Students didn’t seem to have too many problems with rectangular prisms or cubes, but cylinders and cones were a bit more challenging.  Students were able to create the base fairly quickly.  The curved surface was an issue for some.  Many students had trouble creating a large enough curved surface to match the cones and cylinders.  One student mentioned that the curved surface needed to be around 3 1/4 of the length of the circumference.  I enjoyed hearing that as a couple students had a conversation on how to make their shape fit a required dimension. That’s an #eduwin in my book.  Students then attached their constructed structures to the direction sheet.

Students then put the different structures on a map and created a small city.  I’m hoping at some point the students will be able to create a short stop-motion-video using the volume structures.  It might fit in perfectly with our rate/ratio unit that will be coming up after PARCC testing.

## Volume and Fixable Mistakes

My fourth grade students have been exploring volume and area for the past few weeks. Lately, they’ve investigated different methods to find the volume of prisms, pyramids, cones, and cylinders. Through this process, they created their cities of volume and have been studying this topic extensively.  This fourth grade crew has made a lot of progress in finding the volume of objects when given the dimensions.  This particular unit of study is more focused on making spatial connections and using formulas to find volume.  Although the kids have been showing a better understanding, I’m observing very similar errors when I give checkpoints.

• Using inappropriate units (squared vs. cubed)

Students need constant reminders to show appropriate units.  When I whiteout the unit line it’s interesting which students automatically write down the correct units and those that leave it blank.  Lately I’ve been bringing out the base-ten blocks to show the difference between linear measurements, area, and volume.  Students tend to not have any issues with telling the difference at that time, but when concentrating on formulas, the units are sometimes omitted.  I’m currently looking at different ways for students to show their understanding of the differences between square and cubic units.  I don’t want to heavily focus on this, but I’m noticing it as more of a student afterthought than something that they think of while answer a question.

• Find the lengths of a side or the circumference with volume is given

Students seem to be efficient when trying to find the volume of prisms and cylinders.  When given the measurements of each side, students tend to perform the calculations correctly.  It’s a bit of a different story when students are given the volume and are asked to find other dimensions.  Some students rock this and do well, others not so much.  The class reviewed these types of problems by using a variable for the missing side or circumference.  We then created a few different steps that can be taken when tackling these types of problems.  I’d say the majority of issues with this specific problem came when students were given the volume of a cylinder or cone and needed to find the volume.  This is something that the class is still reviewing.

• Remember that in r^2 actually means r * r and not r * 2

I’m going to chalk this up to not having enough practice with exponents.  At this level, students have used exponents, but more so to show Scientific notation.  When students hear “to the second power”, some hear that the word second and just multiply the radius by two.  Some students also problematically use the diameter and call it the radius.  Digging deeper into this issue has also revealed that some students aren’t using the Order of Operations to solve for volume.  Next week I’m planning on co-creating an anchor chart to address this.  Also, Pi Day (3/14/18)  is coming up soon and the class will definitely address the vocabulary and formulas associated with that soon.

These three issues have come up fairly consistently during the past week.  I’m looking forward to addressing them next week, but also having the students become more aware of what fixable mistakes exist so we can be more proactive. I’m also looking into having students create a culminating volume activity.  Putting that together is in my plans for tomorrow.

## Area and Volume Skills

My fourth grade students finished up a unit on volume about a month ago.  This past week I gave the same group a cumulative assessment on the first two units.  After grading the assessment I started to notice trends.  Many students had issues with converting square units to cubic units.  Students also mislabeled units related to measurement.

This is my first year using a new version of a district-adopoted math resource.  This year’s scope-and-sequence had students encountering area first and then volume was discussed in a completely separate part of the unit.  I believe that isolation made students think that problems in the different sections were either 1) related to area or 2) related to volume.  The assessments that I graded indicated that students needed some bolstering in applying area and volume.  Combining them would be a bonus.

Early this week I came across Graham’s Tweet about test questions.

I clicked on the article and found some amazing questions.  I definitely geeked out after trying out a few. These types of  questions made me think beyond one math skill or idea and I thought it would move students in that direction too.  I decided to use the area question with my students.

You see, in the past students have been given the length, width, and height, and then asked to use a formula (often given to them) to find the volume.   In this case, students were given the area and had to use that to find the side lengths.  This type of task in Graham’s Tweet was definitely different problem for them.

I gave each student a copy of the sheet and had them work on it individually for about 10 minutes.  Students initially thought of adding all the area sides together, but then they realized that adding them wouldn’t help in the process.  I redirected students to look at what the question is asking.  There were a few minutes of frusturation as students were looking for ways to find the length, width, and height.

Students were then put in groups to work out the problem.  Eventually, students started to think of factors as they started to investigate numbers that  work for the length.  Some went the route of using a factor rainbow, while others used a trial-and-error method.

More frustration ensued, but students still moved forward.  A few groups were confident that they had a solution.  I briefly looked over all the responses and saw that no one had the correct answer, but I pokerfaced it and had the students work it out at home.  That evening some of the students tackled the problem and came back with a solution.  I was impressed with the perseverance and also how these students applied their understanding of area to find volume.