Exploring Volume: It's More Than a Formula!

This week we have transitioned from area to volume. Students started the investigation using 3D boxes and centimeter cubes to estimate how many cubes would fill the space of the cube. This year, I removed the "lines" that traditionally are preprinted on the cubes. This removal of lines dramatically changed the types of estimates that were offered from students.  

Eventually, students were encouraged to fill the boxes with the cubes to determine the actual number of cubes needed to fill the space of the box. 

Our next investigation involved a book by Jo Boaler which you can find in the book Mindset Mathematics. Want to see the book? Find the link here. After our first investigation of filling the boxes, it was evident that students were still developing their ideas of volume and how the different views of each face can help us find the volume.  This task is not about "finding the volume" rather how we can rotate and turn the cube and making sense of the images. I compare this activity to solving a Rubik's cube and at the end discovering that you have one solo tile that is out of place. A bigger challenge than meets the eye!

  

Students will continue to finish the investigation as they progress through the volume unit. 

As we continue to experience volume, students were asked to build cubes and rectangular prisms with given dimensions (see below). This is reinforcing What is length? What is width? What does that number represent? An observation that became clear was many students believe that just rearranging the order of the dimensions could "change the size" of the prism. This opened up a conversation about what those numbers mean.  We rotated their prisms and showed how rearranging the dimensions does not change the shape's presentation. I noted that this is the commutative property of multiplication.  

 To help students see how they could "change" the dimensions without changing the volume, I returned to a number string that I had opened the lesson with. I asked how the part squared off in red could help them with problem number 3 on their worksheet? The conversation was productive and students were revising their dimensions with greater success.  

 

Nouns: A Person, Place, or Thing

We are working on parts of speech and reviewing nouns with an emphasis on proper nouns and capitalization. Students are categorizing nouns, pronouns, proper nouns, and adjectives through a variety of word work activities. 

Whole group introduction:

I cut pictures out of magazines to drive our choice of words. Students identified the part of speech and offered adjectives to describe the noun.

Then, students gave the same exercise a try working in small groups. They chose the pictures from the magazines and they categorized the words.

Students completed an individual categorization and that proved to be informative to my next teaching points!

Growing Butterflies

 

 During one of the first days of school, as students were getting to know each other, a question that was posed to students was:

What was your favorite grade in school and why?

 A student answered that second grade was his favorite because they grew butterflies. I remember the joy of watching the life cycle of a butterfly when I taught Kindergarten and knew that in the time we are in, our class could use something to bring joy. We have learned so much while feeling such care and concern for our little caterpillars!

The first big discovery for me: there are lots of different kinds of milkweed native to Missouri. Well of course! As an avid gardener, why does this surprise me? But my experience with milkweed was limited and knew that before I could commit to the caterpillars that I had to secure the food source. A walk around my subdivision proved fruitful however learning that there were a few milkweed plants on our school grounds provided an even more accessible resource of food. Our school has a swamp milkweed plant that I ended up using for the caterpillars. 

Swamp Milkweed

This is the milkweed that I could identify with ease. I call this old school milkweed.

Second discovery: The "J" formation

This means that the caterpillar is about ready to hit the chrysalis stage and it should happen within 18-24 hours. I tried so hard to watch this actually happen in real time. I did catch a glimpse of a caterpillar between the two phases but I can't describe it. Sort of looked like the chrysalis was wet as it was forming outside the body.

Chrysalis in the forefront and a caterpillar behind the chrysalis.

 This is where we currently are. All six caterpillars are in the chrysalis phase and we are patiently waiting for them to emerge. We will be tagging the wings of the monarchs and hope to follow their journey!  To be continued! 

Rabbits in a Pen: Area and Perimeter

 Recently, I finished my master's degree in elementary math education with a certification as a Math Specialist. I learned a lot and hope to put in the next steps necessary to put the information to use in my classroom and grade level. 

One of the problems introduced in my Geometry class was called Rabbit and Pen.  (Credit unknown but will name Dr. Webel for sharing it.) This problem opens the door for so many concepts to emerge!

• Perimeter
• Area
• Counting for Area
• Multiplying for Area
• Perimeter and Area are not necessarily equal

I encourage teachers to share the problem with some tools for students to explore. If you have large Geoboards, a Geoboard app (found here), or graph paper for students to model their thinking on.

Here is the student version that I made here.  While I thought I retained the images from the whiteboard app that the students created, I apparently did not save them! However, I want to provide a visual of the work that shows the types of models that the kids created that sparked our discussion.

This activity reveals to students that while the perimeter is “fixed” (you have the same amount of fence to use, like 16 ft)  the dimensions produce a different area. The students might also realize that there is a method to making sure they have all of the different combinations possible. If they are not methodical, you could ask how they know they have thought of all of the possible ways to make the most space for the animals? I hope students would ask or wonder if they used a square (and squared numbers) would that always give you the most space? This lesson certainly lays the groundwork for students to wonder if this is a possibility.

16	20	10
1, 7	1, 9	1, 4
2, 6	2, 8	2, 3
3, 5	3,7
4, 4	4, 6
	5, 5