Volumes of Prisms Play-Doh

Friday was a fun day (mostly). For one, it signaled the end of the last full week of school. Yay! Let's face it - we all need a break. It was also a fun day because use used Play-Doh in geometry. The lesson was an introduction to volume of prisms (we focused on rectangular and triangular) as well as volume of cylinders. This lesson was modeled after Julie's (@jreulbach)  lesson at ispeakmath - HERE.

The kids had a regular-size cup of Play-Doh for every 2-3 people. They split the play-doh and had plenty. First, we crafted rectangular prisms. Then we sliced them into 1 cm cross-sections. Students analyzed the shape of one "slice" and found its area. We decided, then, that we could simply multiply this area by the number of slices we had (it's height) to find the volume. We repeated this process for triangular prisms and cylinders. Students derived the formulas for the volumes of all three. One student informed me that "[Volume] was the easiest thing we've done all year". Good. It's easy because they really understand the formula. Great day.

Some kids discovered some other geometric properties... Hello octagon!

...And we still managed to have a little fun!

Finishing Up Surface Area - Spheres

Today was our last day of surface area. If I had time, I'd actually do one more day, since we really need a day of practice. I just can't take one more day, though, because I have to get in volume before finals. I only have two days for volume as it is (and then two days of review).

Today, we did a hands-on lesson on the surface area of a sphere. The idea was guided by Jennifer Wilson 's (@jwilson828) blog post on the Surface Area of a Sphere.

To do this activity, I knew I needed to get my hands on lots of oranges, since I have 110 kids in geometry. I called our local Food City, and -bless them- they donated 55 oranges. 1 orange per group of two. Thanks Food City!

The kids really enjoyed this activity. It was messy, but i think - sometimes - learning should be messy. The janitor didn't agree. Oh well. You can't win 'em all. The biggest problem I kept running into was that kids were skimping on filling their drawn circles. There would be lots of white space, and the kids would think they filled 6 circles. I would go around and have the groups start disassembling one circle, using those pieces to fill in the gaps.

At the end of the day, the kids had fun, and they really KNEW the formula for surface area of a sphere. Oh - AND my room smelled strongly of oranges instead of smelly high school kids. It was lovely.

Area and Perimeter Culminating Project

School is nearing its end for this year. I'm not mad about it. The kids are basically already hanging from the ceiling. My last unit is always area/perimeter and volume/surface area. Last week, to finish our area/perimeter portion, I assigned two geometry sections to complete the Apartment Remodel Project from Sarah at Everybody is a Genius. I modified her assignment slightly in order to incorporate the perimeter piece. All I really did was add a perimeter bullet and blank to the answer sheet.

My kids loved it. They mostly worked in groups of three to complete the assignment. I told them they were roommates (There are three bedrooms in the blueprint I used. It's the same one from Sarah's blog). I also redrew the 3D model on floorplanner.com. (Link to mine: HERE) The way the kids got into the flooring selection process and argued over it was hilarious. When one group finally calculated their total flooring costs with tax, the boy in the group screamed and said he was going to have to work overtime and buy on credit. He also noted that he was doing it "for the kids", asking his female partner where he wanted her to lay the floor when discussing the sample selections. I swear we all had too much fun with this project. It's probably my favorite project I've ever assigned. The kids learned SO much and had lots of fun with it. I think it was a good reality check for some of them, too. DO THIS PROJECT!

Composite Area Assembly Lines Activity

Since it is the end of the year and my kids are extra disengaged in class (read: way hyper and ready to get out of here), I've tried to really make this last unit fun. In some ways I've succeeded, and in some ways, I've failed. However... this activity was a big success.

Before I did the activity, I split my kids into groups of 3 - heterogeneously by skill level. One person in each group needed a phone for the purpose of reading the QR codes. This person was partner #3 Then the other two numbered off as partners #1 and #2. I borrowed ( I read their terms of use, and it said it was fine.) a bunch of composite figures from Math-Drills.com. However, I modified them a lot. Several of the measurements made no sense. For instance, there were several "right triangles" where all three side lengths were given, but they didn't satisfy the Pythagorean Theorem. So, in publisher, I used a lot of white rectangles to cover up nonsensical measurements. Anyway, partner #1 finds the area of shape #1; partner #2 finds the area of shape #2; and partner #3 finds the area of shape #3. Partner 3 then adds the three answers together to get the total area of the figure. Finally, the partner uses his/her phone to scan the QR code. If the answer is correct, they go to the next card. If the answer is incorrect, the card goes back to partner #1 to check his/her work and find the error.

My initial hope was to laminate these cards, so student could write their partial areas on the cards before passing them to the next partner. However, this didn't happen. I just ran out of time. That's my next step.

I'm attaching the PDF. I think I've fixed all the weird measurements. If you catch one, be sure to let me know.

Also, I know problem #1 is weird... it's really just two steps - area of a trapezoid and of a rectangle, but I wanted to split it into three to show kids you could do it with rectangle/triangles rather than the trapezoid.

Download the PDF File (HERE)

Editable Publisher File (HERE)

An Idea for A Culminating Volume/Surface Area Project

As of this week, my geometry classes have begun the final unit of the year - area/perimeter and surface area/volume. I threw out my old unit and am starting anew (let's face it - the old unit was junk). I have some neat hands-on stuff lined up for learning all these concepts. I also am using the apartment project from Sarah at Everybody Is a Genius as my culminating area/perimeter project. I have been considering what to do for the volume/surface area part of the unit as far as the assessment goes. I've done a lot of googling and have found some interesting projects but none that really got at the depth of inquiry and thinking that I want.

So... here's my idea. I'll put the kids in groups of 4. Each group will receive 12-15 nets of 3D figures. I will already have calculated the volume and surface area of each figure. Using combinations of these 3D figures, I will give the groups certain composite 3D figures to assemble with given volumes.

For Example (just making these numbers up):

Group #1 (Each group will have different figures/scenarios):

Combine your figures to make composite 3D shapes with volumes of

(1) 66 cubic in.

(2) 54 cubic in.

(3) 40 cubic in.

(4) 82 cubic in.

Here, I will assess with a rubric for correctness and calculations before students move to part II.

After student groups have successfully grouped their 3D figures, they'll then have instructions on how to assemble them according to surface area calculations.

For instance:
(1) Assemble the figures with a volume of 66 in sq. so that they have a surface area of ________.

(2) Assemble the figures with a volume of 54 in sq. so that they have a surface area of ________.

(3) Assemble the figures with a volume of 40 in sq. so that they have a surface area of ________.

(4) Assemble the figures with a volume of 82 in sq. so that they have a surface area of ________.

The students will tape their figures together appropriately to meet these specifications. I will then grade groups on the correct assembly of their composite 3D figures with a rubric.

Okay, MTBoS.... will this work? What would you change? All input is appreciated.