Geometry 7.4 Project

We have been in Chapter 7: Solids, studying volume and surface area of prisms, cylinders, and pyramids.  My 2nd period seems to be divided into thirds:  a third get it, a third are getting parts of it, and a third are lost or disengaged.  My 6th period could also benefit from looking at these problems a different way.  I decided we need to have a chance to apply these formulas and have the students do some problem solving.

I haven’t yet had the students do a project that’s longer than 1 day, but talking to an Infotech teacher and a Spanish teacher has me wanting to try a project that’s several days long to re-engage more students.  I’d initially planned on 2 days and a presentation on the 3rd day.  The students worked really hard during the first 2 days and few were ready for the third day, so I extended it to 3 days in class and presentations on the 4th day.

I developed a project for teams of 2 to 3.  Most teams were 2, and I had just 2 teams of 3. Because I was anticipating some low-ability students to want to work together, I intervened with some groups and suggested partners where the students were just waiting without a partner.  One drawback to partner work is with attendance.  On the 2nd day, two students were absent, so their partners were stuck working alone.  I redirected some students to work on just one shape (choose either the cylinder or the prism).  On the 2nd day, I also suggested the students trade contact information in case they needed to call each other.

The engagement was definitely improved and far greater than the previous 2 days.  In each class, one or more students said, “we should do this more often” and “yay!”   When I kicked off the project, I had a student from each class ask me if the restaurant was real.  Having a can of tomato sauce and a box of pasta in my hand also triggered curiosity.

On the second day, I noticed that some students didn’t understand the emphasis on being environmentally conscious by reducing surface area.  I used another problem (doubling the volume of tomato paste) to demonstrate my point with two different nets.  Some students changed their design based on this discussion.  Having the visual aids really helped.  I could see the light bulbs turning on in a few faces.

Here’s the project handout with directions for the students

Here’s the Powerpoint slide that was my background as I explained the project

Here’s the rubric. Students were given this as well.

This project had higher cognitive demand than I’d initially realized and required many different skills, including time management and organization.  There were a lot of parts to it, from volume calculations, trying several surface area calculations, building nets, working with a team member, writing a script, and presenting the work.  Next time, I will have stages of deadlines and will probably give them a week.

In each class, I had 4 presenters.  I’m posting 3 examples of student’s projects and reflections.  Example 1  Example 2  Example 3

Overall, I was very pleased.  I shared the plan with the other Geometry teachers.

Geometry 7.3 lesson plan and reflection

Reflection

Today’s lesson was to have students be able to find the  surface area and volume of a pyramid.  I’m posting my Powerpoint and lesson plan for 6th period.  I taught it 2nd period, didn’t like the flow of it, and so adjusted it for 6th period.  I would do this the same way next time, except to write the objective on the board, and possibly have a net of the pyramid.  Also, consider making a second prism and pyramid, perhaps a hexagonal prism or a rectangular one but twice as tall as the one I used today.

This lesson had students thinking about architecture and structures from around the world.  It had a demonstration using manipulatives (prisms, pyramids and popcorn), and got students out of their seats.  It took the idea of volume and made it accessible, as students saw the volume of popcorn changing in the clear prism and pyramid.  It had team work and collaboration, as students talked with each other as they made conjectures and predictions.

The lesson plan is in the notes section of this Powerpoint presentation.

Geometry 5.2 lesson plan and reflection

Reflection

In today’s lesson, I tried to have students keep their goals in front of their minds and engage in dyads.  I wrote out a couple of questions to ask in the dyads.

I felt we might run short on time, so I cut out large, colorful parallelograms and trapezoids on cardstock and put them on a grid paper background so that students could see how the area could be rearranged to form a rectangle.  In retrospect, I think this worked for only some of the students, but not all.  Next year, I’ll have the students draw parallelograms and trapezoids on their own graph paper and see for themselves how the parallelogram and trapezoid formulas were derived.

Geometry 5.2 lesson plan

Student reflections on their goals (sample1)

Student reflections on their goals (sample2)

Geometry Ch 5 day 1

I’m trying the get my students to take more ownership over their learning.  I am trying this through having them write their own goal, and then to have them reflect on it.

In this lesson, I wanted to start the new chapter with very general concepts, before we build to the specific.  I plan to activate prior knowledge about area and perimeter, and ensure students get the differences and units straights.  I’m planning on filling a t-chart on poster paper that will stay up for the chapter.  On one side, we’ll have perimeter, and on the other, area.  I anticipate there might be some confusion, so I’ll point to examples from real life, like the carpet for area and trim for perimeter.

I’m trying to plan turn-and-talks and dyads, so that students have definite times to engage.

Geometry 5.1 Lesson Plan

Reflection:

I got through the lesson plan, so it worked well.  I’m glad I decided to activate prior knowledge.  We had a few students that knew all the answers, so they could help the class with examples for the t-chart.   Students who’d been struggling with proofs seems to be glad for something that was familiar and seemed relatively easy.

When I had student dyads, not enough students participated.  They are using this time to turn and talk about other things besides math.  I am trying to have students write their dyad thoughts on their notebook, so there’s something to read if they can’t think  when I call on them, but there’s not much written.  We are showing examples of student work under the document camera.

Jan 12 Geometry Lesson plan

Today we constructed parallel lines with a compass and straight edge.  The circumstances of this lesson are that the math department wanted to have a portfolio piece for 1st semester, and it was agreed that construction should be part of that piece.  The students had construction in September, but not since then, so it was like starting all over again with the compass.  I was student teaching in September, so this is the first time that I’d done construction with these students.

The lesson plan can be found at http://docs.google.com/Doc?docid=0AXxJ1gaN0eqJZGYzd2M1bV8zNGhwZno3emM0&hl=en

I started the lesson by first demonstrating the construction on the board with a large compass, then on the document camera with a regular compass, then having the students try it on their own on a handout with 3 practices, while I walked around and helped students.

Reflection

Constructions:  The state expectations are that students make constructions with software or with compasses.  I can’t imagine any workplace wanting my student make parallel lines with a compass, but I can think of many positions where they have to do it with software.  While I’d taught the students the constructions on paper because of the portfolio piece, I will promote with the other teachers that future assessments of construction have a software option.

In chapter 5, we will cover constructions in detail.  Thinking over how this lesson went, I will block the computer lab for those days and plan on giving the students ample time to get comfortable with Geometers Sketchpad.  If there are students without AUP’s (computer use agreements), I’ll have to have them bring compasses and construct on paper.  One thing for sure, I’ll plan extra time for developing comfort with either tool.

Dec 14-15 Geometry lesson plan

In geometry, we are studying polygons. My students did an activity to find the rule that governs the sum of the measures of internal angles of polygons, and the rule that governs the measure of each external angle of a regular polygon.  Here’s the lesson plan,  rationale,  reflection and activity sheet.

Artifact commentary:  The activity sheet is provided by the textbook publisher.  It’s printed from a file on a CD.  I took the activity sheet and added four polygons to the back of the page.  I thought that providing this intermediate step would help students identify the data to fill in the table and thus make the sheet more accessible.  I had the students start on the back page and use the data to fill the table on the front page.  This particular artifact is the copy I used under the document camera to show the class what to fill in, and later, after the class had completed the activity, what I used to complete the table with the student’s data.