Exploring Perimeter

My third graders have been investigating perimeter and area for the past week.   I find when the terms are isolated, students are able to define them fairly accurately.  When put together it’s a different story.  Students tend to switch them around or heavily rely on one term based on what the class has been working on for that day.  So this year my students worked on a project that focused specifically on perimeter.  Area is part of it, but only if a teacher wants to pursue that avenue.

Students were put in groups and given two sheets.

Students outlined the map and personalized the city.  The construction zone is intended to be used for the actual city piece.  After the maps were distributed, each group received a centimeter grid.  The grid was used for students to cut out and create a city based on a certain criteria.  Each group received one sheet that indicated certain dimensions.

Students then filled in the rest of the grid to match the dimensions.  Some of the dimensions were non-negotiable, like the height for the school or perimeter for the police department.  Others had some leeway.  There was a lot of erasing and rewriting for this sheet.  Once they completed the sheet students started tracing and cutting out the centimeter grid paper.  Trial-and-error was part of the process.  Students then cut out the buildings, put together some supports and glued them to the construction zone.

Students put together the cities and attached the dimension sheet to the bottom.  I’d say that around half of the class is finished and the rest are making some great progress.  I’m looking forward to seeing how the rest of them turn out and the gallery walk that will happen afterwards.  Here are the files that I used and feel free to use it in your own classroom.

Making Math Projects Worth the Time

My fourth graders are in the midst of math project. They’ve been studying measurement and are completing a project involving creating nets, assembling them and finding the volume.

I’ve used this task in years past and students spend a decent amount of time planning and putting together their rectangular prism cities.  It’s generally one of the “favorite” activities of the year as indicated by student surveys that I give in June.  The engagement is great and students are proud of what they create at the end.  Now to the challenging –  It takes an LARGE amount of time to complete these types of projects.  Students have the potential to lose focus and stray from the concept/objective.  I’m certainly not a pro with math projects, but I’ve found certain things work, while others don’t.  The bullet list below could apply to other long-term (>3 class sessions) projects beyond math. I’m tackling the points below before I plan out a fifth grade project that’s scheduled to take place in April.

• Clearly define directions, expectations and criteria
• I spend a good 15-20 minutes explaining the project and directions with the students.  During this time I’ll answer students’ questions and elaborate on the criteria for success.  I tend to also reinforce the expectations of how teams should work together (because all teams works great, right??) and what goals they’ll accomplish by the end of the project
• Objectives … Objectives … Objectives
• I remind the students of the objectives and skills that the project will be addressing.  The projects are fun and engaging for the students, but I want to ensure that they understand the reasoning behind the project.  Teachers understand why the project is happening, but it’s also good to have a list available when an admin stops by your room and students look like they’re creating something massive with paper, iPads, scissors, glue and other materials.  Also, the SMP‘s can play a huge role here.  I personally find it challenging to pinpoint exactly where the SMP’s become directly evident in lessons (it’s usually a vague “hey look we’re using attend to precision here” type of statements.  Math projects are full of the SMP’s and this aspect can be part of the objectives and emphasized in a self-reflection activity – see last bullet point.
• Eliminate specific models/examples
• This might irk some people, but I’m not a fan of showing examples of what their project should look like.  Providing really vague or general examples are okay in my book.  I tend to get questions asking if a certain aspect of the project could look like _____.  I tell students that if it follows the criteria it’s good to go. Ideally, I’d like students to work together and create something original, not copy what I show as the example.  This allows students an opportunity to focus on the criteria and not “what the teacher wants” type of mentality.
• Create a timeline
• I find creating a timeline is one of most important pieces when introducing the project.  Adding in checkpoints along the way where teachers “check-in” on what’s happening gives students (and me) an added accountability piece to make sure we’re sticking to what’s expected.
• Be flexible
• Sometimes timelines need to be changed.  Assemblies, snow days, fire drills, (insert an event that impacts your instruction) happen.  Be upfront with the students that the time will need to be extended.  Most of my students give a sigh of relief when I tell them that they’ll have an extra period to work on the project – so do I as I want to make sure that they make a quality product.
• Include self-reflection
• Students need time to process the math that they’re using while completing a project.  I like to give students time to write down how they’re using the time that they’re given and what was accomplished during that session.  I find providing this time gives me an insight to how each group is progressing and also adds an emphasis on what skills are being addressed.  For math projects, I find that adding a reference to the SMPs can be an added bonus as most of them become apparent as students create their projects.
• Sharing is caring
• After everyone has finished I like to share the projects to people outside of our classroom community.  I might share a link out on Twitter and have the students submit their projects to SeeSaw.  Sharing with other classrooms in the district has an added bonus.  Plus, students are creating their projects for an authentic audience and they have the potential to receive feedback.  That adds another quality component in my mind.

I find that having these components in place before assigning a long-term project to be helpful.  It makes the project worth the time as students are more efficient during that time and the quality of what’s created tends to be better.

The Marshmallow Challenge in the Elementary Classroom

Approximately two months ago I noticed a Twitter post about something called the Marshmallow Challenge.  The tweet led me to this TED video.  Many of the examples indicated that the challenge could be used with adults as well as students.  The official Marshmallow Challenge website offers many useful instructions and tips for facilitators.  I decided to use the challenge with a fourth grade classroom.  The session, from start to finish, took approximately 45 minutes.  The standard 18 minute time limit to work on the project was perfect for my classroom.  Of course the focus of this project emphasizes teamwork, but I decided to add a few measurement standards. For example, the students were required to measure the length of each pasta stick used and find the volume of the marshmallow (as a cylinder).  The total height of the structure was also measured.  Here are a few pictures from the event:

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The class had a debriefing session after the event.  During this discussion, students revealed their strategy.  Here were some of the questions that were discussed.

• What will the base of the structure look like?
• Will we use all of the materials?
• What are our roles?
• How will we work as a team?
• How does working as a team help us succeed?
• Will we wait to put the marshmallow on top at the very end or test it throughout the project?
• Should we write out a plan in advance?
• How should we work together?
• What are other groups doing?

Overall, this learning experience gave students an opportunity to use critical thinking in a collaborative setting.   I’m planning on having students complete a plus/delta chart and complete an entry in their math journals next week.

*Picture credit: Stoon

Measurement and Mini Golf

Approximately a week ago I was paging through my math curriculum. Through a pre-assessment I found that students were in need of a review on angle classification and measuring skills.  The curriculum lessons offered a number of worksheets and angle measuring drills.  Although these lessons seemed beneficial, I felt the need to create a more memorable learning experience for my math students.   At this point, I decided to search for measurement projects. While following #mathchat, I came across this Edgalaxy site.  The project seemed to match many of the objectives that needed strengthening in my class.  I changed up the directions and modified some specifics in order to best meet the needs of my students.

So … a week has passed and almost all of the projects are complete.  I listed the project steps below.  Feel free to use any of the ideas below in your own classroom.

1.  Had out the direction sheet.  Here is a Word template (via Google Docs) for your use.

2.  Review many of the different vocabulary words associated with the project: acute, obtuse, right, parallel, perpendicular, trapezoid, etc.

3.  Show possible examples.  I tend to show just a few examples as I don’t want to give them a mini golf course to copy.

4.  Group the students into pairs.  If you prefer, this project could be implemented as a collaborative group activity.

5.  Students choose their construction paper color (11″ x 20″)

6.  Students draft their course in pencil (on grid paper).  The draft gets approved by the teacher and then is transfered to scale on construction paper.

7.  Students present their final projects to the class.

Number Line Concepts

Image by:   D. Rizzuti

Lately, I’ve been having conversations with colleagues regarding how to communicate number line concepts in the classroom.  Specifically, I’ve been giving examples of how understanding number lines may lead to a more stable mathematical foundation. In the past, my class has created various products related to the number line.  My original inspiration came from this number line below.

The project in this post emphasizes the idea that percents, fractions, mixed numbers, and decimals are all related  This basic understanding helps develop number sense skills.  Here are the generic steps for this project:

• Students cut out percents, decimals, percents, and fractions out of the template
• Students draw a number line on a piece of construction paper
• Students glue/tape each number on the number line

Here are a few sample photos (click to enlarge):

The project seems simple, right?  Well … it took about 20 minutes for the cutting, coloring, and gluing.  I then facilitated a classroom discussion after the number lines were presented.  The math curiosity (I really like that term) and discussion that followed the project seemed beneficial.  It’s truly amazing to see what type of concepts can be discussed when observing the number line through a variety of lenses.  Our conversations touched on the concepts of absolute value, positive/negative numbers, fractions and mixed number conversions, addition of negative numbers, and place value.  In fact, the math conversation lasted 30+ minutes.  Having these types of “math chats’ with third graders was a phenomenal learning experience.  All of the concepts discussed will be introduced later in their academic career, and hopefully I gave my students a quick preview to what is to come.