Scale Factor – Part Two

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During the last week of school one of my classes explored dilatations.  It was a rather short lesson since there were only a couple days of school left.  After some review, I pulled out a project from last year and thought might be applicable since it addressed the same standard for that particular day. I looked it over and made a few changes so this year it would run smoother.  Here’s what changed:

  • I had the students create an exact 4cm by 6cm grid using rulers.  This was different than my initial project.  I made sure to check each grid before students moved on to the next step.  I’m not a fan of having a simple mistake or unclear directions derail an entire project (which it did for some last year) – so I decided to check each students initial grid.

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  • I also created a random piece to the amount of dilation this time around.  This picture is from last year’s post.update.pngLast year students already knew the grid to use and basically used a “paint by number” approach to fill in each square.  Although that was fun, it didn’t really hit the objectives as much as I’d like.  I had students roll a die to determine the dilation this time.  This gave four different options for students.

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  • I put together a criteria for success component where students could check-off items when completed.  I set up the different dimension papers on one of the tables so students could easily grab them depending on their dilation.  I also added a short debrief piece near the end of the project where students discussed how they increased the size of the image.

These changes helped improve this particular project and I believe it created a better learning experience for the students.   There are times where I completely scrap a project and other times I make tweaks in order to make it better.  I opted for the second option this time around.

* Next year I’m planning on updating the project to include dilations that involve reducing the size of an image.

Reflections and Takeaways

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The school year is coming to a close. This Monday would’ve been the last day but the midwest weather had other plans and an additional three days were added to the schedule. Classroom walls are starting to look bare and teachers are packing away their things for the summer. Boxes and labeled containers have started to accumulate in classrooms as some teachers know that they’ll be moving classrooms.  As I pack up my room I’m reflecting on this past year. Here are a few takeaways and potential changes that I’m contemplating over the summer.


Takeaways – I’ll keep these winners for next year

  • Give out study guides at the beginning of a unit

After reading Making it Stick last summer I decided to give out my unit study guides at the beginning of a unit.  It takes my classes around 1-2 months to complete each unit of study and I used to give out and review the study guides (basically chapter reviews) the day before the test.  This year I gave them out during the beginning of the unit and students worked on them throughout and then the class reviewed them together the day before the test.  I had to make a trade-off seeing that students would need to complete them at home or if we had extra class time, but that didn’t seem to be an issue.  Also, I gained about an extra day of instruction per unit by using this so it ended up being a winner in my book.

  • Create an agenda slide for each class

For the last couple years I’ve used an online planner to create my plans for each class.  I’ve found it helps me with organizing the structures of lessons a bit more and allows for a quick copy and paste to a slide for students to see.  The goal is in the left corner and it’s something that the class reviews each day.  Most of the students look at the activities for the day and then take out the materials that might be needed.  This year I had a handful of students with special needs and this visual cue seemed to help with anxiety related to the expectation for that particular day.  Plus it helped keep me organized, which is why I did it in the first place.  Do I always follow the agenda – nope, but it’s there to provide structure and an expected outcome.

  • Use math routines more consistently 

This year my 3-5th grade classes used math routines from day one until the end of the school year (counting these last four days).  I also used them during test days. There’s something important about starting with the math and the students expecting to start the day with a specific task.  My third grades used Estimation 180, fourth Who am I, and fifth AlgebraByExample.  It became part of our daily routine and I believe it helped with cycling through concepts and skills throughout the school year.  I plan on continuing to do this next year.

  • Instructional Balance

My classes this year have been much more balanced as far as math instruction is concerned.  This year I used Desmos, Quizziz and Nearpod more frequently and relied less on problems from the text book or worksheets (making sure to state that there’s nothing wrong with a worksheet).  Having that interleaved practice and time to discuss topics with partners has benefited students as they apply their math learning in different situations.  I’ve also changed the sequence in which some math topics are taught and gave students more time to explore concepts with manipluatives first before diving into more of the abstract.


Potential Giveaways – I might change these for next year

  • Homework

Ugh.  That sticky issue of homework has come up again.  This year I gave students homework around 2-3 times per week at the beginning of the year.  I slowly started giving less and ended up with 1-2 times per week during Feb-May.  I found that it was beneficial for those students that completed it, although the students I wanted to complete it rarely brought it back.  Also, I found myself giving homework to increase the amount of time in my math class – not a good reason.  A few years back I decided to give students links to the homework incase that they forgot it at school.  It still wouldn’t be completed.  I’ll still be giving homework next year, but I’m thinking of changing the format to be more of a retrieval practice model.  What that looks like will depends on the next couple months.

  • Projects

My students completed a couple different projects this year.  In a few instances I believe the time in which students worked could’ve been more structured.  I’d like to create more of a daily schedule for these projects and include time where students “check-in” with the teacher to ensure that we all finish.  Unfinished student projects feel like a failure and I’d like to limit these.

  • Grade Less and More Accurately

Next year I’d like to have specific points within a units to formatively check how students are in relation to the standards.  These won’t be formally entered into the grade book, but used for students to reflect on their progress and for me to look at where I need to emphasize my instruction.  I used a reflection tool that was helpful for my third graders this year and I’m planning on extending it to other grade levels.  Who thought emojis could be so powerful?  Also, every year around this time I wonder if the students’ grades actually reflect where students are in relation to the standard?  Sometimes yes, other times no.  At some point in time my district will be consistently using standards-based grading, but we’re certainly not there yet.  I’m hoping that this will help students and parents to see where students are on a continuum compared to the expected standards.  In the meantime, we still have the letter system that parents and students have grown so accustomed to and expect to see when the report cards are delivered.


Events that spurred growth – I’d like to continue to seek out these opportunities

  • Conferences

This year I had the opportunity to co-present at IAGC on the the topic of math routines with my colleague Cheryl. Most of my learning came in the time creating the presentation and discussing potential ideas.  The conference was well attended despite the extremely cold temperatures.  I had a sub for the day but ended up not needing them since school was canceled – go figure.  I also had the opportunity to travel to Wisconsin and attend WMC to present on feedback routines.  I was only able to attend one day, but it was great and meeting many members of my PLN face-to-face was amazing and long overdue.  Special shoutout to Adrianne , Sonja , Mary and Chris for being so welcoming and I enjoyed our conversations.

This past week I received confirmation that I’ll be able to attend all three days of NCTM in Chicago.  I’m in the process of putting together a couple proposals and look forward to meeting, sharing and learning with colleagues.  Attending conferences and meeting with other educators outside of my district brings a different perspective.  That different perspective and ideas is refreshing and helps me think of ways to improve my practice in ways that I didn’t think of before.

  • Book studies

Last year I participated in a Making it Stick summer book study and it was a great experience.  It’s one thing to read a book solo and another to read it along with other educators.  There’s an accountability piece that keeps me reading and more critically analyzing what I’m taking away from what I’m reading.  I’m looking forward to Culturally Responsive Teaching And The Brain this summer.  The book arrived at my doorstep about a week ago and I’m looking into diving in with my highlighter next week.

  • Podcasts

I recently started listening to Podcasts and have found a couple that I’ve been sticking with over the last couple months.  These podcasts help me think about practices that I could improve and just gives me a different perspective in general.  Right now I’m listening to The Cult of Pedagogy, Estimation 180, The Creative Classroom and The Minimalists.  I’m sure my list will change over these summer as more non-education related podcasts enter my queue.  I need to have more of balance with the types of podcasts I listen to but this is a start.


 

Measurement and Reasonable Solutions

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My fourth grade students finished up a project involving area last week.  Students were asked to find the area of different playing areas for certain sports.  They first calculated the areas of the playing field by multiplying fractions and then found the product.

The next step involved creating a visual model on anchor chart paper.  Students worked in groups to put together their athletic park involving the field areas.  They were given the area of the park and then had to place the fields where they wanted according to the team’s decision.  Students also added additional facilities for their athletic field and then presented their projects to the class.

While presenting, students in the audience were required to either 1) ask a question or 2) provide a constructive comment.  Most of the questions that were asked related to why certain fields were placed in specific areas on the field.  One question stood out more than the others … does the distance make sense?

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The locker rooms had to be adjusted (see whiteout) as one student said, “It doesn’t make sense so I changed it to match the 120 yd.”

 

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Students were looking at the length of the fields and observing whether it was reasonable or not compared to the total length.  The class then had a conversation about the terms reasonableness and proportions.  The discussion involved how a double-number line and a grid could’ve helped visualize how the distances match.

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I’m hoping to revisit this idea during the next few weeks as the school year finishes up.

 

Reflections and Math Routines

 

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This year I’ve been using number sense routines* with my 3rd-5th grade classes.  The routines have specifically been put into place to help students strengthen their place value and estimation skills.  The routines last around 5-10 minutes and generally occur during the first part of class  The routines is the first thing on the board as students enter.  Students use a template, complete the routine independently and we discuss the results and process as a class.

Two of the more productive routines this year have been Estimation180 (3rd grade) and Who am I (4th).  Both ask students to use hints or models and then use those visualizations to solve problems.  Students document their thinking on an individual page and then we discuss it as a class through a debrief session.  While working with students this year I noticed that not all students participated to the extend that I’d like.  The conversations were decent and students were engaged, but the reflection piece wasn’t as thorough.  So this year I’ve decided to add an individual reflection component for these specific tasks.  The reasoning actually came from a book that I read back in April that emphasized how sentence stems can be used to help students reflect on their mathematical thinking.

 

I put these sentence stems into practice and added them to a reflection sheet.  I added extra space after the “because” to help encourage students to write more about their own thinking process.

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Students complete each one of these around 2-3 times a month.  Students complete the reflection sheet, discuss the writing with partners and eventually put them in their folders.  The sheets are revisited throughout the year to see the growth over time.


* The images from this post are from a math routines presentation on 5/3. Feel free to check out the entire presentation here.

 

 

 

Spaced Retrieval Practice

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There’s around one month of school left and it feels like the home stretch.  The next month is full of changes.  The weather changes from chilly temps to sunny days (at least in the Chicago burbs), class lists and sections are starting to take form, driving to/from school with the windows down is the norm, and planning for that final month is in full swing.  The majority of my math classes just finished a unit assessment and there’s one unit remaining.  So often I find that students perceive the end of a math unit to “close out” the learning on a particular skill set.  I observe that this idea often gets pushed out as grade deadlines approach.

As my classes start a new unit I’m pausing to reflect on how my practice has changed.  Last year I read How to Make it Stick and I intentionally planned to use more retrieval practices. This year I’ve incorporated more review opportunities through online formative quizzes and by trying to make implicit connections to past learning.  I’ve often asked students how today’s objective connects to this week’s learning.

While digging through my resource materials early this year I found optional mid-year and cumulative assessments. Generally, I find that there’s not enough time to complete all of the assignments/tasks in the resource so these particular tests aren’t used frequently.  This year I decided to use them to help with spaced retrieval practice.  Instead of using a mid-year and cumulative assessment directly following a unit I decided to space out these assignments and take off the grading emphasis.  These types of assignments take multiple days to complete and I often have students work with partners to reflect on their progress.  So far I’ve seen positive progress as students this year are referring back to past skills more quickly and bridging the connections on a frequent basis.  I’m looking forward to using a similar strategy next year.

Classifying Polygons

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One of my classes is in the middle of a unit on geometry and measurement.  They’ve identified shapes before, such as rectangles, squares, triangles and hexagons.  Earlier in the year they found the area and volume of shapes involving rectangles, squares and triangles.  The current unit investigates how polygons (specifically triangles and quadrilaterals) are similar and the study of shapes progress as students create hierarchies.

  • CCSS.MATH.CONTENT.5.G.B.3
    Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

 

In order to dig deeper into the above standards the students starts the classification process.  This was fairly new for most of the students.  I explained what classification meant and gave a few examples related to the characteristics of triangles and quadrilaterals.  Students were given a sheet of quadrilaterals to cut out and classify.  The next question I was asked was related to how each shape should be categorized.  The class reviewed different vocabulary words associated with polygons and then I left the students create their own categories.

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This student decided to split up the shapes into three categories.  3-sides, 4-sides and 4+.

After discussing equal side lengths and parallel sides two of my students created the classifications related to those terms.

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Almost every student had a different way to organize their shapes.  Students went to different tables and observed how their peers classified the shapes and then the class discussed similarities.  Next week students will classify the shapes with a hierarchy chart.  I’m looking forward to seeing what they create.

Making Math Projects Worth the Time

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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.

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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.