Roller Coasters and Math

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One goal this year is to have my classes complete more interdiciplinary projects. These projects move beyond district-adopted texts and often involve multiple subjects and student groups.  I find value in having these projects as students often need to work in teams and apply their mathematical thinking in different situations.

Back in September I came across the tag #paperrollercoaster.  After completing a quick search I came across multiple pages where teachers had students create paper roller coasters and answer questions.  The questions were often related to math/Science objectives.  I thought this had potential so I finalized a decision and ordered a set from here.  My thinking was that if one worked out well I might order more.

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The materials arrive around a week after I placed the order.  I decided to use the project with a third grade class.  After a brief explanation, students were placed in three groups.


One group drew out and created an outline for the base on a piece of cardboard.  The group was asked to create six square bases where students would be placing support columns. The second group scored, cut out and attached the base columns together to be placed on the outline of the first group.  The third group was in charge of creating the support beams. Students scored, cut out and opened up both ends of the beams so they could be added to the columns.

All groups had approximately 20 minute to work in their group.  They were supplied with tape, scissors and directions.  Afterwards, the class met in the front of the room and we started to build the base for the roller coaster.  During that time the class started to discuss some of the math vocabulary we’ll be using as the building continues. Most of the terms will be coming from the geometry and measurement math strands.  The terms area, surface area, volume, length, formulas, speed and height were all discussed before the students left for their next class.  I appreciate the multiple math entry points available through the use of this project.  As the project progresses I’m planning to add activities/sheets that we use.  In the meantime, feel free to check out a few lessons here.


Multi-digit Multiplication Strategies


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This past week my third grade class investigated different ways to multiply numbers.  Before diving into this concept I asked the students their thoughts on multiplication.  A few students explained to the class their view on the topic of multiplication.

  • repeated addition
  • double or triple “hopping”
  • using arrays
  • “timesing”
  • Increase the number by “a lot”

Most students were able to showcase examples of the above.  Even though their vocabulary wasn’t exactly spot-on, students were able to come to the whiteboard and show their thinking.

I received different responses from the students when asking them about multi-digit multiplication.  Actually, it was more of a lack of response.  I feel like some of this is due to exposure.  A few students raised their hands and asked to show their process to multiply multi-digit numbers. These students showcased their ability to use the traditional algorithm. The class reviewed this method with a few examples.  Although students were finding the correct product they had trouble explaining the process. Students weren’t able to communicate why it worked or another method to find a solution.

On Tuesday my class started to explore the partial-products algorithm.  Students were able to decompose individual products and find the sum.  This made sense to students.  Students were able to connect an area model with the partial-products method.  They started to write number models right next to each partial-product.

Later in the week students were introduced to the lattice method.  This method seemed “fun” for the students, but didn’t make as much sense as the partial-products method.  Students were able draw the boxes and create diagonals to find the product.  Some students had trouble with laying the boxes out before multiplying.

During the last day of the week students were asked to explain in written form how to multiply multi-digit numbers.  Even though all of the students could use the traditional, partial-products and lattice methods, they were stuck for a bit.  Soon, most students started to lean towards using the partial-products method to explain how and why this method works.  I asked one student in particular why it made sense and she said “I can see it visually and in number form.”  Although most students were able to use the other methods effectively they didn’t seem confident enough to explain why the strategies worked.

Students will be expected to multiply multi-digit numbers on the next unit assessment.  The method to multiply these numbers will be determined by the student, but I’m wondering how many will gravitate towards the strategy (not just the process) that they understand.



Mindframes and Teaching

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This last Thursday I was fortunate enough to attend a conference around the topic of visible learning in schools. The conference had so much information.  I had to filter and compartmentalize the discussions and presentation.  One of the discussions revolved around John Hattie’s effect size and how schools can make learning visible in classrooms. The last day was dedicated to organizing a school plan that’ll be carried out through the remainder of the school year.

One of the more memorable pieces of the conference were the discussions that happened between the school teams.  My school sent a team of four teachers and two administrators to this particular conference. Discussing our views on teaching and learning was a powerful experience. Many members of the team don’t regularly work with one another, so meeting to discuss these issues brought about other views as we’re all in different roles . Not everyone thinks the same and each member of the team was willing to hear out different perspectives. As a team, we agreed that our school has some great initiatives happening right now. That affirmation was great to hear, but at the same time, we felt that there are steps we need to make to become better. In order to put these initiatives in place the school has to communicate the importance and reasoning behind these proposed changes.

This brought up another discussion about how change will not happen unless stakeholders are truly committed to the cause. Even if they’re committed, the initiative doesn’t reach its full potential unless the organization and individuals have mindsets that are aligned with the initiative. This type of thinking falls in line with Hattie’s Mindframes for Teaching. Teachers have beliefs that impact their teaching. That belief often stems from a self-developed mindframe. Understanding your own mindframe can help stakeholders better define their own role.  The mindframes are explained in the video below.

All of these mindframes are discussed in Hattie’s Visible Learning book.

Early in September my school was introduced to the idea of teacher mindframes. A staff meeting was designed to have educators analyze Hattie’s mindframes and reflect on their own. We plan on revisiting this topic throughout the school year. Understanding deep-seeded beliefs about our role in education can help bring awareness to how we think.  I believe that thinking impacts instructional decisions that influence student learning.

Exploring Criteria for Success


This past week I’ve been observing how students reflect on their learning. This observation originated from a brief conversation that I had with an administrator about the need for students to be aware of the mastery learning objective. Depending on the lesson, I feel like being aware of the goal upfront is important as students have an understanding of what’s expected. Although posting an objective brings awareness and is easy to check-off during a class walkthrough, it doesn’t necessarily impact student learning.  At the most, posting the objective may direct students to informally question the connections that they’re making in relation to the goal. To ensure that students are making a personal connection to the goal I believe they need to have ample opportunities to reflect on progress made towards the goal.


That reflection process becomes important as students start to recognize their own growth over time. This year I’ve been giving students time to review assessment results and compare their results to specific math standards. In the past students have used math journals and a reflection sheet to document their progress. At this time of the year students are using it every 2-3 weeks and it’s a bit sporadic. I’m trying to become more consistent with giving students time to compare their academic progress to the expected goal. In general, I want students to become more capable of self-assessing their own progress. I believe moving towards a criteria for success model may help.

criteriapicI first heard of criteria for success during a Skillful Teacher class that I took awhile back.  This past year I’ve been experimenting with using it more frequently.  I’ve been finding that the criteria for success communicates what meeting the standard looks like. It also tells students if the product that they created is good enough to meet the standard. I think of it has an expectation gauge. If students can recognize that they’ve met the criteria for success then they’re meeting the minimum expectation for that particular assignment. Josh Hattie has been quoted as saying a visual learning school is “when kids know what success looks like before they start.” See Hattie’s video here for a more in-depth dialogue on his view on criteria for success. My first thought of criteria for success revolves around the idea of rubrics. But it doesn’t end there. A decent rubric can tell students if they’ve produced work that has met the standard. Personally, I feel like a rubric can’t be used for all assignments and projects. A criteria for success can also take the form of a checklist or list that describes the qualities of a proficient project.


Should the criteria for success be used for every lesson? Right now I’m tackling this question. I’m wrestling with it because students complete so many activities and assignments that narrowing it down to just one a seems unmanageable. Also, sometimes students work on projects that last a couple of days. In those cases, does the criteria for success stay the same and do students periodically revisit it accordingly?

I’ve been using criteria for success checklists over the past few days and am analyzing the results. I’m finding that students are intentionally reflecting on whether they’re meeting the posted objectives. Students that analyze their own performance have opportunities to also set goals and move forward. I see potential in using this model as students become aware of their own performance level compared to the standard.


Student Reflections and Assessments


This past week my third grade class took their third unit assessment.  This particular unit focused on computation of single-digit numbers, data analysis and order of operation procedures.  While grading the assessments I started to identify a few patterns in the student responses.  Specific problems were missed more often than others.  This isn’t an anomaly on assessments, but these particular problems stood out.  One skill area that seemed to jump out to me dealt with the skills of being able to identify the median, mode and range of a set of data.  These skills were introduced during the first few weeks of school and the class hasn’t revisited them in some time.  Also, I found that students were having trouble identifying the differences between factors and multiples. Some of the student responses mixed up the terms while others seemed like guesses. Both of these skill are necessary moving forward as the third grade class explores prime and composite numbers next.  A colleague and I and came up with a limited list of reasons why we thought the problems were missed.

1.) Students aren’t yet able to apply their understanding of the skill

2.) The question on the test was confusing

3.) Students made a simple mistake

Optimistically, I’d like to say that most of the mistakes fall into category two or three. I don’t think this was the case with this particular assessment.  After looking over the class results I concluded that most students that missed skill-associated problems fell into category one.  In addition to not grasping a full understanding, I felt like students were not given enough time to practice the newly learned concepts.

I believe students should be given additional opportunities to show understanding.  Coming from that thought line, I decided to have students reflect on their assessment results in their math journal.  I’ve done this in the past but I wanted to also include an addition to the process.

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After completing the page above students reflected on their performance in relation to the expectation. Students were then given a list of four problems.  The problems were similar to the most missed skills on the assessment.  Students were asked to pick three of the problems to complete.  Students were encouraged to pick skills that were missed or topics that they felt needed strengthening.

After both sheets were completed, students brought their math journals up to me and we had a brief 1:1 conference. This time is so valuable. The student and I identified skill areas that showcased strengths and areas that needed strengthening.  We then reviewed the responses to the questions on the reflection sheet.  I spent around 2-3 minutes with each student.

Students were then asked to work independently on another assignment that I planned for the day.  Overall, I thought this reflection process has helped students become self-assessors.  Students have a better understanding of their own skill level in relation to the expectation.  I plan on using this strategy a bit more as the year progresses.

Computation and a Growth Mindset

Encouraging growth

This past week my third grade class started to use multiplication and division strategies to solve world problems.  They’ve used arrays before and are now applying their understanding of multiplication and division.  That practical application can be a challenge for some and I feel like it’s partially because students aren’t yet fluent with their facts. In an effort to collect a bit more data on what particular facts students were struggling with I gave the class a short 17 question Kahoot! quiz. The quiz was related to multiplication and division facts.

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In the past I’ve used Kahoot to review concepts and skills in a game-based format.  I’d estimate that the majority of Kahoot quizzes have a limited amount of time and points are scored.  This is fine and I’m not against using this format, but it didn’t work for my purpose.  I wanted students to take their time and diligently pick an answer.  So, each student grabbed an iPad and completed the quiz on Wednesday.  It took about five minutes or so and students reflected on how they thought they did on the quiz.  The class then reviewed multiplications strategies and connected how multiplication and division are connected.  The homework for that evening also reinforced some of the computation strategies that we’ve been practicing in class.

The next day students were given the same Kahoot quiz.  The question order was changed and students were allowed to take as much time as needed.  I printed out both the first and second quiz results for the students to see the difference between the scores.  Students glued both sheets in their math journal and were asked to respond to the journal prompt below.

“Was there a difference between your first and second scores?  If so, why do you think the results changed?”

Some of the responses are below.

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As you can see, some of the students are connecting the idea that improvement, effort, and growth is important.  I’d say this is a move in the right direction.  This year my school is emphasizing the idea of Dweck’s growth mindset.  Teachers are encouraged to use terms like persevere, not yet, and effort fairly frequently.  Students are hearing this type of speak and even being asked by administrators questions related to having a growth mindset.  By doing this activity I feel like students are starting to internalize that effective effort helps produce better results.  Instead of just talking about growth mindset and the benefits, students need to be able to make a meaningful connection between effort and achievement. I feel like preaching that effort alone will reap success isn’t the whole story.  I feel like students need to be able to document their journey and internalize the connections. I’m hoping to continue to use these types types of reflection activities throughout the year.