Tag Archives: phases of the moon

Agenda: Embolden Your Inner Mathematician (10.24.18) Week 7

Week Seven of Embolden Your Inner Mathematician

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

Course Goals:
At the end of the semester, teacher-learners should be able to say:

  • I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
  • I can exercise mathematical flexibility to show what I know in more than one way.
  • I can make sense of tasks and persevere in solving them.

Today’s Goals

At the end of this session, teacher-learners should be able to say:

  • I can implement tasks that promote reasoning and problem solving. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them. (#SMP-1)

From Principles to Actions: Ensuring Mathematical Success for All

Implement tasks that promote reasoning and problem-solving: Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Learning Progressions for today’s goals:

  • I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them.

Tasks:

  • Poetry and watercolor (a.k.a., the beauty of mathematics)
  • Phases of the moon (See slide deck)

What the research says:

From Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5

In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners.  The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy.(Smith, 4 pag.)

Equitable teaching of mathematics focuses on going deep with mathematics, including developing a deep understanding of computational procedures and other mathematical rules, formulas, and facts. When students learn procedures with understanding, they are then able to use and apply those procedures in solving problems. When students learn procedures as steps to be memorized without strong links to conceptual understanding, they are limited in their ability to use the procedure. (Smith, 93 pag.)

Evidence of work and thinking:

Slide deck:

[Cross posted at Sum it up and  Multiply it out]


Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.

FAAR – Connecting Peer Observations to Learning for Life

As part of our formative Faculty Assessment and Annual Review (FAAR) plan, we engage in a process of peer observations. We also have a new Learning for Life vision statement.  With his permission, I am publishing my peer observation of my friend and colleague, BC.  As I reviewed my notes taken during his class, I realized that he, in this one lesson,  seized the challenges and opportunities of the 21st century by promoting all six essential actions called for in our Learning for Life vision statement.

____________________

Focus of the observation (if any) and class context:

Algebra I team’s lesson study on Phases of the Moon.

Teaching methods and practices observed (strength-based)/Indicators of student learning.

  •   Integrated Studies
  •   Project-based Learning
  •   Learning Spaces
  •   Teachers working in teams
  •   Assessment and feedback
  •   Content that connects us to the larger world and the world to us.

Assessment and feedback, Teachers working in team, Project-based learning
BC uses inquiry to engage our learners in the context of the lesson.  He solicits prior knowledge to have learners take an active role in driving the lesson.

Integrated studies, Teachers working in teams, Content that connects us
CB used multi-media, a video from the History Channel (http://www.youtube.com/watch?v=nXseTWTZlks), to confirm the students’ prior knowledge and introduce necessary vocabulary not discussed by the students.

Teachers working in teams
In the face of no network access, BC calmly transitioned to the team’s Plan B.  Rather than using  the resources for Phases of the Moon on our Google Site, he used a Keynote presentation.  This modeled for our learners that we continue to learn; we do not stop because “we have no Internet.”

Teachers working in teams, Content that connects us, Learning spaces
While the students did not leave the classroom, they definitely utilized spaces.  The students used their MacBooks to find answers and questions concerning the moon.  CB addressed visual and kinesthetic learning styles by having the learners graph the illumination of the moon over the days of a month.

[Note:  Video evidence inserted here.¹  ]

Some questions to consider:

Did you like teaching graph interpretation this way?
How can we have more classes like this?
Where do we turn for more resources to find integrate lessons that engage our students and connect their learning to many disciplines?

What did I observe that I would like to incorporate into my own teaching/Other notes:

This is an awkward question since we built the lesson together.  We observed each other; we all went to DD’s class as a team.  DD and I went to BC’s class while WB was teaching Algebra II.  It is difficult to say what I would like to incorporate since we observed, learned, and tweaked the lesson as it was delivered to all Algebra I learners.

____________________

Our new technology made this observation a richer experience from my team.  I used my iPhone (forgot my Flip camera) to collect video snippets of examples so that we could review and analyze what happened during class.  I used my MacBook with Pages to import the video into my notes in class during the observation.  My team and I had my raw notes from the observation right after class.  (See my raw notes from the observation at the end of this post.)

If a picture is worth 1000 words, what is video worth?

  • How does technology help us learn?
  • Is it “good enough” to do things the way we’ve always done them?
  • Do our learners need different than what we need?
  • How are we practicing?
  • What one thing could you explore, experiment with, and practice that would blend learning?

Our challenge as learners is to learn by doing, to practice new techniques, to use technology do things better, and to make connections.  The video artifacts in this observation allowed us to “view” parts of the lesson over and over.  The video doesn’t just make the observation different; it makes it better.  We have the opportunity to see what we might otherwise have missed.  We have “replay” to continue to question and observe.

As a learner, I had the opportunity to blend my learning.  I observed a colleague deliver a common lesson designed by our team.  I practiced with technology by integrating the use of video into my note taking.  While I don’t have as many written notes, the video tells the story is a way that my written notes could never tell.  As a team, we have evidence that we are taking steps to transform our traditional classes in order to align learning with our vision.  We had the opportunity to learn together as we revised and refined the lesson between “shows.”

____________________

¹  School policy prevents me from showing you the video of the learning that occurred during this lesson. [Awaiting permission.]

Phases of the Moon…Middle School Connections with Trigonometry and Science

My learners struggle to read and interpret graphs for meaning.  It makes me wonder…How are we teaching them to read and interpret graphs? When our learners get to precalculus, are they adept at reading graphs for meaning so that they can concentrate on mathematical modeling?  Wouldn’t it be advantageous for a new-to-precalculus or new-to-physics learner to already have a context with which to identify when presented with periodic data?

What if we integrated the ideas of plotting points and interpreting graphs with some earth science?  We are not going to have middle school students model this data, but we are going to have them interpret the data and label the graph.  We are going to expect them to connect the math and the science.  I’m pretty sure that there’s a great connection to periodic poetry too.

I believe that somewhere in 6th or 7th grade science we teach our learners about the phases of the moon.  The geometry is awsome.  (Take the Lunar Cycle Challenge.)  In pre-algebra and algebra, we work on plotting points on the Cartesian coordinate plane.  What if we practiced plotting points and pattern-finding by plotting real data?

In terms of diagonstic assessment, ask:

  1. Can you name the 8 traditionally recognized phases of the moon?  
    Then wait…6th and 7th graders know this, which means that older learners will need a little time for recall.  Wait time is critical.  Full moon and blue moon almost always occur.  Generally the vocabulary will come back to any group of learners.  This is a great place to integrate teachnology.  Let them find the answers.
  2. Is there an order to these phases?  Are there any patterns?
    Ask your learners to sketch a graph of what they have described.  You might want to check their understanding of the vocabulary and the images.
  3. Are the phases identifiable when not in order?
    To reinforce the geometry, you can use the Lunar Phase Quizzer.

 For the lesson, ask

  1. Can we find data for the percent of the moon showing every day?
  2. If we plot this data, will there be a pattern?
  3. How much data should we plot to see the pattern?

Let’s look at the data for January and February 2011 from the United States Naval Observatory.

Questions to ask to check for numeracy, geometry, and understanding of the vocabulary:

  1. Is the moon waxing or waning on January 1, 2011?  How do you know?
  2. Is the moon crescent or gibbous on January 1, 2011?  How do you know?
  3. Sketch the moon’s illumination on January 1, 2011.  Check using Today’s Moon Phase.

Don’t you think that these are great TI-Navigator formative assessment questions?  You can repeat those three questions about any date in January and/or February until you have consensus.

Let’s discover if there is a visual pattern in this data.

This graph always gets a big WOW! if you are using TI-Nspire and can see the points animate into place.  Questions to ask to check for graphical interpretation and connection between the graph and the earth science:

  • When was the full moon in January of 2011?  How do you know?
  • When was the new moon in January of 2011?  How do you know?
  • When was the first quarter moon in January of 2011? … the third quarter moon? How do you know?

Again, you can check using Today’s Moon Phase.

Deeper questions connecting to writing and interpreting inequalities with connections to more vocabulary:

  • Name one day in January of 2011 that the moon was waxing?… waning? … crescent? … gibbous?  How do you know?
  • Over what days in January of 2011 was the moon a waxing crescent moon? … waning gibbous?  etc.

Pretty good stuff if your students are struggling with writing inequalities, particularly compound inequalities.

Now for patterning…

  • Will February’s data look like January’s data?
  • How are these data similar?  How are these data different? 
  • What would the graph look like if we graphed the percent of the moon showing vs. the number of days since December 21, 2010?  (In other words, February 1 would be day 32.)  Would the pattern continue?

How cool is that?

  • Can you identify all of the above questions for February?
  • Can you predict the day of the full moon for March?

Please use Today’s Moon Phase to check!

Here are the burning questions for me…

  • Can middle school students plot these points?
  • Will they find connections between the math and the science?
  • Will these connections help them understand how to interpret graphs?
  • Will these connections help them understand the moon and its phases?

If  our students would start off in trigonometry and physics understanding the connections between the math and science and could interpret what they see, would they be more likely to find success modeling the data?

If you teach trigonometry or physics, there is a clear path from the graphical interpretation to finding a function that models this data.

TI-Nspire Resource Files
  • Phases of the Moon Diagnostic Assessment
  • Phases of the Moon PublishView document
  • Phases of the Moon Data .tns file

From my webpage….

During every month, the moon seems to “change” its shape and size from a slim crescent to a full circle. When the moon is almost on a line between the earth and sun, its dark side is turned toward the earthThe moon’s cycle is a continuous process, there are eight distinct, traditionally recognized stages, called phases, which are ordinarily adequate to designate both the degree to which the Moon is illuminated and the geometric appearance of the illuminated part, to the extent that Moon visibility has relevance to everyday human activities.

In this activity, we will investigate the fraction of the moon seen each day for a month and then for a year.

  1. Identify the eight traditionally recognized stages of the moon’s cycle.
  2. Find the approximate period of the moon’s cycle.
  3. Extract the fraction of the moon showing from the United States Naval Observatory, for the days of the year.
  4. Set up a scatter plot of the fraction of the Moon showing in January versus the day of the year.
  5. From the data or the graph, determine the amplitude and the vertical translation.
  6. Find the cosine function that fits this data.  Identify the phase shift for this function.
  7. Find the sine function that fits this data.  Identify the phase shift for this function.
  8. Edit the data to graph the fraction of the moon showing in January and February versus the day of the year.
  9. How well do your functions fit this extended data?
  10. Determine which day of the year corresponds to today’s date.  Predict the phase of tonight’s moon.
  11. Check the accuracy of your prediction using Today’s Moon Phase.
  12. Take the Lunar Cycle Challenge.