Learning Sync

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One of my classes finished up a unit on multiplication strategies last week.  Before the test I usually have students review a study guide and I meet with small groups to determine if certain skills/concepts need reviewing.  This time I changed up the schedule.  Instead of a study guide I went the route of using a brain dump.

I’ve heard of the term brain dump before, but didn’t really have a way to organize and use it effectively in the classroom setting.  I learned how to refine and apply it based on the examples in the book Powerful Teaching.  I thought I’d try it out with one class, see how it went and then possibly use it with other classes.  If all went well then I’d move to

So I gave each student a prompt.  The prompt was “write everything that you know about multiplication strategies.”  It was in 12 point font at the top of a 8 x 11 sized paper. Below the prompt was a massive canyon of space.  After I passed out the papers I had about a third of my class raise their hands.  Apparently they weren’t used to this type of prompt or activity.  I told the students that I’d answer questions about the prompt, but wouldn’t give them any examples.  Some students were confused at first.  I told them that they would have five minutes to complete the task and drawings to show strategies were certainly okay.  A few students gave sighs of relief.  I started the timer and the students were off to writing.

I walked around the room and observed the visual models and strategies that were filling up the white space on the students’ papers.  After the time was over I randomly grouped the students in pairs and they shared their individual strategies.  I used the questions directly from the book p. 58.

Is there anything in common that both of us wrote down?

Is there anything new that neither of use wrote down?

Why do you think you remembered what you did?

The entire experience took about 25 minutes and it was worthwhile.  Afterwards, students asked about being able to use this activity for our next unit.  I think it worked well with multiplication strategies, but I’m a bit unsure of other concepts.  I’m definitely willing to try it out though.  The class decided to change the name.  We came up with a couple names and then I mentioned Learning Sync from the book and it stuck.

Nice to Meet You Area Model

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This week my second grade students have been exploring multiplication strategies.  We started off early in the year looking at arrays and using doubling strategies.  Then we moved to helper facts.  These are still used to this day, but we introduced a new tool this week.  Enter the area model.  Hello!

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Students transitioned from arrays to squares, but didn’t sit at that spot long.  Through the area model, students take apart numbers and partition (yes, we say partition at second grade) the rectangle into parts.  Each part is a partial product.

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I’m fortunate in my position to see this strategy used at multiple grade levels.  The rectangle evolves over time.  As students progress, I find that place value and advanced decomposing strategies become more prevalent.  You can learn quite a bit about a student’s understanding by checking out their math work with an area model.  How they split up the numbers can also tell a story.  Why did they split up the rectangle that way?

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I find quite a bit of value in using this strategy.  For one, it doesn’t immediately move students towards the standard algorithm and it helps build/show conceptual understandings.  My 2-6th grade math students use it in a variety of capacities. My 5th grade crew has recently been using them to multiply fractions. Short story: It makes an appearance at every grade level.  It’s also a a fairly smooth transition to using the partial-products strategy.

Even though it’s a useful resource, I find there are a a couple things that irk me about using this tool.  Sometimes organization skills can hamper the effectiveness of drawing and organizing.  I’ve had more than a handful of students draw boxes that overlap or numbers that might not be decomposed correctly.  Also, it’s not to scale, but that’s not a game changer for me.

As students progress through elementary school they encounter a variety of math tools and strategies.  Manipulatives are generally used to help students build a better understanding of math concepts. The CRA model is often emphasized at this level. Many tools are brought out to help fill gaps and others are continually used.  At some point, I’m assuming the my students will rely on the standard algorithm to quickly multiply numbers (if they don’t have a calculator handy).  They probably won’t understand why the algorithm works, but it just does.  The area model shows multiplication in a concrete way.  Don’t get me started on lattice.

Surface Area and Improvements

Last year I taught a lesson on surface area that bombed.  I thought it’d be great to have students measure the surface area of a state using a scale model.  This task was found in my course adopted resource pack. Looking back, it wasn’t a bad idea or problem but the execution was far less than stellar.  The problem asked students to find the surface area of the state of Nevada.  They were given a model and a scale at the bottom.

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The class completed this mostly in whole group (which in hindsight was not the greatest idea).  I asked students to use the scale to find the surface area.  Students used rulers and decided to find the area by dividing the shape into one rectangle and one triangle.  After giving students about 10 minutes I surveyed the class and the answers were all over the board. Some debated on the word “approximate” as the class was asked to find the approximate surface area.  Other students thought the 0-100 km was a guideline and could be rounded. While others decided to neglect the missing piece near the southern border of the state.  Needless to say it didn’t go as well as planned.  Looking back, one of the problems was that this activity was completed whole group.  Students didn’t get time to discuss with each other what or how to measure.  There wasn’t a determination of what to do with the missing piece in the south and how to divide up the state.  The class eventually came to a consensus that there was one right answer and we moved on.  I put a note in my planner to do things differently next year.


So it is now next year (2020) and I have a different class.  This year I gave the same problem, but did things a bit differently.  I first front-loaded information about the state itself as a whole class discussion.  The class discussed the shape of Nevada and how it’s not exactly one rectangle and one triangle.  I reinforced that we can’t just neglect the small corner of Nevada.  It may be helpful to find that area as well.  Students were then randomly selected and placed in small groups of 2-3 students per group.  I asked the students what was meant by the scale in the bottom left and how they could use it to help them find the area.  Student groups had time to discuss and report out how they would use it.  Some students even found that the 0-100 km was actually 1 centimeter. I then gave each group a ruler/straightedge to help construct shapes within the state itself. Students had approximately 15-20 minutes to discuss and find the surface area using the tools that they were provided.  Students were busy slicing up the state and using a straightedge to find the approximate surface area.

The class then came back as a whole and each group submitted a response.  I received all the responses and students were given time to think about their submission and possibly make a change.  It’s interesting how peer pressure and consensus will sometimes make you second guess a decision.  In this case students mostly received affirmation and there was justification that came along with that decision.  All but one group was in the ballpark and that group didn’t initially convert the scale.  There answer ended up being extremely small compared to others.  Some of the groups decomposed like this:

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The majority of the class was within the approximate range and it was a productive discussion.  If you’re wondering, the surface area is approximately 278,000 square kilometers.  So now you can win a trivia contest.


I put a note in my planner to use this method next year.  Last year it bombed and this year was much better. Part of teaching is improving your craft and I had more than a couple pieces of humble pie last year. I tend to hear the phrase best practice thrown around in the field of education. I’m more of the mindset of emphasizing better practices and looking forward to tweaking this even more to make it a better experience next year.

Exploring Perimeter

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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.

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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.

Class-generated Quizzes

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One of my classes explored multiplication, factors, multiples and arrays in December. Students solved problems involving using different multiplication strategies and we thoroughly discussed how arrays can be arranged using the rows and columns as factors.  A unit assessment is scheduled for January so students were given a task before break.  Students were asked to create a problem involving multiplication. They had to write out the problem, provide three close but incorrect answers, and one correct answer.  Students could use dice or a random number generator to create the problem.  Most opted to create an original problem.

Students picked problems involving arrays, while others decided to add to the challenge and have students identify factors and distinguish between the product and factors.  Other students created square array problems.  I found that in the creation process many students had to erase their model and start over.  They had to be clear and I reiterated that everyone in the class would need to be able to clearly distinguish the rows, columns and total of an array.  Students realized that the array had to be in the form of a rectangle or square and some used a ruler for precision purposes.  Yay!  Others didn’t. I collected all of the potential questions and answers and brought them home over winter break.  I didn’t look at them again for another two weeks.  I

Yesterday evening I took pictures of the drawings with my iPad and inserted each question into a quiz.  It didn’t take as long as I originally thought to put all the questions and pictures into the quiz.  Feel free to access the actual quiz here.

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Today I paired students up and they took the class quiz.  Students were stoked to see their question on the quiz and the excitement was contagious.   It took the students around 15-20 minutes to complete the quiz and the class reviewed each question together.  The author of each question revealed themselves as we went through the questions and drawings.  Students gave feedback on the questions and I was impressed with how close the incorrect answers were to the actual solutions.   They wanted to make sure the students actually read the questions carefully.  Good call!

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In the future I’d like to add more topics to the quiz.  Adding variety will also give students more options to review the topics discussed in class.  I feel like this idea has legs and I might use it again later in the year.

Pixel Reflections

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It’s nearing the end of 2019.  It’s hard to believe, but in just a few days it’ll be 2020.  Near the end of the year I like to take stock and think about last year and what ended up being successful and what didn’t.  Last year I came across an image on Twitter that showed a different way to reflect on the year.  Not sure where I exactly found it, but I believe the image was pulled from this site.  In 2019 I wanted to purposefully reflect more throughout the year.  I decided to jump on this trend of using highlighters, a notebook and pixels to analyze how I felt throughout the year.  I ended up creating my own sheet with rectangles modeled after some of the pictures that I came across.  I wanted to originally use squares, but that didn’t happen when I printed it to fit to the page so I just went with it.

Highlight per day

I tried to stay consistent with filling out the sheet daily and at the same time.  That didn’t happen every time, but I became better as 2019 rolled forward. As the year progressed I started to notice a few trends in my own analysis of how a day went.  I became more clear on what events/activities/notices indicated an amazing day compared to a frustrated day.  The list below is certainly not all-encompassing and isn’t perfect, but used as general guidelines as I filled out each rectangle.


Amazing (orange) – Feel well-rested, vacation time, visits with family, able to get outside in the sun, time to read, drinking my coffee slowly,

Really good (purple) – Feel productive, time to plan, able to get outside, exercised, get to bed on time

Normal (blue) – Feel good, able to accomplish what’s needed for that day.  Feeling a bit tired but productive, sleep patterns are a bit irregular,

Exhausted (yellow) Lack of sleep, too much or too little coffee, traveling day, didn’t exercise, wasn’t able to get outside, too much work, evaluations, not feeling as productive, starting to feel sick

Frustrated (green) – Sick, bad news about family, medical issues, rejection letters

Sad (red) – I ended up not using this one and probably won’t in 2020


Moving forward, I’m thinking of continuing this process in 2020.  I have my highlighters ready I think there’s power in being able to reflect and categorize how the days make you feel.  Taking the time to write it down has been a valuable experience.  I also have to be a more critical in how I categorize a day.  Everyday isn’t going to be perfect.  I need to be reasonable with expectations.  For example, does getting bad medical news for 5 minutes negate having a terrific day? Not sure and I don’t have an answer here.  Looking at the data is interesting as I can make generalizations, but my takeaway is the time spent being mindful of how daily events impact my perspective.

Here’s to 2020!

Distributive Property Discussions

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My fifth grade class is in the middle of a unit on pre-algebra concepts.  We explored the different associative, commutative and distributive properties earlier in the week.  Students were able to use the first two with modest success, but the distributive property was causing some issues.  I believe some of the reason is because students were confused with what the parentheses meant, while others needed a visual model to make a better connection.

The class reviewed a few different examples and we went back to a concrete representation.  I find this is the place where solid understanding is developed before we  move to more abstract models.

Students have been use to using base-ten blocks, counters and unifix cubes to put together and take apart numbers.  Students were asked to use cubes to show an understanding of the distributive property.  They used a dice to create a multiplication problem and then split it into two parts.  They then wrote on the desks (who doesn’t love that?) to show multiple number models to indicate the total.

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This student didn’t show the partition, but displayed the different number models

One issue was trying to figure out how to divide or create the partition.  Some students used dice to indicate where to split the model.

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I appreciate how this model shows the different representations

From here, students transitioned to problems involving larger numbers and in an abstract form.  They were more successful this time around.  Students then worked in groups to complete this OpenMiddle problem.  They worked in this task for about 15 minutes using whiteboards in the process.  This was a quality activity that has students trying out multiple numbers to make the equation work.

 

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I’m looking forward to revisiting the distributive property when schools starts back up in January 2020.


Friday was our last day of school for about two weeks.  We’re officially on winter break, but it doesn’t feel like it yet.  I’m sure it’ll sink in on Monday when my alarm clock doesn’t go off at the normal time.