Put it in Perspective

12 days. In 12 days my students will cross the threshold of my classroom. In 12 days dozens of eyes will be waiting for me to guide them and instruct them. In 12 days my class will begin engaging in the messy business of learning. But where do I begin?

Each summer I use my time to plan and prepare, designing and modifying both lessons and activities. Having been away at overnight camp this summer, aside from reading, I’ve done little to get ready for those first few days.  I now find myself 12 days before the start of school struggling to get started. There are so many things I want to do differently and focusing on all of them simultaneously is absolutely impossible. 

I can’t help wonder if selecting only one goal is a failure of sorts. Why does it feel like if I want to focus on that goal there is a trade-off, like I need to sacrifice my vision for my classroom? My students are not ready for my ideal and time is a gigantic stumbling block. I cannot possibly do it all right now. And that feeling sucks. 

So now as I sit at the airport waiting for a flight, I go through my mental checklist and prioritize. I think my first goal will be developing a greater number sense in my students. I hope I effectively design and execute lessons or activities that lead my students towards that goal, all the while maintaining the integrity of my vision. I hope I can put everything into perspective and take comfort in it. The achievement of that goal means that I am one step closer to my ideal. 

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Comfortable with Uncomfortable

Division with decimals, particularly decimal divisors has always been a challenging topic for me to wrap my head around. Based on my own procedural understanding of this concept, it was impossible for me to conceive of teaching division with decimals for understanding. Then, Kristin Gray posted this exploration of decimal division. I read the post and was inspired. The closed mindset voice in my head screamed, “Impossible. There is no way that my students could ever construct responses like that!” Kristin’s post was quickly pushed to the far reaches of my mind.

Fast forward one week to the evening I posted this tweet.

A short time later I had my first response. From Kristin, nonetheless! The conversation pushed me out of my comfort zone and forced me to struggle with my own conceptual understanding, particularly when it came to decimal divisors.

Forty-five minutes later minutes…

The next morning, with only the remnants of the trepidation felt a week ago, and armed with a greater understanding of division with decimal divisors, I kicked off our division unit. Posed to my fifth graders was a question similar to that posted on Kristin’s blog. My students were instructed to use a drawing to support their responses. As everyone buckled down and delved into the problem, I kept my fingers crossed.

IMG_9012 IMG_9013 IMG_9014 IMG_9015 IMG_9016 IMG_9019 IMG_9022 IMG_9021 IMG_9020 IMG_9018 IMG_9017  IMG_9022

Nothing. But. Amazing.

Of course, some students did struggle to make sense of the problem and I look forward excitedly to see how their understanding develops through our exploration of division with decimals. I look forward to watching their uncomfortable become comfortable, the way mine did.

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It Doesn’t Have to Be All or Nothing

October 29, 2014. That was the last time I posted to my blog.  Somewhere along the way I’ve imposed upon myself this “rule” that a post must be lengthy, detailed, and eloquent. There must be something spectacular to share or a great epiphany that must be shouted from the rooftops. Do you hear my insecurities and self-consciousness creeping in? Then, there is my perfectionist, type-A personality. Unless a sentence and those preceding it are exactly the way I want them, composing a new one is out of the question. Even a “quick” thought or idea to share translates into to my self-imposed “rule” about blogging and makes a post seem cumbersome. Add to the equation a full time teaching position (I teach two different grade levels and serve as a coach/specialist for grades 3-5) and a family with four children, time has become a valuable commodity and time to blog a supreme luxury. Blogging has become “all” or “nothing”.

But I miss blogging and the opportunity for reflection. And the timing for a new series of missions and prompts from Exploring the MTBoS could not be more welcome. The first mission; read a blog post, comment on it and post a comment here. Scrolling through my Feedly for inspiration, the title “Sometimes, Life Just Gets in the Way” grabbed my attention. So I clicked on the article, read Lisa’s post, and was reminded not only of why I blog, but that being selfish also means being selfless. Though enthused about rekindling my blog, the reality for me is that composing a post seems like a daunting task (don’t even ask how long to took to write this post!).

Exiting the Grand Ballroom at NCTM Boston following Dan Meyer’s presentation on mathematical modeling, I asked one of my colleagues for his thoughts. He cited the presentation as interesting, but felt there was nothing that he could incorporate into his classroom. “Of course, you can!” I retorted. “You don’t need to do all of it, like Dan said. If you use the textbook word problems, at least ask your students what variables might affect the solution. Just start the conversation. Let them think about it.”

Then it hit me. Perhaps I should take my own advice. It doesn’t have to be “all or nothing”. It’s simply about starting the conversation, expanding your comfort zone, and letting go.    And it’s not only for the classroom. It’s for life.

Though I might not be there yet, I am taking baby-steps to get there. And it’s starting with this blog post.

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Counting By, Number Lines and Decimals

The concept of Counting Circles was introduced to me by Sadie, either during TMC or Global Math (thought, I’m not sure exactly). Jessica Shumway’s book, Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3, taught me a little more. Last year, I found a template here to use for counting routines. Eagerly I printed the template on card stock and laminated them, all ready for use in my classroom. But, they sat on the shelf. It took me quite a while to integrate them into my classroom. The perfect opportunity came when my 5th graders began their exploration of rounding decimal numbers.

Counting by tenths or hundredths, after all, is a prerequisite skill for rounding to the nearest tenth or hundredth. Right before our break, we compared decimals by creating a huge number line.

IMG_7295.JPGThat work led us directly into counting forwards by one-tenth starting at 0.6. Each student used a dry erase marker to record his or her counting on the template. When reviewing the counting, the numbers were read aloud by the students (which gave me a chance to quickly assess how accurately students can read decimal numbers), and were recorded on a number line. My students moved seamlessly through the “count by one-tenth” examples when the only digit was in the tenths place, easily regrouping ten-tenths as 1 whole. We then started counting by one-tenth starting at 4.28. That was definitely trickier for some, who thought that 4.29 was one-tenth higher. But as soon as I asked “Is 4.29 one-tenth more or one-hundredth more than 4.28? Why?”,  those students realized that they increased the value of the wrong digit. We did some additional practice counting both forwards and backwards by tenths and hundredths (next week I would like to count by 0.2 and 0.02).IMG_7318To transition into the rounding portion of the lesson, my students wrote a number on their whiteboards between 0.8 and 0.9. Applying what they already know about rounding whole numbers, I asked students to go to one side of the room if their number rounded to 0.8 and to the other if their number rounded to 0.9. Students on each side of the room discussed why they were standing where they were.  Of course, the prevailing explanation  was a recitation rounding rules. But, I pressed my students to explain why the rules work. With some guidance, they determined that since 0.85 is halfway between 0.8 and 0.9, numbers greater than or equal to 0.85 would round to 0.9 and any number less than 0.85 would round to 0.8. After a few more practice examples, we repeated the activity again, this time writing numbers between 0.88 and 0.89, and rounded them to the nearest hundredth. The exploration continued when I asked students to again go to one side of  the room if their number rounded to 0.8 and to the other if their number rounded to 0.9.

After a few seconds one student cried out, “But we are all going to be on this [0.9] side!”

“Why?” I asked.

“Because all of our numbers are greater than 0.85, so we all round to 0.9.”

To challenge their thinking even further, the students were asked to write numbers that round to a particular place. Some of the examples are pictured below. As students shared their numbers, they were recorded on the board and the reasonableness of each was determined.

IMG_7317.JPGThe lesson continued with rounding numbers to a particular place. My students had to prove their solution by using a number line. I quickly assessed their understanding with an exit card. Students were asked to write two numbers, one greater than 0.5 and one less than 0.5, that round to 0.5. That card gave me valuable insight to their learning.

While placing numbers on the number line was challenging for some, the lesson was an overall success! With more practice counting by tenths, hundredths, or even thousandths, students will gain greater confidence and comfort with decimals.




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How Much is That?

How Much is That? is an activity I created for the 4th graders studying money. Students roll the dice to determine the number of quarters, dimes, nickels and pennies. The total value of all of the coins is then calculated. The same coins are then used to make different $1.00 combinations.

It was interesting to see the strategies used to find the total value of the coins. A handful of students drew each of the coins and then used the drawing to find the total value (i.e. circling coins that make $1.00). Most used the standard algorithm. One student employed a slightly different approach in her solution, first chunking coins together (i.e. the quarters with the dimes and the nickels with the pennies) before finding the total value. She then went on to justify her work by recording the totals for each type of coin.

IMG_7276Reflecting on that particular lesson nearly 2 weeks ago (it’s been a bit hectic with all of the Jewish holidays ), I started to wonder whether or not this student would have applied the same strategy if the value of her quarters was $0.75, $1.25 or $1.75. My guess is yes! This student was one of the few who demonstrated flexibility, embraced the openness of the $1.00 question, and persevered to find multiple solutions based on her coins. (There were additional solutions on a second whiteboard.)

IMG_7277Most students were entirely perplexed by the openness, uncomfortable with finding multiple solutions. Isn’t the question answered when one solution is found? With some encouragement and guidance from the classroom teacher, myself, and several successful classmates, most students were able to find multiple solutions.

It’s definitely time for more open-ended questions in this classroom!






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On Your Mark, Get Set…

One of the crazy things about me is that until all of the organizational components of the school year are addressed, it is impossible for me to prepare for those first few days of school. My first priority is always a plan book. Finding one that suits my schedule and needs has been impossible, so last year I created my own. This year’s version is similar to last’s, but has some awesome modification. After perusing the internet and Pinterest, I improved my monthly calendar, refined the “List” spaces, specified “Notes” sections, and created a pocket folder. When all was printed out, my book and I headed to Office Depot for binding (with a clear plastic cover and black back page).

Tired of the chevron pattern used in my previous book, I opted for quatrefoil. I am quite obsessed with this repetitive pattern that is available in a host of bright colors. Fortunately, I will teach two consecutive math periods in the same classroom for the first time in 6 years, which means decorating. And that means there will be lots of quatrefoil! (Stay tuned for a classroom tour!)

IMG_7019 The first section of my book is “Lesson”.  Supplementing the standard lesson plan pages are “Getting Ready” pages (new this year!). Often I find content on blogs or websites that I want to refer back to as the summer ends and preparation for the new year begins. “Planning Notes” pages provide space for me to jot down the tasks, activities, or random thoughts I’ve gathered along the way, as well as help me direct those thoughts towards a particular grade level.


Space to plan for the beginning of the year for my 5th and 6th grade math classes.

I’m a huge fan of checklists. There is something very gratifying about placing a neat check mark in the small little box alongside a thought. All of the lists in my plan book, therefore are checklist templates. Some of the new lists  that I designed are dedicated to preparing my classroom and for the first few days of school. There are handouts to print and posters to laminate, supplies to gather and decor to hang. I love having one place to record all that needs to be done. It sure beats random scraps of paper and post-it notes scattered about the house. And, when next summer rolls around, I will have a list to work off of.


Space to list what tasks or handouts need to be printed, laminated and/or copied.


Lists to keep on top of everything needed to get my classroom set up, including any organization of the room or supplies needed.

My lesson plan pages are almost identical to last year’s. On the left-hand side there are spaces to write my 5th grade advanced math and 6th grade math plans, and a spot for planning notes. I’ve used that space in the past to jot down important information for upcoming lessons or notes for the following week.

On the right-hand side there are spaces for my math coaching responsibilities (i.e. write notes, brainstorm tasks, reflect) and of course, checklists. Last year the “To Do List” on the right ran the length of the page. Since most of my “To Do’s” referenced printing, copying and/or laminating, this year I decided on two separate lists.


Lesson plans for 5th and 6th grade are on the left-hand side and math coaching (and lists to keep on top of things) on the right.


The second section of my plan book is “Calendar”. Each month in the calendar is now a two-page spread (as opposed to the two months per page). I always wrote in all of the important meetings, closures, events, and holidays. Except last year. So this year, I opted to type all of those dates directly on to the calendar. Definitely smarter (and neater)!


The monthly calendar has important dates included.

To encourage myself think about planning more broadly, I added some “Year at a Glance” pages.


There are Year at a Glance pages for my grade 5, grade 6 and math coaching responsibilities.

The final section in my book is “Notes”. In addition to general “Notes” pages, I added identified some of them for scheduling (i.e. to keep track students in my Organizational Skills groups, math times in grades 3-5), meetings, and students.


I can keep track of scheduling changes and meetings here.

My favorite addition to my book is my double-sided pocket folder made from 3 sheets of paper and joined together by some clear packing tape.

IMG_7026.JPGThough the entire process took a bazillion hours due to computer crashing, images not cooperating, and printer issues, I am very pleased with the results and ready to get planning!


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Let’s Rock and Roll!

Practicing reading and writing decimal numbers can be a bit monotonous. So, why not spice it up with some dice?

20140512-165523.jpgOne of the games I learned from Jane Felling’s Power Play session at NCTM Baltimore was called “Rock and Roll.” This game (also perfect for those few extra minutes at the end of class) reviews naming numbers, place value and comparing numbers. Players shake and roll out a given number of dice before quickly arranging them to form the greatest number possible.  When a player has created the greatest number he places his hands on his head and shouts, “Rock and Roll!”

Players then read their numbers aloud, with the first player to shout “Rock and Roll!” scoring 1 point (or was it 5?). The player with the larger of the two numbers also scores 1 point (or was it 5?). But, to earn the points, a comparative statement must be made (i.e. four hundred thirty-four is larger than one hundred fifty-five). Each player then writes his or her number on a recording sheet in both its standard and expanded form.

Though my 5th grade advanced students previously played this game back in October with whole numbers, today we played with decimal numbers. Each player used three 0-9 dice (though spotted dice would work, too!) and arranged them to form a decimal number to thousandths.

This game is simple to differentiate! Variations include:

  • Adjusting the number of dice to increase or decrease the values of the numbers.
  • Arranging the dice to make the smallest number possible, or if playing with 3 players (because classes don’t only come in even numbers) a number that might be in between the other two numbers.




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