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.
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.
Last week I read through chapter five of Becoming the Math Teacher You Wish You’d Had. Reading this chapter made me wish that school was still in session. There were times when I was reading that I stopped and reflected on how I manage expectations in the classroom. Specifically, I thought about how I emphasize the need to be precise during math lessons. More often than not, the precision aspect is related to computation mistakes as well as issues related to missing or incorrect units. I address this so many times during the year. So many that I can’t count the amount of times that it’s mentioned. I think most math teachers have been there. In most cases I’ve observed students being able to show their understanding of a particular concept, but they don’t show it on assessment. A label might be incorrect or a one-digit calculation completely changes an answer. I see this all the time with adding units related to linear, square, and cubic measurements. A student may get the answer correct, but the label doesn’t match. I have issues when students place cm^2 when the label should be cm^3. There’s a big difference there and it has me questioning whether the student understands the difference between area and volume. There has to be a better way than just reminding students to check for errors or make a reasonableness check.
A couple of the examples that were showcased also emphasize using precise language. Avoiding the word “it” and being specific are highlighted. I find myself repeating certain phrases in class. Not using “it” to describe a particular unit would be on my repeat list. Instead of using that devil of a word, teachers can emphasize and have students label the ambiguous “it” into something more accurate. Incorrect labels are a killer in my class, so this is something I continually emphasize.
Estimating can also play an important role in attending to precision. My third grade class uses Estimation180 just about every day. We made it all the way to day 149 last year. We were pretty pumped about that much progress. It was a productive struggle and heartening to see how much progress was made. As time went on students became more accurate with their estimates. That thought process transitioned to other aspects of math class. I asked the students to have reasonableness checks before turning in an assignment. The check doesn’t always happen, but when it does it’s a golden opportunity. I’ve had some students use a checklist to record whether they’ve estimated first to see if their answer is reasonable. Again, it’s not always used but I believe it benefits students.
Games can be great opportunities for students to be reminded to attend to precision. Some games are great for this, others aren’t and bring an anxiety component to the table. I was reminded of the negative impact of timed tests and elimination games. I’m not a fan of timed fact tests in the classroom and haven’t used them for years. More recently, I’ve used timed Kahoots or other elimination games. Some students are more engaged when there’s a competition component. This chapter brings awareness to how emphasizing speed can be damaging. Most of the time these games are low-risk, but they do bring anxiety and can cause some students to withdraw.
Guided class activities like pattern creation can be helpful in reminding students to attend to precision. Using student-created patterns ( ___, ____, 56, ____, _____ ) to develop unique solutions can be utilized to show understanding of numbers. Students can create a multitude of patterns with this. It also challenges students to find a pattern that no one else has. I’ll be keeping this in mind as I plan out next school year.
It seems that students will always need to be reminded to add correct units, review their work and attend to precision. Having strategies and tools available to address this will be helpful moving forward.
My school finished its ninth day of school yesterday. It’s been a journey as students are understanding class routines better. At this point in the year, students and teachers are starting to become more solid in their processes. Many of my students arrive to class at different times. Some students are at an elective or leave class a bit earlier/later than the rest of their peers. Regardless of the arrival time, when students enter the room they follow a flow chart. Students have their own folder and materials inside that are ready to go. I usually have some type of visual brainteaser for the week and a grade specific Scholastic math magazine. In the past I’ve used different types of math warm-up activities to start class.
This year I adapted my warm-up strategy. I wanted to individualize the type of responses within that warm-up time slot. After researching a few different tools, I decided to try Andrew Stadel’sEstimation180 this year. I think of Estimation180 as an opportunity for students to develop a stronger sense of numbers and practice estimation skills in the process. Initially, I thought that the site would be great for middle or high school students. I then found the below sheet and site that seemed helpful. This is one way in which student can document their thinking. The template also includes lessons that could link to Fawn’sVisual Patterns site.
This template inspired me to adapt the sheet to fit an elementary classroom. I changed the template a bit to work with a third grade math class. A few colleagues and I will be using this sheet early next week.
So now, students enter the classroom, pick up their folder and begin to work on their daily estimation challenge warm-up sheet. The estimation is displayed on the whiteboard. Students pick a high, low and exact estimate. I ask the students to prepare to tell me about the reasoning that they used to come to the concluding estimate. The class then completes the online portion of the site and submits a response. We then look at other responses and reasoning.
After a brief discussion the result is revealed. Students write in the correct numbers and find the + / – . The entire activity takes about 5 – 10 minutes.
I’m planning on using Estimation180 a few days a week and incorporate Visual Patterns for the rest of the days. The template also includes a few different reflection pieces. I feel like these activities provide students opportunities to produce a product and reflect on the results. At some point I’d like to add a journaling component to encourage more reflection and possible goal setting.