Daily Explore plus Four

The start of school is looming and I am spending some time thinking about how I'd like to change-up some of our learning activities. With all the attention on the Common Core in our District, and with the commitment to Launch-Explore-Summary lesson structures, I am once again tweaking Daily Five for math.The basics of the philosophy and research behind the Daily Five, whether it is in math or literacy, always are there.  Clearly stated and modeled expectations (10 Steps to Independence), choice, brain research-based lesson structures (thank you Michael Grinder!).  Now, however, we are fitting this into our Launch-Explore-Summary lesson structure.My newest iteration of the Daily Five for math is the Daily Explore Plus Four.  Using Launch-Explore-Summary, the target lesson follows our District curriculum modules in mathematics.  A focus lesson, approximately 10 minutes long, introduces the day's math exploration.  Students can then begin to work on that exploration while I monitor who is able to persevere through the problem or activity and which students needs some additional support.After about 20 minutes of independent work, we will re-gather as a group.  For this focus lesson, there may be an opportunity to share solutions (or partial solutions), talk about what was uncovered in the Explore, or continue with another 10 minute whole group learning activity.Before dismissing students to work on other math activities, just as we do in the Daily Five for literacy, students will indicate what activities they plan to participate in during remaining independent times. Here is where most students will participate in the 'plus four' activities (Strategy Games, Drills and Fact Practice, Technology, Problem Solving).During the second independent time (another 30-40 minutes), while students work on their chosen independent activity, I will be able to meet with a small group or meet individually with students who struggle with a mathematical concept.  For teachers who are already deep in to the Daily Five in Literacy, think individual conferences with a mathematics focus.At the end of the math period, we will once again, re-gather as a whole group to summarize what our math goal was - and process whether or not we feel like it was accomplished - and 3 or 4 days of the week I plan to implement a 5-10 minute "Math Talk" based on Sherri Parrish's Number Talks book.  On the fifth day, I'll use the time to check on math fact fluency (a requirement for 3rd graders in the Common Core standards).This is a flipped version of what we've traditionally done in math class.  In the past, the planned lesson based on the pacing criteria took about 60 minutes and the intervention/small group instructional block was 30 minutes.  With the knowledge that some students will choose to keep "exploring" during the second independent session, the model has flipped so that launch and explore are accomplished within the first 30 minutes of math.Why do I think this is a good move? Well, for starters, I know I will get a better use of time by meeting with smaller, focused groups - the same way I see improved focus during individualized reading conferences.  Secondly, by strategically choosing strategy games that align with the standards currently being taught, students will have additional opportunity to practice those skills in a fun way. Analyzing test data will allow me to target and  support additional skill and strategy practice where students need it in the 'plus four' as well. The flexibility is endless.The start of a new school can be exhilarating and frightening all at the same time. I am definitely looking forward to a change-up of our math time; one that I think will be more beneficial to my students.

Two Great Math Resource Sites

I haven't been able to write much lately. We're in the middle of state testing - again - and now getting ready for that paperwork marathon known as end-of-the-school-year. Not a big fan of paperwork. Does anyone ever really read all that stuff?So I procrastinate. Which sometimes is not as much of a time waste as it sounds.This time, my procrastination(s) proved fruitful.  I've discovered two really useful - in my opinion - websites that I've already started using in math classes with students.Learnzillion is a video treasure of lessons started by a charter school in Washington, DC and recently opened to teachers willing to shared taped lesson snippets.  In addition to being tied directly to Common Core Mathematics Standards, a teacher can sign up for a (FREE!) account and create a playlist of videos. Teachers with more technology available to them that I currently have in my school, or than my students' families have, may find using a playlist with "homework" that confirms whether or not the students has viewed and understood the concept presented powerful. But even without this piece, I thought the video lessons were quite strong. Anyone who uses Lucy Calkins Units of Study will appreciate that the videos begin by addressing students as "mathematicians".Currently the videos support Common Core standards in Grades 3 through 9. And while not all standards are in the video library, there are plenty of visual lessons to help students understand math concepts.Another new to me site is K-5 Math Teaching Resources.  These are not video lessons but they are wonderfully constructed explorations of mathematical concepts. The activities are categorized by grade level, linked to the Common Core Mathematics Standards and, for the most part, are free.  The only for-fee sections appear to be the downloads of math projects, math vocabulary wordwalls, and math journal problems. Each of these downloads are $7 for a single-user PDF file. 

Daily Five Math, Common Core and Investigations

That's right, I am incorporating all three of these things in one classroom.  I've been a fan of the Daily Five and Literacy CAFE for a couple of years. Last year, I started to use the structure of the Daily Five in mathematics.  I did this for a couple of reasons - first and foremost is that I hate segmenting curriculum areas into compartments.  If something works well in one area, it should work well in another.  And it does.Admittedly, I have adapted D5 to suit my own needs as a teacher and the needs of my students.  This year has been a little tricky. The Common Core implementation ALONG SIDE continued attention to the 2004 Mathematics Framework makes me feel like I'm straddling a fairly fast moving river as the water level rises.This week - school vacation week here in Massachusetts - I spent some time getting my bearings again for what universal or landmark games I can rotate in and out of the Daily Five.  Here's what my current list looks like (this is on wikispaces, feel free to join in).

Using Daily Five Math to Support Common Core

This summer was partially spent in aligning Common Core Mathematics curriculum (Massachusetts-style) with the district's universally available materials and laying out a scope and sequence that makes sense vertically and horizontally. As anyone who has looked at the Common Core in depth can attest, it's an on-going process full of starts and stops.A particular challenge to 3rd and 4th grade teachers in this transition year - this year our students will be MCAS-tested on 2004 Curriculum Frameworks - is, while we work to transition there is a great  need to keep a close watch on those standards that have been moved from our grade level. Particularly the standards for which our students will be accountable but were not previously taught to mastery.To my thinking, this is where using the Daily Five in Mathematics makes perfect sense. I can still launch my core lesson - the Common Core-based lesson, have my students work for a period of time on the activity (notice I'm not saying worksheet!), reconvene for a summary discussion and refocus students on continued work using one of four categories: Strategy Games, Facts-Clocks-Money, Problem Solving, or Math Tools.Yes, I know that the Sisters don't use this terminology.  These are the terms that I use because of the mind-blowing task of straddling two curricula while transitioning to full Common Core implementation.As a third grade teacher, I know the bulk of my mathematics intervention - the dance to catch kids up on things that are now receiving more emphasis - will be on number sense and operations (CCM: NBT, OA) . Prior to this year, there was no explicitly spelled out requirement that students master addition and subtraction to 18s in second grade.  We've got some wood-shedding to do here.To keep things sane, and to allow me to meet several small groups, I have a few strategy games that I call "landmarks". In our current multiplication unit, those games include array cards, Marilyn Burn's Circle and Star game, as well as Close to 100 (or 1000) and Collection Card games (Investigations in Number Data and Space) we used to introduce 3-digit addition/subtraction. The teaching challenge is to pick out universal games where "rules" stay the same, but the ante is pushed to make it challenging for all students no matter what their level of mastery.As most students use the four choices to continue to build mathematical concepts and skills, I can meet with small groups of students needing intervention support  in place value, or understanding of addition/subtraction or some other yet undiscovered area of need.How can I do that? Because my students are Independent Learners, I know that when I attend to the small group, the rest of the class is engaged in some meaningful practice and learning. The same Daily Five expectations for Literacy - get started right away, do math the whole time, work quietly, work on stamina - are applied to independent explorations in mathematics.For me, the Daily Five principles applied to the mathematics class make this differentiation possible. My implementation certainly is not perfect, but knowing my students are getting what they need without the teacher being pulled away by monitoring what is going on in other areas of the classroom makes the work ahead possible. And definitely more enjoyable.

Another Look at the Daily Five and Math

How does that saying go? If you're not green and growing, you're rip and rotten. One of the key components of the Daily Five - teaching learners to be independent - is not only appealing, but imperative. After some false starts last year (based on my reading of both the D5 and Cafe books), I attended a Daily Five workshop. And the whole thing is becoming less muddled.Typically, my students don't do well with a million and one different teaching models thrown at them. We already have a Launch-Explore-Summary model in place for our mathematics instruction. There is a great need for small group/individualized math conferencing and intervention, particularly this year when we transition from the Massachusetts 2004/2009 Frameworks to the Massachusetts version of the Common Core Curriculum. There will be gaps, that is certain.To address both the transition to a new curriculum and my students' need for consistency, I have decided to make a go at implementing a Daily Five model during mathematics instruction. What are the five areas going to be? Well, here's what my current thinking is:

• Exploration activities based on the launched mini lesson (a "must" do)
• Strategy Activities. Through the use of games and other constructive activities, students will address computational and conceptual gaps.
• Problem Solving. All of my students, but particularly second language learners need practice in the structure of problem solving situations. This will be a weekly assignment with time built into our schedule for students to discuss how they solved the problem (rigor! perseverance!)
• Basic Fact Games/Practice
• Technology Tool (a chance to use the accompanying programs for our math program OR the interventions found in the Galileo program).

I'll need a minimum of 85 minutes; 90-100 would be better. That means getting back to class and started on our mathematics work right after recess. Hopefully the stamina-building and direct instruction in expectations for independence will give us greater success. On paper it looks do-able, in reality - I am hoping so.

Planning out the block comes next.  Suggestions welcome.

Common Core and Clarity

The Massachusetts Common Core Curriculum implementation starts this coming school year.  As a District Team, we've looked at how the standards are expressed with increased attention to Focus, Coherence, Clarity and Rigor.  In Lowell, we began our look at the new standards by defining exactly what these four terms mean. One idea that has stuck with me as we work on preparing materials for our colleagues is that  the standards are not "intended to be new names for old ways of doing business. They are a call to take the next step...."Where this becomes apparent is in looking at clarity as applied to the Common Core. I've been taking these standards apart since early June now, and each time it amazes me at how clearly each grade levels' responsibilities for student learning is spelled out.As a Third Grade example, our former Frameworks (2000, 2004) 3.N.10 asks students to "Add and subtract (up to four-digit numbers) and multiply (up to t2o-digit numbers by a one-digit number) accurately and efficiently".  This standard corresponds to the Common Core 3.NBT.2, "Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction."For me the new standard is truly packed with specifics. Fluently add should mean that no matter what the strategy, students can perform the operation without hesitation.Using strategies and algorithms based on place value does not mean the standard algorithm -- in fact the standard algorithm does not become specified until later grade levels (Grades 4 & 5).  What this standards tells us - clearly - is that all students need to be able to perform addition and subtraction within the thousands place using relationships - such as friendly number strategies - or using a process reliant on place value (decomposing and then adding partial sums for instance).While we may have students who are ready to record these problems using a standard algorithm, unless the student thoroughly understands and can explain the use of the standard algorithm - thereby demonstrating that the student is ready to use a standard algorithm - the student should use some other process for computation. Blindly applying a process without the knowledge of the what and why is no longer accepted.To me, this is refreshing - a recognition that understanding and comprehending a mathematical topic with depth, and rigor is of importance.  The wording itself of the standard is clear and direct.As we explore the Common Core, we discover that there is much more clarity about the level, or depth of thinking, to which we need to bring our students. And that is a good thing.