I am thankful for so many things...and no matter how difficult life can get, this is the perfect time of year to reflect on all that we have that we are grateful for. I am so blessed to have TWO jobs I love--teaching by day, and creating resources and blogging by night! I have a wonderful family and great friends...I have a more-than-ample roof over my head and go to bed with a more-than-full belly every night.
Today I am joining together with some other wonderful bloggers in a special link up to celebrate all our blessings--and to show our gratitude to YOU by offering some special gifts to make your lives easier at this busy time of year. We have a couple of fun things planned for you.
First of all, each one of us is offering up a gift for you--we are taking one of our products and making it FREE for you, our loyal readers! Just stop by my store on Sunday, November 18 or Monday, November 19 and grab this "Thinker Task" for free! If you want to try doing an in-depth problem solving activity that is rigorous, differentiated, and FULL of teaching ideas, this is for you! This resource is one of seven included in a bundle of Thinker Tasks AVAILABLE HERE if you are interested. This offer is only good for those two days, so mark your calendars. Click the image below to take you to the resource, but remember it is only free on Sunday and Monday!
In addition to the great resources we're giving away, each blogger is also hosting a raffle for a $25 TpT certificate! That gives you 16 chances to win, so be sure you don't miss any of the blog hop stops!
There are three ways to enter to win my gift card--the more you do, the more chances you have to win! If you want to join my newsletter and get freebies and other offers, just click the image below to take you to the sign up form. That's the first way to enter! Following my store or my IG account are the other ways--following my store will help you see what new items get added, and following me on Instagram will show you lots of teaching ideas, resources in action, and glimpses into my "real" life!
a Rafflecopter giveaway Remember, all of the resources are usually for sale in our TpT stores, but we have made them free for JUST TWO DAYS only. Be sure to grab them before you go to bed on Monday night, November 19th, because they will be set back to their normal price shortly after midnight. Hope you enjoy all the great freebies.
NEXT STOP:
Below, you'll see thumbnail images of each resource. Simply click the next stop in the list to download the free resource and enter another raffle. Best of luck with the raffles, and have a wonderful Thanksgiving holiday.
One question I get all the time is, "How do you work your thinker tasks into your daily instruction?". Today I thought I'd share a little more about how I use these project-based learning experiences!
First of all, if you haven't seen my "Thinker Task" collection, this video might give you a better sense of what they are and what they involve. I hope you'll see the benefits of getting students doing "real-world" problem solving and how much math discourse and critical thinking they can evoke.
Ready to see more?
Thinker Task Holiday Feast - YouTube
How do I use Thinker Tasks?I think what I really love about these tasks is how many different uses they have. I thought I'd list a bunch of different teaching suggestions for you--but I bet you can get even more creative!
Sometimes I use Thinker Tasks with my whole class. I introduce them to everyone and then students can work alone or collaboratively at their own pace.
At other times, I use this as a "fast finisher" activity. Everyone has a copy, but some students get far more time to work on it because they need less "me" time for instruction on other things.
Perfect to use as a station in math workshop or guided math. Once students know what to do, they can be totally independent.
These tasks are great to help explicitly teach students about the Standards for Mathematical Practice where students can work to justify their thinking, model with math, make sense of problems, persevere, work with precision, and more!
Two words: Math discourse! These tasks instantly get students talking about math, critiquing each other's reasoning, defending their thinking and more. They also have multiple opportunities to WRITE about math, something missing in most math series.
Perfect for special education in middle school. Teachers have raved that the tasks don't look "baby-ish" but work hard to get students both solving problems AND working on critical computation skills.
Enrichment groups for grades 2-4. Students love the challenges and teachers love that they can do meaningful work while they work with the rest of the class. The fact that the task itself is challenging is great--but the page of additional extensions means that with very minimal planning, this task can provide meaningful math work for weeks.
Sometimes I take a few days in a row and we do the complete task. Other times I introduce the task and then students work on it after they finish their other work. In other words, it can be a replacement activity or an extention activity. Perfect to introduce before having a sub--because students are so engaged.
Wonderful to use to model great math thinking for observation lessons. Administrators love to see students involved with such meaningful math!
What Thinker Tasks are available? I have very few resources that are "holiday" based because I like the flexibility of using different lessons and ideas when they are the best fit throughout the school year. That being said, sometimes those seasonal times of the year are the trickiest times to keep students engaged in their learning!
For my Thinker Tasks, I have created some of each. I have versions available that can tie to seasons (back to school shopping, a Thanksgiving feast, holiday cookie baking, or Valentine's Day), but others that can be used at ANY time...students can enjoy working on a sleepover task, an amusement part problem, or an animal rescue problem any time!
How do I differentiate these math tasks? Another question teachers often have relates to differentiation with Thinker Tasks. Fortunately, there are a ton of options for teachers wanting to use them with students at different levels. Check out these ideas!
Most of the tasks come with two "Math by the Numbers" sheets with the numbers at different levels. For example, in the Valentine task, one version uses only whole numbers like "$5" while the other uses decimals with amounts like "$4.95". This, of course, makes the task more rigorous.
The tasks can be differentiated by providing different amounts of scaffolding. By giving students the chance to be completely independent, they need to "make sense" of the problem on their own and dig in with no guidance. By working with explicit directions and, perhaps, working with students step by step, the task becomes more manageable and easier to tackle.
Providing students with tools like calculators and manipulatives can make a challenging task more accessible. A child who cannot subtract with regrouping CAN use a calculator to solve a task involving subtraction.
Working in partners or small groups is an instant way to give students support and still have access to rigorous, quality math.
Working in differentiated teams allows you to tailor these tasks to small groups with different needs.
I hope this helps answer some of the questions YOU might have had about Thinker Tasks and how I use them throughout my school year. Each is available separately, or you can buy the bundle and save. Just click the image below to see the bundle. Each individual resource can be accessed from that link. Enjoy!
Today is my day to blog over at Upper Elementary Snapshots, and I hope you'll stop over to check out some of the lesson ideas I am sharing to use with whatever read aloud YOU are using right now! Just CLICK HERE or the image above to take you there!
I am excited to announce a HUGE back to school giveaway that I am a part of--and I would LOVE for one of MY PEOPLE to win one of these amazing prices...do you see the SEVEN prizes listed below? I can only imagine that you could use a little extra cash at this time of year. Take a peek at the rafflecopter below and enter for your chance to win one of these great gift cards.
I've been getting busy in my classroom, so I hope to have some classroom updates soon for you...but make sure you follow me on Instagram and Facebook because that's where my "day to day" updates happen! So...enter this amazing giveaway--and I hope you WIN!
As you know, the purpose of a graphic organizer is to help students (or adults!) make sense of information and organize it into a visible, usable fashion. Sometimes using an organizer is all we need from students—a way for them to represent the information we are asking for. Sometimes, however, we want students to organize information for other reasons…like to do a piece of writing. I wanted a way for my students to be able to track their thinking about the texts they read, but also for them to be able to use those notes to complete a short piece of writing to show me their thinking and depth of understanding about a text.
All year long I share novels, picture books...students read during independent reading, book clubs--you get the drill. There is never enough time to confer with everyone and get as much information as needed to see how deeply students are thinking so, part of the time, I do rely on some written work to check for that depth of understanding.
The more I thought about it, the more I wanted to be able to be able to quickly consider what skill or learning target I wanted to focus on, and then have a low ink (or digital) way to get students thinking—and then writing about texts.
I have books and books of graphic organizers, but could I find what I was looking for? Nope!
There are countless resources out there filled with different graphic organizers--none of which were going to do what I needed them to do. I decided to create my own for a number of reasons. Graphic Organizers That Help Teach Reading
•The organizers have teaching tips/mini lessons worked right into them! (see the image above!) •This resource has the print AND digital versions of these organizers so you can use them either way.
•This set also has a written component so students can use the organizer to jot down their thinking—but then can “write long’ about them to deepen their thinking and work on their writing skills in a meaningful way.
•These organizers are meant to dig deeply into rigorous standards and get students really thinking deeply about texts, not just fill in the blanks. Assessing Student Thinking with Graphic Organizers
When I ask students to write about texts, I am looking for a few things:
•Are they able to find examples in the text? •Can they explain clearly? •Can they write coherently? •What is their “depth” of understanding? •How reflective are they as they read? •How much scaffolding or “coaching” do they need to make sense of the text? •Does their written work seem to match their reading level? •What instruction needs to happen to support them as readers and writers? •Do the texts they are reading seem to be a good fit for them?
When Do I Use Graphic Organizers? The sky is the limit—but here are some ideas for you!
•Use these to model your own thinking about texts you share with the class…read aloud novels or picture books. Show how you track your thinking on the organizer AND how you take that information and turn it into a piece of writing.
•Use this as “ready to go” work for book clubs where students can read, reflect, write, and then discuss!
•Use this as an assessment…either have students use these organizers to show their thinking about a book you have shared with them or their own reading.
•Have students work in partners to get them talking about books and finding those essential ideas and text evidence.
•Work to fill out the organizer as a class (or as a part of a small group) and then have students work independently to do the reflective writing.
•Use this as a way to get more writing instruction into your day. Teach about paragraphing. Show them how to use transition words to connect ideas. Show them how to write topic sentences and supporting details. Show them how to cite evidence from the text.
So if you think you might be interested in trying something like this...just click the link here to see my fiction graphic organizers or click the image below.
Well, here we are...our final day of the summer math challenge! I hope you have enjoyed the series and have made some plans to try some new things this year!
Today's final challenge involves asking you to do some reflecting on how you actually organize your math instruction. I am constantly getting teachers asking me what my math block "looks like"--and it's just not that easy of a question to answer! Mine looks different every day...because the math looks different every day.
There has been a lot of push to do "math workshop" or math "centers" in recent years. Sadly, this has resulted in some unfortunate results. I'm going to redefine some things the way I like to keep them in my mind...and I hope some of what I have to say resonates with you.
Here goes.
In my mind, I like to think of math workshop as being "ways to give as many students as possible JUST RIGHT instruction for as many minutes per day as possible". Does that work for you?
If so, then we have to be mindful of how we do that. right? Some of our best intentions often go south, so today I'm going to share with you 5 ways that you can plan your instruction to try to get students in that "math zone" as often as possible. You will notice--each strategy has pros and cons. We need to make professional decisions based on the math content, our students' knowledge, and countless other factors. Let's see what you think.
By the way...if you want a freebie that has all the images from this post to help you with your own planning, here you go!
Whole Class Math InstructionFirst of all, I want to give the disclaimer that "whole class" instruction is NOT the whole class instruction I had growing up! There are no podiums or lectures involved! Instead, students are given some meaningful instruction and then are immersed in a task or set of problems/activities. The teacher then circulates and coaches. Students may be working alone, in pairs, or some other collaborative combination. In order to be successful, the task has to be within reach of all students or small groups--whether that be through the instruction, differentiation, tools (like calculators), or through intervention on the teacher's part.
This can also be an extremely effective strategy when presenting content that is new for all students...a new concept that students need to be immersed in as an introductory lesson or meant to trigger discussion. A perfect example of an activity that is perfect whole class instruction is my math concept sorts. My goal as a teacher is that I WANT to be the observer and coach so I can see what my students know and what misconceptions they have.
Splitting the Class in HalfThere are times when trying to keep the attention of 24 students is simply impossible. Splitting the class in half and teaching the lesson twice might be just the ticket! The beauty of this is the flexibility. You can teach the exact same lesson twice and just have a smaller, more focused group OR you can teach the lesson at two different levels so students are challenged at just the right level and just the right pace.
Remember, when doing two groups, there is no rule that says each "half" needs to get the same amount of time. I frequently teach the lesson to my more capable learners in about half the time I spend with the other group. You can also bring out different tools or scaffolds for the group who needs it--so a win/win for all. Be mindful of what you have the students who are NOT with you do...we don't want to fill their time with busywork or off-level work. It's a perfect time for collaborative problem solving, computation fluency work, or other "just right" practice.
Math Centers and StationsWell, here we go. "Centers". "Stations". "Math workshop". This instructional strategy involves grouping students (either by ability or not) to rotate through a number of different activities--one with instruction from the teacher. Ideally, this instruction is tailored to the needs of the small group--or there really is no value in the rotations, right?
Here's the deal. Whether we set up 3, 4, or 5 stations, the simple truth is that students are under direct supervision of the teacher for only a small percentage of the math block. That means students need to be doing MEANINGFUL, on-task work for a large percentage of their math class. This requires a great deal of planning. We know we have many, many different ability levels in our classes, and creating meaningful "just right" centers for all of them is a challenge, indeed.
So if we can create meaningful work at these stations, we also do need to make sure that student behavior creates an atmosphere conducive to quality work. Since students are only getting direct instruction for one rotation, the teacher must be completely free of managing those other groups. This takes a great deal of time up front to make sure the groups function well, know expectations, and can manage them without teacher assistance. When they work well--this can be a great way for teachers to really tailor instruction...but we must be mindful that students aren't wasting 75% of their math time doing centers that aren't "just right" or where behavior interferes with productivity.
Math Minilessons and Focus GroupsThis organizational strategy is a nice combination strategy...it allows the teacher to teach a focused minilesson to the class and then tailor the instruction AFTER that to different groups of students. Here's an example...let's say I wanted to explicitly teach the strategy "draw a picture". I could do some modeling with the entire class...show my thinking...maybe even have students work in partners to try a similar problem.
After that, I could pull small groups to work on that very skill--but at different levels. Again, like with the "half and half" strategy...there is no rule that says that these focus groups need to be equal lengths of time. For some of my better problem solvers, I might start with a challenge problem to watch them work, listen to strategies, coach on organization and precision issues, and then send them off to try some more on their own or in partners.
For a group of students needing more, I could use much simpler problems, walk through them more slowly, model in different ways, and keep the students much longer for extra practice and coaching. Like with all the other structures, we just need to make sure the students NOT with us are doing meaningful, independent work!
Math Menus and ChecklistsWhen the instruction you really need to do is one on one or small group work...using a menu or checklist can be an amazing strategy to really free you up for an entire math block. I especially like to use this toward the end of a unit when students are working toward fluency with the different skills and maybe even have some longer term projects underway like Project Based Learning Thinker Tasks which can be a meaningful way to spend some work time. Sometimes I'll even have the students working on some of my alternative assessment options to keep them really doing meaningful work. I can then circulate and coach...pull intervention groups...reteach...or whatever else I need to do to make sure all my students are getting what they need.
So there you have it! Although this certainly doesn't cover what my math block looks like EVERY day, it gives you a little glimpse into some of the deliberate structures I use to really maximize the time students spend working on meaningful math--and to make sure I feel as effective as possible with all the different needs in my class.
So....that's it! Seven posts that I hope have given you some food for thought this summer as you move into your school year. To celebrate, I'm going to do a little giveaway! I hope you'll take the time to enter--because who couldn't use $100 to spend on TpT supplies, right?
There are a ton of ways to enter...and you can do some each day if you want to rack up the entries! Thanks so much for being a part of my summer challenge--and good luck!
To make things even MORE fun...I am putting my ENTIRE store on sale for July 25 and 26 (Wednesday and Thursday) to say thank you for being a part of my little project! Just click below to stop by and check it out!
Click HERE for Challenge 1 (yearly planning) Click HERE for Challenge 2 (math talk and mindset) Click HERE for Challenge 3 (word problems and problem solving) Click HERE for Challenge 4 (math organization) Click HERE for Challenge 5 (math assessment) Click HERE for Challenge 6 (meaningful problem solving)
Did you miss signing up for the FB group? CLICK HERE! (And make sure to answer the screener questions!)
A few challenges ago, I talked pretty extensively about problem solving as it related to word problems with tips and suggestions and food for thought. Today I want to talk about problem solving "experiences" that are NOT word problems so that we can adjust our thinking and plan for meaningful math instruction. So here we go...some ideas to get you thinking about problem solving!
Presenting math problems and concepts in new waysAs defined by the NCTM (National Council of Teachers of Mathematics), problem solving is:
"The term "problem solving" refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development."
When using that definition, it's easy to see that word problems are no the only way to help students achieve this state of "intellectual challenge". In fact, one thing I like to consider when planning math experiences for my students is simply to try to engage them in a concept in a new, different way. So often math series do just the opposite in their attempt to help students know what to do...they might have a task in one lesson, then do a similar task in a follow up lesson (perhaps with larger numbers) and so on.
Instead, I feel we really need to ask students to USE the math they are teaching, to practice in different ways, and to make as many neural connections as they can while they work. What this does NOT mean is explicitly teaching a rainbow of different strategies. It simply means that we allow students to do math in different contexts. Let's take simple computation as an example.
When we want students to learn to add, subtract, multiply, and divide, we have a number of different strategies we can use to help them. We build deep understanding through manipulatives, number lines, picture models, and so on. Once students have deep conceptual understanding, we want them to work toward fluent and accurate work. This can be done with practice pages, games, and so on.
Take a peek at how these different activities ask students to use their brain in different ways as they work toward fluency.
This is one of my favorites...totally computation--but forces students to estimate, reason, think, and persevere. I put it up as a bulletin board, but you don't have to...everything students need is right on the reproducibles. Each set has 5 challenges, and each challenge has 2 parts for differentiation...and then there are bonus challenges at the end. TONS of practice but really asks students to use their brains in different ways. It's a challenge--but students love it!
This little video clip shows another way to get students working on computational fluency in a new and creative way. It forces them to really think about numbers and number combinations. I use this several times a year in different ways to get them really deep ways. See what you think!
Another set of problems I use throughout the year is this one...these problems require students to draw from different strategies they have learned and to really just dig in and TRY. I love having them share their strategies and solutions with the "learning poster" component that I've included.
Using open ended math tasks to build engagement and sustained math focusAnother type of problem-solving activity I like to use involves what I call "open ended tasks". These tasks are meant to last a class period or more, can be done independently or in pairs or groups, and can be done at varying levels of sophistication.
The benefits of these tasks are immeasurable--for the students AND you as a teacher! Here are just a few...
Students talk about math. A lot.
Students learn there are multiple ways to tackle a problem.
Students practice applying the math they have learned.
Students learn to read critically and look for multistep parts of tasks.
Students learn that there are real-world connections to math.
Students learn to sustain math thinking over extended periods of time ("stamina")
Teachers can use this time to watch, notice, and coach.
Teachers can use this time when students are being productive to pull individuals or small groups--either to work on the task at hand or other skills needing intervention.
Teachers can tell whether math concepts that have been taught are transferring to unique tasks.
Teachers can help students prepare for standardized tests where they will see "novel" tasks and need to use their toolbox of strategies to solve them.
Teachers can help build excitement for math.
Teachers can help students develop growth mindsets and perseverance with challenging tasks.
Here are a few examples of the kinds of tasks I'm talking about. I use these ALL year long in my class and love them for all the reasons listed above. The first one has 18 tasks that are perfect for one day lessons or for fast finishers. They range from focusing on basic computation (addition, subtraction, money) to more sophisticated concepts like area/perimeter and measurement and more. Directions are simple...students can work alone or collaborative...and they totally free me up to coach and work with students. (Added bonus--awesome and easy for sub planning!)
The second one involves seven more complex tasks...they are differentiated so students can work at different levels, but these tasks are designed to take place over multiple days. In fact, I have them divided into sections so that you can use some or all of each one...and some students may do more than others. I want them digging in and doing math, writing about math, and then there are a ton of extension activities suggested as well. I love these for students to do during math workshop when they are not working with me because they get totally engaged and don't NEED ME! I tried to write tasks on real-world concepts I thought they would like, and I use one of these tasks about every month of the year. Increasing algebraic thinking and number senseOne thing I have learned over my twenty-sixish years in the classroom is that we don't spend enough time on number sense and we don't immerse students in algebraic thinking experiences nearly enough.
I think the number sense concept is talked about more often. We need to immerse our students in number talks, using number lines (I have a ton of posts and resources to help with this!), and helping students develop a deep understanding of how our place value system works.
What we don't talk about enough is algebraic thinking and how students need to be flexible with numbers and equations--understanding concepts like "equal", recognizing patterns, and knowing how to flexibly "halve" and "double" things--all concepts critical to algebra work in later grades.
This can be accomplished in many ways...but one of my favorite things to do from the very first day of school is work on the concept of equal. I have an entire blog post where I talk more about algebraic thinking if you are interested, and you can CLICK HERE to check it out.
One of the tasks I mention in it is one of the first math questions I give at the beginning of the year...and it really helps me take the temperature of my class and their understanding. See how many write "12". See how many write "15". See if any write "9". It is so telling about how we present number sentences to children from an early age. Anyway--I would encourage you to check out that blog post linked above for more thoughts about incorporating this kind of thinking. The card below is from a set of task cards I use under my document camera for this very purpose (they get WAY more complex as they go!)
I also have a set of math concept sorts that I use to help with algebraic thinking as well as lots and lots of pattern work. Even being selective about the kinds of word problems we choose--making sure the "variable" moves and we aren't always looking for the end result. I've linked a few resources below...see what you think!
Making math more "real world"Another way to help students think more deeply about math is to make sure we are giving them real world math to do! I thought I'd throw out a couple of suggestions for ways to keep students engaged in the process and excited to dig in. See what you think!
Use student names whenever you can...it keeps them engaged and makes it meaningful.
Get to know your students' interests--especially your reluctant ones--and use that information when writing or selecting problems. I had a HUGE sports crowd in my class last year so I used a ton of sports examples.
Find things in your OWN life to use. Check out this freebie below--it's an example of an easy way to use "real world" math. This was at an apple orchard...but you could do SO many things like it.
Find meaningful math around your school...students per class. Length of lunch hours. Minutes of recess. Students CARE about math that touches their lives.
Have students create their own word problems on a topic they enjoy or love...favorite foods, sports, hobbies, and so on. Great for sharing with the class!
Do you want a freebie to help you do some reflecting on these ideas? Here you go!
Click HERE for Challenge 1 (yearly planning) Click HERE for Challenge 2 (math talk and mindset) Click HERE for Challenge 3 (word problems and problem solving) Click HERE for Challenge 4 (math organization) Click HERE for Challenge 5 (math assessment) Click HERE for Challenge 6 (meaningful problem solving)
Did you miss signing up for the FB group? CLICK HERE! (And make sure to answer the screener questions!)
"Planning for assessment" is a phrase that we might not use that often. PLANNING for instruction? Isn't it just something we DO? I think a proactive approach to assessment leads to better instruction, less stress, and more efficient use of our time. I want to bring up some different topics related to assessment as food for thought.
Math Content AssessmentWe all know that we need to measure how well students are learning the content we are teaching. If our standards dictate that students need to be able to "round numbers through hundred thousands to a given place", then we have to have the tools by which we check for that math understanding.
Often math series, if used, have this type of assessment--in varying degrees of quality. Here are some points to ponder!
Do your content assessments ask students to showcase their understanding in more than one way, with more than one or two problems, and in multiple attempts? (So often series only provide end-of-unit assessments and many standards are measured with maybe one or two questions)
Are many of the questions multiple choice or matching? Do students have to actually DO the math to get questions right or could your data be inaccurate because students can guess or narrow down the answers because of how they are written?
Do the assessments really tackle the content at the level or depth of understanding needed to really show they have learned it?
Are there opportunities to measure understanding throughout the unit or just at the end?
After you have studied what you have available to you to help you measure student learning, then you can begin to craft a plan to fill in the missing parts. For me, I am not provided enough assessment to help me feel confident that I know where my students are with their learning, so I am always needing to supplement.
Math Practice Standards and Student Self-Assessment Whether or not you GRADE the standards for mathematical practice (more on that later!), I do think it's important for us to be not only tuned in to our students' math content understanding, but the math practices as well--and that we are making that public to them! Students can only hit a target that they can see, so we need to make these math practices visible and meaningful.
I have found a few things to be true.
Students often don't realize how important math "behaviors" and practice are to their learning.
They often feel that speed and accuracy are the most important components of math work.
Students often overgeneralize--they don't realize how complex math is and we need to help them realize their strengths and goal area.
Students need help finding ways to meaure their own progress and successes.
There are so many ways to help with these things...from full class discussions to 1:1 conferences with students, to anchor charts and checklists. I spend a great deal of time at the beginning of the year to help students understand the standards for mathematical practice...to break them into student-friendly terms, and to work on math that allows them to practice them and reflect on them. We make anchor charts, look at student work, and more! I use these assessment checklists as well to help students understand how complicated the practices are--and to realize that they may, indeed, be doing PART of the standard and that they can they identify smaller areas to set goals and make improvements. Just click HERE or the image below for more details.
Formative AssessmentAs I alluded to earlier, I am huge believer in formative assessment. I don't EVER want to get to an end-of-unit assessment and be shocked at how a student performs. A few nuggets to think about as you plan for your formative assessment:
Formative assessment doesn't have to be all paper and pencil (see "Observation")
You do not need to only assess what you taught that day. Bring back concepts from weeks earlier to check for understanding.
Try doing an "entrance" slip when students walk in the door and use that information to group students.
No need to grade and score all assessments...as students turn them in, sort them into "Got it!", "Maybe" and "Oh my!" to help you know who to work with later.
Thumbs up/thumbs down can give you a quick "check"--as long as you have built the culture where students are comfortable admitting that they are stumped
Student self-assessment can be formative as well!
One way to informally assess students is to make an optional "coaching session" for students wanting help...students can self-select (or be placed by you!) into this review group.
Be mindful that you don't simply mimic the questions on the end-of-unit assessment. Present things in as many different ways as you can and make students really show they understand!
I use lots of different "tools" to help with formative assessment, but I seriously couldn't do my job without print exit and entrance slips. I've use many from this bundle which has slips for 6 key math areas. I try to print them before I teach the unit and use throughout the unit and then even AFTER the unit to make sure students are retaining the concepts taught. Click the image below if you are interested.
Sometimes I want to assess something in a different way (or in a different subject!), so I use these to make my own! I make a copy of the page I want...write in my content, and then make copies!
ObservationI think it's really important that we realize that assessment doesn't need to be written down. A huge percentage of what I learn about students happens as I watch, listen, ask, and notice. In order to get good information about students and their thinking, we need to put students in situations where they will do the type of work we want to see.
If we want to see if they can compute accurately, we can give them a page of problems to do. If we want to see how they think, how they process, how they explain, or where they go wrong--we need to get them doing rigorous work so we can see how they tackle it.
This work can be done as a part of a whole class activity...in a small group...as a center that we are facilitating, as we walk around and coach. This is really the BEST kind of assessment because we can intervene at the time of difficulty rather than wait for students to struggle with misunderstandings that they then show us on paper later.
One of the trickiest parts about assessing in this way is record keeping. There are a ton of different ideas out there for tracking your anecdotal notes--but before you stress out about how much work this is, let me just ask a question.
Is this information you will need to remember later?
If it is...then you will need to find a way to document it. You can use sticky notes. A Google doc. A spiral notebook. Whatever works for you...but keep in mind that good teaching involves constant assessing...so be mindful that spending more time writing down what you see than COACHING what you see isn't, in my opinion, the best use of time. Instead, use your time and energy to refine your observation skills--and I hope the freebie I'm sharing with you below will help you with this!
Depth of Understanding When we are looking to assess student understanding, I feel I would be remiss if I didn't ask you to do some reflecting on the types of problems, questions, and tasks you are giving your students. If we ask students to fill in the blank on a problem like this, does this tell you how well students understand equivalent fractions? If they can answer 2 of these? 8 of these? Will you be convinced that they understand the concept of equivalence? What other questions might help you really determine how deeply they understand equivalent fractions?
What about a question like this: There were two pans of brownies at the baseball picnic. P The coach cut each pan of brownies into equal portions. Jamal had 2 portions from one pan, while Daniel took 4 portions from the other pan. They both took the same amount of brownies. How is this possible?
Or this: Write two fractions that are equivalent. Prove they are equivalent using at least three different methods. Explain your thinking with words and pictures.
Or this: Sam said 4/5 and 9/10 are equivalent because each fraction is one piece away from a "whole". Is he right? Explain your thinking.
Or how about a combination of all of them! My point is this...if most of your assessment tasks are asking students to fill in a blank, generate an answer, or come up with a computational response, it might be time to do some research about how to assess students at a deeper level. (NOTE: Many students will put the number "6" in that white box because it is a logical guess...it doesn't in any way guarantee they understand equivalency.)
Another way to assess the depth of student understanding is to give them a much more open-ended assessment option. I use these throughout the year...and it really helps me see if student understanding is superficial or more in depth. I have a blog post where I show more about if you are interested--just CLICK HERE. The image below will take you to my fourth grade assessment set if you want ot check them out!
Assessment and GradingI just want to preface this section by making it clear that assessment and grading are related but not equivalent. I think the terms are sometimes used interchangeably--and shouldn't be. We use assessment as teachers to help us understand how our students are doing--and for students to assess how they are doing.
We also need to be cognizant that we DO have to report out--in some format. Whether we have to be ready to talk to parents at conferences, do report cards--or even just send parents an email, we must be able to take the information we observe and collect to make our decisions, to communicate to families and students about how students are progressing.
A few hints:
Remember that finding "averages" of scores doesn't necessarily show where students are NOW.
Often, scores mean very little to parents, so finding ways to EXPLAIN with comments, checklists, or other more clarifying examples.
Getting students involved with their own assessment and grading makes a difference in how students understand why their grades are what they are.
We want students to understand that grades are a VERY small representation of who they are as students and people!
I hope this post has gotten you thinking a little bit--and might give you inspiration to make your assessment practices more in-depth and varied.
Want to grab the freebie to help you with some assessment planning?
Today I want to talk to you about mindful classroom design and organization--organization that leads to efficient teaching and learning. We often get so caught up in planning lessons and activities that we forget that the space we teach those lessons in can really impact our teaching--and student learning!
Space PlanningEvery classroom is so different--it's hard to give clear direction on this one! I have a few tips to keep in mind.
Consider the role of your teacher desk. I use mine as storage and a place to put my document camera. I don't sit at it. Ever. The last thing I want is to have my students have to interrupt their thinking to come find me--I am moving around to coach THEM. Some people can live without a teacher desk to free up space in their room. I wish that were me. I have too much junk. #truthbomb
Consider carving out multiple "floor spaces". I want my students to have multiple floor spaces to work--whether they are in pairs, trios, or larger groups. When I do a new desk arrangement, I seriously count the number of work spaces I have on the floor to make sure we all have room to function without getting up into each other's business.
Desks in small groups--always. I switch up the number of desks in each group and how they are arranged (last year I had a challenging group, so more students were facing forward in their groups than usual!). I use cooperative grouping nametags to help me quickly form groups when I need to. We work cooperatively ALL. THE. TIME.
Consider where to put math supplies (more on this below!) to make sure students have easy access.
Make sure all students have easy view of your main teaching area(s) and key anchor charts and displays.
Consider traffic flow. I am huge on transitions (like we practice them) because I cannot stand wasted time. If there are hard-to-navigate areas in the room, streamline them.
Make sure to avoid "hidden" areas where students might get off task when you are working with small groups.
Consider having a crate, bin, cart, or table where you keep your intervention supplies and notes so you aren't digging for things all the time.
Find an easy storage system for games. Bins, crates, those fun rainbow carts--whatever the system, make sure students know how to use it and that it won't interrupt others when they access it.
I'm sure you will have tons of other ideas to share as well!
Anchor Charts, Walls, and MoreStreamline your walls
One thing I have done more and more as I've gotten more "seasoned" is actually pared down what I put on my walls. I want the items I have posted to be USED, so I don't want a lot of distractions. In the hallways, the sky is the limit! That's where I put student work, projects, and so on--but in my classroom, I keep the walls as learning tools. I have even stopped hanging things from the ceiling to make sure my students can easily refer to my walls.
Create anchor charts you and students use
I firmly believe that anchor charts are meant to be created WITH and FOR students. That being said, I want them to be useful as well. For that reason, I work with students on a "rough draft" anchor chart...then we group things together, cross things out, and so on--and then I recopy it in a neat (well, relatively!) fashion so it's easier to read and understand. I want students to use these charts independently, and I want to be able to send students to them--both for content information AND for expectations on how to function in my class. Here are a few examples of charts that hung in my room last year...and each year I "remake" them with my new group so they are a part of the process--and they evolve along the way!
Be mindful of bulletin boards and take advantage of that real estate
Bulletin boards can be great reference tools for our students! I keep up my growth mindset bulletin board all year and add to it as we learn new things. I refer to it often--as do the students.
Even displaying the Standards for Mathematical Practice posters (in kid-friendly language) is a great way to use bulletin board space--IF you actually use it as a teaching tool. Simply hanging up the posts (or any anchor chart, for that matter) does nothing...we need to refer to these tools, talk about them, and encourage students to use them. Click the image below if you want to check out this poster set (I have several versions in my store to match different room decor!)
I'm sure you will think of other great bulletin board ideas that can make a difference in your teaching...whether it's for math or other content. I love displaying other work too--but I want to make sure my classroom is a place for learning and inspiration as much as possible! Math Manipulatives and SuppliesWe want students to be independent "users" of our supplies
One thing that I constantly talk about is the need for us, as teachers, to get out of our students' way. We do too much! We think for them...we make decisions for them...and we need to learn to let go. Here's an example.
Let's say I'm going to be doing a lesson on elapsed time. To help, I put a few Judy clocks at each desk group to help them model their thinking. Great, right?
Wrong. I did the thinking for them. I essentially said, "This is a problem you need a clock to solve."--but really, it is not.
Students could draw a sketch. Or make a number line. Or get counters out to represent minutes. Or use a ruler to measure out passed time. Or use fraction circles where a "whole" represents a whole hour. Or maybe they will use tally marks or some sort of computation where they "trade" hours and minutes. It doesn't matter--by giving them clocks, 9 times out of 10--they will use the clocks.
So...the moral of the story is this. Have a bounty of resources in your classroom. Have them at student-height. Have them available--not in a closet. Teach the students where they are and how to use them. Create the climate where students know they can go grab whatever they need whenever they need it.
Consider small storage containers or toolboxes
One way I help make this happen is to store math manipulatives in easy-to-use containers. Snack sized plastic storage containers are great for individual sets of counters--easy to grab and take back to students' desks with no fuss or hassle. You can use little cubes, fun mini erasers, bingo chips--whatever you can find!
I also love my toolbox as pictured below:
Each drawer pulls right out and students can take it right to their desk. I fill the drawers with different counters so students can pick what they like!
All other supplies...pattern blocks, base 10 blocks...rulers...Judy clocks--ALL of it--is on open shelves and ready for students to use when needed.
Teach students about where things go and how to access them
Because of this easy access, I do make sure my students know how to use the tools, where to get them, and HOW TO PUT THEM BACK! This takes some training at the beginning of the year, but it saves so much time eventually because when students find dice on the floor or a ruler--they can just deal with it without interrupting me. #timesaver #sanitysaver
It's not just math supplies either! Get a stacking tray and fill it with lined paper, white paper, different grid paper, dot paper, blank number lines--anything! Students can realize that paper itself is a tool...and it may inspire them to solve problems in different ways.
Don't assume students have supplies
One thing I didn't think about when I was a younger teacher was that some students may not have supplies. Our supply list has things like rulers, glue sticks, and protractors--but I know not all students come with them--for a variety of reasons. I always have this type of supply on hand in my math area so there is never any embarrassment or need to ask. Again, I want students to be independent and to have access to any tool they need.
Other Organizational Tips and StrategiesThere are other people FAR more organized than I am who can write a better post about classroom organization. That being said, I thought I'd share a few more tips of things that actually seem to improve the quality of instruction (or efficiency) for me. Colored paper in hanging files I like to use colored paper to shake things up sometimes...for problems that I have students glue in their notebooks, for directions at stations, or for headings for math sorts. I used to have to go foraging, but by biting the bullet and buying some hanging folders, my beeyooootiful paper is easily within reach at all times.
Zipper bags for math gamesI like to use gallon zip bags for my games most of the time because they are so inexpensive and easy to replace. I like that you can write on them--and I even will write what supplies are needed, how many people can play, or other directions.
For the games I use for interventions, I do put them in these nice bags from Seat Sack. I like that they are oversized, super durable, and have a spot to put a label. These are all the games I have as a part of my bundled math centers...4 games and the labels to go with them! Click here to see what I mean. I love how durable they are and that I can grab what I need and hang it on a tack on the wall next to my table so it's ready for me. They are big enough to put several sets of the game and dice, counters, or whatever is needed.
(These are the bundled game sets with labels if you are interested)
Premade exit slips and word problemsAnother time saver that REALLY helps me is that for each unit, I print off the word problems and exit slips I want to use, get them cut, clipped together, and marked with a sticky note for the day/lesson I want to use them. Realistically, I don't get through them all which is GREAT! I put the extra word problems in a vertical letter holder to use as warm ups over the next week ( I love to keep using problems as review even when the unit is finished!) and the exit slips in a different one. I am a firm believer in continuing to measure skills--so if we finish our unit on partial products, my students can count on exit slips on partial products sprinkled in for the rest of the year. This is so important as I plan interventions--to makes sure students retain their learning and get reteaching when needed.
Get a mobile math cart!Seriously. I use this cheap piece of plastic ALL. THE. TIME. It stores my whiteboards, a bin of markers and erasers, and then whatever else I want...fraction pieces if I am meeting with a fraction group...task cards if I need those...and I can move it to wherever I want. I often move my "teaching area" around the room based on how much space I need, so it's awesome to be able to relocate this "hub" either to where I am--or far away from me if students NOT working with me need it.
Want a FREEBIE to help you do some classroom planning of your own?
Here we go! On to challenge 3. If you are just joining us, I have linked to all the other posts related to this summer math challenge at the bottom so check them all out1
Today's challenge is all about reflecting on problem solving--how we teach it AND how we make it accessible to students. I am hoping something in this post resonates with you--and if it does, please consider dropping into the Facebook group and sharing your thoughts!
Let's get rolling...
First of all, I want to go on record as saying that I think it's crucial that we, as teachers, understand that teaching the act of "solving problems" is very different than using word problems to practice already taught skills. My point is this. We can give students word problems that ask them to multiply. Or compare fractions. Or add money. But the act of TEACHING students how to solve problems is another entity all together. They are both important--but we need to be mindful of what we are working on when we select our problems.
Secondly, we often use the term "problem solving" and "word problems" as if they mean the same thing. Students can be provided MANY situations where problem solving is required--but are not word problems. More on THAT later! Today's post is about incorporating more word problems or "story problem" into your day. As we know, making math meaningful with real world applications is critical. Word problems can be a great way for students to see how math ties to the real world--as long as we find good problems! Teaching Problem Solving Strategies
First of all, I think it is really important to give students problem solving "tools" in their toolbox. So often our textbooks teach one strategy in each chapter...so they might have to wait until chapter 9 to learn that they can draw a picture to solve a problem! I'm not a fan of that approach, and prefer a problem solving "boot camp" at the start of the year to get students thinking about and using different strategies.
That way, as different problems come up throughout the year, they can draw from this foundation. Knowing how to work backward, draw a picture, make a table--these are all so important not just on the one page of the math textbook, but for their rest of their mathematical lives! Although I won't go into this in detail in this post, these strategies are integrally tied to the Standards for Mathematical Practice and other rigorous math "behavior" standards.
The image below is the set of task cards I use at the beginning of the year to teach 7 different strategies. I explicitly teach each one--then the last set of cards asks students to apply what they have learned and select an appropriate strategy. It's also available in a digital format. Just click the image or HERE if you are interested. (Also available in a DIGITAL FORMAT)
Word Problems As Warm Ups
Another way I like to get students problem solving is to mix things up. Research has shown that the first ten minutes of math class is the time when students are most "ripe" for engagement--and so often that ten minutes is spent doing procedures or correcting homework! I'm a firm believer in moving RIGHT into math with a quality warm up. Whether this be a number talk, a math discussion--or a word problem--getting students engaged with and talking about math is so important.
I do this in a few different ways...see if any seem like they could work for you!
I project one problem on the board and students first talk about it, then solve independently, then share solutions and thinking.
Each student gets a copy of the problem to glue into their math notebook, they work to solve independently, then share in pairs or bring it back to the whole class for a discussion.
Provide a problem (maybe a task card, maybe projected) where a small group first discusses strategies that would work (no paper and pencil!) and then students go back to try it on their own.
Students work to solve a problem on their own and then different students share their strategies with the class or under a document camera. This can also be a great time for students who organized their work really well to showcase that!
Solve a problem as a whole class and then send students off to try writing a similar problem.
Use a problem that has blanks instead of numbers and then give three choices of numbers to use...students can pick their level of challenge
And so many more!
I think it's a lot more engaging when you mix up the problem solving in different ways--and it gets students really "doing" math in those first minutes of class.
Word Problems on Display
Another great way to incorporate more problem solving is simply to have tons of problems available at all times! Problem solving is ALWAYS an option if students have extra time in my class...never is there a "What should we do?" because no matter what, there are ALWAYS problems around! You can even find ways to differentiate...by printing on different colors, putting them in different colored pocket charts, or labeling bins at different levels of challenge. This is a perfect way to help students do a little self-assessing about their readiness for different tasks--and if they have a true growth mindset, it is fun to watch them push themselves toward more rigorous problems!
Whether it be on one of my problem solving pocket charts or a bin of problem solving task cards, there are specifically chosen to either complement the content we are working on or to merely engage the students in meaningful, motivating problems. This is a perfect time for me to pull out some of my seasonal problems or problems that have "cool" and extreme facts or that pique their interest. I love writing problems with students' names and interests in them as well! Once they have the tools in their toolbox, my students actually gravitate toward these problems when they have extra time!
Cooperative Problem Solving in a Math Workshop
Like previously mentioned, having problems around the room is a great way to provide students with problems. It's also a great way to build a center or station if you are using math workshop. Students can work alone OR collaboratively on problems that are chosen for them--or that they can freely select as mentioned above. In other words, you can have problems around the room for fast finishers, but you can also have those problems be a part of a math workshop plan.
Perhaps you might have one problem that is "required" and then students can use the rest of their rotation to select from other problems. Or you might ask students to solve a problem in two different ways...or make a "mini poster" of their problem that clearly shows their steps. I do this once in a while as a sort of "final copy" of a problem...where students can really look at the work they did and make improvements to their precision, accuracy, and organization and then can use that poster to showcase their work. You have tons of options--and by getting problems ready ahead of time, this is an easy station to use...and you can mix it up just by asking students to approach the problems in different ways.
Ways to Differentiate and Scaffold Problem Solving
One of the many "truths" about teaching as that no two students are ever in exactly the same place. There are times when working on the same problem is meaningful, but there are other times that we need to be mindful of these differing abilities. Here are few nuggets to ponder.
Sometimes students can tackle the same problem if you make "tools" available to them. If you are truly working on the problem solving process and not a skills (like subtraction), why not make manipulatives or calculators available? That way students who don't have the math computation skill can still work to understand the problem itself and work to solve it.
One of my FAVORITES (and this is why so many of the word problems I write do this) is to have problems that have a "part 2"...a "challenge" component for students who easily manage the first part. This puts students on equal footing for the first part--but allows those who are ready to move on to the next part. This also would allow you time to meet with those who need help on the first part while the others tackle the second part.
Work in pairs! This is a great way to make problems more accessible to students.
Do a "presolve" meeting with anyone who is interested. What I mean by this is...invite (or require!) students who need a quick discussion or read-through of the problem to meet with you first so you can get them off on the right foot. Don't give everything away...but read through the problem with them, ask them what they notice, maybe even ask them to share out what strategies might get them started--and THEN send them on their way.
Put "hints" up someplace in the room. A simple piece of folded paper taped to the board with a hint inside can free students up who get stuck beyond "unsticking" without needing teacher help. Even a series of hints can be useful!
Have students offer to be problem coaches for the day...people other students can go to for ideas and hints. You WILL have to teach students how to give hints rather than do the work for them...and sometimes teaching students to ask questions is the best way to do that. It works for you too--teachers often give away too much to students. Try asking questions like, "What do you know already?" or "What have you tried?" or "What is confusing you?" instead of SHOWING them the next step.
Use problems that have different number choices (see above)
Have your problems around the room categorized...maybe a green pocket chart for "go ahead" and try for easier problems and a yellow chart for "slow down" before you choose? Color coded envelopes or bins? Or check out this post for some other ideas.
Teaching Fractions? Then Why Are They Solving a Money Problem?
One thing that I have stated over and over for years is that we often take away our students' thinking by how we make our teaching decisions. This is certainly true when we teach math.
In particular, after twenty-six years (and counting!) of teaching, I have heard things come out of the mouths of babes (and teachers) that make me stop and reflect. About 15 years ago, I was teaching a math lesson and was listening in to a conversation two students were having about a word problem and I heard this:
"Well, we have been working on multiplying all week, so this must be a multiplication story."
And it stopped me in my tracks. Since that day, I have made a CONSCIOUS effort to immerse my students in true problem solving...the kind where they have to "make sense" of the problem on their own, choose from their bank of strategies, and then try out their plan. So when we are immersed in fractions, students may find themselves warming up with a money problem. Or when we are working on partial products, students may need to divide to solve a problem. No longer do I do the thinking for them (by choosing a fraction word problem during your fraction unit, you have done part of the work)...at least some of the time! Of course, when I teach multiplication, we DO need to solve multiplication stories...but that's not the ONLY time we do so. In my class, problem solving is like a box of chocolates...you never know what you're going to get.
One thing I think is important to reflect on are the "verbs" we associate with teaching and learning with problem solving. Do we observe? Coach? Question? Guide? Listen? Watch?
I think so often we don't. We rush. Tell. Help. Do.
And what about the students? Do they think? Listen? Watch? Try? Adjust? Or do they wait? Freeze? Ask? Quit?
One great thing to do is to lay out some of these verbs for ourselves--and our students. Making an anchor chart of "my job" and "your job" is a great way to help craft that culture of math investigation and mindset. Give it a try--see what you and your students can come up with!
One shared responsibility teachers and students DO need to have is assessment and self-monitoring (more on this in an upcoming challenge!) but since we are on the subject of problem solving, I thought I'd link to a problem solving rubric freebie if you are interested in trying one version of a rubric. It might help you and your students get on the same page for the complex world of problem solving--or might inspire you to write one together!
So...if you want to do some thinking about problem solving and word problems in YOUR classroom, I put together a little freebie of "thinker questions" and space for notes if you are interested!
Here are some of my favorite word problem resources...see what you think! (and shhhh....I'm putting them on sale for just a few days so grab any that seem appealing!)
Now if you missed the other blog posts--here you go!
(Link to join the FB group is in each of those posts)