Fractions and Decimals Made Easy

Fractions, Decimals and Percents hanging from a ribbon across a wall.
Hang rational numbers from a clothesline to generate great mathematical conversations about comparing numbers!

If teaching fifth and sixth graders has taught me anything, it’s that fractions and decimals can be ABSTRACT and TRICKY… and that kids have to be developmentally ready to perform operations on them. The good news is- the standards aren’t encouraging us to get kids to add, subtract, multiply and divide 5/32 and 16/71! We make equivalent fractions as a strategy, we multiply and divide to resize, or scale– so there’s more purpose behind the work than there was once upon a time! An activity that never gets old- and grows number sense- is comparing numbers. As a result, we compare fractions and decimals in a variety of ways in the upper elementary classroom. My favorite- is the clothesline. This is super easy to DIY and to differentiate on the fly.

Clothesline Activity

Index Cards, Markers, String/ Yarn for a clothesline

To prepare: fold index cards in half so that they can “hang” on your clothesline. Write a fraction, decimal or percent on each card. String your clothesline across the board or wall and attach with magnets or tape (or tie to something).

Pass 6-8 cards out to students. Tell them they will take turns coming up and placing their card where they think it belongs on the clothesline. In the end, cards should hang from least to greatest. When a student hangs a card, they need to explain to the group why they placed it where they did. This is a great opportunity for communicating our math thinking. It’s also a learning opportunity for everyone listening!

Tent cards with fractions, decimals and percents in red, green and blue on white index cards
Fold index cards in half to create a stack of cards in no time.
Considerations
  • The first cards are awkward to place because the clothesline is empty! Code the first and last cards in the range green, and invite those students first. Then the board is “set up” for play. It’s also an opportunity to differentiate. Strategically hand out those green cards! Maybe you have a student who needs a confidence boost?
  • Set norms around discussion. What do you want students to do if they disagree with a placement? This is where the most growth and learning happens! As students’ number sense develops, the distance between hanging cards will become more important! They will want to “slide” cards over. How should they communicate that they’d like to do this? I usually try to hold “sliding” off until the end- but when it’s a major slide- they can’t contain themselves:)
  • Some cards will be equivalent. I usually have kids stack them. If you have a magnet board you could put them above and below the clothesline.
And Also…
  • Partnerships build communication skills and confidence. Sometimes I send 2-3 kids up together with one card. And other times I pass cards out and have students chat with a neighbor about their card before we start building the clothesline. This helps decrease anxiety and pressure some students might feel and gives students one more opportunity to talk math!
  • Color coding is great for differentiation! So color code the cards for yourself so that when you pass them out- you give kids a green, blue or red card on purpose.
  • 0-1 is a boring range!!! So is -1-1. Kids are always looking at symmetrical number lines. That’s not real life. Mix it up! Try 3-4 or -0.50-2.
  • Reflection. Even if this activity lasts 10 minutes, your kids’ brains will be working overtime. Capture it somehow. A math journal, an exit slip… Post a cellphone picture of the clothesline in your Google Classroom and have students comment. Do something:) There are some reflection sheets here too!

Here are three games that build Fraction & Decimal Flexibility that could be used in centers, small groups or even as a whole class!

Have fun! And get flexible. This is a great Class Opener that has a huge return on investment. Also, “the ones who are doing the talking are doing the learning” so there’s lots of learning going on here!!!

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Classroom Word Game

You know that buzz of collaboration and learning that you hope for everyday? It happens when we play this game. Every. Single. Time. If you like Boggle, you’ll love this game. Word Wrangle is a fun classroom word game inspired by my love of Boggle and also my love of quiet. Once upon a time, I bought SIX Boggle games for my first year teaching sixth grade. I let my students open the shrink wrap (for effect- because this was going to be so awesome)… and then I heard it. The sound of 25 solid letter cubes banging around in a hard plastic echo chamber, multiplied by six. After that, the Boggle games went away.

Why I Love This Game

This is absolutely my favorite game to play with my class. I make it a point to teach this game early in the year as we are learning procedures and routines. As a result, this is an amazing back up plan, sub activity and party game in my classroom. We start by playing as a whole group until students understand how to play. After that, I group students in so many different ways! I often think about their spelling success as I group them. The game is more fun when kids play against others with similar skills. When this kind of grouping is done- every board is challenging to every student! I never see my strongest students work as hard as they do when they are Wrangling Words against other students who are just as strong in reading and spelling. Likewise, students who often give up on challenging tasks, expecting they won’t have the skills to succeed- LOVE this game. I group them thoughtfully, so that they are playing against others with a similar skillset- and they are always begging for one more round. Lastly, every year I am surprised to find some struggling learners who excel at this game. So, mix up those groupings often, and you will learn so much about your kiddos!

Teacher Hack

I print out my game boards on different colors of card stock. When my class plays in small groups, every group plays with the same game board. at the same time I do this so that after each group has determined a winner, we can share out some of the winning words from each group. As they share, players’ eyes dart around their card searching for each word. I hear lots of “oh man” and “how did I miss that?” Every minute of this game is a learning experience. Usually, I place two game boards at each group so that in a group of 4-6, no one is looking at an upside down card. I do not give students their own game boards because I think managing the materials and sharing is an important part of this game. I set a 3 minute timer for students to hunt for words. When the timer goes off, we switch gears and start the the share out and cross out part of the process.

5 multicolored word grids, game boards
Color coding my Word Wrangle boards helps me manage multiple groups at once with ease!

 

Building Community through Discussion

Class Discussion Norms

(In my class, these become our Community Norms and replace any “rules”)

A world community painted on hands with doves
Build a community of empathy and caring in your classroom through academic discussion.
  • Equity of Voice: Monitor your airtime. As a group member you are responsible to be a speaker AND a listener. You are also responsible to invite others to speak. Equal(ish) airtime is the goal. Our community values all voices.
  • Active Listening
: Eye contact, nodding, being sure you respond to a comment with a related question or comment. Build on what others say. Our community believes everyone should feel heard.
  • Respect for All Perspectives
: You will not agree with everyone’s ideas. Work to understand their thinking. Our community values diverse perspectives.
  • Safety to Share: Your language, tone, body language and overall behavior should invite others to share differing opinions. Approach others’ ideas with curiosity and an open mind. The goal is never to be right, it is always to learn. Our community values safety.
  • Self-monitor use of Electronics
: It’s hard to feel like your ideas are important when you are speaking to the top of someone’s head because they are staring at their phone or their laptop screen. Our community values you and your ideas.

*Adapted from the norms used by the New Teacher Center during the best trainings of my life!


How Can We Create A Community that Values these Norms?

I gradually release student responsibility. Here’s how:

  • Sentence Stems & Explicit Instruction. Require their use. Fishbowl small groups. Analyze their discussion as a class. Data collection tip- let observers record tic marks for certain sentence stems or behaviors you’ve agreed are important. Current Events Discussions are a great way to practice these skills within an organized structure!
  • Conduct whole group discussions- focusing on the norms and sentence stems. REALLY focusing on them. With the same vigor you focus on routines and procedure in September. You hate yourself when you relax about them in November and vow you’ll never do that again. Do better with this. They need the structure to feel safe.
  • Pull small groups for discussions (maybe even half the class). Coach them. Invite a few students to be observers/ analyzers with you. Share the highlights with the whole class. Find observation sheets here.
  • When you feel they are ready, divide the class into small groups (4-5 students max). Let them discuss! While you monitor, record excellent phrases and interactions and share them publicly as soon as it’s over! Provide students an opportunity to reflect on paper after discussion. Download my free Discussion Reflection Activity when you subscribe below.
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Current Events Discussions

Current Events. It’s been done to death. And I get that. What I’m going to share with you is not about current events at all. The context just happens to be Current Events- but it could be anything. It’s about academic discussions- conversation. Do kids really know what that is these days? Chances are they do more discussing in school than out of school- but wouldn’t it be nice if there were more conversations happening everywhere? Fewer interactions, with cell phones in hand- and more eye contact, active listening and questioning? Ahhhhh!!! My teacher brain is in heaven just thinking about it! And my mom brain is pretty psyched too.

Rocks on a beach with text in front of them about discussions

A few years back, I was inspired by some AMAZING parents in my classroom. These parents were involved- I’m talking Family Book Club at 7:00AM before school involved. They would do ANYTHING. As a result, I tried to incorporate some type of authentic home school connection in all of our subject areas. These families inspired this series of activities- and it’s been successful with many classes since… even classes without that crazy- involved crop of parents;) What has remained the same though, is that having quality discussions in class- where everyone is set up for success– leads to more discussion at home (and in the lunchroom, and the hallway, and art class). When kids are engaged in a topic- ENGAGED- and have opportunities to discuss it in a safe space (our classrooms), momentum builds… and those discussions continue. And if we take our time, really go slow to go fast… they take those discussion skills and apply them to all of the relationships in their lives. They debate important topics with integrity, challenge one another, and change the world for the better. (No pressure!)

The Making of  Amazing Current Events Discussions

*Interact with an assigned topic. Listen to a podcast, watch a news broadcast, read something.
*Process that new information. (Complete assigned response sheets in Events in Our World)
*Participate in a class discussion focused on the questions that were answered while processing that new information. Check out my tips!
*Engage an adult in your life in a discussion about the topic. (More details in Events in Our World)
*Participate in a short class discussion focused on new perspectives from that discussion with an adult.
*Reflect & Self-Assess your discussion skills (Get my free guide when you subscribe below)

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My Takeaways

All kids participate when they are prepared and encouraged. For me, that meant that when I had some students who would not do homework- I made sure not to assign steps 1 and 2 as homework. Sometimes I assigned all students that work in class. Other times, I found opportunities for a few students to accomplish these tasks during the day. In all cases- those students participated in class discussions and engaged an adult. Also, I use “an adult in your life” very purposefully. For some students that has been a family member, for others a dance teacher and for others- the adult supervising Office Detention. All of those work.

beach scene with quote about discussions
When I worry about the success of a lesson, my inner control freak comes out. Early in the year, when we are beginning the work of discussions- everyone interacts with the same assigned topic and reads the same article or watches the same news broadcast… in front of me. But, guess what? It’s fine!!!! We make our way to the place where lots of differentiation is happening and my blood pressure stays under control. So- know yourself and do what makes you feel comfortable. Go slow to go fast. You are building a community.
I’ve also learned that kids are proud of their grown ups. Even the “too cool for school kids” who hate getting parent signatures. I’m totally shocked by this EVERY YEAR! I always devote way more time than I mean to in the beginning, to that- “how was last night’s conversation at home” discussion. Eventually kids discuss it in groups, so in 10 minutes everyone gets a chance to share and I can get the highlights. In the beginning though- it’s important that Joey and Alison both share about their discussion publicly if their hands are up. And they beam with pride!!!

 

3 Classroom Discussion Musts

Using Sentence Stems and Explicit Instruction for Classroom Discussions

Teaching discussion skills can be daunting! You know you want productive, positive discussions… but how do you get there? Here’s some of what works for me!

  1. Body Language & Politeness Matter
  • Eye Contact: looking directly at the speaker lets them know they have your attention
  • Inviting Posture: Facing your body toward the speaker with an open posture invites them to share. Avoid crossed arms if you can!
  • Use your group member’s name when addressing them.
    Ex. “Dan, can you tell me more about what you thought the author meant by…”

man crossing arms

2. Paraphrasing lets the speaker know you have listened and understand.

  • So,…
  • In other words,
  • …It sounds like…
  • There are some key points you’re bringing up…
  • From what you’re saying,…

3. Clarifying lets the speaker know you have listened but do not fully understand.

  • Would you tell me a little more about…?
  • Let me see if I understand…
  • Can you tell me more about…
  • It would help me understand if you’d give me an example of…
  • So, are you saying/suggesting…?
  • What do you mean by…?
  • How are you feeling about…?

Let students collect data on their use of these important behaviors! Encouraging them to formally reflect on their performance after each and every discussion instills in them the importance this work.

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Using Current Events as the Context for Structured Academic Conversations

Building a Classroom Community through Academic Conversations

DIY Projector Screen

You finally have your own classroom!!! No more shuffling around on a cart, lugging your whole life with you every period of the day… no more “borrowing” other teachers’ classrooms and hoping you left them as neat as you found them.

Now What

Now, you’re ready to make this new space work for you. One of the biggest challenges to classroom set up is that projector screen. It’s no one’s fault. It was hung uniformly, matching all of the other classrooms… probably with an antique overhead projector and transparencies in mind. More importantly though, moving it is not topping anyone’s to do list… there are much bigger fish to fry- from a property services standpoint. But, in your world- a thoughtfully place projector screen could make ALL the difference. It did for me! When I added this DIY projector screen to my classroom, things changed- and FAST! No more distractions for kids working on the class warm up. The problem wasn’t just that occasionally a classmate would block someone’s view while walking to their seat- it was that staring at the warm up on the screen in the front of the room at the start of class, provided an unintentional “social check in” for my easily distracted kids. empty classroom with projector screen in front

It didn’t matter if I moved their seats- it didn’t help them to “pay attention”… they were! But- every minute or so one of their besties walked right into their line of sight. That’s REALLY HARD for a middle schooler to ignore. For weeks I had joked with Distracted Danny that if he could pick where the screen went it would be better for everyone. Every couple of days he’d remind me, “you know, if you just move it up high and in the corner, we’ll all be able to see it better…” He was right. But I would never get anyone to hang a screen in the corner!

projector screen in classroom hanging from ceiling

So What

So, I tried a white sheet. I tried chart paper. I tried a regular sized piece of foam board… and finally this. An extra large piece of foam board from the Custom Framing department at Michael’s Crafts. I stuck some Command strip hooks on the back of it and used string to tie it to the ceiling tile spacers in my classroom. About $10 and 10 minutes to make a significant impact on student learning.

messy papers behind student reflection sheets              Projectable slides in front of book shelves base ten blocks on student worksheets

Getting Students to Use that Feedback

I used to cringe watching students stuff papers into their folders to be lost in the locker abyss… after I had spent so much time thoughtfully providing feedback on their work!! I spend so much time writing thoughtful questions about their math thinking and comments aimed at pushing their scientific curiosity… It was killing me to know that none of my feedback was likely going anywhere but the bottom of a messy locker!!! The ultimate frustration.

A few years ago I decided to tackle this problem head on. I knew that students could learn and grow if they sat, and really thought about my feedback. So- I made some changes. I decided to protect some time for exactly that. How could I expect students to read my notes, review the content and reflect on their learning if I didn’t show them how? Students needed to see that I valued their interaction with those assignments if I wanted them to value it too. And so began RRR&R. I dedicate a class period every few weeks to this and students and parents alike have seen the benefits.

My Goal: Students will think about the content, their work habits, and their progress.
This work is not about simply giving students time to change their answers and fix mistakes. This is the time when students will reflect upon the better answers they can come up with for the science test they weren’t proud of, and realize the study guide would have helped! Students need time and repetition to make those connections and draw those conclusions. And, they need to do it themselves.

Things that Matter

Oftentimes, I give students a few choices of assignments they may work on during this time. I don’t want anyone revising spelling homework or a math quiz with a score of 98% correct- I want students to dig deep and to grow. There are many times that I will notate right on an assignment (when I am grading it) that I want it revised. Sometimes I do that when I think my feedback is particularly powerful or if I feel a student is on the cusp of a breakthrough.

Home School Connection

These assignments and reflections might go home to families (there’s a Celebrating Success at Home Page), but ultimately end up back in student portfolios in our classroom. These make great conversation starters for student and family conferences. Students are empowered by their growth, and the language they develop as they learn to describe their learning is powerful.

I hope that this serves you and your students and families well!

Messy papers with student worksheets on top

Subtraction with Renaming

Trading to Rename
Standards for Math Practice 4

We have moved on to subtraction with renaming (2.NBT.7). You might call this regrouping… but really- if we think literally about what’s happening- we’re also giving the values new names! 50+10 is a different name for 60. So, renaming, regrouping… you know what we’re doing!

What’s Working

I’ve been doing a lot of this work with students in small groups and it’s amazing  to see students talking and thinking about making trades, or renaming numbers. In a small group full of dialogue, students physically traded one of the ten rods that makes up 60 for 10 unit so they can more easily subtract 13. We talked about the value of 60 at the start, during and after the trade. Students giggled about how I could still buy exactly 60 $1 ice cream cones- no more, no less; at every phase of the trade. They knew that whether 60 was composed of 6 ten rods (60+0) or 5 ten rods and 10 unit cubes (50+10), its value remained constant. We worked through a few more bare number problems that also required renaming to get more ones and I really emphasized how accurately our recording matched their physical manipulation of the base ten blocks as well as their thinking. Students recorded on white boards, just as I had… and I expected we were good to go! Not so fast. About 1/3 of my students were not able to demonstrate their learning with much independence… even with 60-13. Even if I talked about ice cream cones. These students seemed to rely heavily on the scaffolding that came from our discussion throughout the trading process.

Now What?

So, I decided they needed a trading center- a place where they could be successful and independent with the skills that this high level work demanded. Here are some of the recording sheets that are guiding their work. I needed them to build confidence and more deeply conceptualize the equality of the value of the numbers they were composing, both before and after renaming. They needed to deepen their understanding that values can be represented in multiple ways. After observing students’ success with this work in centers, I realized this center had potential value for all of my students. It provides an opportunity for students to focus on and practice their recording, outside of the context of the subtraction problem itself.  Additionally, it is forcing some of my higher level students to build, revisiting a more concrete experience with numbers. This helps me prepare them to rename to get more tens, hundreds etc. They are finding the challenge numbers particularly fun to work with, and I appreciate the opportunity for students to grapple with these situations in isolation, as opposed to in the context of a subtraction problem. Having this more isolated experience, makes them more confident, and less distracted by the challenge in the midst of a problem. I hope these ideas work as well for your kiddos as they did for mine!!

Alicia:)

 

PS… Here are some Place Value Games we love and here’s a Place Value FREEBIE to try with your kids today!

Concerns About Counting

In my second grade classroom, I’ve recently identified a troubling gap in my students’ learning… Counting. I know how important counting is… and we have been counting all year. We count while we wait in line, we count backwards and forwards, by 2s, 3s, 5s, 10s and more. We start in the hundreds, we start in the teens… So, why (I’ve asked myself and anyone who will listen) am I observing students struggle to cross decades when counting in the midst of double digit addition and subtraction?!?! Here’s what I mean: We are working on adding multidigit numbers and I stumble upon a student who is heading toward the wrong answer. As I listen to her explain her thinking, I realize when she counts from 19 to 20, there is a question mark in her voice and she looks up at me for reassurance. From 38, 39 she heads to 60 with the same inflection and eye contact. The scariest part… she’s not the only one. I’ve realized this is a symptom of a few more serious issues, one of which is patterning in base ten… and conceptualizing the magnitude and difference of numbers.

So what are we doing about it? After consulting with some of my favorite math teachers… here’s the plan. First, I’ve been doing an activity we call Sound of a Number for a few minutes each day.The kids love it and they are exercising an important part of their math brain. For this activity, I hide behind a cardboard study carrel with a pile of base ten blocks. Students listen hard to attempt to identify the value of the blocks I drop. We start each lesson with a quick review. I drop of each of the pieces, unit, ten rod and hundred flat; a student identifies each by sound and explains some of the different ways each could be made. For example, we could make a hundred flat with ten ten rods or 100 unit cubes etc. This helps to deepen the concept of base ten.

Continue reading “Concerns About Counting”

Classroom Teacher: Reality Check

The view from down here.
“It all falls on the classroom teacher, it always does” she reminded me. This was my mother. A retired elementary school teacher, who had made it the long haul. In the classroom for her entire career, advocating for kids, mentoring new teachers- reminding me when I express frustration in the system that, I shouldn’t be surprised because “other people just don’t get it. Everything is the responsibility of the classroom teacher.” In other words- s#!t rolls down hill. I’ve been hearing it for years. But, honestly I didn’t quite get it until recently.
I’ve spent most of my career as a middle school teacher. I guess I have that genetic mutation that appreciates the sass and limit-testing of the adolescent. Continue reading “Classroom Teacher: Reality Check”