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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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”

Formative Assessment Checklists

clipboard How do you capture all of the learning that occurs during discussions, hands-on exploration and collaborative group work? When there is a written product… we know we can collect and correct (ugh)… but that’s not always my first choice. When I collect and correct too much, I lose the ability to catalog and analyze and make instructional decisions based on the evidence. Instead, my school bag gets heavy Continue reading “Formative Assessment Checklists”

Dittos & Worksheets & Packets, Oh my!!

So, your school department actually has a manual for you and it’s full of printables… They were designed by educators and statisticians… and people that must know more about teaching this content than you do… so why aren’t you students engaged? Well, I am writing this post to make sure you don’t “throw out the baby with the bath water!” Before you throw away every workbook and ditto in your classroom… let’s put our heads together.

You are right, experts did design these materials, so there’s probably something that works in here…

 Don’t reinvent the wheel- Re-purpose it instead!

Here’s a template for a cube (as well as other amazing ideas- amazing wiki). Why not put the best questions from your packet on the 6 sides of the cube and let students roll and discuss in pairs? Your goal (with the packet) was for students to think about the questions, right? Imagine all the ideas they’ll get from their partner when rolling the cube??!! Two heads are always better than one.

You could listen in on student conversations and assess their Speaking & Listening Skills or their content knowledge. Another idea is to assess student learning with an exit slip at the end of class. When you encourage students to have conversations, arm them with sentence stems and accountable talk to make it as productive as possible.

What will you re-purpose this week? Let us know in the comments & you may inspire someone else to take a similar risk!

Marker_Signature

PS… I’m looking to give away a TpT gift certificate to a lucky blog commenter this week! Spread the word- bring a friend!

Student Engagement… Strategy #1

Jigsaw it! jigsaw

Regardless of the subject, brain research tells us we need many rehearsals (+20…yikes!) for new learning to stick! Learners rehearse learning when they are actually engaged in it. And, just to be clear… a worksheet with 20 math problems does not equal 20 rehearsals…( awwww, maaaan!) So, let’s consider the value of a jigsaw!

Continue reading “Student Engagement… Strategy #1”

Student Engagement- Week 2 Educator Challenge

If you are back for round two… congratulations on your successes during week one! If you’re just joining us, welcome~ we’re thrilled to have you here and hope you join the conversation! Let’s think about where we are starting!

Level 1: Projects, activities and assignments lack challenge, are inappropriate, or do not cognitively engage students. -> Level 2: Projects, activities and assignments inconsistently challenge all students appropriately and only cognitively engage some students. -> Level 3: Projects, activities and assignments are appropriately challenging for all students, require 21st century skills, and cognitively engage almost all students in complex learning. -> Level 4: Projects, activities, and assignments are appropriately challenging for all students, require 21st century skills, and cognitively engage student in complex learning.

With these descriptors in mind, which level would you say best describes your daily teaching experiences? Continue reading “Student Engagement- Week 2 Educator Challenge”

Improve your Teaching Practice: Take the 1-week Challenge!

Dear Fellow Teachers,

Let’s roll up our sleeves, take some risks and be proud of the outcomes! It’s February and by now you have a good idea where you want to focus your attention. Maybe you’ve been observed by a colleague or administrator and you have some actual feedback to guide you (yes!!) or maybe you’ve known for months and have finally dug yourself out of that pile of paperwork and are ready to go!

Mountain of Paperwork

However you got to this place of wanting to grow- I’m glad you did. All we need is some focus and a little bit of persistence and together we will make change happen! Over the next four weeks, I will post practical tips you can use right away to make change happen in your classroom! We will focus on a different area each of the four weeks, and connect the work directly to the RI Teacher Evaluation System (based on the domains of Danielson’s Framework for Teaching). We will self-assess, implement a strategy and reflect. Any comments or feedback you leave will help me to generate the next post. I will respond to your needs… Based on teacher requests, we will start with Questioning/ Prompts and Discussion Techniques.

There are lots of rubrics out there! Here are two you can use to self-assess, reflect and set a purpose for our work together around questioning!

RIDE_Questioning_Rubric     I3_Questioning_Rubric

Let’s support each other and celebrate success using feedback, comments, Facebook & Twitter. Subscribers will receive additional tips along the way, so if you haven’t already subscribed- make today the day!

So excited to get started!!

Alicia