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.
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!
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.
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!
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!
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.
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!!
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.
Lately, many of the teachers I support have been expressing a desire to take risks with new and different teaching strategies. One strategy many teachers are investigating is station teaching. Over the next two weeks I will attempt to respond to their needs as best I can through group work sessions, classroom observations and modeling.
Here are some videos from Teaching Channel.com that provide examples!