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First to 5
I am the first to admit, I’m not the biggest fan of worksheets. Too often when students are working independently on worksheets they are not fully engaged in their learning. They are going through the motions or mimicking what the teacher just did in the lesson. The assignment is not memorable. The worksheets are normally a lot of similar problems over and over and over.
I much prefer to have my students working together and doing activities that are memorable and meaningful. Over the years I have created so many of my own games and activities to have my students complete instead of the independent practice that the district provided curriculum provided. I’m not saying curriculums are bad, there are some really good ones out there. Many of them though don’t have a whole lot of the why behind the how in their instruction and the independent practice is just a worksheet full of problems.
A few years back I created First to 5. This is a perfect example of how students are getting practice multiplying whole numbers by 1/10, 1/100 or 0.1 and 0.01. The game is always varied and unpredictable. This particular skill is a 4th grade standard here in Ohio, but many 5th graders still need work with multiplying whole numbers by fractions and decimals. The game could be changed up by changing how many tenths or hundredths the students are multiplying by. This is a very easy way you can differentiate the game based off of your specific students’ needs. Change the fractions and decimals to 2/10 or 5/100 to multiply by.
I created a quick 10 minute video to show you how the game is played.
The image below shows you what the game looks like as it’s getting played. You can see how the equations on the right are shown in the “whole” on the left for the conceptual part of the game. When we multiplied 11 x 1/100= 11/100 = 1/10 + 1/100 , you can see how we colored in a whole tenth and then another hundredth in green.
If you decide to have your students play this game in your classroom, let me know how it goes and what modifications you made to it in order to differentiate it for your specific students’ needs.
Blank Regular Dice from Amazon– 40 blank dice for $9.50
Blank Dry Erase Foam Dice from Amazon – 7 for $12.99
Chunky Dice from Box Cars– $1.75 each
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Reflection Journals
The start of a new year is a time where a lot of people take time to create “New Year’s Resolutions” as they reflect on how their prior year went and changes they want to make going into a new calendar year. That’s a BIG task for adults let along some of our young learners. I saw something like this a few years back and loved implementing it in my classroom with my students. I cannot remember where I got it from, but I remember loving it!
The idea is simple. At the end of the day, your students take a minute to reflect on their day and color in the box for that specific day according to the color code to the left. This should be a minute activity. Students can keep these in their take home folders so their parents could also see how their days went. If you’d rather, keep them at school, that’s great too. It’s completely up to you. As the teacher, I took a look through my students’ reflection pages weekly so that I could take a few minutes to chat with a student who had a few bad days in a row and see what’s going on.At the end of the month students can pause and take a look at how their month went by taking quick glance at the colors. From there students can write out a reflection page and write out things they have control of to make the next month better than the one had before.
Their reflection pages will only be partway filled by the time they leave you in May, but it creates the habit and maybe, just maybe they will continue with their daily reflection. This would be a great things to start at the beginning of the school year as part of your SEL lessons. Feel free to change the color meanings. This would also be GREAT for teachers and admin to complete as well!
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Puzzling Tree
Throughout my career I enjoyed doing activities and projects with my students that got them thinking and problem solving. I knew they were learning when there was progressive struggle. The students enjoyed this activity by the end of our time allotted for it, but there were moments of frustrations for sure. In many of my classes throughout the years, I had a few students each year who found elementary school to be rather easy. As a teacher we are constantly trying to differentiate our instruction and activities to meet all the needs of our students; those approaching “grade level”, students who are “at grade level”, and those students who are “beyond grade level”. This is a fun holiday activity that gets kids thinking, but also in the wintery and holiday spirit.
You simply need:
- green construction paper for the trees
- brown construction paper for the tree trunks
- your choice of background for the trees to be glued on
- rulers
- pencils
- scissors
- glue
- small shapes cut out using di-cut or stickers
Students will get a piece of green paper that have four 1 inch thick rows that are each 9 inches long. Construction paper is 9 inches wide, so you just need to have 1 inch thick lines on the green paper like the image below. I had the lines printed from letter paper printed from a word doc, but printed on construction paper like this since construction paper is wider than letter paper. This never bothered my students, but if you need, just use a ruler to draw your lines for 1 in thick lines on the 9 inch wide construction paper. The red paper you see is what my students were gluing their trees on.
Each student will receive the 4 rows of green lines and be asked to measure and mark the following lengths: 1 inch, 2 inches, 3 inches, 4 inches, 5 inches, 6 inches, 7 inches, and 8 inches. Students will struggle with this. Most want to start measuring out 1 inch, then on the same line measure 2 more inches and so on. See what is a common mistake below and then a required measurement will be missing and the top and bottom will be a wasted piece. There should be no extra pieces.
I let kids struggle and encourage perseverance. I keep reminding my students to have a growth mindset. After a good amount of time, 15 minutes or so, I may give them the hint to think in terms of part-part-whole. Some students will start to have light bulb moments, some will still struggle. Let them struggle.
To save yourself time of having to make more copies of the green paper, students have to get teacher approval before they are allowed to cut their pieces apart.
For students who continue to struggle, encourage them to measure the whole wide of the paper. We are looking at 9 inches. Have students go back and look at the lengths we are trying to measure out and remind them we are thinking in terms of part-part-whole. You’ll hear a bunch of “ah ha” moments.
You can take this activity a step further and have the students decorate their trees with di-cut shapes or stickers. When I’ve had students decorate their trees I have then made shapes worth values. In 4th grade I would the values be a bit bigger so my students were then working on multiplying with multi-digit numbers.
Lastly, if you want to take it even a step further, you can have white paint out and use Q-tips or their finger tips to add “snow”.
Let me know if you decide to do this activity with your students. I’d love to hear how it went and see some of your students trees!
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Holiday Shopping Project
As I have talked with my teacher friends and teachers that I work with, a common consensus is that the weeks between Thanksgiving Break and Winter Break are some of the roughest weeks of the school year.
Procedures and routines need reviewed coming back from an extended time off, whether you had the whole week off last week or just Wednesday-Friday off.
Students are excited about the holiday season that is quickly approaching and have a hard time staying focused on their school work or have a hard time being responsible and respectful while at school.
Last year as some of my students were getting squirrely and I needed to find something that worked on skills they needed more practice on (addition and subtraction with regrouping), but it needed to be an activity that they would enjoy while being fulling engaged. The Holiday Shopping Project was born!
The idea of The Holiday Shopping Project is to get students to think about gift giving and what someone else would like, while also working on adding and subtracting. You can add an economic piece to the project as well, since the students will have a budget, just like many people do when it comes to holiday gift giving.
I love that this “project” isn’t focused on a specific holiday. I have always had students who were English Language Learners who celebrated different holidays in my classroom, so it was important to me that this be holiday neutral and all students felt included. Last year I brought in actual shopping magazines I received in the mail, but that was a bit overwhelming for my students. There were so many options for them to pick from that they took forever to pick just the right gift for their recipients. After that, this year I created 2 levels of shopping cards for you to use with your students if you wish. One set has mostly whole numbers for some of our youngest learners to use for their shopping. The second set has more realistic pricing and works on addition and subtraction with decimals for our 4th-6th graders.
Teachers will determine the students’ budget to spend. There’s a place on the student recording sheets for you to put in their allotted budget. I have found it’s fun to have various budget amounts on slips of paper folded up and put in a jar or bowl, then students come up and pull their budget one at a time. It’s a fun moment in class to watch the student reactions. That also mimics real world scenarios where different people have different resources and amounts of money they wish to spend on gift giving.
I have the project set up for each student buy gifts for 9 people Feel free to adjust this to what you feel is appropriate for your students. Some of my students chose to buy for people they actually knew and some chose to buy for people they made up. With each student having a different family dynamic, I let this part be very flexible. I loved watching my students last year get excited to pretending to buy their mom or sibling something. Their hearts were definitely in the right place.
I have the Holiday Buying Project pages set up so that if you copy them front to back, take one set and have them stacked up, you should be able to fold them in half like a book and staple them together in the bind.
Please let me know what you think and if you decide to try this out with your class. I would love to hear how it goes!
Holiday Buying Project – Black and White Copy
Holiday Buying Project – Color Copy
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Division continued…
I had a friend who teaches 5th grade recently reach out and ask how we can help students who struggle with dividing by a 2-digit divisor. I made a quick 9 minute video to help her make the connection between a 1-digit divisor.
While we were going back and forth with our messages it was apparent that her students were not doing the thinking, they were mimicking her work. This is common in classrooms. When we teach with the concept of “I do. We do. You do.” the students are copying what the teacher is doing. That turns into memorizing steps and procedures. Students need to view the math and think about the problem using their prior knowledge, not how the teacher attacks the problem. Allowing time for students to share how they solved the problem is critical. School is a social environment and popular education philosopher Lev Vygotsky was known for Sociocultural Theory of Cognitive Development. This means our social interactions influence our cognitive growth. When students work together and share their ideas and thoughts with one another, they are able to further build upon their initial thoughts and teach and learn from one another.
As you watch the video below, hopefully you’ll notice the opportunity students have to decompose the dividend of a problem so that it is friendly for that particular student. We want students to have the freedom to thinking about numbers flexibly. I just wanted to walk through a couple more problems to help you and eventually your students truly understand how we can make problems friendly for students.
I also suggested to my friend to pull the students who are really struggling with what division means in general (conceptually) into a small group and work through the basics of division with place value materials. A great game I play with students is called Cookies. It’s adapted from the game Leftovers by Marilyn Burns.
The Cookies game directions and recording sheet are linked below. I’ve also added a video of Kristin from Making Math Make Sense and I to walk you through how to this activity should work. Please let me know if you have any questions.
Cookies to print – I use construction paper cut into 3″x 3″ squares and 2-color counters or Cookie Crisp cereal when I play this game in person. Below is a video by my friend Kristin on how to play with hands-on materials. https://youtu.be/fCobQnWJQc8
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Division with Multi-Digit Dividends
This may be an unpopular opinion, but the traditional algorithm for division is outdated and needs to go away.
Let me explain. The traditional algorithm for any computation (addition, subtraction, multiplication and division) is a procedure and when taught alone does not make math meaningful and make math make sense to students. We as adults need to remove our “algebra glasses” and recognize that students need to learn new topics conceptually first. Students need to discover how they can use ideas they already know to solve a new given problem. During reading instruction I’ve seen a lot of teachers relate a texts to other texts, texts to real world, and have students relate the text to themselves.
Are we doing the same in math class?
Are we expanding the world of comprehension with your students?
Do your students…
- Create mental images?
- Use their schema?
- Ask questions?
- Make connections?
- Determine importance?
Let’s build problem solvers. Problem solvers do these four things consistently.
I was recently asked to created a quick video for some 5th grade teachers on other ways they can teach division to their students. This video isn’t “quick”… it ended up being about 35 minutes. Sorry! I do think that all 35 minutes are valuable though. I don’t rush through things, I tried to take my time and make the strategies meaningful for you to understand.
Making the shift from teaching procedurally to conceptually to discovery based is hard. It’s uncomfortable for us as adults because that is not how we were taught, but that doesn’t mean we shouldn’t do it. We owe it to our students to learn how to look at math differently, so that they have a chance to truly understand the math behind the math and not memorize procedures.
Grab a snack, your favorite beverage, maybe even your teaching partner down the hall and give me 35 minutes to see if I can #makemathmeaningful for you.
Let me know what you think and if you want to learn more about how we can teach division (or any other topic) more conceptually.
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Esti-Mystery….
When I get asked the question, “What is one, quick activity I can do with my students to build number sense?” my response just about every time is Steve Wyborney’s Esti-Mystery.
The Esti-Mystery activity is a FREE download from Steve’s website that is leveled to reach all of your mathematicians. You can sign up for emails from Steve as well and the Esti-Mystery arrives in your email daily. How much easier can this be? All you need is a projector from your computer, Powerpoint or Google Slides, and you are ready to go.
His schedule is as follows:
Posting Schedule
Mondays
- 3-Container Estimation Routines (All Grade Levels) will be posted here.
Tuesdays
- Esti-Mystery (Kindergarten)
- Esti-Mystery – Level 100 – (Grades 1-2)
- Esti-Mystery – Level 300 – (Grades 3-8)
Wednesdays
- Esti-Mystery Level 200 – (Grades 1-3)
Thursdays
- Esti-Mystery – Level 400 – (Grades 4-12)
Fridays
New Videos to go with my his book, The Multiplication Advantage: Journey Into Multiplication
As a 4th grade teacher, I had students that were on all different levels. I ended up doing all 3 Esti-Mysteries on Tuesdays and then the ones on Wednesdays and Thursdays. I love how the Esti-Mysteries work on vocabulary at the same time as they work on number sense. Each Esti-Mystery takes about 5 minutes in class. You want to give students time to turn and talk with a classmate about WHY they picked that estimate.
This year Steve is changing things up and has a 3-Container Estimation routine instead of his Esti-Clipboard. I love them both and feel like you can’t go wrong.
I wanted to add a little something to the Esti-Mystery routine in my classroom and created a recording page to help students get their thinking down. The idea is for students to have the recording page in a plastic sleeve so the students can use the same paper each day of the school year.
EstiMystery Thinking Board 100s Chart Bottom Up– NEW 11/15/22
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Mathematical Vocabulary (Anchor Charts)- Part 4
Decorating classrooms is either a perk of being a teacher or just something else on our never-ending to do list.
Some teachers love going into their classrooms over the summer months and creating some of the most magical spaces for student learning. Some teachers would rather not decorate their classrooms to look Pinterest worthy, and set up safe and happy learning environments without all the extra.
My classroom to start the year in 2021. Not a whole lot hanging up. Lots of space to add meaningful learning. Desks arranged in groups for students to be able to communicate thinking with one another in pairs or small groups. Two carpeted areas for students to be able to get down on the floor to play math games or complete activities at. My Daily Number Sense Routine up front on left in a prime real estate location. Either way you choose to do up your room, that’s 100% up to you and there is no judging here. I wrote a blog post a little over a year ago about classroom decor. It can be a hot topic, but my opinion is… less is more to start the year. Take a few minutes and read about why I say this.
Classroom Decor… or Lack Thereof
As I said in the linked blog post, Edutopia has an article and a video about setting up your classroom. Check them out here…
Do’s and Don’t of Classroom Decorations
5 Tips for Decorating Your Classroom
What struck me was the very last sentence “The takeaway: Classroom walls should feel warm and lively but not overcrowded—keep 20 to 50 percent of the wall space clear, and fill the rest with student work, inspiring pictures, and learning aids.”
Vocabulary with operations is key in understanding what to do in real-world problems. In 4th grade I didn’t need to get into the visuals for addition and subtraction as much as I did for multiplication and division. These were made with the students as the student made the same thing in their math journals. I had the pieces cut out and ready to go before class started using an Ellison Di-Cut machine. These posters were made as we went throughout the school year and were not made before hand, hung up, and waiting for the students. This is where anchor charts come into play. Anchor charts are learning aids, but could also consist of student work. I’ve been working in a number of classrooms lately and coaching through Zoom. Much of what I’ve seen and heard from teachers is, students don’t know the vocabulary. My most common suggestion for teachers this fall has been creating anchor charts with their students. A lot of my focus in the last few months has been on building number sense and flexibility with numbers. Many of the teachers I am working with are implementing a Daily Number Sense Routine. Through the various grade levels and the different parts of the DNSR I have noticed a lot of the mathematicians wanting to share their thinking and communicate their thoughts. It’s been amazing seeing and hearing about so many students getting excited about math and communicating their thinking. As I have sat through lessons and had conversations with teachers the same thing comes to the surface, student use of vocabulary is lacking with their explanations.
This takes us back to classroom decor. We’ve all seen the store-bought beautiful posters that cover the topics being taught in our classrooms. We find just the right spot and use all sorts of adhesives to hang them up. Most of the time, students look at them once and don’t use them again (unless you reference them over and over and over). Store-bought posters become more of a decoration than a learning aide.
My suggestion is to make anchor charts with your students! When you make an anchor chart with your students the ownership transfers from you the teacher to the students. The students contribute to what goes on the anchor chart and there is meaning with it. I take it step farther and have the students create the same anchor chart in their math journals/binders.
Everything that goes up in your classroom needs to play a role and have a purpose. Take a few minutes to look around your room. What is the role of each item you have displayed in your room? I’m not saying there’s anything wrong with something that is “decorative”. If we create and reference our mathematical posters (anchor charts) with our students, the connections are created and strengthened each time we and our students use them.
I hang most of my anchor charts on my windows or from the blinds using paperclips. The blinds are not damaged in the hanging or taking down of the posters. I back all of my anchor charts so they have a lining with the sun coming through. 
I have included a few images throughout this post to help inspire you with various ways you can create and display anchor charts in your classrooms. I continue to hang my anchor charts, but if I find I’m running out of room, I move the older ones out to the hallway so they’re still displayed and seen frequently.
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Mathematical Vocabulary (Fractions)- Part 3
When I first started teaching back in 2005, I personally, did not have a conceptual understanding of fractions. To be honest, it wasn’t until about 2010 ( I was 27 years old) and I attended a professional development in Columbus, Ohio that I started to really comprehend what a fraction truly was. I was never taught that a fraction is part of a whole. I was taught rules and procedures. That’s it.
When Kristin was moved from 3rd grade to 4th grade and became a teammate across the hall, we were both on a journey to understand our standards better. We wanted to know more of the WHY not just the HOW when it came to mathematics.
When I changed HOW I taught my students, not only did their learning soar, but mine did as well. One of the first things I changed was the vocabulary I was using. Most students would come to me as a 4th grader and know that the top number in a fraction was called the “numerator” and the bottom number was called the “denominator”. A lot of teachers would be happy with that, but when my students couldn’t tell me what “numerator” and “denominator” meant, I knew I had to rectify that. Kristin and I came together and said, “What do we need students to know when it comes to meaning of fractions?” Here’s what we came up with.
I have had so many students come into 4th grade and struggle with adding fractions with like denominators that I take it back to how our primary friends do one to one correspondence with addition.In kindergarten we ask our students to count like this.
1 bear + 1 bear + 1 bear = 3 bears or 2 rings + 3 rings = 5 rings
The numbers tell us our quantity, the bear and ring says what we are counting or our value.
number = quantity = adjective
object = value = noun
Let’s give it a go with fractions.
1/2 + 1/2 + 1/2 = 3/2
Why? Why is it not 3/6? Let’s dive in…
When we rewrite this same problem in unit form, 1 half + 1 half + 1 half, it allows the students to see that we are adding halves. Halves is the object in which we are adding. They can see that 1 half + 1 half + 1 half = 3 halves.
We are adding 1 + 1 + 1 to get 3 and we are adding halves.
Almost the exact situation happened on the 2nd day of school last year. Take a look at the picture below from when we added our second half for the school year. A student gave the answer of 1/2 + 1/2 = 2/4. I got out manipulatives and we added 1 block + 1 block to equal 2 blocks. I got out fraction tiles and built 1 half + 2 half. The class was able to see that we didn’t have fourths. It wasn’t 4 parts that equaled 1 whole, but 2 halves. We built our way to writing it out below.
The same thing can be used if we are adding bigger values and different units.
3/4 + 3/4= ?
3 fourths + 3 fourths = 6 fourths = 6/4
Some of you might be wondering… What about when we add fractions with unlike denominators? That my friends is for another blog post. 🙂 I’ll be posting that in the coming weeks.
Feel free to download the Fraction Vocab below to use in your classroom to help with fractions in your classroom.
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Number Sheets
Primary friends, this is for you!
I’m going to keep this short and sweet…
I was asked by a teacher for some basic number sheets that have students working on a few things…
- Tracing the spelling of the number
- Number tracing
- What comes before the number? What comes after the number?
- Fill in the ten frame to make the number
- Use tally marks to create the number
Use the link below for the free download.
There are many ways you can use these sheets:
- Copy all pages into one journal and students can work on one page at a time.
- Add this page into our addition and subtraction “Story of a Number” book.
- Each week as you focus on the Story of ____ you can add this page as independent practice.
- Put this into a dry erase pack and the students can complete this multiple times in a week.
Let me know how you used this resource in your classroom !