• Math Picture Books

    Math Picture Books

    Over the course of my career as a classroom teacher and throughout my journey as a mother, I have developed a LOVE of picture books. I love reading books to students, picture books and chapter books.

    What’s even better is when I would read books during our math time.

    Some of my favorites are below:

    (affiliate links)

    One Is A Snail, Ten Is A Crab : Grades 1-3… This is a terrific book to work on counting, various ways to make numbers, skip counting, and more. A favorite extension is to have students make pages they think are missing (teen numbers).

    The Cookie Fiasco: Grades 3-7… This is a great story about 4 friends who have to share 3 cookies. It’s a great task for students to work through in groups. Don’t read the whole story to them. Read part of it and pause to give the students a chance to solve the problem for the friends. When I did this with my class, we then had cookies in class together.

    There are so many good books to use in your math classroom/block. I’ve shared below a link to an ongoing list of picture books you can use in your classroom. The title, author, Amazon link, topics covered, and extension activities are all on the sheet. The books are in alphabetical order on the first sheet, but the 2nd sheet (see bottom of the file) is listed by topic.

    Math Book Sheets File

    If you’d like to share one or more of your favorite books to use in your math classroom/block, please let me know by filling out this Google Form. Math Picture Book Form

  • Top 5 Manipulatives: Ang Legs

    If you’ve taught for very long or investigated any text book series, you’ll notice a variety of things, but one thing that I noticed is that geometry is usually taught towards the end of the school year. Often times teachers think to themselves or talk with their team members about how their students don’t know this or don’t know that in terms of geometry. Think about this… if we are only teaching geometry at the end of every year, students are being exposed to geometry about every 12 months. Every April or May, geometry is being taught, but the students haven’t had much geometry exposure since the prior April or May. I’m a big advocate of using Daily Number Sense Routines to supplement any text book series. Part of my idea of a Daily Number Sense Routine includes the learning standards from the geometry domain.

    The calendar date cards for each grade level in the DNSR that I help teachers use in their classrooms incorporates geometry standards and patterns. This particular image is from 4th grade. The date cards are reviewing types of angles. (acute, obtuse, right, straight)

    I LOVE getting math in my students’ hands. Giving students a chance to feel and build the math enhances their learning and curiosity. Getting manipulatives in students’ hands gives them the opportunity to explore, take chances on being wrong, and make corrections in a low stakes environment. Ang Legs (or manipulatives similar) is one of my most favorite tools to use when working in the geometry domain. I used them all year long in my classroom. I have used them in all grade levels K-5 when doing interventions or coaching.

    Ang Legs are a great tool to get students playing around with shapes. You’ll notice in the images that Ang Legs are made of straight pieces in various colors and various lengths. When introducing them to students, I give them time to just play with them. One of my favorite ways to get students to play with math tools is by first introducing them to students in our Morning Math Tubs. (I’ll write a post on those in the next few weeks. That’s one you do not want to miss.) Allowing students to get acquainted with and explore with a new math tool in a low-pressure, no stakes situation.

    This student used the protractors that came with the Ang Legs to build a bicycle with the pieces. Even through the blur, you can see his smile.
    These students are sharing a set of Ang Legs and building various shapes and angles.
    During morning tubs, this young man made an animal. I love when students use their creativity!
    This young man is building a “house”. Using his time with the Ang Legs during morning tub time gives students a chance to explore and be curious with these math tools.

    The Ang Legs snap together at their end points and can also snap to protractors that are included. Check out how these students are exploring with various connections.

    On top of using Ang Legs with geometry standards, I also like to add some rubber bands and geo boards into the morning tubs and my lesson plans. I have very strict rules about being responsible and respectful with the rubber bands. With the chances of rubber band snapping and shooting across the room, I also have printed geoboards that are handed out to those who cannot handle using rubber bands appropriately. I think in my 17 years of teaching, only 2 students needed the worksheets. Being prepared to have a consequence made the expectation of being responsible and respectful a little more serious.

    Ang Legs can be played with by students K-12 and even beyond. If you teach any type of geometry standard, Ang Legs are a tool that will make your geometry math lessons more engaging and more meaningful.

    *Affiliate links*

    hand2mind: Small Set

    hand2mind: Class Set (This is one of the sets that I have.)

    EAI: 6 sets with dry erase task boards

    edxeduation: includes arcs and circles

  • Top 5 Manipulatives: Pattern Blocks

    Top 5 Manipulatives: Pattern Blocks

    I am a HUGE advocate for using manipulatives in the classroom… at all grade levels.

    I have not always thought this. Early on in my career when I went from teaching Algebra I to 4th grade, I saw teachers in my elementary building using manipulatives as I would walk by and think, “Why are they playing with toys? We don’t have time for that!” Luckily, over the course of my career and constantly learning to grow as an educator and mathematician myself, but opinion on the use of manipulatives has changed. I cannot imagine teaching K-8 mathematics without the idea of a hands-on, concrete approach. Students need to feel, manipulate, and engage in the math before they can make meaning of the abstract stage of learning.

    Over the course of the next few weeks I will be writing about my favorite manipulatives to use in the math classroom.

    Starting off, let’s explore PATTERN BLOCKS.

    In a lot of schools I visit, I see pattern blocks being used in primary grades. Pattern blocks are generally used for geometry, patterns, or to create pictures out of them. Students LOVE using pattern blocks to create images. It’s a way we can incorporate math and art together. You really see joy in students’ faces when they get to be creative in math.

    I’m here to tell you that pattern blocks do not have to stay in the primary grades and should not just be living in the geometry world. In the intermediate grades (3-6) teachers can use pattern blocks to teach concepts of fractions, angle measurements, symmetry, and scale to name a few. Middle school teachers can use pattern blocks to work on the various translations.

    Over the course of my career using pattern blocks became my favorite manipulatives to use to get my students working with fractions. The basic set of pattern blocks include a yellow regular hexagon, a red trapezoid, a blue rhombus/parallelogram, a green equilateral triangle, an orange square, and a tan rhombus. Did you know each side of the pattern blocks measures 1 inch? (except the long side of the red trapezoid) Within the last 8 or so years two new shaped pattern blocks have been created and released. The brown right trapezoid and the purple right triangle have been a much needed addition to the pattern block set.

    Using pattern blocks, my 4th grade students that you see in the pictures below were able to develop a strong sense of:

    • parts & wholes
    • unit fractions
    • fraction equivalency
    • comparing fractions
    • computation with fractions


    Below you’ll find a free download that I created during my time in the classroom that I used to walk the students through identifying what each pattern block represented in relationship to the whole for that set.

    Fractions with Pattern Blocks UPDATED FREE DOWNLOAD

    If you don’t have pattern blocks in your classroom, don’t fret… there are many websites that have interactive pattern blocks.

    Didax : This site allows you to place the pattern blocs next to each other, but not on top or layer them.

    Cool Math 4 Kids : On this one you select images and drag the pattern blocks in to make the picture. It also includes the option to use a protractor to work on angles. You can layer the pattern blocks on this website.

    Math Learning Center : On this one you select images and drag the pattern blocks in to make the picture. It also includes the option to use a protractor to work on angles. You can layer the pattern blocks on this website. You can also create a picture and share it with your class with a code or with a link. Math Learning Center also allows you to change the size of the pattern blocks with the tool bar at the bottom.

    Toy Theater : This site allows you to place the pattern blocks next to each other, but not on top or layer them. On this one you select images and drag the pattern blocks in to make the picture.

    Braining Camp : You need a membership for this site. It’s honestly, my favorite virtual manipulative site. You can layer the pattern blocks on this website. You can also create a picture and share it with your class with a code or with a link. They also have prebuilt activities that you can share with your class. As I was going through the activities, there’s only one fraction one using pattern blocks.

    Room Recess : Here you can select images and drag the pattern blocks in to make the picture.  You can layer the pattern blocks on this website.

    Mathigon : Mathigon is part of the Polypad family. You can place the shapes on top of one another, but there are no pictures to try to create using the pattern blocks.

    If you want to extend your students’ fun with pattern blocks, check out Dan Finkel’s Upscale Pattern Blocks  or 21st Century Pattern Blocks on Amazon.

    • Link to purchase Upscale Pattern Blocks on Amazon here. Today, 4/11/23 they are on Lightning Deal, so act fast!
    • Link to purchase 21st Century Pattern Blocks on Amazon here.
    • Link to check out Dan’s post about his newest versions of pattern blocks, here.
  • Fraction Flowers

    Fraction Flowers

    As I’ve been in schools the last few weeks, I’ve heard teachers talk about the most dreaded part of the school year, State Testing Season.

    As a teacher of 17 years in testing grade levels, I know the stress of testing season. I know the weight you feel to plow through the content. I understand the feeling of, “Have I done enough?” I’ve sat with my plan book and tentatively plotted out what to teach when between now and the testing dates. I’ve done it all. About 10 years ago, I decided I needed to change what I was doing to prepare my students for the test. I needed to continue to teach for understanding, not just plow through the material. I needed to stick to my teaching philosophy to Make Math Meaningful.

    About 10 years ago as we were heading into Spring Break, I wanted a fun activity that my students would enjoy, but get a little bit of extra practice with equivalent fractions. I was teaching in an elementary school and knew I needed something to put in the hallway to bring those who pass it joy, but also display my students’ hard work.

    Fraction Flowers were born!

    If you are a primary teacher, don’t run… you can adjust these to be Fact Flowers instead.

    This activity is high engaging and allows the student to be flexible in their math, but also in their flower creation. When working on Fraction Flowers, students are working on: equivalent fractions, writing a fraction as a decimal, and plotting a decimal on a number line.

    Intermediate teachers, you will give each of your students a fraction. You can use unit fractions or fractions, it doesn’t matter. Be sure to give them fractions that they can find the decimal for by making the denominator a 10 or 100. If you are a 5th grade teacher, you can make the given fractions harder and have your students use division to find the decimal. You can easily differentiate this activity based on the fractions you give your students. Students have to fill out their fraction information before creating their flowers. You can see these answer sheets in some of the pictures above. The students then use those sheets to create their Fraction Flowers.

    If you are a primary teacher and want to try out Fact Flowers, change up the directions. You give each student a number between 10-20 (I’ve even had students roll a 20-sided die to get their number). Students can put their number on the center of their flower and write out different combinations to make that number. For example: 13 goes on the center of the flower, students put 0+13, 1+12, 2+11, 3+10, 4+9, 5+8, 7+6, 6+7, 8+5, 9+4, 10+3, 11+2, 12+1, 13+0 on the petals. Primary students can still create a number line on the stem and mark their number on the number line.

    I’ve also worked with primary teachers who were studying butterflies and had their students create Fact Flutterbys. Aren’t these cute?

    I have included a basic lesson plan and all of the black lines you can use to create your petals. I pick about 5-7 colors and copy each petal in each color. I copy circles for the center of each flower and cut the stems about 2″ wide. Feel free to edit how it works best for you.

    I’ve posted these fraction flowers in the hall in various ways. Copy me if you’d like or create your own display. Please tag me if you post pictures! @makemathmeaningful @KappelEmily @kappelconsultingllc




  • Digital Number Sense SUMmit 2023

    Digital Number Sense SUMmit 2023
    It’s that time of year again! My friend Kristin, of Hilty Consulting, and I are hosting the 4th Annual Digital Number Sense Summit June 13-14. Every year this is one of our favorite things to do, put together a conference to fit the needs of what we are seeing in classrooms and what teachers are asking for.
    This year all sessions fall into 2 tracks–Back to the Basics and Beyond the Basics. The Back to the Basics track is geared toward educators who haven’t had a lot of exposure to math professional development. We will go all the way back to developing part-part-whole relationships and build up to understanding multiple strategies for each operation with whole numbers, fractions, and decimals.  The Beyond the Basics sessions are geared toward educators who are ready for more!
    We also have special guests joining us this year–John & Jane Felling from Box Cars & One-Eyed Jacks will present a bonus session at the end of each day teaching everyone games that can be differentiated for all learners.
    The Summit targets educators in grades K-5, special education teachers, administrators, support staff, and 6-8 grade teachers looking for remediation options. All attendees will receive access to all 7 recorded sessions for each day they are registered. Because of this, you DO NOT have to attend the live sessions if you have scheduling conflicts.
    Please pass along the following information to anyone you think might be interested and let me know if you have any
  • Multiplication Tic-Tac-Toe

    Multiplication Tic-Tac-Toe

    Happy Friday friends! It has been a cold, snowy week here in Ohio. School delays, snow days, and today was a dress up day in many schools to support the Cincinnati Bengals in the AFC championship game vs. the Kansas City Chiefs. During these types of hit or miss weeks, I like to scrap any of my “traditional lessons” and use the time to work on some skills that many of my students needed during Guided Math Groups. Students LOVED when we did Math Stations as did I. During Math Stations, I was given the chance to pull students in small groups to go over things they needed me to go over with them.

    One of my ALL TIME FAVORITE math games that I have done with students and teachers… MULTIPLICATION TIC-TAC-TOE

    If you’ve been to any of my PDs or worked with me this is not going to be a new game for you to incorporate, BUT I have made some changes so you can use this in various situations. This is a game that I have differentiated.

    Take a few minutes to see how I have differentiated the game to meet the needs of your students depending on where they are on their multiplication fluency journey.

    In this next video you’ll see two young men playing the game and how I talked through some of their plays with them. They are freshman now and man I miss them.

    (Sorry the video is sideway. I couldn’t figure out how to turn it in WordPress. You will get the idea of how we can help scaffold the learning during a game with students.)

    A fun digital version of this game was recently released on a FREE downloadable app called Number Hive. My own family loves to play this game together each on our own devices. When I found the game a few weeks ago on Twitter I was so excited because it was a way I can have my own 3rd grader practice her multiplication facts while we are on the go and I won’t feel as bad when she’s on a device at one of her brothers’ games. Let me know if you try Number Hive out with your students or own children. It’s a family favorite here!

    Below you will find the downloadable game boards for Multiplication Tic-Tac-Toe. Let me know what your students think of this game. It’s always been a hit with my students in my classes.

    Multiplication Tic Tac Toe- Foundational Facts 0, 1, 2, 5, 10

    Multiplication Tic Tac Toe- Factors 1-9

    Multiplication Tic Tac Toe- Factors 1-9 Products Mixed Up

    Multiplication Tic Tac Toe- Factors 0-12 Products Mixed Up

    Multiplication Tic Tac Toe-Factors 0-12

    Two Color Counters– Amazon link (I do not make a commission off of this.)

    Clear Bingo Chips– Amazon link (I do not make a commission off of this.)

  • Math Picture Puzzles

    Math Picture Puzzles

    How is math learning showcased in your building? Does each teacher put up their own displays? Do you have building-wide displays for visitors to view? I love walking into buildings where you can see the learning taking place before you ever enter the classroom. Throughout my career I worked hard to improve what I put up in the hall outside my room, but I was always looking for ways to get the rest of the building involved. The last few years of teaching in my classroom, I finally found something new that both teachers and students are loving–

    Math Picture Puzzles!

    I found these upper elementary puzzles from Jennifer Findlay. I gave a pack to my students at the beginning of each month and they’re due at the end of each month. At the start of the school year, my 4th graders typically found them quite difficult, but as the year goes on they learn strategies that make them easier to solve. They are great for practicing mental math and algebraic connections.

    Last year I decided to take the puzzles a step further and post them in the hallways for all students in the building to enjoy. I used two different levels, K-2 and 3-5. This doesn’t mean that K-2 students cannot complete the 3-5 puzzles. I just made the K-2 ones a little more friendly for our younger friends. Below you can see how a 1st grade class in my building sat outside the puzzles in the hallway to solve together. They ended up solving two of the upper-level puzzles as well and wanted to go back to their classroom to start creating their own puzzles.

    Solving these picture puzzles, students will use their knowledge of addition, subtraction, multiplication, and division. Depending on what you want your students working on, stick with those operations. Students will problem solve and make connections from what they already know to what they don’t know. The puzzles give students an opportunity to work on their fact fluency without the pressure of a timed test. The puzzles are themed for the month, so solving them tends to be a little more fun for students.

    I placed the puzzles in a high traffic area of the building. As every class leaves our cafeteria they walk right to the wall where the math puzzles are posted. As I’ve been in the hallway, I’ve heard students whispering to one another, “The snowflake must be 6 if three snowflakes equal 18.” It makes me smile so big and fills my math heart right up!

    I am sharing my file of hallway picture puzzles with you. It will force you to make a copy of the file, so you can continue to create more puzzles if you’d like. I plan on changing out the puzzles in the hallway at my school every other week to keep the kids thinking. Let me know if you use them and how it goes!

    Hallway Math Picture Puzzles

    Hallway Math Numbers


  • Mathematicians Love Hot Cocoa

    Mathematicians Love Hot Cocoa

    Who doesn’t love a good mug of hot chocolate in the cold winter months? When I was teaching in the classroom still, I was always trying to tie in real-world experiences into my math lessons and what’s better than combining math and hot chocolate?

    Do you have that one bulletin board in your building that everyone struggles with an idea about what should go on it? Does your principal randomly assign grade levels and/or teachers to make sure it gets decorated each month? Sometimes it can be a big pain to figure out what should be displayed and find the time to get it done. In the building I taught for 15 years in,  we had this issue. Our 4th and 5th-grade hallway has one of these boards and of course, it is located right by and entrance and exit set of doors. If I’m being honest, the bulletin board was usually neglected and some stuff was just thrown up there.

    I was walking by the week after winter break in 2022 and I was cold, so I was looking forward to getting back to my room and making a hot chocolate. All of the sudden the idea popped in my head…Let’s take a recipe and have the kids adjust it for various amounts of servings. You can see below what I came up with on Google Slides. I really like thinking of ways to make the bulletin board interactive and get kids thinking.

    That night I created a rough idea of what I was thinking and send it to Kristin and to our PTA president, as she’s a graphic designer. I wanted the graphic designer’s ideas on making the bulletin board 3D. (see below my for original idea) She politely said, “Do you care if I take some creative liberty?”

    She’s a busy lady running our school’s PTA, raising a couple of boys, completing some graphic designing projects… but she came up with this.

    When I walked into the building and saw this I was stopped in my tracks and gasped with my hand over my mouth. Let’s take a closer look.

    Here is the recipe card. I wanted the students to be able to make connections in math just like they do with reading. Math to Real World
    THE cutest mug of hot cocoa with adorable marshmallows floating. The hearts on the mug allow this to stay up through February! (winning!)
    I love how the measuring spoons and cup were added to show students how fractions are present in cooking.



























    The math on this particular bulletin board is geared toward 5th grade standards (multiplication and division with fractions). That doesn’t mean 4th graders can’t do the math though. The next week we sat in the hall as a class and worked through the math of the problems. Fourth graders, even 5th graders,  need to make this conceptual with manipulatives or pictures. That’s great… encourage it! We do not want to just skip to the algorithm and rules. This is an activity your students will remember, especially if you serve hot cocoa with it!

    Feel free to create your own interactive Hot Cocoa boards with teachers in your buildings name on the marshmallows. If you do, please share pictures with me!


  • First to 5

    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.

    First to 5 Download

    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



  • Reflection Journals

    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!


    Reflection Journal Download