At the start of every school year, I always have it in my mind that this is going to be the year that I create the ultimate math portfolio. A fluid place where the children’s entire math worked is housed; a place where all of their previous work is easily accessible and they can refer back to review or to aid them in solving a problem; a neatly organized, sequential archive that includes technology, reflection, and assessments. And every year, the idea of this “perfect” math portfolio becomes too daunting and I end up spending the year avoiding such an undertaking and putting it off until the following year.  Well, this upcoming school year 2017/2018 is the year! With the help of our Math Specialist, I am going to work on creating the ultimate math portfolio for elementary children. Wish me luck!

The problem with creating such a math portfolio is that we have so many different ways in which we record our mathematical thinking.  They have a math notebook, individual papers (worksheets, puzzles, scrap paper) that goes into a math binder, a math workbook that compliments our TERC math curriculum, math projects, math games, and math work that they record on their iPads either in Google Classroom or in the Explain Everything app. I understand that this portfolio is not designed to house ALL of the math work they do in 4^th grade but rather, be a mindful collection of work that best highlights a student’s efforts, progress, and achievements.  And I want the portfolio to be an ongoing conversation between our Math Specialist, the student, and myself.

Before school ended last June, the Math Specialist and I decided that we would try and create a digital math portfolio. We have a one-to-one iPad correspondence program at my school and we already do a fair amount of our math work on the iPad.  I can also send them PDFs of assessments or worksheet that I want them to work on through a PDF Annotator on Google Classroom.  Explain Everything is the iPad app that we use most for our math work so I think that this will continue to use this app to create our math portfolios.

“Create, share, and present on any device using Explain Everything Interactive Whiteboard. Use real-time collaboration, a cloud sharing portal, infinite canvas and a wide range of tools to present your ideas and express your creativity.”

The children can draw and annotate; import images, files, and videos; record everything; add text and math equations; share cloud projects; collaborate; and it works with Google Drive. I love the idea of students having video of them talking about math strategies and their mathematical thinking.  Parent/teacher conferences are an added bonus of that video feature.

Now that I have pretty much decided on my format, what goals do I want to accomplish with this math portfolio?  I stated earlier that I wanted a place that houses all of their math work but is that necessary?  A math portfolio should help the children recognize quality work and take some time to select entries that best reflect their effort and process.  Writing this blog has helped me to work out some issues and specifics that I’d like to include. For instance, I think that setting aside a time once a month or once a unit to go through our work would be most beneficial.  The first session, the Math Specialist and I could model how to go through our math work and chose pieces that ill go into the portfolio. We need to communicate our expectations of what kind of work needs to be collected. (and what not to collect needs to also be communicated) A reflection should accompany the work. Work they are proud of and why, work they really worked hard on, worked where they made a mistake and learned from that mistake and where able to correct their work through that mistake.  The reflection can be a PDF that can accompany the work that will then go into a file or a verbal explanation using the actual work as a visual that can be done on Explain Everything.  How great would it be for report cards, assessments, and Parent/Teacher conferences to have a recording of the student explaining their process and mathematical thinking?  Children also love to hear and see themselves on video and will most likely look at and listen to the reflection several times throughout the year further solidifying concepts and skills.

Another important aspect that I want the children to be able to include in their portfolio is the Exemplars they do for weekly homework.  Exemplars are open-ended questions that engage students and help them to develop critical thinking and reasoning skills to solve real-world problems. An example of a weekly Exemplar:

The Exemplars are broken up into content and I assign a different problem a week that aligns with what we are studying.  The children can use any strategy that works for them but they must show all of their work.  If they just simply write down the answer then I have them go back and explain their thinking.  Exemplars become an important part of our math routine and conversations, (we once did a whole end of the year skit on how our class uses habits of Mind to solve Exemplars) and the children become very motivated and determined when solving.  After the Exemplars have been reviewed, I think that I will have the children put them in a folder and later, when reviewing our work for our portfolios, chose some Exemplars to contribute.  They can take a picture of their work and download it into their digital math portfolios.

A big part of our math program is cooperative collaborations, projects, and playing games.  Occasionally I like to give the kids team building challenges.  I get these challenges from the Internet, professional workshops that I have attended or from Odyssey of the Mind – www.odysseyofthemind.com.

Odyssey of the Mind is a creative problem solving competition with teams from all over the United States and they have practice problems on line.  Several times a year, I  present the children with a problem and give them a time limit to figure out that problem.  Divided into groups, each group receives materials, guidelines, and a time frame that is divided into planning, execution and review.  The last challenge we did was “The Newspaper Tower” challenge. Each group got a stack of newspapers and two meters of masking tape. The challenge was to build the tallest structure they could using the given materials.  The children love these challenges and ask to do them often.  I take picture of them at work but they very rarely see all the pictures and I end up sticking them in an end-of-the-year slideshow.

So, what if I made the photos available during our Math Portfolio time and the students could choose what photos they wanted and add them to their own portfolios? This serves not only as evidence of their experience but, if accompanied with a recording, serves as a way to document their learning in ways that do not lend themselves to traditional assessment. I really like the idea of the student’s math portfolios including lots of pictures that include captions or recordings.

In the same ways that we have Writing Celebrations and Parents as Reading Partners, I’d like the children to have an opportunity to celebrate their progress and set future goals.  Math Portfolio Monday? Maybe twice a year where parents, other teachers and students can come into our classroom see the math work we’ve been doing.  We can project some of the work onto our whiteboard via Airplay and others can show their work on their iPad.  And maybe there could be some place where people could comment on the portfolios?

I will not only need the help of my Math Specialist with this endeavor but the help of our IT person and our Director of Library and Research (technology) While writing this blog, I have become very excited about this digital math portfolio and already know that I am going to have my students include the beginning-of-the-year math questionnaire that I hand out on day one. That will be our starting point.

On last thing that I’d like to mention is that I make my own academic goals known to not only my students but to other faculty members and to parents. The children tend to be more technologically savvy than I am and they usually help out a great deal in that area. Colleagues can help you out with ideas or resources and by telling the parents, it keeps me accountable.  Writing this blog will also keep me accountable!

My best memories of my elementary education are all the project-based activities that were embedded into the curriculum. Projects that were based on real-life situations that helped me learn in an innovative and creative fashion. In 4^th grade, I made a large-sized teepee (out of my mother’s good linens), decorated it with Sioux symbols and it sat in our school library for several months and served as a reading nook. I have no idea how I got or secured the lumber but I remember measuring the bed linens and painstakingly wrapping them around the 3 poles and then cutting a flap for the entrance way. I remember being the “authority” on teepee life and sharing my information with classmates who were studying other aspects of Sioux life. I moved to a different school in 6^th grade, a smaller school where there were 2 classes on each grade. When studying ancient civilizations, each class made up their own civilization complete with its own alphabet and culture and made artifacts to represent that culture. We then buried our artifacts in a volunteer’s backyard. (I grew up in a suburb of Chicago with plenty of room) After burying our created civilization, we became archeologists. We excavated the other class’s civilization, deciphered their artifacts and learned about their civilization. I just e-mailed with four of my 6^th grade classmates and they all remember the project fondly and had hilarious anecdotes to share.

STEAM is a curriculum based on the idea of educating students in five specific disciplines — science, technology, engineering, art and mathematics — in an interdisciplinary and applied approach. Our 1978 6^th grade civilizations projects included all of these disciplines. Science and Art are all around us, everyday. Technology is expanding into every aspect of our children’s education lives; my students have their own iPads, store work in Google Docs & Google Classroom and navigate the Internet for research and information purposes. Mathematics is in our everyday lives and Engineering is not only the construction of bridges and buildings but the repairing of broken objects and making environmentally conscious changes to our home.

“In the 21st century, scientific and technological innovations have become increasingly important as we face the benefits and challenges of both globalization and a knowledge-based economy. To succeed in this new information-based and highly technological society, students need to develop their capabilities in STEM to levels much beyond what was considered acceptable in the past.” (National Science Foundation)

I believe very strongly in a STEAM based, interdisciplinary curriculum and usually, given the nature of elementary curriculum, it is social studies based.

When I taught 3^rd grade, we studied Ellis Island Immigration. I loved this unit and living in New York City, there was never a shortage of what and who to study, places to visit, and immigration stories to be heard. We did an Ellis Island re-enactment and a push-cart sale to raise money for a refugee center (2 separate blogs!) But my favorite mini-unit was Tenement Life. We visit the Tenement Museum in the Lower East Side of Manhattan and learn all about turn-of-the-century immigrant life. My class was divided into countries or areas of study – the Eastern European Jews, the Irish, the Italians, and the Germans and each group studied the push-pull factors of each culture, timelines and immigrations numbers, and their life once they reached New York. I would then built a tenement building for the immigrants to move into. I would build it out of cardboard boxes and being the hoarder that I am, I once found a wooden dollhouse on the street that I ransacked for parts (stairs, windows, doors) to use specifically for this project. You are probably thinking, that’s not very STEAM to have the teacher build the tenement but 1. Time was always of the essence as this project was always at the end of our study and we didn’t have time for the building and 2. The building of the tenement wasn’t the take away I wanted for the students. The children decorated and added specific details according to their studies. For example, one group built a fire escape outside their window and hung laundry across it. Another group added an outhouse to the back of the tenement dollhouse. Each country had their own floor and it was their responsibility to decorated accordingly. For example, the Eastern European Jews made their apartment into a sweatshop and the Germans, who were on the bottom floor, made their apartment into a salon. I was the landlord so they had to make sure that the jobs they secured were enough to pay rent and buy food. The majority of their research was done at The Tenement Museum http://www.tenement.org/ as well as from websites and books. When the tenement was all finished, the children then served as tour guides to their parents and other children of other grades.

I want to take a moment to say that A LOT of planning goes into STEAM projects. Organizing groups, making sure that they have age-appropriate materials both for research and building, keeping the chaos manageable and productive, and managing expectations and classroom behavior are just some of the things you need to keep in mind before undertaking projects of this magnitude. I am very fortunate to have a STEAM Integrator and Materials Librarian at my school who can make time in her day to help out when we are working on a project and who has an endless supply of hot glue sticks, wine corks, and duct tape. I also am very lucky that I have wonderful colleagues who love to get involved and help out with their disciplines. After some research, we discovered that the later wave of immigrants had electricity in their apartments so together with our fabulous Science teacher, those groups hung working light bulbs in their apartments. The take away for this unit was how immigrants assimilated to life in the Lower East Side of New York City and what they had to endure to create a better life for themselves and their families.

When I moved to 4^th grade, I was very sad to leave to leave this project behind and quickly started thinking of another STEAM project. In 4^th grade, we study the Eastern Woodland Native Americans, primarily the Lenape and the Haudenosaunne/Iroquois and how they used natural resources to survive, pre contact. This screamed STEAM to me! Building an Eastern Woodland Native American village out of natural resources complete with longhouse and wigwam. I quickly set about designing a STEAM curriculum that included all the information that I wanted the children to learn about this topic. I am a teacher who thrives in controlled chaos and diving into a topic that I knew relatively nothing about, (Remember, I grew up outside of Chicago with the Sioux and the knowledge that the Blackhawks were a hockey team) I had to learn alongside of the children.

First, I want the children to know about the geography and topography of the land before colonization, before contact. We primarily looked at New York state and its rivers, mountains, the ocean, lakes, forests, and farmland. We looked at maps, websites, atlases, and books. Fascinating how little children know about where they live! Since we focus primarily on the Haudenosaunee & the Lenape, we identified where they settled and why and then taking that information, we created our own large-scale map to hang in our classroom for future reference. I gave each student a landmark to research (the Hudson River, the Finger Lakes, Niagara Falls) and it was their responsibility to add it to our classroom map. Once the map was complete, we talked about why we thought the different groups of Native Americans settled where they did. Once we set our scene, the children were ready to research about all aspects of Native American life. Through Internet research, field trips, videos, and books, the children collected the information needed to start creating our village. This time, I provided the land. I went to Lowes and bought 4ft by 8ft green foam insulation board and painted a river down the middle of it. And the children took over. They measured, built, came up with a scale consensus, decided on how to make people, and overlapped on various topics. For example, the 2 children working on the longhouse collaborated with the student working on gender roles and the students working on farming, ceremonies, and The Three Sisters. An added bonus of this project was the children realizing that they couldn’t work in isolation and that every aspect of Native American life was interdependent and the children needed to work together to and learn from one another in order to successfully plan and execute our village.

We had children building women out of clay and taking them over to the students studying clothing to cloth the women appropriately and then taking one of the women with a baby over to the student who was studying transportation to create a cradleboard for the baby and then over to the students studying farming who hung the baby and cradleboard from a tree while the woman was placed in the kitchen garden outside of the longhouse. Parents bought supplies at Michaels, we went to the park to collect bark, the art teacher suggested making rubbings of the bark on butcher paper as to make it easier to measure and place onto the longhouse, the maintenance men cut wood and wire for us and our STEAM integrator manned the hot glue gun and was forever on the lookout for more resources to deepen our knowledge. It took a village to create this village! And all the while, the children were engaged, independently problem-solving, motivated, and happy!

We had a festival day complete with traditional Native American food, storytelling, and the children acting as museum guides to parents and other students.

This project included all the elements of STEAM as well as a 5-paragraph essay about their topic of study and the children wrote their own creation stories based on Iroquois creation stories that we read in class. At the end of 4^th grade, when I asked the children to reflect upon their year, almost every student said that learning about Native Americans and building the our village was the highlight of their year.

STEAM projects, whether they are embedded into the curriculum or standing alone are an amazing way to allow the students to think critically, creatively, and independently while facilitating collaborative teamwork and communication. And isn’t that the type of leaner/real world problem-solvers we want our children to be?

All teachers are inherently hoarders of one kind or another. In the beginning of my teaching career, I would collect everything from eggshell cartons to the Styrofoam trays that are included in meat packaging to spending many of my weekends going garage sale-ing and buying books, games, cooking utensils, stickers… You name it and I had to have it and store it somewhere at home or in my classroom. Many times, I didn’t even have a specific project for these items. I just knew that some day, down the road, there would be an opportunity to use these items and I would be ready. Safe to say that 90% of those precious items I lovingly collected, were thrown out. And I am sure that, at the time, it pained me to throw it away. Now, after more than seventeen years of teaching experience, I am no longer an aimless hoarder. I have become a very specific hoarder; I hoard math manipulatives.

Math manipulatives are essential to math learning. According to Scholastic Parents, “Math has many areas — patterns, measurement, geometry, statistics, probability, and more — and they’re often unfamiliar, abstract, and confusing to students. We need to help children develop the ability and confidence to find their way around in each of these areas, see how they connect, and know what to do should they forget a fact or procedure.” Math manipulatives can help students learn in several ways: they help to make abstract ideas more concrete, they build confidence and aid in more clearly visualizing their reasoning, they are useful tools for problem-solving, and most importantly, they can be interesting and fun.

I have had the advantage of working in the same school for sixteen years and ten of those years have been in the same room. A couple of years ago, when it came time to remodel the classrooms and put in new cabinets and shelving, I asked for 5 x 5 shelving cubbies in which to neatly store my math manipulatives. Each cubby fits in a plastic shoebox container with lid, and is easily accessible. This collection of manipulatives and the way

that I have them stored is my pride and joy. I love having easy access to almost any manipulative a child might need to solve a problem or enough game pieces to play a spur of the moment math game. Math manipulatives help to make math accessible to everyone, all learners and they also help to take the anxiety out of math. And having the manipulatives on hand, at any given moment, help to make them part of the set-up and routine of student’s math practices.

One of my favorite manipulatives is number tiles.

And I especially love the magnetic number tiles. Lakeshorelearning.com has a big selection of magnetic manipulatives (fractions sets, base ten numbers, money, geometric shapes) that I rely heavily upon. Back from my nondiscriminatory hoarding days, I collected a ton of tins in all shapes and sizes. I put the magnetic sets in the tins and clearly label the outside of the tin. Number tiles help children take risks and take away the stigma of making a mistake. Instead of erasing and using up paper to solve a number problem, the children can simply move numbers around until they figure out how to solve the problem. For my age group, the number tiles are very helpful for double-digit addition and subtracting with regrouping and finding the unknown. These number tiles also come with equation signs. The beauty of the magnetic manipulatives is that they are contained in a tin and the lid of the tin can be used to set up and calculate their number problems.

Our lower school uses TERC curriculum and the program comes with a lot of manipulatives and games. The games need to be assembled a head of time and now, after several years teaching 4^th grade, I have my collection of math games neatly filed away in a bin on top of my manipulative shelving. Along with the actual game boards, instructions and recording papers, the games need cards or game pieces. I have a specific cubby for cards and a cubby for game pieces. Playing cards is one of the supplies I ask my students to bring in at the beginning of the year. I find that the playing cards take a beating each year and I like to start each year with fresh packs. The game pieces can be anything that will mark a spot. Anything from small, colored teddy bears to colored ones cubes. I keep the games out all year long and do not put them away once we have moved to another unit. Some children need refreshers throughout the year and I find that playing these skill- building games help to reinforce their skills.

Some of my cubbies also contain math stations onto themselves. I have one cubby that has Tangram Puzzles and Tangram activities. This is especially beneficial for my spatial learners. Years ago, I had a child in 3^rd grade who really struggled in math. He was motivated but concepts and skills did not come easily to him and he slogged through math work and activities. One day, while studying China, I gave each child a Tangram Puzzle and asked them to make a square using all the shapes of the puzzle. This child solved the puzzle in a minute flat. He then went on to complete all of the most advanced configurations in the set. We called him the “Tangram King” and from then on, I have had activities that helped in building and complimenting spatial intelligence. www.tangram-channel.com/tangram-puzzles/ is a great website that I use to download printables for the children to use as guides. I also have a cubby that has KenKen and Suduko puzzles and I encourage the children to use the number tiles to help them solve the puzzles.

Dice, small Judy clocks, calculators, paper money and plastic coins, Dominoes, colored tiles, pattern blocks, rules and tape measures, Unifex cubes, stamps (blank clocks, numbers) and ink pads, and geo blocks are some of the other manipulatives that I have in my collection. I start the beginning of each year by introducing the manipulatives and how and when to use them. I give them an exploration time in which they can “play” and use each manipulative and then steer them towards Use classroom materials and manipulatives in a respectful and appropriate manner as a class rule. I have found that the children love having the manipulatives at their disposal. During their free time after lunch or during Choice time, they will build with the blocks, make intricate designs with the pattern blocks, or calculate hard equations using the calculators.

Having a specific goal when going to garage sales in search of manipulatives has saved me a lot of money and makes the hunt that much more fun. My latest addiction has been multiplication and division flashcards and taking games (Sorry, Candyland) and using the rules, board, and pieces to make a new math game.

From the moment school lets out for summer vacation, anxiety about how to avoid the summer slide sets in. Summer slide refers to the loss of skills many children experience during summer vacation.

As a parent, the idea of “practicing” skills over the summer was dreadful and daunting. Forcing my children to do workbook pages, flashcards or mandated work from school was not my idea of how to best spend our summer vacation. But as a teacher, I want children to practice their skills over the summer so they are sharp and ready for their upcoming year. Not surprising that reading seems to be easier to include into summer. We would have designated times each day where we would all read and weekly trips to the library to check out new books was a part of our summer routine. Math seems to be the activity that gets neglected and according to research, math skills drop more over the summer than any other academic skill.

There are many ways in which to keep up math skills without resorting to workbooks or relying solely on iPad apps. (Though there are so many comprehensive math apps available and the iPad is a great “down time” activity!) Games, sports, cooking & baking, planning a trip, math stories, museum trips, time telling to plan their day, and lemonade stands and trips to the candy and/or toy store or all fun activities to reinforce numeracy skills.

For years, my college friends and our children go on a beach vacation to Rhode Island. And each year, the trip to the coveted candy store is “must do” activity. The trip to the candy store does not come without a lot of frontloading as to how much money they can spend, what kind of candy they can buy, and when they can eat the candy. This year, I brought my 6-year-old godson and since I only see him one or two times a year, and my job is to spoil him, none of the previous rules I had for my own children applied.

Instead, I gave him $5.00 and told him that he could buy whatever he wanted but he had to ask the price of each item and ask the person at the counter to let him know when he had gone over $5.00. Luckily, the woman at the counter was very accommodating and not too busy to help us out. As he was picking up items and asking their cost, I was calculating his possible candy stash on my iPhone calculator and showing him what his items totaled and how much more money he had to spend before he got to $5.00. Unfortunately or fortunately for the sake of this experience, $5.00 does not go far in this particular candy store. He chose Hubba Bubba Bubble Gum for $2.65 and a Whistle Pop for $1.50 for a total of $4.15. I calculated and then showed him that $5.00 minus $4.15 was $0.85 and that was the amount he had left to spend on another piece of candy. I told him that he could spend it now or save it for another trip to the candy store at a later date. He chose to save it and a good thing too because after a brief survey, there wasn’t anything in that candy store that was under $1.50. I had him put his $0.85 in his pocket and he happily exited the candy store with a mouth full of bubble gum. I think that next year I will have him earn the money by doing small chores such as taking the garbage out, sweeping the deck and after he has earned a bit of money, I’ll take him to the candy store. Teaching children the basics such as how to budget, spend and save will establish good money habits for life.

Another “summer slide” activity we like to do on vacation is play games. We are a game playing family and love the down time of vacation to relax and play the games we love.

Shut the Box has been a favorite beach game for forever and appeals to all age groups.

This game can be played with a partner, alone, or with a group and teaches math and logic skills. Younger children can use it as a counting game while older children can use it as a game of strategy. The fun part is that the game takes about five minutes to learn but can take a while to learn how to “Shut the Box”. Players roll two dice (at first) and flip down numbers that equal the sum of the total rolled. Each player continues until he can no longer flip down a tile and then adds up the total of the remaining numbers. The box passes to the next player and the winner is the one with the lowest score (unless someone “shuts the box” and automatically wins by successfully flipping all of the numbers down) I’ve actually seen this game at my local bar and have witnessed adults get into heated round robin competitions of Shut the Box.

This year, my friend introduced us to a new game that quickly became an obsessive hit.

Simplexity is absolutely addicting. It is easy to learn, but sophisticated with multiplayer layers of strategies and can get very competitive (which we like!) The object of Simplexity is simple; be the first player to connect four pieces in row by shape or by color. But, be careful, your next move may actually help your opponent. The nice thing about both of these games is that they are sturdy and are made of wood so that they last a long time and transport is easy. There are so many great games that children can play to reinforce skills whether it be number sense, spatial reasoning, or good sportsmanship, the trick is to find one that your child enjoys playing.

Along with playing games, I love logic puzzles, mind teasers, and math word problems. Last summer I blogged about logic puzzles, brain teasers, & games. They boost brain activity, increase fluency and memory, improves concentration, promotes harmonious group dynamics, and gives one a sense of pride whe they have successfully completed a challenge. Instead of giving my 4^th graders a math packet for the summer, I give them a one big math problem to solve. They can work on it throughout the summer and they can work on it with friends and family but they need to clearly show their work and explain how they got to their answer. I give them Marilyn Burns’ The Double-Dip Ice Cream Problem from the book, About Teaching Mathematics. Marilyn Burns is a well respected math educator and has many math books for children of all ages. She is a wonderful resource for skill and concept extensions, games, and logic problems. She has her own blog that I often use as a resource www.marilynburnsmathblog.com.

The Double-Dip Ice Cream Problem: In an ice-cream store that has 31 flavors,

how many different combinations of double-scoop ice cream cones can you get?

Show your work.

I send this to my upcoming class and have them bring it in the first day of school. I take a look at their work and then group them accordingly as to how they solved the problem. I also tell them that, for this activity, I am far more interested in their process than in their final product. Some kids draw out the whole problem with different colors representing each double-dip ice cream cone until they get to the final answer. Some kids will start out making a picture, will recognize that there is a pattern involved and switch over to a table t-chart to continue the pattern until they’ve reached the answer and some of the children solve the problem using an algebraic operation. Nine out of ten times, the ones who try and solve using the operation, do not get the answer correct and have little work to show for their thinking. I group the children accordingly and have the children go over the problem and compare answers. Each group need to agree on one answer and then explain how they got the answer. The Double-Dip Ice Cream Problem has proven to be an insightful diagnostic tool and tells me a lot about the children as mathematical learners. The problem is also a low stakes way of getting them back into the swing of mathematical thinking. Once all the groups have presented, we come up with the most efficient way to solve the problem and make a class graph that represents our thinking.

It is important to have children thinking about math all throughout the summer and there are many creative ways to make sure that that happens. Here are some websites to give you some additional ideas:

Gideonmathand reading.com

Mathinsider.com

Splashmath.com

I love playing games, doing puzzles, and figuring out a good brain teaser. I do the New York Times Crossword Puzzle everyday and while I struggle in the later half of the week, I love learning new information, keeping my brain sharp, and that sense of accomplishment after I have successfully completed a difficult puzzle. I try to instill this same love of logic puzzles in my students. We love to play, it’s how we learn.

Brain teasers, games, and puzzles boost brain activity, increase fluency and memory, improve concentration, promote harmonious group dynamics, and give one a sense of pride when they have successfully completed a challenge. I always have individual puzzles, such as Kenken or the “Find the Embedded Objects in the Picture”, like the ones in the old Highlights magazines, set out for my students when they finish their work early. I also engage the whole class in brain teasers in which they must work together to come up with the answer.

One of my favorite brain teasers is “Valley of the Green Glass Doors” taught to me by a former assistant who was a life-long camper and camp counselor. Many camp games translate well into the classroom. “Valley of the Green Glass Doors” is played with a group and I usually play it during Morning Meeting or at the end of the day. I begin by explaining that only certain things can be in the “Valley of the Green Glass Doors” and give examples such as, “There can be the MOON but no STARS…” I then give numerous examples. The key being that only words with double letters can be in the “vaLLey of the grEEn glaSS dOOrs.” I make a chart and have it hanging up for reference during the duration of the brain teaser.

At first, it is hilarious to listen to the children try and make sense of the logic. I usually need to provide some scaffolding by encouraging them to “think out of the box” and “try and different approach.” I also need to manage the frustration levels and keep the mood light and jovial which isn’t always easy to do.

Once someone figures out the pattern, they must check with me to see if they are correct and if they are, they then become the person to write down the correct answers and play the role of facilitator. They must also promise not to reveal the pattern to anyone else, which, as you can imagine, is also very difficult but prompts a worthwhile discussion on the benefits of working through a challenging problem on your own and not finding an easy way out when the going gets tough. I also have to inform the parents that we are playing this game and not to let the children go home and look up the answers on the Internet. This brain teaser can go on for several days. I recommend playing this with older students, 3^rd & 4^th grade. Each year, when I do my “End of the Year” reflection, “Valley of the Green Glass Doors” is always a highlight.

Another great brain teaser puzzle that is easier and we can play almost anywhere is “Bagel, Pico, Ferme.” The game begins with one person secretly choosing a number with no repeated digits. I usually start with a 3-digit number. The children attempt to guess the number, and the one who identifies the number correctly, becomes the next facilitator. For each guess that has no numbers correct, they respond: “Bagel.” If they guess a correct number but that number is in the wrong place, they respond: “Pico.” For each number the guess has correct and in the correct place, they respond: “Fermi.” In the beginning, I keep a chart to keep track of their responses but as they get the hang of the game, the chart no longer becomes necessary.

As an example, the number I think of is 489. I let the children know that I have thought of a 3-digit number and using the rules of “Bagel, Pico, Ferme” they will now take turns to figure out my number.

This game helps to improve memory and solidify place value. The children need to remember what number has already been used and in what place. I also use place value language by saying, “The 8 is a correct number but it is not in the hundred’s place” for the 2^nd guess and then, “Yes, the 8 is in the one’s place” for the 3^rd guess. This game is similar to the board game, Mastermind, is a game that I love and always have in my classroom.

Riddles are fun too! “Four is Magic” is my favorite and is fun to play once the kids have worked their way through “Valley of the Green Glass Doors” and know to look beyond the obvious.

3 is 5 is 4 is magic. Why is the number 3 the number 5? Why is 5 the number 4? Why is 4 magic?

Answer: 3 is 5 because there are five letters in the word three. 5 is 4 because there are four letters in the word five. 4 is magic because there are four letters in the word four.

http://www.ultimatecampresource.com/site/camp-activities/camp-games.html is a wonderful resource to find new games, brain teasers, and puzzles. Also, one of my favorite resources, Pinterest www.pinterest.com/explore/brain-games/. I also like to ask the children, many of them who attend camp or play games with their families if they have any they’d like to share.

One of the important things to remember when introducing and playing these games, brain teasers, and puzzles with your children is that there is a lot of teaching, managing, and emotional supporting that goes into these activities. The children need to essentially be “trained” in how to successfully master these activities. Have fun!

posted by Stephanie Forsman

Measurement is an area of my math curriculum that I often feel gets neglected, rushed through, and sometimes, at crunch time, overlooked all together.  As a result, I have worked on infusing small aspects of measurement into the routines of the day.  From linear measurement to volume, weight and mass to telling time, temperature and money, measurement is an everyday skill, “real life math.” It is important that children know how to identify appropriate units and choose the correct tools and technology for measuring those units.

One of my favorite topics that I consistently revisit throughout the year is Time. Even in 3rd and 4th grade, some children cannot tell time and rely on the adults in their life to tell them where they need to be and when. At the beginning of the school year, regardless of what grade I am teaching, I do a quick lesson on Time – 24 hours in a day, AM & PM, the short hand is the hour hand and the long hand is the minute hand. One of my favorite tools to teach Time is a Judy Clock. I have a class set and each student has one in which they practice telling time and learning the concept of elapsed time. A Judy Clock features easy-to-read numerals that show elapsed time in 5 min intervals. The clock makes learning to tell the time simple and fun for children and comes with visible functioning gears that maintain correct hour hand and minute hand relationships.

I will routinely ask the children to show me the time on their clocks or I will pose questions, “if it is 10:45 AM now and we have lunch at 12:00 PM, how much time does that leave us for snack and math?” Another handy time telling tool I have is a rubber clock stamp.

I will routinely ask the children to show me the time on their clocks or I will pose questions, “if it is 10:45 AM now and we have lunch at 12:00 PM, how much time does that leave us for snack and math?” Another handy time telling tool I have is a rubber clock stamp.

When I put up the day’s schedule on the board, I will put the event and the time and then have a blank picture of a clock where the children will draw in the correct time using the hour and minute hands.  I will write times such as “Math – 10:45 AM” with a blank clock next to it and make sure that the child responsible for noting the time will make sure that the hour hand is closer to the number 11 than to the number 10.

Just like my parents did with my brother and I when we were growing up, I like to have a height chart located on the inside of my doorway. One of our beginning of the year activities is to partner up and mark your height on the door. I use a cloth tape measure for this activity and it does require a pre-lesson on how to use the measurement instrument. The first year that I did this activity, I just gave the children the tape measure and had them go at it. I quickly realized that the majority of the children did not know what to do when they had run out of tape measure but still had not completely measured their friend. I have a class set of 60 inch, cloth tape measures that the children use throughout the year. I find that the cloth tape measures are easier to manipulate, cheaper, and easier to store.  After a lessons in which we discuss “How many inches in a foot?” and “If a child measures 52 inches, how would we record that in feet and inches?”, we place our names, the date and our heights against the door. We do this activity 3 times a year and at the end of the year, each child figures out how much they’ve grown through the school year. In our end-of-the-year reflection, we include our physical growth as part of the child’s reflection, “This year, I have grown 3 ½ inches and have become a much more of a risk taker when approaching difficult math problems.”

It is also extremely important to allow them exploration of various types of measurement tools and educate them to which tool is best for which situation.  Measuring how long things are, how tall they are, or how far apart they might be are all examples of length measurements. I expose the children to all sorts of measurement units in which they can use to measure various objects. Centimeters, inches, feet, yards, miles, and kilometers are all the units we use to measure distance, height, and length.

We brainstorm items we’d like to measure and then categorize them according to the units of measurement we’d use.

I like to put this conversion chart up in the classroom for constant reference –

1 foot = 12 inches

1 yard = 3 feet = 36 inches

1 mile = 1,760 yards = 5,280 feet = 63,360 inches

Liquid measurement is another aspect of measurement that when I run across it, often need to look up a conversion chart to make sure that I am measuring correctly. I am not always certain that 2 pints equal a quart since I very rarely use these units of measurement.  Again, this is when a conversion chart comes in handy but we make our own “Gallon Man” with empty, recycled containers that the children bring in from home. We bring in one plastic gallon (milk), 4 quarts (milk or juice), 8 pints (ice cream, yogurt), and 16 cups (yogurt, sour cream). Preferably all plastic and clean. Before I put up a conversion chart, I essentially create a water table and see if the children can come up with the equivalents on their own. “How many quarts equal a gallon?”, “If there are 2 cups in a pint, how many cups in a quart?” After figuring out the conversions ourselves, we create “Gallon Man.” We actually create this by attaching the quarts to the gallon with holes and wires for the arms and legs and then 2 pints to each quart and finally, 2 cups to each pint. We should rename our creature “Gallon Robot” or “Conversion Robot.”

We hang up “Gallon Man” in our classroom for easy reference.

Teaching measurement or any concept for that manner, using hands-on activities, manipulatives, and real-life applications makes concepts more interesting, engaging, and fun for my students. I get a lot of my ideas from Pinterest and often, these “real life math” lessons take little time and don’t take away time from keeping pace with my mandatory math curriculum.

Each morning, my class has a Morning Meeting that consists of a Morning Message, a Greeting, a Share, and an activity. It is a great way to start the day, reinforces our sense of community, and sets the expectations and goals for the day.  These meetings last anywhere from 15 to 30 minutes. While I cover many topics during these meetings, my favorite topic is math. I love a Math Morning Meeting!

I have an interactive Morning Message (a message written on chart paper with an area for the kids’ responses) that the children work on during morning arrival and then later talk about during Morning Meeting.  Anything from identifying and giving the monetary value of coins to measuring various line segments with a ruler using both inches and centimeters, we try to either reinforce what we are working on in math or cover a topic that isn’t heavily hit upon in our curriculum. For example, when working on multiplication facts, I will put up problems that are related and share a pattern.

3 x 3 =

3 x 6 =

3 x 12 =

3 x 24 =

I have a problem for each of the children and one that I use as an example.

For Morning Meeting, we sit in a circle and begin with a Greeting. In keeping with our Math topic of the day, we play Match Card Greeting. I give each child a card on which I’ve written part of an equation. For example, one child gets a card that says “3 x 6”; and another student gets one that says “= 18.” The children move around trying to find the match for their card. When the children find their match, they greet each other. A simple “Hello” or “Good morning” is fine. I always keep a big stack of Index cards on hand for games such as this and this greeting can be adapted and/ or modified for almost any concept; addition, subtraction, shape recognition.

After the Greeting and the children are settled back into a circle, we do a Share. Share can be anything. Topic driven, partner share, a prearranged share in which one student shares something they’ve experienced or an object brought in from home.  During a Math Morning Meeting and when we are working on a specific skill, I will announce a topic for an around-the-circle sharing. Since we are working with multiples of “3”, I will refer back to the Morning Message and ask the children what they notice. “I am definitely seeing a pattern with not only the answers but the problems. Who else is noticing what I am noticing?” The children take a minute to think and then I will start to entertain answers. The children get so excited to share what they notice and there are usually so many extensions and directions I can go based on their observations, that I usually have to jot down notes and table some of their observations for another time.

Since we are working on multiples of “3”, we will play an adapted game of “Ruof” called, “eerht” which ends up sounding like “earth.”  Three spelled backwards. The children stand in a circle for this game. The children count off and on every multiple of “3”, they say “eerht”  1, 2, eerht, 4, 5, eerht… If the they say the multiple of three or make some other mistake, they sit down and the count off starts again.  I play this game for every multiple up to 12 and have even played this game using square and prime numbers. The children love it and challenge themselves to see how high they can count.

After the activity, the children sit back down and we end our Morning Meeting with a heads up about what we’ll be working on during math that day, pretty obvious given our Morning Meeting work and ask if there are any questions, comments or concerns.

Math Mornings Meeting are so beneficial and bring so much enthusiasm to the math that is happening in your classrooms. By 9:15 am, we’ve already had a good 20 minutes of math, the children had fun practicing their math facts, and their minds are warmed up and thinking about math for the rest of the day. I highly recommend the book, Doing Math in Morning Meeting, 150 Quick Activities That Connect to Your Curriculum by Andy Dousis, Margaret Wilson, Roxann Kriete. The book contains math-themed ideas for all four Morning Meeting components: greeting, group activity, sharing, and morning message. Have fun!

Click here to see the link to the book below.

Setting up a nurturing mathematical environment & community is an essential beginning to any school year.  When  getting to know my students, I like to dig deeper and find out what kind of learners they are, where their strengths lie, and what areas they intend to work on during the upcoming year.

Teaching 2^nd, 3^rd, and now 4^th grade for the past 20 years, I have seen so many students arrive on the first day of school declaring themselves “Bad at Math.”  When I push them to expand upon that statement, I typically receive, “I just don’t like it” or “I like reading instead” They have already, at the age of 7 or 8 years old, started to shut down in math. For years, I took the approach of cheerleading them through their difficulties, offering extra support, and diversifying the curriculum with “fun” activities such as puzzles, activities that involved food, and various games instead of focusing on giving these children the emotional tools they needed to work through difficult problems.  A couple of years ago, my school hired a math consultant and she introduced us to Habits of Mind and it changed not only my approach to math and all other aspects of my grade curriculum and teaching.

Habits of Mind are essentially 16 characteristics of what students do when they come across a problem where the answer isn’t immediately obvious. So much of our math curriculums have been about focusing on getting the correct answer. Habits of Mind has us also looking at what the children do when they don’t know the answer. “We are interested in enhancing the ways students produce knowledge rather than how they merely reproduce it. We want students to learn how to develop a critical stance with their work: inquiring, editing, thinking flexibly, and learning from another person’s perspective. The critical attribute of intelligent human beings is not only having information but also knowing how to act on it.” Arthur L. Costa, Learning and Leading with Habits of Mind (An amazing book! I highly recommend it!)

I put these Habits of Mind up on the wall of my classroom and keep them there all year long as a reference. I break them up into 3 categories: the actual Habit of Mind, the short and memorable definition, and what it looks like in the classroom. For example, my favorite Habit of Mind is “Flexibility” The short and sweet definition of “Flexibility” is:  Look at it another way.  The way it looks in the classroom is to change your perspectives, think of other ways to solve the problem, listen to other classmates’ options and strategies.

This is a wonderful Habit of Mind for a student who consistently uses the same strategy to solve a problem despite the results. Last year, I had a student who was very determined to always use the subtraction algorithm despite the fact that he wasn’t always correct and that he wasn’t relying on his number sense to solve problems like 100 – 25.  He resisted adapting strategies such as an open-number line or extended notation. After many frustrating and tear inducing experiences with the algorithm, his classmates encouraged him try out the other learned strategies. Coming from his peers and not mandated from his teacher was a key element in his willingness to try another approach. After playing with several strategies during our subtraction unit, he declared that he was much more successful counting up on an open-number line than he had been using the algorithm which then led to a very rich discussion about what strategy to use when and how important it is to have an arsenal of strategies at our disposal. Developing critical thinkers and empowering the children with the tools they need to become successful problem solvers has helped turn those “I don’t like math” children into successful mathematicians. From that moment on, this student’s Habit of Mind was that he needed to work  “flexibility” and when he became stubborn or adamant during a difficult math session, we, our classroom community, only needed to remind him of being flexible and he was able to switch gears and do just that.

One of the beauties of Habits of Mind is that everyone has something they need to work on. That same year, I had what we call a “high-flyer” She was mathematically savvy, great with rote memorization and up until 3rd grade, had gotten away with relying on her mental math abilities to solve problems correctly. She didn’t like to show her work and while the majority of the time, she solved the problem correctly, she wasn’t able to recognize where she went astray if she happened to solve the problem incorrectly. As the problems started to become multi-step and it all became too much to hold in her head, she began to stumble. “Striving for Accuracy and Precision” became her Habit of Mind to work on.  Check it again!  Show your work!  A desire for exactness, using your Math Journal to show your work and be neat & organized in your mathematical thinking is what it looks like in the classroom.

You can easily find Habits of Mind on the Internet along with so many wonderful and creative ways in which teachers implement them.  We were so dedicated to our Habits of Mind last year that our end-of-the year, written by the students play was based on solving a very tough math problem and using our Habits of Mind to do so. We had children act out each Habit of Mind. There was also a great and almighty HOM (acronym for Habits of Mind) who kept the children focused while solving the problem and a teacher who presented the problem and threw additional obstacles in their way such as time constraints, taking away manipulatives, and adding extensions to the problem along the way. It was adorable!