A pair of four-year-olds in my classroom are happily playing “dice wars,” a simple but fast-paced game. To play, each child rolls a die and the player who rolls the highest number wins. No one is keeping score today—and nobody seems to care who wins each round. 

I watch as Juan shakes the die between his palms, rolls it, counts each pip (dot) on the side that’s facing up and announces, “1, 2, 3!” I rolled a three!”

“My turn!” exclaims Maria as she shakes the die between her hands and rolls it. “SIX! I win! Six is more than three!” Maria doesn’t need to count the pips. She recognizes the pattern immediately and her number sense tells her the value of the pips on the die.

Rolling a die is fun in its own right, but these friends are working on the math skill known as subitizing. When children begin to recognize the pattern on the die and associate it with the number of pips (dots) without counting each pip, that is subitizing!

Children develop subitizing skills in much the same way that they learn to read sight words.

In a previous Early Math Counts blog post, Jen Asimow, M.Ed, explained it this way: “Remember when you learned about ‘sight words’ and how children learn them? According to one school of thought, children memorize sight words by taking a mental snapshot of the entire word. By using context clues, they learn the word as a ‘whole’ rather than as a series of letters. Consider how children learn the words EXIT or STOP.  Both of these words appear in the same way—on signs above doors or on red octagonal street signs—and nearly always in the same colors and typefaces. All of these clues help children form a mental picture of these two words, and they often learn the pictures before they learn the individual letters that make up the words.”

Maria and Juan are playing with a die, so they are only working with numbers ranging from one to six. As they play successive rounds of the game, they are beginning to recognize the patterns on the die without counting the individual pips.

With every roll of the die, Juan’s pattern-recognition skills are growing stronger. Before long, he can recognize the total number of pips on each throw without counting.

According to child development experts, the ability to subitize quantities up to and including four by the age of five represents a significant developmental milestone. 

Subitizing is a fundamental math skill, and dice games are a good way to help foster the development of this skill.

“Hey! Do you want to play that block-building dice game?” asks Pierre as he grabs a die from the jar and joins the group. 

Roll and Build is another dice game that we’ve played in our classroom for years. One child rolls a die and the other children add that number of blocks to their towers. Children learn to recognize four dots on a die, which helps them understand the cardinal value (how many four represents), which they can then link to the symbol (4) and the word (four).

Games like this provide repeated opportunities to interpret the dot images. As children figure out how many pieces to collect or add or how many spaces to move on a game board, they develop their number sense and other early math skills such as counting, number identification, the correlation between numbers and the items being counted and concepts such as greater than or less than.

Keep a jar full of dice within easy reach to give the children plenty of opportunities to practice and make up their own games.

Begin by subitizing quantities of 1, 2 and 3. In a math workshop that I attended, the trainer had blacked out the pips representing 4, 5 and 6 for the younger children.

If a child is having difficulty subitizing, reduce the quantity of dots. 

Dice games help young children develop math and social-emotional skills in a fun and engaging way.  So grab some dice and introduce your gang to subitizing fun! 

Check out our Early Math Counts lessons page for dice game ideas. Be sure to click on the Connect With Families button in the left-hand column of each lesson to download a Parent Letter that you can customize to share the day’s learning activity with parents and other family members.

Math really is fun.  It can be misery trying to teach it, but magic when you integrate it into your child’s everyday life.  

It’s a mystery to me why some children have a natural affinity for numbers while others show no interest or may even resist them.  It may be no different than why I chose to participate in gymnastics as a child while my best friend’s sport of choice was soccer.  We veer toward subjects and activities that come easily and steer away from those that are confusing or tricky.  As a parent of four young children and a learning specialist, I know how difficult it can be to get a child to participate in something they think is hard or boring. Pushing concepts on young children will prove arduous to both the adult and child, so what are some fun ways parents and educators can engage young children with math?

Too often we turn to the computer for answers, .  Or the apps on a smartphone.  While some of these are fun, my children already spend enough time in front of screens.  There are many workbooks that reinforce math concepts, but if your children are like mine, they aren’t going to be motivated by more ditto sheets.  Instead, I propose thinking more organically about numbers and mathematical concepts; they are hiding within so much of what we do everyday.  Very often, we can explore mathematical language and concepts without it ever seeming to our children that we are “working on math”.  If there are two words that don’t go over well with children, the top two might be “work” and “math”.

Some examples of how to bring math into everyday life:

*Put a timer on the microwave. Tell your child how much time you’ve put on the timer. Challenge them to pick up their toys or clean their room before the timer beeps. If they finish early, do a countdown with them while watching the numbers on the clock. You could even hold up fingers for the 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 countdown.  If it was not enough time, talk about how much MORE time could have been added to the timer.  If it was too much time, how much LESS could have been used.

*Have your child study their cereal box in the morning.  Any aged child loves to look at the colors, the characters, and the games or stories on the back of the box.  But cereal offers many other rich math opportunities:

-Talk about the numbers they see in the ingredients. Discuss which character on the box is “bigger” than another. Take the cereal box apart, cut the pieces and measure them with a ruler or just lay them next to one another and decide which is taller and which is shorter.

-Pull a handful of cereal out and count.  How many “marshmallows” are in the cereal  (if you like the junk cereal variety)? Separate by color. Sort piles of like shapes. The amount of opportunities to get the math brain curious is limitless.

*Near your child’s bed, create a Mathematical bulletin board. My youngest son sleeps on the bottom bunk in a bunk bed. I created a beautiful (not too visual so as to keep him awake) collage of mathematical concepts for him to peek at before he closed his eyes at night.

After we read, I count with him. We find numbers. We look to see which number is “bigger”. We play riddle games. “I’m thinking of a number”. When he is tired, I never force it. When things get old, I switch it up. It is fun because he never knows what is going to be on the board next.

*Is your child physical? Make movement mathematical. How many times can you throw the ball back and forth or roll it if catch proves difficult. Create a dart board (out of plain paper) with numbers on it. Make paper airplanes and see what numbers you can both hit.

Get a jump rope and sing a number song or count. Kick a soccer ball and keep tally marks on a sheet of paper to track how many goals are made by each player.

*Cook and bake with your child. Both offer very rich opportunities to sneak numbers in. There are fraction opportunities but also looking at temperature on an oven. Talking about how long the item needs to cook. How many minutes does the batter need to be mixed? Etc.

*Play games. Dice games, card games, matching games. There are a plethora of board games that include mathematical concepts.

-Sleeping Queens (A family favorite- enjoyed from my 5 year old up through both parents!)

-War: an easy way to compare numbers. You can add and have each player turn over two cards. The bigger number after you’ve added keeps all 4 cards.

-Rat a Tat Cat (Another family favorite that involves your wanting to keep the “low” numbers and get rid of the “high” ones)

-Shut the Box: Roll the dice and close the doors on the numbers you roll. Try to “shut all of the numbers” to end with the lowest number.

-Memory: Who could forget Memory? What a wonderful game. The cards can have shapes on them or numbers. While playing and matching, talk about the shapes they see, count the images on the card together before making matches.  

These ideas are not new and this list is far from complete- there are so many more hidden opportunities to learn math. They are things that many parents are already doing with their children everyday. However, when it is not obvious that Math is being taught, it can be easy to overlook the Math hidden right in front of you. Before you turn on a computer or buy a workbook, try to find the hidden math in your everyday life. To insert mathematical language, concepts and games into their life can make all of the difference. After working in a few more of these ideas, I think you’ll see your child building a math brain from everyday life.

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.

While observing a kindergarten classroom the other day, I observed a child counting the pips on a die each time she rolled it.  The lesson asked that children roll one die, read the number of pips, and complete a word chart determined by the number.  Interestingly, this child could both read simple sight words and write them, but could not read the number 3 on a die.

This got me thinking about the activity itself.  It was clearly set up as a literacy lesson, asking that children practice their reading and writing, but the addition of the die asks that children also practice their subitizing skills.  Remember, subitizing is the ability to look at a group of objects, in this case the pips on the die, and know “how many” there are without counting them.  This ability to take a mental snapshot works much like reading sight words does but we work on sight word reading all of the time with children and focus on skills like subitizing much less often.  Even while observing this activity, the teacher worked diligently with the child on sounding out the words, reading them, and writing them down.  However, when the child tossed the die, she was left to figure out the number without the same sort of support.  Why is that?

If I had been supporting this activity, I would have focused on the die as much as on the words.  The math is as important as the reading and writing and deserves equal time.

There are several ways to support children as they begin to subitize.  One thing you can try is to have the child toss the die and then before she counts the pips, pick up the die and see if she can tell you “how many” were on it.  If she can’t, show her the side again and ask her “how many.”  Let her count and tell you how many there are.  The next time, try it again until she becomes more familiar with the patterns of the pips.  With ongoing support a child of 4 and 5 should easily be able to subitize up to 6.

Just like frequent opportunities to read sight words support the development of the skill, so too, do frequent opportunities to subtitize number. In addition to having several kinds of dice and dominoes in the classroom, other materials with small numbers of objects should be available so children can practice. Begin with groupings of 1 to 5 as these will provide the foundation for subitizing larger groups using part/whole understandings as well as composing and decomposing number.

This memory game has small groups of objects with matching numeral cards.  Start with 1-5 and put the rest away for later.

Even though I don’t like flash cards for young children for any reason I think that these cards could be used in interesting ways.

Below is a picture of a traditional “Shut the Door” game which asks children to roll the dice, count the pips (the dots on the dice) and then “shut” the numbered door shown on the dice.  When all of the doors are shut, the game is over.  There are ways to play this game individually or with others.  I especially like this one because it is a noncompetitive game that asks children to work together in order to meet the desired goal (all of the doors shut).

This version is played by as many as 4 children at once.  When children engage in this together, the play moves from being cooperative to competitive which is a natural progression as children get older.

Each time they tossed the dice, the teach tried diligently to get the child to recognize and name the numbers.  She used her best teacher voice saying things like, “Ooooh, what number is that?  Can you count to 4?  Are the number the same?  Are they different?”  Not once did the child respond to her prompts.  He didn’t even look up or acknowledge her attempts at engaging him in the numbers.

I watched this interaction for a little while longer and came to the following conclusion:

The teacher was wasting her time and energy focusing on what she thought was important when using dice as a manipulative rather than observing the child and following his lead to uncover what he thought was important about the dice. 

If the teacher had been paying closer attention to the child’s cues, she would have noticed that he wasn’t rolling the dice to see which numbers came up.  He was rolling the dice to see how close he could get them to travel without falling off the edge of the table.  His game was about space and distance, about near and far, about staying on and not falling off.  His engagement with the dice was intense and exciting.  His game had rules and was fun.  His game didn’t include a relentless string of questions with right and wrong answers.

If the teacher had been paying closer attention she would have seen an opportunity for an authentic interaction between the two of them based on the genuine interests of the child.  She would have found many opportunities to encourage mathematical thinking, spatial recognition and math vocabulary.

Math opportunities exist in all areas of the early childhood classroom and in all sorts of adult-child interactions.  Playing with dice may seem like a super obvious example of an “opportunity” to explore number with a young child.  However, the obvious is not always the best choice.  Follow the child’s lead.  It may take you somewhere far more interesting.

Remember when you learned about “sight words” and how children learn them?  There is a school of thought that says that sight words are memorized when children take a mental snapshot of the entire word, using context clues, and learn the word as a “whole” rather than a series of letters. Consider how children learn the word EXIT or the word STOP.  Both of these words appear in the same way, on signs above doors and on big, red, octagonal signs on street corners.  They are nearly always in the same print and they are nearly always in the same color.  All of those clues help children take a picture of the word, and learn the picture, often before learning the individual letters that make up that word.

Subitizing is like that.

It is the ability to look at a group of objects and know “how many” there are without counting them.  You do this every time you roll a set of dice.  You know what 5 looks like on the side of the die, and you do not have to count the pips to be sure.  When you see a carton that holds eggs, you don’t count each space to see how many there are.  You know that there are 12 because you subitize the quantity.

The other day I was in a center and the teacher was playing this game with the children.  They were choosing a petal and then trying to place the petal on the correct number without counting the dots.  You can see above that the dots that are organized in a logical manner in rows, or in recognizable patterns like those on dice, are easy to recognize. There were petals that also had random dots which were much harder to subitize for the children.

How do you teach subitizing to your children?

6 and the ways those numbers are represented by pips on a die, you can add the dice with signs, just to liven things up.  These are large enough that they can be rolled at group time in the center of the rug.

Roll one of the dice with numerals on the side and let the children figure out what number comes up.  Then roll one of the dice with signs.  Use this as an opportunity to “teach” what each of the signs mean.  Next roll one of the dice with pips.  Let the children figure out “how many” pips are shown.  Now, have them compute the number sentence.  This is going to be very difficult for most children, but if you make it fun, and game-like, they will enjoy getting involved.  Be sure to let the children choose which dice to use and let them have turns rolling them.  For some, this will be the focus of the activity rather than the math.  That doesn’t matter.  These dice will provide additional exposure to signs and numbers in a fun and engaging way.

Even very young children could roll one of these die and, with help, count the pips to find out what number it is.  If you have three children in your group, each one could roll the die, tell their number, and put themselves in order based on that number.  Here is a nice lesson plan that uses dice for counting.

These dice are a bit different.  Rather than pips, they have the number written on each side.  These too are interesting- especially if children are working on identifying integers rather than counting.

Different materials support different learning goals and create different learning outcomes.  Yeah for dice!