Water, Worms and Measuring


posted by Diann Gano

Have you ever seen a child with a tape measure? They are in all their glory! We have small tape measures that sometimes make it on our walks around the neighborhood. We like to measure seedpods, sticks, each other, our shadows, you name it. Did you find a worm? We are measuring machines. We like tape measures that are small enough to fit in a pocket, because you just never know when you will need to measure something. We may not know the numbers or what the spaces means, but it is fun! It exposes them to the concept and the visual number, when their brain is ready the important parts will fall into place.

mesauring tape

Living on the Mississippi River, each spring we get sucked into watching our beloved bald eagles. When we decided we should make our own nest, out came the tape measures! Did you know the average eagle nest is six feet wide? This is the perfect time to grab a tape measure and create a nest!

boys in the shrubs

We use worms to teach length and we sometimes measure them with tape measures but we honestly do a lot more observation and estimating with them because they are perfect just the way they are. We love worms. Did you know that worms don’t have teeth? Worms don’t have pinchers or stingers. They have no eyes, no legs, no arms. They will never hurt us. We try equally hard not to hurt our worms, but when you are two and investigating…well, sometimes it doesn’t end so well.wormsWe love worms because they help create healthy, beautiful lawns, which is hard to do when you have lots of two legged friends playing on it all day. People often ask how we “get” our kids to hold a worm. We read a lot of books about worms, we watch them for long periods of time, and if you have one brave friend, you are pretty much assured the bravery will come. Patience and calm, whispering voices can help also. Worms like moist ground, which leads us to water.

water pump

I love water play almost as much as I love blocks. When you have water in your play area, it is the equalizer among all children. Regardless of their age or language or social ability, water will bring them together. We love water play so much that we created our pump with the help of a buried rain barrel. Water gives us plenty of opportunities to understand volume and measurement and estimation. It turns dirt into mud, which makes it easier to find worms! It is a loose part. It may be my absolute favorite loose part. Be sure to add it in some form to your play area because it is so incredible.

This is one of our favorite stories, about water and time and discovery. We had our pump and I had some fabric in the yard as a loose part for making forts or whatever. These boys decided they wanted to capture water in the fabric.

I knew it wasn’t going to work, but why would I say no to such a learning opportunity. So,

boys measuringthe boys started pumping the water into the bright blue fabric.






HUH????? No way! Oh my goodness! Who knew that fabric was actually waterproof? collecting water  Ha! So now we had ourselves a project!collecting water The boys quickly decided this could create an amazing mote in the sandbox.







boys with collected water

Another lesson learned in giving children long periods of time, never stopping the obvious and the importance of loose parts. Look at the delight on their faces! Okay, well maybe one is carrying most of the load, but the other two are thrilled.


Let them play!muddy mess

So, let’s talk some more about water and containers. Many cities are giving away rain barrels or offering them for sale. These make fabulous sources of water, specifically if you have a spigot for your child to control. Think of the math opportunities of measuring, estimating, mixing.   If you don’t have a water resource nearby, take some out with you. Think about milk jugs or buckets or big thermoses with spigots. Children love spigots. It gives them power to control something. You will also love having a source of water to wash your child before they return indoors.

Oh, how we love to cook. We do a lot of cooking around here, often outdoors, with loose parts and water. We spend hours mixing and stirring and adding and serving. Cooking is a math-athon of opportunities. (Yep, I think I made that word up. I like it!) It is important when you are cooking for play or cooking for actual consumption that children have their own bowls and utensils. It adds to the learning value. Watching your friend is not the same as having your own bowl, measuring spoons and spatula. We have been through many types of pots and pans and spoons and measuring devices. I recently jumped on a deal for a plastic children’s toy tea set to add to our play. I normally stay away from such things, but I’ll admit it, the price and the reviews sold me. Sadly, I didn’t love it. Within six months it was stained, and ugly and just not nice to look at. It didn’t seem to bother the children, but it bothered me. For the same amount of money, I could have purchased A LOT of real pots, pans, spoons, measuring cups and utensils from a garage sale or Goodwill. Keep it real. Include pots and pans, pouring pots for sure, and utensils and most importantly sand and water. We have tried to get away from plastic shovels but they really are nice for what we use them for. Metal shovels are sharper and heavier and just don’t seem to work as well for us. Metal works well for dirt. In sand, we use plastic.

coolking with mud

Sand. I know, I know. A lot of parents hate it. I promise you it will bring you hours and hours of deep, calm, investigative, creative play. The bigger the area, the bigger the creations and the more friends can play. Mud kitchens are all the rage right now and for many of the same reasons. I, personally prefer sand. It’s easier for me to clean up with a household of little friends. Sand, dirt, and mud are essential parts of loose parts play. Think of it as a short-term investment for long-term brain development. Sand and dirt support children on the mathematical learning journey. Children will explore space and measurement and shapes. They will start making comparisons of dry and wet and how that affects what they are building or mixing.

girl wiht leaf

This is where loose parts will come in handy. They are the ingredients and the spices. You will want lots of rocks, flower petals, grass clippings, native prairie grasses, sand, small sticks, and feathers. The more choices the better, because every experience changes the recipe! There’s a whole lot of math going on.

toddler baking wiht mud



cooking mud












If I still haven’t sold you on sand or water play, let’s try rice. We color our rice with liquid watercolor, but plain rice is just fine. I have really gotten away from using our sand and water table very often. They aren’t nearly as easy to use as tubs on the ground. We like to use these big tubs. You could use those long, plastic storage containers for under the bed or oil drip pans from the auto supply store for a fraction of the price I paid for these, and the colors will be much less annoying. The long, plastic storage containers also come with the bonus lid, which is great for storage. We like to lay out a large sheet or blanket to help with clean up. Be sure to add funnels and all the utensils listed above. The measuring and pouring and learning will bring you hours of quiet time. The rice is very calming and it is so very inviting.outdoor sand tables

I watched these four-year-olds as they investigated the rice one day. I knew it was coming.




outdoor sand tables 1







outdoor sand tables 2







………yep, yep, there it is.

sitting inside sand tables


Good stuff that rice is. Just like a day at the beach. Cheap, because that’s math, and we like cheap. Buy the big 25-pound bag because like sand, more is better. Your child may need to crawl into it someday!






The Early Math Experience Matters

posted by Dr. Bilge Cerezci

Traditionally, mathematics education has not been considered developmentally appropriate for young children (Battista, 1999). Math is abstract while young children are deemed to be concrete thinkers, and some cognitive developmental work done in the mid-twentieth century has been used to suggest that young children’s mathematical ideas develop on their own timetable, independent of environmental factors like teaching (Piaget, 1969). Over the past two decades, however, a growing body of literature has indicated that many mathematical competencies, such as sensitivity to set, size, pattern, and quantity are present very early in life (National Research Council [NRC], 2009). magnetic numbers plus symbolsYoung children have more mathematical knowledge, such as an understanding of number and spatial sense, than was previously believed. For example, research suggests that young children have a basic understanding of one-to-one correspondence even before they can count verbally (e.g., pointing to items in a collection and labeling each with a number) (Mix, 2001). Further, young children also enjoy exploring spatial positions and attributes of geometric shapes by building towers with blocks and cubes and by manipulating various materials, such as puzzles and two- and three-dimensional shapes (Clements, 1999; Clements & Sarama, 2008). They also demonstrate emerging awareness of measurement, when they begin to notice and verbalize similarities and differences in the size, height, weight and length of various objects and materials (Clements & Sarama, 2008). In addition, research also suggests that 3 and 4 years-old children engage in analytical thinking as they collect and sort materials by various attributes (e.g., color, size, and shape) and in algebraic thinking as they copy the patterns they observe in their surroundings and create their own patterns by using pattern blocks and other materials (Epstein, 2003; 2006). In fact, as research points out, most children enter school with a wealth of knowledge in early mathematics and cognitive skills that provide a strong foundation for mathematical learning (Clements & Sarama, 2009; Ginsburg, Lee, & Boyd, 2008; Mix, 2001).

There is also new evidence that achievement in early mathematics has a profound impact on later success. For example, Duncan and Magnuson (2009) examined the mathematics achievement of children who consistently exhibited persistent problems in understanding mathematics in elementary school and analyzed it in comparison to children who had stronger early math abilities. The results of the study revealed that 13% of the children with persistent problems are less likely to graduate from high school and 29% of them are less likely to attend college than those who had stronger early mathematics abilities. In other words, the initial differences in mathematics skills in early years may lead children to remain behind their more knowledgeable peers not only in primary grades but throughout their formal schooling (Geary, Hoard, & Hamson, 1999).

Studies also showed the predictive power of early math skills compared to other academic skills, such as reading. Lerkkanen, Rasku-Puttonen, Aunola and Nurmi (2005) investigated the relationship between mathematical performance and reading comprehension among 114 seven-year-old Finnish-speaking children during the first and second years of primary school. The results suggested that the level of mathematical knowledge children have before schooling is very important because these skills are predictive of their subsequent reading comprehension. In other words, early mathematics skills predict not only later achievement in mathematics but also later reading achievement. Similarly, Duncan and colleagues (2007) conducted a meta-analysis of 6 large-scale longitudinal data sets to examine the relationship between early learning and later school achievement. Of them, two were nationally representative of U.S. children, two were gathered from multi-site studies of U.S. children, and last two focused on children either from Great Britain or Canada. The researchers focused on the relationship between school-entry skills (i.e., reading achievement, math achievement, attention, internalizing behavior problems, social skills, and anti-social behavior) and later math and reading achievement while controlling for children’s preschool cognitive ability, behavior, and other important background characteristics such as, socioeconomic status, mother’s education, family structure and child health. Their meta-analysis revealed that only three of the six sets of school entry skills and behavior are predictive of school achievement: math, reading, and attention. Further, early math skills were consistently a stronger predictor of later achievement compared to reading and attention (Duncan, et. al., 2007). Consistent with the educational attainment analyses (Duncan & Magnuson, 2009), early math achievement was found as the most powerful predictor of later school achievement (Duncan, et. al., 2007).

Even though young children are natural mathematicians (NRC 2009) and capable of developing some complex mathematical ideas (e.g., addition) and strategies (e.g., sorting by multiple attributes to analyze data), it is also true that they do not become skilled in mathematics without adult guided rich and intentional interactions with those foundational math concepts. This month, we are going to focus on three of these foundational math concepts (e.g., number sense, sorting and geometry) and how you can provide your youngsters with rich and engaging math experiences that offer for opportunities and structures for the development of deeper math understandings.

Silly Putty Recipe Card


posted by Stephanie Forsman

clockMeasurement 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.


Cooking with Preschoolers

posted by Alison Balis Hirsch

Cooking with kids offers a wonderful array of learning opportunities for young children. It provides practice in language arts (vocabulary and “reading” a recipe), science (chemistry and exploring the senses), and developing social skills (cooperation and turn-taking). The kitchen also provides a range of math practice such as counting, measuring, and understanding order.

IMG_5879In my son’s pre-k class, the teachers and children cooked together almost weekly; the recipes coincided with their Letter Of The Week. So for B week they made banana bread and for O week they made omelets. The recipes were simple enough for the teachers and children (ages 4 to 5-years-old) to manage, each having a minimum number of ingredients. My son LOVED the rice pudding so much that I asked his teacher for the recipe. When I saw how simple it was, I suggested we collect ALL of her recipes and create a cookbook to share with other parents, whom I imagined were equally excited to cook with their kids at home. After all, these were recipes already vetted by our experienced and talented teacher.


As a teacher in the classroom, we sought out parent/caregiver volunteers to assist with cooking projects. Having the child’s special grown-up allowed those participants to engage in the school life of their child, providing them with an opportunity to better know the other children and teachers and also observe their own child in the context of the classroom. It also allowed us to maintain good adult/child ratios while working with small groups of children (typically 4 – 5), in the kitchen. The children who cooked or prepared snack (sometimes it was simply designing bagel faces with cut fruit, vegetables and sprouts) usually delighted in their food and seemed proud to share their creations with their classmates. The learning continued through the service portion of the meal, since the child chefs, with the help of the grown-ups, needed to figure out how to divide what they made into equal portions for their friends. Something like bagel faces required counting and one-to-one correspondence; baking a quiche required cutting it into enough equal-sized pieces to serve everyone.

For recipes that were made frequently, we made recipe booklets that were much more readable for children. Play dough was something we made with children on a weekly basis and for that we created cards, bound by binder rings that had visual instructions and described quantities with pictures.january photos 070

Cooking presents children with plenty of opportunities to learn and is also a great way to teach principles of good nutrition and encourage an adventurous palate: in my experience kids are much more likely to try foods they’ve grown or prepared themselves.


April Showers Mean….

I’m sitting at my dining room table watching the rain pour down so hard that I can’t see out of my windows and although it is 4 o’clock in the afternoon, the sky is as black as the night.  My kids used to love to play in the warm rain and they especially loved to play in a sun shower.  We ran outside and splashed in the puddles and if it rained enough, we brought out the shampoo and washed our hair.  Inevitably, the rain would subside just enough that we could never get the soap out of our hair, but it was totally worth it.

These memories remind me that rain, just like the snow, is one of nature’s ways of providing us with an interesting topic to explore.  How can we create curriculum using the spring rains and support mathematical understandings in meaningful ways with young children?  I usually see preschoolers talk about the weather during circle time.  One of the children is a weather person. S/he walks over to the window and reports the day’s weather and sometimes s/he gets to mark the weather on a graph or the calendar.  Most often, it is an unremarkable part of the morning circle.

If we get a good amount of spring rains this month, how about shaking it up and creating an opportunity for a real exploration of rain?  If it is warm (and there isn’t any thunder and lightning) take the children outside to play in the rain. This will require some planning in terms of rain coats, rubber boots, and extra sets of clothes.  I guarantee the children will find new ways of exploring the same old space.

It might also be interesting to place different sized receptacles outside and near a window so the children can watch the rain accumulate.  You can create a graph so they can mark “how much” rain is in each container throughout the day.  This will also allow them to see that even though the rain is falling into the containers in the same way, the different sizes and shapes of the containers will make a difference about how high the water rises.

Next week, I will write about another exploration of rain that you can try this month.  Let us know what you think or if you have another idea about rain and math.




On Friday, Math at Home presented at the Opening Minds conference in Chicago.  We spoke about the Math at Home site and our upcoming Professional Development series, soon to be available through the Gateways to Opportunity ilearning system.(More to come about that exciting project over the next couple of weeks). At the end of our talk, we presented the attendees with buckets of counting worms and walked through some possible learning activities that could be done with them.  Although the worms we had were a bit different, they reminded me of this post from 2013.

Have you seen these?  These are called Inchworms and they are actually one inch long.  That means they are standard units of measure (because an inch is an inch is an inch) while looking like a non standard unit of measure.  When children use these to measure, they might say, “It is 3 inchworms long,” which also means that it is actually 3 inches long. This is an important step in children’s understandings of measurement, which can be reinforced by laying these inchworms out next to a ruler to show that they really are one inch each.

It might be fun to introduce the “Inchworm Song” as well.  If you don’t know/remember it, it goes like this.

“Inchworm, inchworm, measuring the marigolds
You and your arithmetic, you’ll probably go far.
Inchworm, inchworm, measuring the marigolds
Seems to me you’d stop and see how beautiful they are.

2 and 2 are 4, 4 and 4 are 8, 8 and 8 are 16, 16 and 16 are 32.”

How Tall is Your Pumpkin

A couple of years ago, when we explored apples and one of our Thursday Themes, we took a stab at figuring out the circumferences using string.  You can also use string to figure out how tall your pumpkins are.

Have children hold string next to their pumpkins from the top of their stems to the bottom of the body.  You can help cut the strings so they are about the right length of the height of the pumpkin.  Now, you have several strings of different lengths that can be laid next to one another to create a graph all on their own.

If you use yarn, each child could have a different color so they know which one is theirs.  Otherwise, you need to label the strings so the children can remember which one is theirs.  These varying lengths of string can be used for comparisons, for sequencing and for documenting the different heights of the pumpkins.

Another way to measure the height of the pumpkins is by using Unifix cubes.  The children can put the cubes together until they are the same height as their pumpkin.  You can then count the cubes to see which pumpkin is the tallest and which pumpkin is the shortest.

Hands as a Measuring Manipulative

Sometimes our very best tools are actually attached to our bodies.  I use my feet for all sorts of “opening and closing” needs, and my nose is the perfect choice when I need to turn the page of my ereader and my hands are inside of mittens.

Children’s hands are also a great tool for measuring.  Since each child’s hands vary in size, it is important to use the mathematical language “nonstandard unit of measure” so they all know that their answers will be different depending on the size of their hands.

What can their hands measure?  They can use their hands to measure length, by placing one hand down and then the other right next it, and continuing until they have spanned the length (or width) of whatever they are measuring.  This also works well if the children trace their hands and cut them out, so the cut-outs can be used as the measurement tool.

Hands are also a great tool to measure quantity.  Using the questions, “How many” or “How much” children can explore quantity in meaningful ways.  “How many Unifix cubes can you hold with one hand?” or “How much sand can you carry with one hand?” are realistic activities that can be explored with several children.  They will discover that bigger hands hold more and smaller hands hold less.  However, they will also find out that it takes fewer larger hands to measure a length and more littler hands to measure the same length.  Be prepared for how confusing this might be for them.

Try using hands as manipulatives and let us know  how it goes.

Cuisenaire® Rods Compare Length

Over the winter break from my teaching job, I spent quite a bit of time cleaning and organizing our Child Development laboratory.  We really dug deep, opening boxes that had never been opened and discovering materials that had never been used.  In our excavations, I found a brand new set of Cuisenaire® Rods, complete with a beautiful wooden storage box.  Glorious!

There are few manipulatives out there that are as interesting and beautiful as a wooden set of Cuisenaire® Rods.  Developed 75 years ago by Belgian teacher Georges Cuisenaire these “rods” come in beautiful colors in varying lengths.

Using Cuisenaire® Rods to compare length is as simple as putting shorter rods next to longer rods and seeing how your children observe those differences.  Although these manipulatives were designed for a very specific purpose (units of 1, 2, 3, etc.) I think  it is far more likely that children will explore the rods by laying them out, standing them up, and comparing them.

Most young children will be able to identify which rods are shorter and which are longer, especially when they are laid out next to each other.  It is far more difficult for children to compare several rods of differing lengths simultaneously.  Putting many of them in order from shortest to longest is really challenging because it asks children to think about 2 things at the same time; which rod is shorter than these – but longer than the others?

If you look carefully at the above photo, you can see that the units of 1 are white and the units of 2 are red, 3 are green and so on.  They provide a visual representation of number units, up to 10, or for today’s purposes shortest to longest.


Giant Chain Links

Since I had my babies long ago, people have developed really interesting things to hang on strollers. We were lucky to have working harnesses so our babies didn’t fall out onto the street.  Nowadays, folks hang all sorts of stimulating and educational things from the tops of their strollers to keep their children’s attention and to keep them entertained.

Links are one of those really versatile manipulatives that children will play with throughout their young lives.  As infants, they will use them as chew toys as well as to connect their other toys to something.  Later, children will connect them to make chains that are “long” or “longest” or to go across the room.

They can also be used to show numerical differences over distance. For example, stretching a 10-link chain next to a 5-link chain shows that it is twice as long.  You can also explain that the 5 link chain is half as short.

Links provide children with a nonstandard unit of measure. Here is a great lesson plan that uses links as way to measure common household areas.

Click here to see a video of a child using large connecting links in a whole other way.