Tag Archives: math

How to Get Your Child’s Hands On Math

Numbers can be a pretty abstract concept for a preschooler to wrap her mind around.  But just as a storybook turns abstract letters into a meaningful story, the abstract concepts of numeracy, patterning, and comparison find real meaning in the objects they represent.  Putting these real objects into the small hands of young children makes the abstract concrete as we connect these math terms and concepts with experiences and  understandings they’ve been building over  a lifetime.

I began thinking of some of my favorite math manipulatives to use with young children and found that while my thoughts began with formal sets you can buy from an educational supplier, my mind soon drifted to those wonderful home-spun manips that are cheap or even free (some of my favorite words when it comes to describing educational supplies).  And of course with these thoughts buzzing in my brain, I began to notice all the ways to turn everyday experiences into a hands-on math experience.

And so, in those categories, here are a few of my favorite math manipulatives to use with young children.

Manips You Can Buy:

Unifix Cubes:  I love these versatile blocks!  They’re great for counting and stacking as a visual representation of numbers.  It’s easy to see that 8 is bigger than 2 when you see the two standing side by side!  They’re perfect for a quick and easy bar graph as well as pattern building and hands-on adding and subtracting.  Plus, if you hand a basket of these to a group of children, they could explore, play, and create freely for quite some time.  That’s always a good sign of a wonderful manip!

Pattern Blocks:  If you really want children to understand shapes, they have to hold them, build with them, make patterns with them, sort them, and compare them.  Pattern blocks fit the bill here, and kids love them!

Cheap or Free:

Largely, the purpose of math manipulatives is to provide a concrete, movable object to represent each part of a number in a one-to-one ratio (one object, count one number).  This gives meaning to numbers and story problems and turns math into an experience instead of just another subject.  You can buy counting bears, but really all you need is an assortment of physical items that can be counted and sorted.  Here are a few items that meet those requirements without a trip to a specialty store:  buttons, dry beans, craft pom poms, plastic lids, coins, bottle caps, beads. 

Invent hands-on games using dice or number cards (I like using spare Phase 10 decks).  Add either one to a board game you already have or create one by simply drawing a path of squares.  Use favorite toys like cars, animal figures, or little people to advance along a counting game you can create together!

 On the Fly:

We’ve all heard the complaint from someone somewhere along the road: Why do I need to know this stuff?  If you really want the children you love and teach to see math as something that they use in the real world, well, then you have to take advantage of opportunities for them to use it in the real world!  Here are a few ways to do just that:

Let them use the scales at the grocery store.  Count apples as you add, read and compare the weight.

Use snacks to sort, count, make patterns, and of course, subtract! 

Make your own counting travel mix.

Find patterns in striped socks, polka-dotted ties, and checked shirts.

Set the table together!  One plate for each person is one-to-one counting in action.

Make collections of treasures to sort, count, and compare.

What are your favorite ways to make math a hands-on experience for the little ones you love and teach?

Top photo by John Evans.

Button photo by Zsuzsanna Kilian.
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What’s in the Number Bag?

bagI’m trying something new this year, in an attempt to combine a little bit of a show-and-tell opportunity and a numeracy activity.  I’m calling my experiment “The Number Bag”.  You might want to try it out too, and let me know how it works for you!

My magical, mystical number bag is simply a cloth drawstring bag.  The bag is sent home with a card with a number  written on it (1-5 for starters), along with the activity instructions in case any parents need a reminder.  The child can bring anything they want in that quantity.  For example, for the number 3 they may want to bring three toy cars or three cool rocks.    (I will let parents know that if their child has something really special they want to share, they are welcome to use some creativity to make it work for the number bag.  For example, if the child has a new doll she wants to share, but has the number 3, you might put in three dresses the doll might wear, or a dress with three buttons, and then include the doll to share as well.  Or send the doll along with two other dolls of some kind.) 

After taking the bag home, a child will bring it back to share on the next class day.  The child will give clues to help the children guess what the object(s) is/are.  After guessing the object(s), we will count them together and match them to the correct numeral.  Then the child will have a few moments to tell more about what they brought.  This activity will help with counting, numeral recognition, and sorting like objects as well as fostering the confidence, social skills, and language skills necessary to speak in front of a group.

Taking into consideration the size of your group, you may want to do this during large group time, or you may want to assign one child in each small group and do it during small group time.

So if this sounds like something that might add to your program, give it a try, and chime in here to share how it’s working for you!

For more ideas as you head back to school, click here!

Photo courtesy gotscolios.

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Post It! Simple Graphing with Preschool Children

dscn1243When you think of graphing, you probably think back to stale worksheets in your third grade class, or to more complicated parabolas in high school calculus.  Graphing starts out as a very simple concept, one that can and should be explored with preschool children, particularly the four year-olds.  One of my favorite ways to do that is with a Post-it graph. 

The easiest way to start with the concept of graphing is to chart the  number of boys vs number of girls in a group.  It is a clear-cut dichotomy (in preschool anyway :)) .  Start by having the children look around.  Do they think there are more boys or more girls?  In a larger group, this is often harder to do just by looking.  We need to organize the information to make it easier to compare.  Show your prepared chart, with a grid divided between boys and girls.  Explain to the children that you will be using this grid to graph how many boys and how many girls are in your class.  Ask each of the girls, one by one, to come up, get a Post-it and place it on the chart above the “Girls” label.  Remind them that each person only gets one sticker, and that when we build a graph, we climb up the chart like a ladder: one sticker per square.  Next, invite the boys to do the same thing. 

Once all of the Post-its are up, ask if the children can tell, just by looking at the graph if there are more boys or more girls.  Often, they will quickly acknowledge that the tallest line represents more.  Next, invite them to count each group to compare to each other and to verify the first answer.

This activity not only introduces graphing in a very basic way, but also incorporates counting, sorting, and categorizing, all of which are important preschool math skills!

You can use Post-its to make other graphs based on the children’s input, such as socks and no socks, pets and no pets, or how many brothers and how many sisters each student has.  Once your children have experience with graphing only two groups, you can go on to multiple answers: which of three apple flavors; tie shoes, velcro shoes, buckle shoes, and slip-ons; or eye color.  Graphs can be used in a myriad of ways to help preschoolers sort information and make it concrete and visual.  By using Post-its to do it, you can make grids, laminate them if you wish, and use them multiple times quickly and easily!

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Preschool Math

Photo provided by pk2000.

Many people believe that preschool math begins and ends with counting.  In reality, there are so many facets of mathematics addressed in the preschool years that truly lay the groundwork for the algebra and calculus to come!

Classification / Sorting / Seriation

Young children are often natural collectors.  Observe them as they play on their own with these prized collections.  Do they separate the race cars from the monster trucks?  Do they sort their favorite candies into piles according to color?  Do they line up their self-sheared pretzel sticks shortest to tallest?  These types of activities that often come naturally (or easily with a little suggestion), and display an important early math skill.  The ability to identify the different characteristics within a group, plays a key role in concepts such as recording and interpreting data, charting and graphing, and predictions and probability.

Numbers and Operations

These are the concepts many automatically think of when they think of math.  Numbers, adding, subtracting.  There’s more to it, however.  Many children learn to “count” early, reciting a memorized list of number names, but to actually count they must understand that one number name goes to one item in the group.  It also includes the concepts of “more than” and “less than” (something preschoolers grasp very quickly when candy is involved).  Recognizing written numerals and connecting them with their number names is another task often overlooked as a learning objective all its own.  Once again, we must remember that written numerals, even number names, are abstract concepts when compared with raw amounts – our “piles of stuff”.  Children need hands on experiences, with interactive discussion, to fuse together the concept that this “pile of stuff” is the same as the word “seven”, which is the same as the numeral “7”.  Once they understand the link between grouped items and quantified terms, they can advance to justifying their claims of “He has more than I do!” by saying, “He has 9 and I have 4”.  Further operations can be explored to find out how, exactly, justice can prevail, and both parties end up with equal amounts. 

Time and Sequence

Most preschoolers are too young to learn how to read an analog clock, but they do need to build the foundation for time and sequence by using and understanding terms such as “yesterday”, “tomorrow”, “in five minutes”, or “last week”.  Sequential terms such as “before”, and “after” and ordinal numbers (first, second, third, etc.) also build the concepts of time and sequence.  Recognizing the days of the week and their typical activities (“Today is Monday.  We go to the library on Mondays.”) also strengthens this skill.  Involving children in regular conversations about and throughout the day goes a long way in building this foundation.  Talk with children about what you’re doing, what you’ll do next and about how much time has passed.  Make picture schedules to show the order of routines.  Talk about future and past events and make comparisons of time.  (“Lunch is in one hour.  That’s about as long as Sesame Street.”)


Children should be exposed to the concept of measurement, not necessarily in the sense that they would use inches and feet, but other familiar standard units.  How many blocks long is your foot?  Which uses more blocks to measure, the door or the window?  Compare weight by using a basic balance and discussing heavier/lighter.  Volume is often compared using containers in the sensory table.

Geometric Shapes

In the preschool years, children begin to learn basic geometry when they learn to identify and create simple shapes, such as circles, squares, triangles, diamonds, and on and on.  Children generally first learn the shapes in isolation, but then may also learn how to identify shapes within a picture (that tractor wheel is a circle) or create a new picture using shapes. 


Unlocking the mystery of patterns is the foundation for many mathematic and scientific breakthroughs.  It begins simply for preschoolers, with the basic ABAB pattern (circle, square, circle, square).  Children first learn to complete the pattern and then learn to create it on their own.  Children then progress to more complex patterns, such as ABBA, or AABBAA, and on an on.  You can expose your children to patterns in riddle form with almost any repeating objects.  You can use shapes cut from felt, black and red checkers, or even silverware on the table.  Start out the pattern, “Here’s a fork, spoon, fork, spoon, fork.  What comes next?”  You can present it as a riddle or a game, “Guess the Pattern”, or even “Read My Mind”.  As children become more familiar with patterns, it will not only open the door to more complex math concepts, but it will also increase logic and reasoning skills.


Fractions may seem like a concept far beyond a preschooler’s grasp, and as a formal, worksheet type concept, it is.  As a foundation concept it is not.  At the preschool level, children can experiment with the concept of halves, and that a whole can be divided into parts.  Think of dividing an apple.  You can slice one into eight slices, but you can also place them back together to reveal that you still have only one whole apple.  This is a concept preschoolers can understand, and when they do, they are primed for the more complex concepts to come.

Talking Math

Math is a very abstract concept.  The terms and operations mean little when taken out of context.  (What does the word “two” mean if you’ve never held a group of two objects?)  Use concrete objects as often as possible when working with young children.  Take advantage of authentic experiences as they arise in the day to use math terms.  (You have 5 crackers and I have 3.  I have less than you do!)  Encourage them to verbalize as you work together so that they can gain ownership and an authentication of the concepts, building connections in their own minds to make the concepts firm.


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