Teaching Number Sense to Toddlers

This article outlines some techniques and materials, including a storybook, which can be used by parents, grandparents, and teachers to improve a child’s cognitive development and academic success.  The activities incorporate learning strategies that have a basis in educational research in order to engage young children and strengthen their vocabulary, creativity, and understanding of some math concepts.

In addition, ideas within this article can be used by parents, grandparents, or teachers as a template to develop future teachable moments. [Note: Some applicable national education standards for kindergartners are listed within this article that relate to the incorporated techniques and/or subject matter.]

Storybook:   Little Goblins Ten by Pamela Jane

The above storybook can be accessed online, at a library, or at a bookstore and can be read over-and-over again to young children in order to build their thinking and communication skills. In addition, this storybook and others, can focus young children on some of the math-themed activities detailed below.

The Importance of Number Sense:  Success in early math has lifelong implications. Researchers have found that children arrive at school on the first day of kindergarten with wildly different levels of math knowledge.  These differences in children’s initial understanding of math have long-term implications for their success in school and in life. In fact, mathematical knowledge (particularly number sense) at the point when a child enters kindergarten is the strongest predictor of a child’s later achievement in school; it is a stronger predictor than reading skills (Duncan, 2007).  In addition, success in math during kindergarten is an early predictor of math achievement in middle school, as well as an early predictor of one attaining a financially successful career. However, on average, only about 3% of the amount of preschool instruction is spent on math.

There is broad consensus on which components of math knowledge young children need to gain in order to succeed.  Researchers have identified a specific, well-defined set of concepts and skills that can make the difference between a child’s success or failure in mathematics in the early years.  Gaining an understanding of these three mathematical insights is key:

• Numbers represent quantities.
• Spoken number names (“one,” “two,” etc.) and formal written symbols (1, 2, 3, etc.) are just different ways of referring to the same underlying quantities.
• The quantities represented by the symbols have inherent relationships to each other (7 is more than 5, for example) and it is this property of the quantities that allows us to use the symbolic number representations to solve certain kinds of problems (such as putting objects in order; counting to determine how many objects are in a set; understanding that if you take one item away from a set, you have less items in that set; etc.).

The above network of concepts and skills constitute what is called Number Sense and these research-based insights are embodied in the most recent guidelines for teaching mathematics in the Common Core State Standards for Math (National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010).  [See some of these math standards for kindergarteners attached at the end of this article.]

Little Goblins Ten storybook:  Below are some (1) key themes, (2) reasons why this storybook was selected for the article, and (3) reading strategies for adults.  This story:

• Is tied to a holiday/seasonal theme: For example, this storybook is great to read during the Halloween season.
• Provides an opportunity for counting items/characters and for making detailed observations of specific items found in the storybook pictures.
• Promotes associated extended learning opportunities during trick-or-treat events, visits to pumpkin patches, carving jack-o-lanterns, etc.  (See some suggestions on the following pages.)

Themed Activities at Home to Strengthen STEM (Science, Technology, Engineering, Math) Education and School-readiness Skills

Practice the following activities at home with your children/grandchildren.

Size of Pumpkins

• While at the grocery store, farmers’ market, pumpkin patch, or at home (if you purchase multiple pumpkins) have your child use words, such as small, large, and medium, to appropriately describe the relative size of pumpkins.  
• To build language skills, also use similar words interchangeably: small/little/tiny; large/big/huge; medium/in-between size/not too big or not too small.  
• Hold up or point to two pumpkins at a time and ask, “Which is bigger?”  “Which is smaller?”
• If you have really large pumpkins, see if your child can wrap his/her arms around them.  Then have them wrap their arms around you to see which is bigger.
• Older toddlers can use a piece of yarn or a tailor’s cloth measuring tape to gauge the distance around an object as a comparison.

Sorting & Counting – Number of Seeds & Size of Seeds

• If you plan to carve a single or multiple pumpkin/s for a jack-o-lantern, take out the seeds, wash them in salty water, then use them as simple counters.  [Afterward, these seeds can be placed in a warm oven and roasted as a treat (in a 300 degree F. oven for about 45 minutes; some melted butter can be drizzled on the seeds at the beginning, along with a sprinkle of salt; the entire seed with the shell is edible).]
• Depending on the age of your child, have him/her line up the seeds in a row or group them into piles of ten, counting them each time, explaining that each pile is the same as each other.  
• With different amounts of seeds laid in lines or in loose groupings, have your child determine which grouping has more seeds or less seeds than the other.  
• If there is enough difference in the size of the seeds, have your child sort the seeds by size or use hulled and non-hulled pumpkin seeds (white shelled pumpkin seeds versus pepitas) to separate into two lines or piles for counting.  
• The white pumpkin seeds can be colored with markers and glued onto paper to create fun mosaics, faces, flowers, or other designs.

Sorting & Counting – Color & Shape Recognition

• Use and describe the characteristics of flat foam shapes (as can be purchased in a craft store) to have your child practice shape recognition, identification, and the use of names, such as circle, triangle, rectangle, square, etc).  The foam shapes can also be sorted and named by color.
• Counting and describing relative sizes (small, medium or large) can be added to the above activity.  
• A foam pumpkin template can become a creative jack-o-lantern by using the various shapes as eyes, noses, mouths, and even ears.  Encourage your child to stack some of the shapes on top of each other as well, such as a small circle on top of a large triangle to create the eyes of the jack-o-lantern.  Create several faces before sticking the shapes permanently onto the pumpkin template. Note: you can use small pumpkins, gourds, apples, or pears to apply the sticky foam shapes onto, in order to create a more 3-D look to the jack-o-lantern craft.  

Sorting & Counting – Trick-or-treat Math

• A great use of trick-or-treat candy, such as M&Ms or Skittles, is to have your child sort the candies by color into individual cups or onto pieces of colored paper.  
• For an older toddler, once the candies are sorted, have him/her line up the candies using gridded paper (such as graph paper), one row for each color of candy, so that he/she winds up with a row of red candies, a row of orange candies, and so on.  Once the sorting is finished, he/she will have created a bar graph. Ask your child to name which color of candy he/she has the most of? Which does he/she have the least of? He/she can also count the number of each color of candy that he/she has.  
• If your child doesn’t eat candy, substitute colorful goldfish crackers.

Dress Up, Role-playing & Use of Imagination

Halloween events gives children the chance to dress up and take on the role of an imaginary person or thing.  Stretching one’s imagination leads to creativity and portraying a different persona encourages children to build their vocabulary, confidence, and problem-solving skills, as they rescue a doll, fight an imaginary beast, or set up a tea party.  Role-playing, especially when it happens with other children, encourages taking turns, sharing, cooperation, and socialization.

Kindergarten Common Core – Counting and Cardinality

In preparation for Common Core State Standards for Math – Kindergarten: These are national education standards which many states recognize and utilize in the classroom. Notice how the standards below align with the suggested material to be taught.

Know number names and the count sequence.

• Count to 100 by ones and by tens.
• Count forward beginning from a given number within the known sequence (instead of having to begin at number one).
• Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).

Count to tell the number of objects.

• Understand the relationship between numbers and quantities; connect counting to cardinality (Note: cardinality is defined as the number of elements in a set or other grouping, as a property of that grouping).
• When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
• Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
• Understand that each successive number name refers to a quantity that is one larger.
• Count to answer “how many?” questions about as many as 20 things arranged in a line, a  rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Compare numbers.

• Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.
• Compare two numbers between 1 and 10 presented as written numerals.

Kindergarten – Geometry

• Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
• Correctly name shapes regardless of their orientations or overall size.

You might also enjoy this recent article about introducing Language and Literacy to Toddlers.