“Quantity is an attribute of a set of objects, and we use numbers to name specific quantities”
-Erikson Institute’s Early Math Collaborative
Did you know...infants notice a difference between small groups of 1, 2 and even 3 objects? This ability makes them ripe for learning math.
“Learning the number words and relating them to a set of objects is a major new kind of learning done by toddlers and preschoolers at home and in care and education centers...children who acquire this knowledge at earlier ages are provided with a distinct advantage.” -National Research Council, 2009
“Distinct Advantage” As a parent and teacher, I want the children I work with to have a distinct advantage, don’t you?
This activity is about developing a sense of number and how numbers are used. Very simply, we want children to learn the amount of something can be an attribute of the set (just like color, shape, etc.). When children label small sets with a number word they learn that number words can be used to describe the set.
Hand me the yellow leaves. Hand me the three leaves.
I want round crackers. I want two crackers.
Practice counting and labeling sets of items. Begin with 1, 2, 3. Don’t rush to higher numbers. Start small, build, and have fun.
Playful Invitation
1. Prepare: a small assortment of natural materials and a piece of chalk. I will use sweet gumballs and magnolia seed cones.
Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.
2. Invite: Use 2 seed cones to begin. Look at what I found! Aren’t these amazing! Tell me, how many do I have? If necessary-Allow time for the child to think.
3. Play: The child may immediately call out a number, count each item, or guess.
Ask: How do you know I have that many? Observe their response.
Model thinking if needed: Lets count together 1, 2. There are 2 seedcones! See how I count the gumballs and the last number I say is how many we have.
Continue the game gathering new materials and counting how many. Use chalk to write the number on the ground next to the items to show a connection between the materials, the amount, and the numeral.
Ideas for keeping it playful:
Hide materials behind your back and say, “Now I’m going to challenge you! How many do I have this time!” Reveal a new amount each time.
Let the child take the lead, Now it’s your turn! You choose a few things and I’ll tell you how many!” Play back and forth as long as the child is interested.
4. Reflect and Assess: Was the child able to verbally label small groups (1, 2, 3) or larger groups (4, 5, 6) with a number? Did they count each item using one to one correspondence? Did they restate the total amount when asked, or did they recount the items each time (repeat the count errors occur when the child does not understand the last number counted is the amount of the group)?
Ready: The ability to label small quantities with a number develops over time with counting and one-to-one correspondence. Practicing one skill reinforces the other two. Counting and labeling sets can be done with infants and toddlers, but grows in importance as the preschool child shows an interest in numbers and counting.
Ready to move on: If the child easily labels a group of items 1, 2, 3 and beyond.
Extend: Ask the child to find 1, 2 or 3 items. Hand me three rocks? Now hand me two leaves? Do they produce their own sets?
Next, draw a circle and write a number. Have the child practice finding different small sets of materials.
Finally, count larger groups of items. When you finish counting ask, So how many were in that group? If the child restates the number without recounting, it shows the child is developing cardinality and understands the amount counted is the quantity of the set.
Math Language
Attribute-characteristic of an item. Examples include color, shape, texture, size, type, number, etc.
Set- items that are grouped together in a meaningful way.
Sort- to organize items based on characteristic/attribute.
Quantity- the amount of something. The “how many or how much.”
Cardinality- understanding that the last number counted represents the quantity of the entire set.
Rote count- the ability to recite the count sequence in the correct order without understanding.
One to one correspondence- when counting a set, each item should be counted only once matching one number word to each item.
Resources
Nguyen, Laski, Thomson, Bronson, & Casey, 2017*
Cordes & Brannon, 2009*
NRC, 2009 pp 60-66 “Evidence for early understanding of number”*
*full citation can be found on the Research page