“Who wants more!?” Growing up in an Italian household, this was a common phrase that was heard at the kitchen table. I can just picture my father checking in on all the kids to make sure we had enough food to make us full. The concept of more or less is learned at a very young age. Think of infant children. Aren’t adults constantly asking the child, “Do you want more?” Because of this, children have an unconscious sense of a change in number within the first few months of life. This change could be with very small collections such as 1 or 2 objects, or with larger collections, such as double the number of objects.
Comparison In Early Grades
When students enter the classroom in Kindergarten, the idea of comparing a collection of objects still stays the same. Teachers provide students with two groups of objects to compare and determine which has more and which has less. Teachers make sure it is obvious which is more or less, so that students do not need to count to compare. This is because the focus is on developing the vocabulary of “more” or “less” and then transitioning that language to “greater than” and “less than” further in their learning.
Still having a hard time picturing how a five-year-old can determine more or less without counting? Here are some strategies students may use to compare in the kindergarten classroom. These strategies are explained in detail in the book The Common Core Mathematics Companion: The Standards Decoded, Grades K-2 by Linda M. Gojak & Ruth Harbin Miles.
Things to Remember
There are a few important notes to remember about the early stages of comparison thinking. When you first start talking about comparisons, make sure to provide an abundance of opportunities to compare obvious amounts in order to help support the new vocabulary. Obvious amounts mean more than just one or two more. Your child needs to really SEE that one group of objects is more or less than the other. Furthermore, it’s also important to note that this idea of comparison is grounded in concrete representations. Let your students play with two different sets of objects and use prompting questions to elicit a conversation of more or less. It’s okay if they’re unsure at first! Multiple exposures will continually reinforce the vocabulary.
Games to Practice Comparison
Games are a great way to engage young learners, and the idea of comparison can easily be practiced during a math game! Below are three simple games you can play with young learners to practice the concept of more or less. These games will also reinforce the concept of subitizing, since all you need to play is a deck of subitizing cards!
Comparison Game #1: More or Less?
Two players decide if they are playing more or less before starting the game.
Players split the deck and each player takes the top card from their pile and places it face up. Whichever card is more/less wins both cards.
The player with the most points/cards wins the game.
DIFFERENTIATION IDEA: If your students struggle with the pictorial representations, have them recreate the image using concrete objects!
Comparison Game #2: More or Less War
Players split the deck and each player flips over the top card from their pile.
The first player to say the quantity that is less keeps both cards as points.
The player with the most points/cards wins the game.
DIFFERENTIATION IDEA: Playing this game with older students? Use multiplication subitizing cards instead of five or ten frames!
Comparison Game #3: In Betweens
Two players split the deck in half and each place one card down face up. These are the two target numbers. If they are equal, redraw.
Players take turns flipping over their top card. If the card is in-between the two target cards they keep that card as a point. If it matches a target card or is outside the range, it goes to the discard pile.
Players continue alternating turns until all the cards have been played.
The player with the most points/cards wins the game.
The Number Sense Trajectory
If you’re interested in finding out more about the early number sense trajectory, here are some other posts that will be helpful!
The Power of Early Number Sense: How to Support Curiosity in K-2
How to Investigate Subitizing Through Games to Spark Early Number Sense
Resources to Help
Grab and Go
Remember: Depending on what you are using the subitizing decks for, you may need to make multiple copies.
K-2 Learning Trajectory Document
Deep Dive
Learning and Teaching with Learning Trajectories- This website will provide a wealth of information on specific learning trajectories for learners of all ages!
Learning and Teaching Early Math: The Learning Trajectories Approach by Clements & Sarama
The Common Core Mathematics Companion: The Standards Decoded, Grades K-2 by Linda M. Gojak & Ruth Harbin Miles
