Little Brains, Big Concepts: Comparing Quantities

This post is part of the Little Brains, Big Concepts series. Check out the previous posts: Introduction, Number, Counting Strategies, Part-Whole Relationships, Understanding 10, Place Value

Children naturally compare quantities starting at a young age. Does “hey, they got more than me!” sound familiar? Finding the relationship between amounts and groups is at the heart of number.

Let’s take a look at 6 and 7. They’re next to each other in the number word sequence, but what does that actually mean? Well, it means that 7 and 6 are different numbers (not equal), that 6 is less than 7, and that 7 is more than 6. While this seems obvious to us, children need a lot of experiences with numbers and groups in order to develop this understanding.

The Concept

Children first look at equality through the lens of one-to-one correspondence. You can determine if two sets are equal by pairing them off, one object from Set A with one object from Set B. If there are no objects left over, Set A and Set B have equal amounts. Any number of leftover objects means that the sets are unequal.

Unequal groups have two important relationships: less than and greater than. Once you have put the groups into one-to-one correspondence, you can see which set has more and which set has less. In the example above, there are more iguanas than turtles because there is an iguana left over. On the flip side, you can also see that there are less turtles than iguanas.

Notice how you don’t necessarily need numbers to define these relationships!

Equal groups have an important property called conservation. This means that two sets that are equal stay equal, even when we change the configuration. In the image below, you can see that even when we spread out the turtles, there are still the same amount of turtles as iguanas.

Interestingly, children’s brains tend to be distrustful of arrangements, and they will count the iguanas and the turtles all over again, even if they had just determined they were equal!

Experiences that Build Understanding

Children need a lot of practice physically working with equality and comparing quantities.

Compare Quantities in Daily Activities

There are opportunities to compare groups all around you. All you need are 5-15 objects that your child can hold or move – no special counters or cubes required! If you’re making cookies, use the chocolate chips. When you’re eating a snack, use the Goldfish or fruit snacks. When you’re folding laundry, use the socks. Your child loves playing with the dinosaur toys from the Dollar Store? Perfect.

Start by creating two groups – this is a great opportunity to sort if there are distinguishing characteristics! Then, ask Does each group have the same amount? Which group has more? Which group has less?

You can extend the activity by adding more to a group or taking some away before repeating the process.

Explore Built-in Equal Groups

Take a look at the happy monsters below. Notice there that the monsters, hats, and eyes are in one-to-one correspondence: 1 monster – 1 eye – 1 hat. Images with built-in equal groups are great for extending children’s understanding of equality.

Consider the following questions: How many monsters are there? How many hats are there? How many eyeballs are there? As adults, we can easily determine that because there are four monsters, there are also four eyes and four hats.

However, this type of thinking isn’t obvious for young children. When asked about the number of eyeballs and hats, three-year-olds won’t use the number of monsters to infer the number of eyeballs and hats. Instead, they will count each eyeball and each hat. By the age of four, children are better about using equal groups to infer amounts.

Using images with built-in equal groups are great for deepening your child’s understanding of equality. Now that you know to look out for images like this one, you might be surprised how often you see them. Picture books are a perfect place to find these images – check out this page from one my personal favorites, The Very Hungry Caterpillar!

Take Action

  • Choose one moment to leverage a daily activity to compare quantities.
  • When reading with your child, be on the lookout to find built-in equal groups.

References

Feikes, David., Schwingendorf, Keith. and Gregg, Jeff. (2018) Children’s Mathematical Learning. Retrieved from this website.

Dougherty, et al. (2010). Developing Essential Understanding of Number and Numeration: Pre-K-Grade 2. National Council of Teachers of Mathematics.

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